PEACE INITIATIVE: To Carl and Ozan

Dear Carl and Ozan,

Please let me express my regrets for any negative part I may have had
in a "debate" which is clearly intruding on the positive purposes
of the group and creating more heat than light.

As wisely suggested by Kraig, I have taken a pause in order to
reassess the situation and consider what this "debate" might be about,
and whether the positions are necessarily even incompatible.

Thanks also to Robert the Inventor for some wonderful common sense
about mathematics, music, and the Tuning list that, along with
insights from other contributors, set the theme for what follows!

Carl did indeed "debunk" a misconception that maqam music is
traditionally performed in polyphonic or barbershop-like textures
featuring sonorities like 18:22:27. As we know, maqam/dastgah music is
above all a melodic art, although Ozan and I and others are indeed
producing polyphonic pieces, and some use neutral third sonorities of
various kinds. However, correcting anyone's misimpressions as to these
points should hardly cause the kind of stir which has resulted.

What are the real issues, not necessarily or solely factual, in
question? Well, my own position could be summed up about like this:

(1) Medieval Islamic theorists describe tetrachords and modes
which are beautiful and can and should be applied to medieval
and modern maqamat at least some of the time in some contexts;

(2) Some of these tunings are closely approximated by current
tunings in practical use in various parts of the Near East;

(3) Just ratios both simple and complex, as well as values in
cents, commas, savarts, etc., can be useful in describing and
analyzing current Near Eastern practice; and

(4) Superparticular or other divisions of the medieval theorists,
as well as some modern variations, can nicely evoke the state
of _tarab_ ("enchantment" or "ecstasy") sought by performances
and audiences as an aspect of the maqam tradition.

Carl, please correct me if I am wrong in seeing your main points as
follows:

(1) You observe that a 24-EDO model can nicely fit some maqam
perforamnces.

(2) You regard medieval Islamic theory, and likewise the
theory of Ptolemy, insofar as it involves superparticular
or other rational ratios of medium to high complexity, as
having little reference to either the practice of those
times or of today -- doubtless allowing an exception for
those of us who deliberately study and then set out to
implement these tunings.

(3) You associate concepts such as "11-limit" with a
harmonic context where various prime factors are in
operation (e.g. 2-3-5-7-11, or possibly 2-3-7-11),
rather than simply a melodic system using ratios such
as 12:11. If we change "JI" to "RI" (rational
intonation), and speak of "ratios of 11," then you
might be happier.

(4) You generally find complex integer ratios more
confusing that illuminating, and would really prefer
simply to see measurements in cents.

While even factual matters in this kind of art often involve a degree
of judgment and opinion, I'll certainly agree that some Near Eastern
performances nicely fit 24-EDO, and suspect that any reasonable person
would agree that some modern tunings of tetrachords and modes nicely
fit rational medieval models, or can be seen as variations closer to
those models than to 24-EDO, for example.

Other than that, it's mostly taste, artistic perceptions, and
opinions.

Ozan, please let me also give examples of a few of your insights,
sometimes the collective insights or you and your colleagues,
including Can Akkoc, in the paper "Weighing Diverse
Theoretical Models on Turkish _Maqam_ Music Against Pitch
Measurements: A Comparison of Peaks Automatically Derived from
Frequency Histograms with Proposed Scale Tones":

(1) The AEU or mostly Pythagorean model (often featuring
schismatic 5-limit approximations) for modern Turkish music
actuals fits some flavors of perforance in maqamat such as
Rast and Segah, but does not represent important flavors such
as Rast with rast-segah at around 16 commas or in the
neighborhood of 360 cents (e.g. 16/13), and fails radically
to account for prevailing intonational style in maqamat such
as Ushshaq and Huseyni.

(2) As shown in the earlier work of Akkoc, flexible-pitch
performers tend to focus on regions or "clusters" for a given
perde or step in a given maqam: for example, evidently,
peak areas around either 360 cents or so (16/13) or 380 cents
(5/4) for perde segah in Maqam Rast.

(3) In Maqam Ushshaq, the second step above the final peaks
around 130-140 cents (with 129.7 and 142.2 cents as the
autopeak envelop and average, dare I say ~14/13 and ~13/12),
in contrast to the 8 commas or 180 cents specified by AEU.
Interestingly, however, the neutral sixth when it occurs as
an alternative to the minor sixth is much higher, peaking by
either measure at around 872 cents. (Scott Marcus reports a
similar distinction in Maqam Bayyati (generally corresponding
to Turkish Ushshaq) in informed Egyptian practice, where the
neutral second step is around 5-15 cents lower than the
24-EDO value of 150 cents, but the neutral sixth somewhat
_higher_ than 850 cents.)

(4) In Maqam Hijaz, the autopeak envelope for the second step is
around 105 cents and the autopeak average around 120 cents,
while the major third step peaks at around 380-385 cents,
just below 5/4. The AEU formula of 5-12-5 commas (around
113-272-113 cents) thus fits the data rather nicely, while my
favorite tunings for Hijaz are notably off. For example,
while Qutb al-Din al-Shirazi's 150-267-81 cents is one of my
most commonly used models, closely approximated in most of my
favorite maqam keyboard tunings, as a representation of modern
Turkish practice it is "Not close, and no cigar," as you
might say.

Thus while some facts seem fairly clear, about 90% of this "debate"
involves opinion, taste (musical and/or theoretical), choice of
emphasis in the selection of materials, and also differences in
musical orientation.

Carl, what I mean by "differences in musical orientation" might be
illustrated by your response to a piece of Elizabethan music, _Come,
Sirrah Jack, Ho!_ by Thomas Weelkes. From your post, I might guess
that you are more oriented to 18th-19th century tonality, and are
experiencing this composition from around 1600 from that perspective.
From my perspective, when listening to 18th century music, I tend to
look for moments that could be heard as evoking a familiar
16th-century modal context. Either viewpoint is equally real for
the person experiencing it, although curious to someone more
attuned to the other period.

The same music can, and should, evoke different experiences in
different people. For you, as I read your account, there was an
interesting contrast between features that might fit an 18th-century
framework and those diverging from such a framework. When I heard the
piece for the first time around 1976, I'd guess, on an album of the
King's Singers, it sounded to me routinely pleasant, without anything
standing out. This might simply show that we have internalized
different musical expectations in certain contexts. And that is fine!
Your analysis fits the theory I've been exposed to over the years:
certain kinds of degree inflections or fluctuations I tend to take for
granted, and indeed to cultivate when I'm composing or improvising in
a Manneristic meantone style, are often noted by modern writers as
notable or unexpected from a tonal perspective.

<http://www.bestII.com/~mschulter/IntradaFLydian.mp3>
<http://www.bestII.com/~mschulter/IntradaFLydian.pdf>

Anyway, I'm wondering how this discussion of maqam music became a
"debate," much less a "debunking," when the people on various sides
are mainly making assertions of taste or opinion, which we know "are
not to be disputed"; when there are some empirical facts to support
the style of tuning that each party is focusing on or offering
examples of; and when we know that Near Eastern tunings are, in fact,
incredibly diverse.

Agreeing affably to disagree, and continuing constructively with
musicmaking and supportive discussions -- whether in maqam/dastgah
styles or others -- would seem to me the best resolution of this
unfortunate episode, for you, Carl and Ozan, for me, and for us
all who share this friendly and quirky virtual space.

Best,

Margo

Hi Margo,

> Please let me express my regrets for any negative part I may
> have had in a "debate" which is clearly intruding on the
> positive purposes of the group and creating more heat
> than light.

Thanks for saying so, but I didn't feel you had any negative
part in it. On the contrary, I enjoyed the messages we
exchanged and thought they were a good example of how such
things can go. I hope this sense was mutual but if not, it
certainly wasn't my intention and please contact me offlist
if you would like to discuss it further.

> What are the real issues, not necessarily or solely factual,
> in question? Well, my own position could be summed up about
> like this:
> (1) Medieval Islamic theorists describe tetrachords and
> modes which are beautiful and can and should be applied to
> medieval and modern maqamat at least some of the time in some
> contexts;

...Don't see how anyone could disagree with this.

> (2) Some of these tunings are closely approximated by
> current tunings in practical use in various parts of
> the Near East;

Seems likely, though the word "closely" can be troublesome.
The central point I would stress is that we really don't have
much idea what tunings are currently in use, because of a
paucity of data. That ought to lead to some humility, which
would be good for all of us.

However we can say certain things are unlikely. For instance,
choose a rational number R at random, num(R)*den(R) < 10,000
and 1 < R < 2. Let's say 55/27. What are the odds it is used
systematically in maqam music (that is, it is the target of
some bearing plan, fret placement instruction, vocal training
regimen, etc, used by more than one musician... that
musicians/craftsmen have some means of communicating about it,
not necessarily by name, but in *some* fashion)? Answer: the
odds are low and we wouldn't believe this unless evidence was
plainly extant, de novo, of such a bearing plan, fret placement
instruction, etc. etc.

> (3) Just ratios both simple and complex, as well as values
> in cents, commas, savarts, etc., can be useful in describing
> and analyzing current Near Eastern practice; and

I would dispute this beyond the 7-limit. Within the 7-limit
it's unclear, but plausible, and Weighing Diverse seems to
support it.

> (4) Superparticular or other divisions of the medieval
> theorists, as well as some modern variations, can nicely evoke
> the state of _tarab_ ("enchantment" or "ecstasy") sought by
> performances and audiences as an aspect of the maqam tradition.

I'm not sure how to evaluate this. Beyond the 7-limit I know
of no property of superparticular intervals that makes them
special in a melodic context, and even within the 7-limit
harmonic context, intervals such as 5:3 and 7:4 are on par
with superparticulars in terms of their stand-out psychoacoustic
properties.

> Carl, please correct me if I am wrong in seeing your main points
> as follows:
> (1) You observe that a 24-EDO model can nicely fit some
> maqam perforamnces.

Yes.

> (2) You regard medieval Islamic theory, and likewise the
> theory of Ptolemy, insofar as it involves superparticular
> or other rational ratios of medium to high complexity, as
> having little reference to either the practice of those
> times or of today -- doubtless allowing an exception for
> those of us who deliberately study and then set out to
> implement these tunings.

I know of no evidence they're connected.

I know of strong evidence these theorists would have had no
alternative but to use rational numbers to express their
scales.

Of course I allow that exception.

> (3) You associate concepts such as "11-limit" with a
> harmonic context where various prime factors are in
> operation (e.g. 2-3-5-7-11, or possibly 2-3-7-11),
> rather than simply a melodic system using ratios such
> as 12:11. If we change "JI" to "RI" (rational
> intonation), and speak of "ratios of 11," then you
> might be happier.

Generally the point is that ratios (dyads) of 11 are not
tunable by ear either harmonically or melodically. In triads
like 10:11:12, 4:7:11 and so on, available on dulcimers and
the like, more can be said of a tendency to gravitate to 11.
However I have never heard these relationships in recordings,
and Santoor tuning instructions I have seen have not mentioned
them. Now, maybe I should just get out more, which is why
I keep asking for examples. I get accused of insincerity, or
just ignored, when I do this.

> (4) You generally find complex integer ratios more
> confusing that illuminating, and would really prefer
> simply to see measurements in cents.

I find that rationals numbers are used in a quasi-religious
fashion by people purporting to do music theory. That goes
far outside the maqam realm. If somebody has a religious
fascination with rational numbers, that's fine by me!
Just say so from the start, and for heaven's sake don't make
objective claims about historical or contemporary musical
tradition(s), supposed health benefits, etc. That's dishonest,
disrespectful to the practitioners of said tradition(s),
offtopic, and likely to arouse those with allergies to such
things, such as myself.

> (1) The AEU or mostly Pythagorean model (often featuring
> schismatic 5-limit approximations) for modern Turkish
> music actuals fits some flavors of perforance in maqamat such
> as Rast and Segah, but does not represent important flavors
> such as Rast with rast-segah at around 16 commas or in the
> neighborhood of 360 cents (e.g. 16/13), and fails radically
> to account for prevailing intonational style in maqamat such
> as Ushshaq and Huseyni.

While waiting for Ozan to confirm or deny these details, I can
say I will hardly be surprised if existing theoretical
proposals, of whatever vintage, are found wanting.

I will add: there is no guarantee that a single master tuning
exists for all the maqamat. Of course tunings of arbitrary
precision, like 1200-ET or 12,000-ET would probably do the job.
But that would be too easy. Any such master tuning must
justify itself via some explanatory power, much like a
scientific theory. It must 'explain' or reveal common features
of the maqamat, much like Newton's laws of gravitation
explained a variety of different observations of motion made
by different people at different times. Otherwise we can be
perfectly happy knowing a tuning for each maqam, or even at a
finer level of detail (regional, tetrachordal, etc.) as
necessary.

The master tuning of the West, 12-ET, does in fact have such
explanatory power over Western music, yet it doesn't go all
the way. We need the notion of adaptive JI, along with the
idea of disposing of only those commas assumed to vanish in the
score, to get the rest of the way. Prior to this list I'm not
sure this had ever been fully realized. Though people like
Bosanquet, Groven, Fokker, and Mathieu were definitely on the
right track.

> Carl, what I mean by "differences in musical orientation" might
> be illustrated by your response to a piece of Elizabethan music,
> _Come, Sirrah Jack, Ho!_ by Thomas Weelkes. From your post,
> I might guess that you are more oriented to 18th-19th century
> tonality, and are experiencing this composition from around
> 1600 from that perspective.

It's hard to say. My Dad was an early music geek so I grew
up with such things -- and sang them in high school and
college. But perhaps my tonal indoctrination runs deeper
than I know.

> The same music can, and should, evoke different experiences in
> different people.

Absolutely.

> When I heard the piece for the first time around 1976, I'd
> guess, on an album of the King's Singers, it sounded to me
> routinely pleasant, without anything standing out.

I wasn't alive yet in 1976 but I too first heard this
particular piece on probably that very same King's Singers
recording. It sounded completely normal until I tried to
learn the parts.

> <http://www.bestII.com/~mschulter/IntradaFLydian.mp3>
> <http://www.bestII.com/~mschulter/IntradaFLydian.pdf>

Thanks for reminding about this piece. Loved it in 2005 as
much as now.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

>
> Seems likely, though the word "closely" can be troublesome.
> The central point I would stress is that we really don't have
> much idea what tunings are currently in use, because of a
> paucity of data. That ought to lead to some humility, which
> would be good for all of us.

Paucity of data? YouTube alone has more hours of maqam music than you can shake a stick at.

>
> However we can say certain things are unlikely. For instance,
> choose a rational number R at random, num(R)*den(R) < 10,000
> and 1 < R < 2. Let's say 55/27. What are the odds it is used
> systematically in maqam music (that is, it is the target of
> some bearing plan, fret placement instruction, vocal training
> regimen, etc, used by more than one musician... that
> musicians/craftsmen have some means of communicating about it,
> not necessarily by name, but in *some* fashion)? Answer: the
> odds are low and we wouldn't believe this unless evidence was
> plainly extant, de novo, of such a bearing plan, fret placement
> instruction, etc. etc.

So, you find 81:64 an unlikely bit of numerology? As I have already pointed out to you- and as you should already know- the "complex" intervals that actually are in discussion (not "random" intervals) turn out not to complex at all in context. It takes a nice bit of fractal mathematics to describe a "paisley" shape, but all you have to do is make a fist, press the edge of your hand onto wet dye, and voila.

>
> > (3) Just ratios both simple and complex, as well as values
> > in cents, commas, savarts, etc., can be useful in describing
> > and analyzing current Near Eastern practice; and
>
> I would dispute this beyond the 7-limit. Within the 7-limit
> it's unclear, but plausible, and Weighing Diverse seems to
> support it.

I agree insofar as, beyond this point it is a matter of choice as to what you call what you have.

>
> > (4) Superparticular or other divisions of the medieval
> > theorists, as well as some modern variations, can nicely evoke
> > the state of _tarab_ ("enchantment" or "ecstasy") sought by
> > performances and audiences as an aspect of the maqam tradition.
>
> I'm not sure how to evaluate this. Beyond the 7-limit I know
> of no property of superparticular intervals that makes them
> special in a melodic context, and even within the 7-limit
> harmonic context, intervals such as 5:3 and 7:4 are on par
> with superparticulars in terms of their stand-out psychoacoustic
> properties.

Why don't you test to see if such a property exists? I claim it is tangible from the point of physical performance, that is, you can feel it in the instrument as an easiness/smoothness, but I honestly don't if it really is perceptible beyond that, or if that same feeling when listening to others' music is due to other factors. I'm perfectly willing to be tested on this, still waiting for Igliashon to get the chance to make a test.

>
> > (2) You regard medieval Islamic theory, and likewise the
> > theory of Ptolemy, insofar as it involves superparticular
> > or other rational ratios of medium to high complexity, as
> > having little reference to either the practice of those
> > times or of today -- doubtless allowing an exception for
> > those of us who deliberately study and then set out to
> > implement these tunings.
>
> I know of no evidence they're connected.

I just presented you with evidence, a year-old instrument methodically fretted to yee anciente intervals found in olde textts. I must admit that I was taken aback at the measurements myself, so I don't expect you to be convinced. I'm not convinced beyond "it could very well be some people do indeed either deliberately take intervals from old texts, or there are unbroken fretting traditions of great age".

To Margo: if you take these things into hand on acoustic instruments, and spend a long time doing so, you will discover that "complexity" is mostly a numerological term here. The physical realities of the allegedly complex ratios in the classic writings are actually delightfully simple.

>
> Generally the point is that ratios (dyads) of 11 are not
> tunable by ear either harmonically or melodically.

This is simply not true. I find it difficult NOT to sing 11:8 ( within a couple of cents when shooting for a "low tritone". Kind of a pain as the tuning scheme I primarily use has low tritones closer to 7:5.

>
> > (4) You generally find complex integer ratios more
> > confusing that illuminating, and would really prefer
> > simply to see measurements in cents.
>
> I find that rationals numbers are used in a quasi-religious
> fashion by people purporting to do music theory. That goes
> far outside the maqam realm. If somebody has a religious
> fascination with rational numbers, that's fine by me!
> Just say so from the start, and for heaven's sake don't make
> objective claims about historical or contemporary musical
> tradition(s), supposed health benefits, etc. That's dishonest,
> disrespectful to the practitioners of said tradition(s),
> offtopic, and likely to arouse those with allergies to such
> things, such as myself.

And I find that rationals are simply practical names for what I actually think in, which is sounds. It doesn't have to be exactly 16:13 to sound "dusky red" to me, but why should I not name this after the nearest address in coincident partials? Better than a wanna-be-scientific attempt at describing it in cents, because the "window" of cents changes with timbre and context, whereas the nearest lowest coincident partials remain the ones called 16 and 13. Though they could just as well be called Groon and Bethsheba.

>
> I will add: there is no guarantee that a single master tuning
> exists for all the maqamat.

I think a major cause of contention here is that you don't seem to have noticed that there is a practical real-life problem which Ozan has been attempting to solve as best he can. This problem is not finding a philosopher's stone for "all maqam music", but tuning an actual instrument (quanun) to be as flexible and excellent as possible.

I don't get you, man. Don't you want the "regular temperament paradigm" to see some real action? Ozan advocates 41-equal as a good realistic smaller set of intervallic possibilities for maqam music (so much for bizarre straw characatures of unrealistic expectations of accuracy), and I can tell you from experience that "marvel temperament" in conjunction with tetrachordal modal music works very well indeed. Yet you relentlessly jeer and sneer at the very people who are among the few who both understand the "RTP" and have the means to implement it in ways that might be very very groovy.

-Cameron Bobro

Margo seems to make it very clear that, in many ways, you were BOTH right in
many cases (and wrong in a few)...and my take is that sort of thing is to be
expected since music is an art: that it's possible to have more than one
intelligent theory on the exact same topic.

>"Carl did indeed "debunk" a misconception that maqam music is traditionally
>performed in polyphonic or barbershop-like textures featuring sonorities like
>18:22:27. "...(and Carl regards, according to Margo) "superparticular
or other rational ratios of medium to high complexity, as having little
reference to either the practice of those times or of today"

...Meanwhile
"Medieval Islamic theorists describe tetrachords and modes which are beautiful
and can and should be applied to medieval and modern maqam at least some of the
time in some contexts;"..."the mostly Pythagorean model (often featuring
schismatic 5-limit approximations) for modern Turkish music actuals fits some
flavors of performance in maqamat such as Rast and Segah, but does not represent
important flavors such as Rast with rast-segah"..."and fails radically to
account for prevailing intonational style in maqamat such as Ushshaq and
Huseyni."

So it seems to follow that
A) Indeed Pythagorean theory works in several cases of Maqams and is generally
used melodically and not harmonically...but Pythagorean theory fails to
summarize certain important Maqams and by no means should be considered a
complete summarizing theory for Maqam music.
B) Margo and Ozan's "non-traditionally" polyphonic music shows a good bit of the
true potential of Maqam music to be performed with harmony and to employ the
kind of tetrachords Islamic theorists describe. Easy example: Ozan's
composition "Saba Storm" winning a microtonal contest with "polyphonic Maqam".
In other words...while "harmonic" Maqam is not done often traditionally, it sure
seems to me we should be working to push it to full potential instead of
complaining how that practice does not meet past practices! :-)

------------------------------------------
Another important note: Rational Intonation vs. Just Intonation. Now that
Margo has made the distinction I think it's fair to say when I mentioned "dyadic
JI" in Arabic and Persian scales I meant Rational Intonation in proper terms.
And, in fact, I get the feeling Igs and several others have made the same
terminology mistake.
Carl (repeatedly) seems to assume when others say a "chord" they mean a
segment along the harmonic series (IE under the 25th harmonic or so) and that,
for example, something like 4:5:6:7 is a valid JI chord but something like 1/1
5/4 15/11 23/17 isn't because it doesn't reduce well in non-dyadic form. The
thing is some of us, arguably, believe in "dyadic JI" IE Rational
Intonation...and I don't think it's fair to expect people to jump ship and
switch to your favored JI theory because you believe JI involving lower straight
harmonic series chords is so superior. Personally when I force myself to deal
with only fairly low-limit chords (IE with 11 or so as the highest triadic or
tetradic limit/number AKA Margo's 2-3-5-7-11 example)...it may sound a bit
better (granted, due to things like the resulting chord having a shorter period
in many cases) but the number of chords possible per scale (compositional
flexibility) if you force yourself to that are so reduced that it's not worth it
to me.

Cameron wrote:

> > Seems likely, though the word "closely" can be troublesome.
> > The central point I would stress is that we really don't have
> > much idea what tunings are currently in use, because of a
> > paucity of data. That ought to lead to some humility, which
> > would be good for all of us.
>
> Paucity of data? YouTube alone has more hours of maqam music
> than you can shake a stick at.

Yes, and I'm the only member of this list to post analysis
of some of it. That's data. Since I do have other things
to do, I only spent about 20 minutes on it. I did ask, at
least ten times since, for others to submit data, since we
have a severe paucity of it.

> So, you find 81:64 an unlikely bit of numerology?

Dude, I've only written to you four times so far that
Pythagorean intonation is perfectly plausible. Do you
read what you reply to?

> > I'm not sure how to evaluate this. Beyond the 7-limit I know
> > of no property of superparticular intervals that makes them
> > special in a melodic context, and even within the 7-limit
> > harmonic context, intervals such as 5:3 and 7:4 are on par
> > with superparticulars in terms of their stand-out
> > psychoacoustic properties.
>
> Why don't you test to see if such a property exists?

Plenty of tests have been done. No such property is
known (that is significant here).

> I don't get you, man. Don't you want the "regular temperament
> paradigm" to see some real action?

I don't think the regular temperament paradigm can help us
understand maqam music. If I did, I certainly would say how.

> Ozan advocates 41-equal as a good realistic smaller set of
> intervallic possibilities for maqam music

Ozan advocates a lot of things, but 41-ET happens to be
what I'd suggest based on the data I've seen, if we aren't
allowed to bend notes.

> I claim it is tangible from the point of physical performance,
> that is, you can feel it in the instrument as an
> easiness/smoothness,

We're really down to a disagreement over how to think here.
You don't seem interested in objective thinking. That's ok
by me, but it doesn't work on a mailing list. Unless the
other person just pretends to understand what you've said and
says something interpretive back, and you just go around
like that.

-Carl

An enlightening post on many levels especially on the tuning in this area Margo!

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Dear Carl and Ozan,
>
> Please let me express my regrets for any negative part I may have had
> in a "debate" which is clearly intruding on the positive purposes
> of the group and creating more heat than light.
>
> As wisely suggested by Kraig, I have taken a pause in order to
> reassess the situation and consider what this "debate" might be about,
> and whether the positions are necessarily even incompatible.
>
> Thanks also to Robert the Inventor for some wonderful common sense
> about mathematics, music, and the Tuning list that, along with
> insights from other contributors, set the theme for what follows!
>
> Carl did indeed "debunk" a misconception that maqam music is
> traditionally performed in polyphonic or barbershop-like textures
> featuring sonorities like 18:22:27. As we know, maqam/dastgah music is
> above all a melodic art, although Ozan and I and others are indeed
> producing polyphonic pieces, and some use neutral third sonorities of
> various kinds. However, correcting anyone's misimpressions as to these
> points should hardly cause the kind of stir which has resulted.
>
> What are the real issues, not necessarily or solely factual, in
> question? Well, my own position could be summed up about like this:
>
> (1) Medieval Islamic theorists describe tetrachords and modes
> which are beautiful and can and should be applied to medieval
> and modern maqamat at least some of the time in some contexts;
>
> (2) Some of these tunings are closely approximated by current
> tunings in practical use in various parts of the Near East;
>
> (3) Just ratios both simple and complex, as well as values in
> cents, commas, savarts, etc., can be useful in describing and
> analyzing current Near Eastern practice; and
>
> (4) Superparticular or other divisions of the medieval theorists,
> as well as some modern variations, can nicely evoke the state
> of _tarab_ ("enchantment" or "ecstasy") sought by performances
> and audiences as an aspect of the maqam tradition.
>
> Carl, please correct me if I am wrong in seeing your main points as
> follows:
>
> (1) You observe that a 24-EDO model can nicely fit some maqam
> perforamnces.
>
> (2) You regard medieval Islamic theory, and likewise the
> theory of Ptolemy, insofar as it involves superparticular
> or other rational ratios of medium to high complexity, as
> having little reference to either the practice of those
> times or of today -- doubtless allowing an exception for
> those of us who deliberately study and then set out to
> implement these tunings.
>
> (3) You associate concepts such as "11-limit" with a
> harmonic context where various prime factors are in
> operation (e.g. 2-3-5-7-11, or possibly 2-3-7-11),
> rather than simply a melodic system using ratios such
> as 12:11. If we change "JI" to "RI" (rational
> intonation), and speak of "ratios of 11," then you
> might be happier.
>
> (4) You generally find complex integer ratios more
> confusing that illuminating, and would really prefer
> simply to see measurements in cents.
>
> While even factual matters in this kind of art often involve a degree
> of judgment and opinion, I'll certainly agree that some Near Eastern
> performances nicely fit 24-EDO, and suspect that any reasonable person
> would agree that some modern tunings of tetrachords and modes nicely
> fit rational medieval models, or can be seen as variations closer to
> those models than to 24-EDO, for example.
>
> Other than that, it's mostly taste, artistic perceptions, and
> opinions.
>
> Ozan, please let me also give examples of a few of your insights,
> sometimes the collective insights or you and your colleagues,
> including Can Akkoc, in the paper "Weighing Diverse
> Theoretical Models on Turkish _Maqam_ Music Against Pitch
> Measurements: A Comparison of Peaks Automatically Derived from
> Frequency Histograms with Proposed Scale Tones":
>
> (1) The AEU or mostly Pythagorean model (often featuring
> schismatic 5-limit approximations) for modern Turkish music
> actuals fits some flavors of perforance in maqamat such as
> Rast and Segah, but does not represent important flavors such
> as Rast with rast-segah at around 16 commas or in the
> neighborhood of 360 cents (e.g. 16/13), and fails radically
> to account for prevailing intonational style in maqamat such
> as Ushshaq and Huseyni.
>
> (2) As shown in the earlier work of Akkoc, flexible-pitch
> performers tend to focus on regions or "clusters" for a given
> perde or step in a given maqam: for example, evidently,
> peak areas around either 360 cents or so (16/13) or 380 cents
> (5/4) for perde segah in Maqam Rast.
>
> (3) In Maqam Ushshaq, the second step above the final peaks
> around 130-140 cents (with 129.7 and 142.2 cents as the
> autopeak envelop and average, dare I say ~14/13 and ~13/12),
> in contrast to the 8 commas or 180 cents specified by AEU.
> Interestingly, however, the neutral sixth when it occurs as
> an alternative to the minor sixth is much higher, peaking by
> either measure at around 872 cents. (Scott Marcus reports a
> similar distinction in Maqam Bayyati (generally corresponding
> to Turkish Ushshaq) in informed Egyptian practice, where the
> neutral second step is around 5-15 cents lower than the
> 24-EDO value of 150 cents, but the neutral sixth somewhat
> _higher_ than 850 cents.)
>
> (4) In Maqam Hijaz, the autopeak envelope for the second step is
> around 105 cents and the autopeak average around 120 cents,
> while the major third step peaks at around 380-385 cents,
> just below 5/4. The AEU formula of 5-12-5 commas (around
> 113-272-113 cents) thus fits the data rather nicely, while my
> favorite tunings for Hijaz are notably off. For example,
> while Qutb al-Din al-Shirazi's 150-267-81 cents is one of my
> most commonly used models, closely approximated in most of my
> favorite maqam keyboard tunings, as a representation of modern
> Turkish practice it is "Not close, and no cigar," as you
> might say.
>
> Thus while some facts seem fairly clear, about 90% of this "debate"
> involves opinion, taste (musical and/or theoretical), choice of
> emphasis in the selection of materials, and also differences in
> musical orientation.
>
> Carl, what I mean by "differences in musical orientation" might be
> illustrated by your response to a piece of Elizabethan music, _Come,
> Sirrah Jack, Ho!_ by Thomas Weelkes. From your post, I might guess
> that you are more oriented to 18th-19th century tonality, and are
> experiencing this composition from around 1600 from that perspective.
> From my perspective, when listening to 18th century music, I tend to
> look for moments that could be heard as evoking a familiar
> 16th-century modal context. Either viewpoint is equally real for
> the person experiencing it, although curious to someone more
> attuned to the other period.
>
> The same music can, and should, evoke different experiences in
> different people. For you, as I read your account, there was an
> interesting contrast between features that might fit an 18th-century
> framework and those diverging from such a framework. When I heard the
> piece for the first time around 1976, I'd guess, on an album of the
> King's Singers, it sounded to me routinely pleasant, without anything
> standing out. This might simply show that we have internalized
> different musical expectations in certain contexts. And that is fine!
> Your analysis fits the theory I've been exposed to over the years:
> certain kinds of degree inflections or fluctuations I tend to take for
> granted, and indeed to cultivate when I'm composing or improvising in
> a Manneristic meantone style, are often noted by modern writers as
> notable or unexpected from a tonal perspective.
>
> <http://www.bestII.com/~mschulter/IntradaFLydian.mp3>
> <http://www.bestII.com/~mschulter/IntradaFLydian.pdf>
>
> Anyway, I'm wondering how this discussion of maqam music became a
> "debate," much less a "debunking," when the people on various sides
> are mainly making assertions of taste or opinion, which we know "are
> not to be disputed"; when there are some empirical facts to support
> the style of tuning that each party is focusing on or offering
> examples of; and when we know that Near Eastern tunings are, in fact,
> incredibly diverse.
>
> Agreeing affably to disagree, and continuing constructively with
> musicmaking and supportive discussions -- whether in maqam/dastgah
> styles or others -- would seem to me the best resolution of this
> unfortunate episode, for you, Carl and Ozan, for me, and for us
> all who share this friendly and quirky virtual space.
>
> Best,
>
> Margo
>

Hi Carl, Cameron, Ozan, etc.

Just a thought, don't know if it will help.

The issue seems to be that some instrumentalists think they can feel high ratio intervals which according to theory don't seem to be intervals it would be possible to hear as special in any way from nearby intervals just a fraction of a cent away.

Well the thing I've observed which may be relevant is - when you listen to two notes played together on an instrument such as stringed instrument rich in harmonics, you get a very complex pattern of not just one set of beats, but often many beating pairs of partials (from the two notes) all sounding simultaneously at many frequencies.

So - well any ratio between partials up to say 20 or whatever is the number of partials you can hear in each note if you listen for them individually - you may be able to hear the beats between the actual partials for the ratio.

Beyond that, for something like say 81/64, which you would originally learn by chains of 3/2s probably - but you might get used to something distinctive about the way the beats in the various frequencies interact with each other. Like maybe some of them nearly coincide at regular intervals, or whatever. Basically you are listening to a complex polyrhythm in all the beats at all the beating frequencies from the interacting partials in the dyad, and it may well be distinctive sounding even when there is no simple ratio between any of the notes sounded.

It might help to resolve this and help to explain how instrumentalists may be able to hear something you would expect to be imperceptible.

Just a thought. At anyrate perhaps suggests the question is a bit more complex than one might perhaps think.

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:

> It might help to resolve this and help to explain how instrumentalists may be able to hear something you would expect to be imperceptible.

It seems to me you've put the cart before the horse. Before explaining the effect, we need to show it exists.

Love it or hate it, here is my PHI sections scale :-)

The original scale foundation is:
0.618^1 + 1 = 1.618 (the period)
0.618^2 + 1 = 1.3819
0.618^3 + 1 = 1.236
0.618^4 + 1 = 1.145
0.618^5 + 1 = 1.09
...the other part is simply PHI / (the results above) ("reverse logarithmic")
IE....
1.618 / (0.618^2 + 1) = 1.17085
1.618 / (0.618^3 + 1) = 1.30906
1.618 / (0.618^4 + 1) = 1.4131
1.618 / (0.618^5 + 1) = 1.4844

-------------------------------------------------

The "JI tweaked" approximated version is (note = here means "approximately
equals")
1.618 = 13/8 (the period)
1.4844 = 3/2
1.413 = 17/12
1.3819 = 11/8
1.30906 = 21/16
1.236 = 16/13
1.17085 = 7/6
1.145 = 8/7
1.09 = 12/11
1/1

When an experienced instrumentalist says they hear something - my inclination would be to assume that it does exist as a working hypothesis.

It's not really assuming it exists. But it is like in physics where you start with observations, which at that stage don't need to be particularly accurate or well presented or well analysed. You then make up a theory. Then you can test it.

E.g. when Einstein made up his theory of General Relativity - I'm choosing that just because it is a clear example of the process of theory and confirmation - then the evidence for it was very poor indeed. No-one could say it was confirmed at that stage, just an idea. But you couldn't go on to the confirmation of the theory until it was clearly spelt out.

Then he predicted that you would get a certain effect during a solar eclipse. First prediction he made was incorrect, but luckily it was impossible to confirm it - and by the time it was possible to observe the eclipse, the theory had been refined and was spot on (so a bit of luck came in there as well).

But anyway that's the scientific process. Very unlike how maths is done. In science you should welcome untested theories. But not accept them as valid until tested.

Robert

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
>
> > It might help to resolve this and help to explain how instrumentalists may be able to hear something you would expect to be imperceptible.
>
> It seems to me you've put the cart before the horse. Before explaining the effect, we need to show it exists.
>

BTW what I gave wasn't a theory yet. It is just a proto theory, not really well enough articulated to start testing it.

But you could as a next step then ask the instrumentalists if they do hear the polyrhythmic beat patterns or can hear them if they listen out for them.

Though gets a bit tricky there as they might be described as a "texture" not so analytical as a particular polyrhythm or they may be influenced by beats that are so quiet they don't actually hear them as such - not consciously - but our brains filter out a lot of stuff so even things you don't hear may influence other ways you perceive the interval, same cause but reported using different language.

But anyway you'd find out a bit more about what it is about the interval that makes it feel smooth, can this be articulated in any way at all?

Not necessarily even start testing at that point. You start testing once you have a clear theory. But it might be that instrumentalists are onto something, but that they sometimes get it wrong, sometimes tune to 81/63 or something (I mean that particular number is unlikely) - some nearby numbers that have a similar "feel" to them - that would then show up as a disproof of the conjecture if you did a simple test of whether they can distinguish 81/64 exactly - but after you refine the theory, much like Einstein's General Relativity example - it might then be confirmed even so.

So - tests can disprove a fully worked out theory. But can't disprove a proto theory or idea or a hunch that there is something there to be explained. That needs more work than just a simple yes / no test of whether they are able to distinguish the interval. Though if someone is reliably able to tune an exact 81/64, then that would be a confirmation, but if they think they can and can't that's not a disproof as it is not enough to disprove a proto theory which is work in progress and not yet fully worked out.

Hope this helps. I didn't do much philosophy of science, in my studies, as my focus was on foundations of maths rather than science, but did do a bit on it as a related subject, and it is a subject that interests me.

Robert

--- In tuning@...m, "robert_inventor5" <robertwalker@...> wrote:
>
> When an experienced instrumentalist says they hear something - my inclination would be to assume that it does exist as a working hypothesis.
>
> It's not really assuming it exists. But it is like in physics where you start with observations, which at that stage don't need to be particularly accurate or well presented or well analysed. You then make up a theory. Then you can test it.
>
> E.g. when Einstein made up his theory of General Relativity - I'm choosing that just because it is a clear example of the process of theory and confirmation - then the evidence for it was very poor indeed. No-one could say it was confirmed at that stage, just an idea. But you couldn't go on to the confirmation of the theory until it was clearly spelt out.
>
> Then he predicted that you would get a certain effect during a solar eclipse. First prediction he made was incorrect, but luckily it was impossible to confirm it - and by the time it was possible to observe the eclipse, the theory had been refined and was spot on (so a bit of luck came in there as well).
>
> But anyway that's the scientific process. Very unlike how maths is done. In science you should welcome untested theories. But not accept them as valid until tested.
>
> Robert
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> >
> > > It might help to resolve this and help to explain how instrumentalists may be able to hear something you would expect to be imperceptible.
> >
> > It seems to me you've put the cart before the horse. Before explaining the effect, we need to show it exists.
> >
>

Sorry I mean, if they can reliably tune 81/64 it's a confirmation that there is something going on. Not a confirmation of the proto theory since while it is just a proto theory there isn't enough substance to it to confirm it.

Anyway general message is, science is much more messy than maths, and that untested theories are to be encouraged and - you start with intriguing or unexplained observations - and then get working on proto theories which you refine using more observations - then eventually at some point you feel confident enough to build a fully fledged theory with clear cut experimental consequences which you can then test.

If the experiment fails - even at that stage, you mightn't throw away the theory - it is perfectly valid to continue to refine it, and it is a matter of individual judgement whether tweaks to a theory are acceptable, or whether it has got so complex that you are better off starting from scratch with a new theory. So even evaluating whether a theory is correct or not isn't the black and white thing it is in Maths. E.g. Ptolemy's epicycles theory did continue to work if you keep adding enough new epicycles - but the ellipses theory was simpler, so much so that it became increasingly hard to uphold the complex Ptolemy approach.

As for things like Charles Lucy's theory - well the actual explanations are eccentric. But - his thesis that there is a special healing or therapeutic effect of pi based tunings - that's hard to disprove. It's not enough to just say that it is no more than a particular type of meantone which seems to have nothing special about it. Because - there may be other ways of looking at it. It may be part of a proto theory not yet developed which will show something special about pi based tunings.

You just can't tell. Not in science. It's really such a different subject from Maths - well you get a bit of this sort of thing in Maths too when you get to foundational work particularly - or if you look at the process of discovery rather than the methods of confirmation of proofs - but anyway don't want to go into that right here as this is about tuning which is essentially an area of science rather than pure maths or even applied maths. Fascinating though the connections are with pure Maths, and even though it is perfectly possible to spawn an area of pure Maths from the science and then pursue it on its own as a field of its own (e.g. you could say study of tuning lattices is an area of applied maths, possibly even pure maths at times, inspired by its applications in an area of science).

Robert

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> BTW what I gave wasn't a theory yet. It is just a proto theory, not really well enough articulated to start testing it.
>
> But you could as a next step then ask the instrumentalists if they do hear the polyrhythmic beat patterns or can hear them if they listen out for them.
>
> Though gets a bit tricky there as they might be described as a "texture" not so analytical as a particular polyrhythm or they may be influenced by beats that are so quiet they don't actually hear them as such - not consciously - but our brains filter out a lot of stuff so even things you don't hear may influence other ways you perceive the interval, same cause but reported using different language.
>
> But anyway you'd find out a bit more about what it is about the interval that makes it feel smooth, can this be articulated in any way at all?
>
> Not necessarily even start testing at that point. You start testing once you have a clear theory. But it might be that instrumentalists are onto something, but that they sometimes get it wrong, sometimes tune to 81/63 or something (I mean that particular number is unlikely) - some nearby numbers that have a similar "feel" to them - that would then show up as a disproof of the conjecture if you did a simple test of whether they can distinguish 81/64 exactly - but after you refine the theory, much like Einstein's General Relativity example - it might then be confirmed even so.
>
> So - tests can disprove a fully worked out theory. But can't disprove a proto theory or idea or a hunch that there is something there to be explained. That needs more work than just a simple yes / no test of whether they are able to distinguish the interval. Though if someone is reliably able to tune an exact 81/64, then that would be a confirmation, but if they think they can and can't that's not a disproof as it is not enough to disprove a proto theory which is work in progress and not yet fully worked out.
>
> Hope this helps. I didn't do much philosophy of science, in my studies, as my focus was on foundations of maths rather than science, but did do a bit on it as a related subject, and it is a subject that interests me.
>
> Robert
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> >
> > When an experienced instrumentalist says they hear something - my inclination would be to assume that it does exist as a working hypothesis.
> >
> > It's not really assuming it exists. But it is like in physics where you start with observations, which at that stage don't need to be particularly accurate or well presented or well analysed. You then make up a theory. Then you can test it.
> >
> > E.g. when Einstein made up his theory of General Relativity - I'm choosing that just because it is a clear example of the process of theory and confirmation - then the evidence for it was very poor indeed. No-one could say it was confirmed at that stage, just an idea. But you couldn't go on to the confirmation of the theory until it was clearly spelt out.
> >
> > Then he predicted that you would get a certain effect during a solar eclipse. First prediction he made was incorrect, but luckily it was impossible to confirm it - and by the time it was possible to observe the eclipse, the theory had been refined and was spot on (so a bit of luck came in there as well).
> >
> > But anyway that's the scientific process. Very unlike how maths is done. In science you should welcome untested theories. But not accept them as valid until tested.
> >
> > Robert
> >
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
> > >
> > > > It might help to resolve this and help to explain how instrumentalists may be able to hear something you would expect to be imperceptible.
> > >
> > > It seems to me you've put the cart before the horse. Before explaining the effect, we need to show it exists.
> > >
> >
>

Oh, and the way science is presented in nearly all films and popular literature tends to reinforce this completely wrong but prevalent idea of how science is conducted.

In fiction a scientist observes something and then immediately moves to an explanation of what it is, even a new fully fledged theory based on a single observation (e.g. often in Star Trek this happens).

But in science proper you observe something - and your initial observation is something you can't quite categorize or describe very well often. Because often you need a bit of theory before you can even make the observation - need to know what to measure, and how to measure it, which needs some theory about what you are looking for, in order to do it.

Then over a long period of time sometimes, sometimes decades, gradually the observations and the theories are simultaneously refined.

Then rather than a single theory often you have many theories that come and go, and often several of them at once at any time (e.g. discovery of DNA many ideas of what it's structure might be before the final "discovery" of the double helix).

Many of them completely untested even. As e.g. is the situation at present in cosmology where String Theory is completely untested and doesn't even have any observations that could be made to test it known at present (or if there are any now certainly for many years it had none). Yet it is a perfectly respectable theory and many theoreticians devote their lives to studying it. Basically it is a proto theory - not yet clearly enough formulated to be tested. Even though very elaborate - there is still something missing which may be needed to turn it into a true verifiable theory.

Robert

Then - makes the situation even less like Maths - in a way no theory in physics is really confirmed.

E.g. General Relativity - though most physicists if asked would say it has been confirmed to many decimal places - yet if asked how it fits in with Quantum Mechanics - will then answer that the two theories are inconsistent. General Relativity describes how space is curved in the presence of matter - but there is no known way to explain the matter itself within General Relativity in a way that is consistent with the theory.

Other theories may supersede GR - but they too may not be immune to later flaws being discovered.

I suppose strictly speaking it's not the theory that is confirmed, just its predictions are confirmed, and that then is used as a basis for believing other predictions from the same theory, especially so if every single prediction it makes is confirmed to many decimal places.

So - Newton's theory was confirmed in that way and can still be used in situations where it is accurate enough - still valid to some extent even though incorrect and superseded.

Anyway said enough now I'm sure.

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:

> Many of them completely untested even. As e.g. is the situation at present in cosmology where String Theory is completely untested and doesn't even have any observations that could be made to test it known at present (or if there are any now certainly for many years it had none).

The difficulty with presenting this analogy in connection to LucyTuning is that with String Theory *is* a theory. GR was immediately deemed interesting because of its strong theoretical logic, and String Theory has held interest for so long precisely because there is a compelling theory. LucyTuning does not have a theory which passes the test of the most cursory rational scrutiny, and so we need to defend it, if we choose, on Michael's ground, that it sounds better than closely related tunings. So far this claim has received zero evidential support.

It's not good enough to claim I can't prove it isn't special. I can't prove that it's false that every time a bell rings, an angel gets his wings, but this doesn't mean that running up and down constantly ringing bells to help out the sad case of the wingless angels would be rational behavior.

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> When an experienced instrumentalist says they hear something - my
> inclination would be to assume that it does exist as a working
> hypothesis.

A quick survey of money paid by experienced instrumentalists
for various gimmicks sold to improve the sound of their
instruments puts that hypothesis in question.

-Carl

Carl>"A quick survey of money paid by experienced instrumentalists for various
gimmicks sold to improve the sound of their instruments puts that hypothesis in
question."

Especially for things like amplifiers, effect pedals, compression and/or
multi-tap delay boxes, special softsynths, specific MIDI controllers,
etc...except I don't think it puts the hypothesis into question but rather often
proves the opposite.
Especially in electronica, musicians do crazy things like optimize
delay/reverse-spring-reverb/quantization/different frequency
drums/phasing/filters and more to make break-beats. In fact, much if not most
of what's done for that sort of thing is by experimentation...and even the
parameters use for those effects vary widely among experienced artists: many
have completely different technique "gimmicks" they use to get the same audible
feel. The most common one I can think of is stereo delay vs. reverb...though
many prefer delay is it often sounds less "muddy".
There is no scientific formula for "how to make a break-beat have flow" be it
by timbre/effects-used/timing/etc....yet there's no need to present one to prove
that a positive audible difference is there "even" though the way people obtain
that feeling is "random". I've asked for ages on forums what the magic trick
is...and just got a huge list of possible effects, use of ghost notes, and the
general tip not to make drum timbres overlap...but that's about it far as
"breakbeat science" and the general statement "every artist has their own
combinations...and it's mostly experimentation to find what works well
together"..

I don't want to end up going on too much...but another example I can think
of is the more "basic" gimmicks of portamento and vibrato...IE can you give me
any specific formula I can use to fade into portamento between any two notes in
such a way it always sounds natural? There's a logarithmic portamento built
into my CS6X...but I know from experience it does not sound natural and most
musicians I know adjust portamento as it happens by feel alone...so portamento
"curve/rate-of-change" can differ dramatically even from song to song.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> A quick survey of money paid by experienced instrumentalists
> for various gimmicks sold to improve the sound of their
> instruments puts that hypothesis in question.

Hardly scientific. I know you did it for the lulz, but that was weak.

On Wed, Nov 3, 2010 at 12:55 AM, jonszanto <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > A quick survey of money paid by experienced instrumentalists
> > for various gimmicks sold to improve the sound of their
> > instruments puts that hypothesis in question.
>
> Hardly scientific. I know you did it for the lulz, but that was weak.

Go to the AES convention sometime if you want some scientific proof.
It's pretty much a staple of AES that some outraged audio engineering
professor (or some panel) comes up with a paper or presents some
master class on what things actually matter and what things don't in
terms of instrument acoustics, electronics, digital signal processing,
you name it. There's lots of theory and listening examples and test
and statistical analyses, and in general, lots of numbers. There are
lots of numbers.

Don't go to one of these sessions if you've ever paid tons of money
for "oxygen free" monster cables.

-Mike

Jon wrote:

> > A quick survey of money paid by experienced instrumentalists
> > for various gimmicks sold to improve the sound of their
> > instruments puts that hypothesis in question.
>
> Hardly scientific. I know you did it for the lulz, but that
> was weak.

I didn't do it for lulz, this is a well-established
phenomenon. I see Mike just mentioned AES -- audiophiles
are notorious. Wine tasters, medical doctors, the list
goes on and on. I think this came up last time we had
this argument about golden eared just intonation
practitioners.

-Carl

you might try running these through Brun algorithm or Gene's Crunch Algorythm to see what variations you might get. I think it would spread out the intervals a bit. just a thought

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Love it or hate it, here is my PHI sections scale :-)
>
> The original scale foundation is:
> 0.618^1 + 1 = 1.618 (the period)
> 0.618^2 + 1 = 1.3819
> 0.618^3 + 1 = 1.236
> 0.618^4 + 1 = 1.145
> 0.618^5 + 1 = 1.09
> ...the other part is simply PHI / (the results above) ("reverse logarithmic")
> IE....
> 1.618 / (0.618^2 + 1) = 1.17085
> 1.618 / (0.618^3 + 1) = 1.30906
> 1.618 / (0.618^4 + 1) = 1.4131
> 1.618 / (0.618^5 + 1) = 1.4844
>
> -------------------------------------------------
>
> The "JI tweaked" approximated version is (note = here means "approximately
> equals")
> 1.618 = 13/8 (the period)
> 1.4844 = 3/2
> 1.413 = 17/12
> 1.3819 = 11/8
> 1.30906 = 21/16
> 1.236 = 16/13
> 1.17085 = 7/6
> 1.145 = 8/7
> 1.09 = 12/11
> 1/1
>

One has to question if they are trying to 'improve' their sound as much as either enjoy being able to do what they have heard others do, or just in pursuit to sound different

--- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > A quick survey of money paid by experienced instrumentalists
> > for various gimmicks sold to improve the sound of their
> > instruments puts that hypothesis in question.
>
> Hardly scientific. I know you did it for the lulz, but that was weak.
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I didn't do it for lulz, this is a well-established
> phenomenon.

That many people might be fooled by some of this does not mean *everyone* is. Your statements come across as blanket assessments, as if there are literally *no* instrumentalists that, through their experience and their talents, don't have a special insight into how their instruments behave.

You are talking to a guy who had his trumpet cryogenically
frozen. Did it change the sound for better or worse?
Nope. I could go on with such embarrassing things... at least
I was always skeptical.

Howabout the notion that you can hear the difference between
Duracell and Energizer in your active bass pickup?

I could go on...

-Carl

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:
>
> One has to question if they are trying to 'improve' their sound
> as much as either enjoy being able to do what they have heard
> others do, or just in pursuit to sound different
>

If you use solar it gives you a fuzzy feeling in your stomach:)

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> You are talking to a guy who had his trumpet cryogenically
> frozen. Did it change the sound for better or worse?
> Nope. I could go on with such embarrassing things... at least
> I was always skeptical.
>
> Howabout the notion that you can hear the difference between
> Duracell and Energizer in your active bass pickup?
>
> I could go on...
>
> -Carl
>
> --- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@> wrote:
> >
> > One has to question if they are trying to 'improve' their sound
> > as much as either enjoy being able to do what they have heard
> > others do, or just in pursuit to sound different
> >
>

No, of course it doesn't prove Lucy Tuning, or that there is anything to it at all.

Yes I agree that String Theory is unusual as a theory that is so thoroughly developed over many years, and yet still not a scientifically testable theory.

However, if you look at its history, it is messy just as is normal in science. And there isn't just one String Theory either.

http://en.wikipedia.org/wiki/String_theory#History

It's certainly valid to criticise the theoretical ideas of Lucy Tuning - e.g. if it is based on the idea that pi enters in because of the spherical nature of sound waves, you can point out, maybe, that chords sound the same when you listen to them from a great distance when the waves incident on the ear are almost exactly flat. He might have an answer to that, I don't know, or he might need to go away and attempt to refine his theory.

You can say that you aren't convinced by it. You can say that in your own personal opinion the theory isn't worth exploring - but that can only be a personal opinion.

Also if he makes clear testable predictions, then you can investigate whether those predictions are true or not. If he doesn't, then you can just discuss ideas. whether they seem interesting to you, what needs to be done to put them on a more scientific basis, that sort of thing, and explain why you think it isn't yet a theory proper.

In science, often there will be many proto theories around and some will lead nowhere and be given up by everyone including the original theorists. Some will be just vague ideas that don't get developed very far.

Some become a minority idea which only a few scientists hold to, maybe just in one university e.g. Fred Hoyle's ideas about panspermia and life carried from place to place on comets and evolved in outer space not on a planet.

Some are just on the fringe of science, to the extent that nowadays few respectable scientists even look at them, such as cold fusion - but not really disproved. One easily repeatable experiment or better still, actual energy generating device, would change the entire nature of the field and make cold fusion once more mainstream.

And all that is stuff that gets published in physics journals. When you are presented with hard to explain data you may briefly at least think of much more "whacky" ideas, which never get to print, such as e.g. the original ET hypothesis for pulsars - which never got to the stage of even a proto theory, just a very natural thought that passed through the mind of the researcher, enough to mention it to colleagues, but soon dismissed once there were several separate very similar pulsars at widely spread locations in the sky. If we had the modern internet at that time, then the scientists involved might well have discussed that idea briefly in a forum like this :).

And that's mainstream science. I think a forum like this should encourage "fringe science" as well since the focus is as much on creativity and music composition and inspiration as it is on the development of tuning theory.

Fringe science can be interesting and inspiring and lead to new ideas and theories and especially new art works even when it never even reaches the status of a proto theory in scientific sense.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@> wrote:
>
> > Many of them completely untested even. As e.g. is the situation at present in cosmology where String Theory is completely untested and doesn't even have any observations that could be made to test it known at present (or if there are any now certainly for many years it had none).
>
> The difficulty with presenting this analogy in connection to LucyTuning is that with String Theory *is* a theory. GR was immediately deemed interesting because of its strong theoretical logic, and String Theory has held interest for so long precisely because there is a compelling theory. LucyTuning does not have a theory which passes the test of the most cursory rational scrutiny, and so we need to defend it, if we choose, on Michael's ground, that it sounds better than closely related tunings. So far this claim has received zero evidential support.
>
> It's not good enough to claim I can't prove it isn't special. I can't prove that it's false that every time a bell rings, an angel gets his wings, but this doesn't mean that running up and down constantly ringing bells to help out the sad case of the wingless angels would be rational behavior.
>

On Wed, Nov 3, 2010 at 4:37 AM, robert_inventor5
<robertwalker@...> wrote:
>
> You can say that you aren't convinced by it. You can say that in your own personal opinion the theory isn't worth exploring - but that can only be a personal opinion.

Why hold the reasoning behind our criticism of Charles' ideas to a
higher standard than the reasoning behind the ideas themselves? Let's
go back to the "1d waveforms are invalid because sound waves propagate
in 3 dimensions" idea. That's simply an illogical idea, and my "logic
heuristic" is throwing out red flags all over the place.

But rather than us sitting here talking about heuristics for whether
ideas are worth exploring or not, shouldn't it be up to Charles to
explain WHY 1d waveforms are invalid, and why acoustic equations
dealing with the propagation of spherical wavefronts should have
anything at all to do with the VF effect?

-Mike

Has it escaped the attention of everyone that music is a social/cultural artform just like all other art forms and is not necessarily dependant on a set of cold empirical data that comes out of the laboratory?

Granted, the tools of science and mathematics can be deployed (very successfully sometimes) to understand and explain acoustical phenomena and the mechanics of sound; however science certainly does not - at this stage - account for "absolute" tastes and pleasures that in fact emerge from and rely solely on a cryptic metaphysical world of consciousness (perception and conception) that elude any sort of empirical, tangible quantification.

So long as "human awareness" cannot be established to have physical grounding that is testable and falsifiable, music theory remains a jargon that describes "rules" and "traditions" that comprise "correct music-making norms" in a particular (existing or invented) human culture.

Hence the general division of sciences into "natural sciences" and "social sciences". Hence again the plethora of diverse scales and music-making traditions around the world often at great odds with each other.

Oz.

--

✩ ✩ ✩
www.ozanyarman.com

genewardsmith wrote:
>
> --- In tuning@yahoogroups.com, "robert_inventor5"<robertwalker@...> wrote:
>
>> Many of them completely untested even. As e.g. is the situation at present in cosmology where String Theory is completely untested and doesn't even have any observations that could be made to test it known at present (or if there are any now certainly for many years it had none).
>
> The difficulty with presenting this analogy in connection to LucyTuning is that with String Theory *is* a theory. GR was immediately deemed interesting because of its strong theoretical logic, and String Theory has held interest for so long precisely because there is a compelling theory. LucyTuning does not have a theory which passes the test of the most cursory rational scrutiny, and so we need to defend it, if we choose, on Michael's ground, that it sounds better than closely related tunings. So far this claim has received zero evidential support.
>
> It's not good enough to claim I can't prove it isn't special. I can't prove that it's false that every time a bell rings, an angel gets his wings, but this doesn't mean that running up and down constantly ringing bells to help out the sad case of the wingless angels would be rational behavior.
>
>

Mike,

Sorry I've not expressed myself well. I wouldn't regard Lucy Tuning as a testable theory in the sense of physics. That's why it doesn't have to meet the scrutiny of physics - because it isn't a theory in that sense.

And yes - proto theories and things like strange dreams or out of the blue ideas that don't fit anything yet - they don't have to fit the normal criteria of physics and theories. Since they haven't yet reached the status of a theory, they can't yet be criticised and tested in the way you can test a theory proper.

Yet - is still interesting to talk to people with these ideas, listen to what they have to say, and pick up on the points in common, use constructive criticism and so on.

And - no obligation to believe it or think there is anything in it at all. Just to let people have their say, listen to them, and if you don't feel there is anything in their ideas - you can say so but at the end of the day it is their idea and if they want to continue to pursue it then it is their decision to do that, not yours.

And on a forum like this I think we should encourage people with fringe ideas. Also let them talk to each other too. You normally get lots of fringe ideas. And they won't agree with each other either chances are. But generally one can coexist amicably and learn from the experience.

I think the main thing is that if participants in the discussion genuinely believe what they are saying, and they aren't trolling or spamming, then their point of view deserves to be heard, however strange or hard to understand it may be.

That's all I'm saying.

And if it doesn't strike a chord with anyone else at all then the topic will probably not develop very far. If one or two are interested in the same fringe or proto theory then you can get an interesting discussion develop between them. And others to whom the whole thing doesn't mean much and just seems like nonsense - well does no harm to let them get on with it, and it might, like dreams or sci fi or whatever still bring up ideas of interest more generally from time to time, and sometimes even some crucial insight that no-one ever thought of, comes out of the blue.

I think if you looked into the history of inventions and of science you would find quite a few ideas that came out of theories that were pretty crazy at the time and maybe never lead to anything except that one innovative idea.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

>
> > So, you find 81:64 an unlikely bit of numerology?
>
> Dude, I've only written to you four times so far that
> Pythagorean intonation is perfectly plausible. Do you
> read what you reply to?

I know that you have said that Pythagorean intonation is perfectly plausible. That is why I remind you of this. Why do you make up implausible complex ratios and ratios out of context instead of addressing the complex ratios, in context, which are actually presented in medieval and ancient texts?

You'll find that you have a great number of Pythagorean intervals. You'll find that you have bearing plans and mechanical tuning instructions- not just "numbers".

You claim that "most scholars" consider the work of the medieval and ancient theorists to be number games. Yet when I go to implement ratios from ancient and medieval texts, I find simplicity and practically all over the place. I find that "complex" intervals are simple in context. I wouldn't claim to be able to tune 28:27 directly by ear, but I can tune it with ease when I address it in an original context: pure fourth up, pure fourth up, 7:6 up, octave down. Whoops, it's not dubious numerology violating the claims of "harmonic entropy" at all. It's practical way to implement ratios of 7 within a tetrachordal system.

The bulk of "complex ratios" in ancient and medieval texts are the result of Pythagorean and very simple intervals, simple mechanical operations (really, "fretting"), and the interrelationships of these intervals. Spend tons of time with John Chalmer's Divisions of the Tetrachord, and hours every day for the next year or so working with these ancient and medieval tetrachords- with acoustic as well as electronic instruments- and you will see that what I say here is very sensible.

Or you could just go on trying to find new ways of pooh-poohing everything I say while others watch on and get ever more curious about the discrepancy between the reasonableness of what I say and your
insistence on its lack of reason. :-)

>
> > > I'm not sure how to evaluate this. Beyond the 7-limit I know
> > > of no property of superparticular intervals that makes them
> > > special in a melodic context, and even within the 7-limit
> > > harmonic context, intervals such as 5:3 and 7:4 are on par
> > > with superparticulars in terms of their stand-out
> > > psychoacoustic properties.
> >
> > Why don't you test to see if such a property exists?
>
> Plenty of tests have been done. No such property is
> known (that is significant here).

Could you show me these tests? (I have access to JSTOR.) I've never
seen any such tests.

>
> > I don't get you, man. Don't you want the "regular temperament
> > paradigm" to see some real action?
>
> I don't think the regular temperament paradigm can help us
> understand maqam music. If I did, I certainly would say how.

Noone said that the RTP would help us understand maqam music. I meant, it's curious that you harangue those who could be implementing the RTP.

Now that you mention it, though, it is my opinion that the study of tempering and commas is relevant to maqam intonation. Ozan may disagree, even strongly, but I suspect that a lot of the ancient and medieval tuning writings might actually assume the tempering out of certain intervals. I imagine that the Pythagorean interval which is two cents from 6:5 might very well have been meant to be 6:5 (there is a reproduction of an old Pythagoren tanbur fretting scheme presenting this interval at Ozan's site, IIRC).

-Cameron Bobro

I have been enjoying and concurring about what you are saying Robert.
I think one difference in the arts is often one comes up with theories afterwards in order to explain phenomenon to themselves.
This is true of quite a few composers i can think of who just write music and "justify " it later.
Being in such a science heavy society, i think many artist feel they have to explain their actions or directions.
Which i think is unfortunate.

--- In tuning@yahoogroups.com, "robert_inventor5" <robertwalker@...> wrote:
>
> Mike,
>
> Sorry I've not expressed myself well. I wouldn't regard Lucy Tuning as a testable theory in the sense of physics. That's why it doesn't have to meet the scrutiny of physics - because it isn't a theory in that sense.
>
> And yes - proto theories and things like strange dreams or out of the blue ideas that don't fit anything yet - they don't have to fit the normal criteria of physics and theories. Since they haven't yet reached the status of a theory, they can't yet be criticised and tested in the way you can test a theory proper.
>
> Yet - is still interesting to talk to people with these ideas, listen to what they have to say, and pick up on the points in common, use constructive criticism and so on.
>
> And - no obligation to believe it or think there is anything in it at all. Just to let people have their say, listen to them, and if you don't feel there is anything in their ideas - you can say so but at the end of the day it is their idea and if they want to continue to pursue it then it is their decision to do that, not yours.
>
> And on a forum like this I think we should encourage people with fringe ideas. Also let them talk to each other too. You normally get lots of fringe ideas. And they won't agree with each other either chances are. But generally one can coexist amicably and learn from the experience.
>
> I think the main thing is that if participants in the discussion genuinely believe what they are saying, and they aren't trolling or spamming, then their point of view deserves to be heard, however strange or hard to understand it may be.
>
> That's all I'm saying.
>
> And if it doesn't strike a chord with anyone else at all then the topic will probably not develop very far. If one or two are interested in the same fringe or proto theory then you can get an interesting discussion develop between them. And others to whom the whole thing doesn't mean much and just seems like nonsense - well does no harm to let them get on with it, and it might, like dreams or sci fi or whatever still bring up ideas of interest more generally from time to time, and sometimes even some crucial insight that no-one ever thought of, comes out of the blue.
>
> I think if you looked into the history of inventions and of science you would find quite a few ideas that came out of theories that were pretty crazy at the time and maybe never lead to anything except that one innovative idea.
>

Many cultures tune up intervals by describing it property as the emotional quality for instance. While western theory might be precise it lacks breath of methods,
such as these, relying on something more closely related to auto mechanics than poetic nuance.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> Has it escaped the attention of everyone that music is a social/cultural
> artform just like all other art forms and is not necessarily dependant
> on a set of cold empirical data that comes out of the laboratory?
>
> Granted, the tools of science and mathematics can be deployed (very
> successfully sometimes) to understand and explain acoustical phenomena
> and the mechanics of sound; however science certainly does not - at this
> stage - account for "absolute" tastes and pleasures that in fact emerge
> from and rely solely on a cryptic metaphysical world of consciousness
> (perception and conception) that elude any sort of empirical, tangible
> quantification.
>
> So long as "human awareness" cannot be established to have physical
> grounding that is testable and falsifiable, music theory remains a
> jargon that describes "rules" and "traditions" that comprise "correct
> music-making norms" in a particular (existing or invented) human culture.
>
> Hence the general division of sciences into "natural sciences" and
> "social sciences". Hence again the plethora of diverse scales and
> music-making traditions around the world often at great odds with each
> other.
>
> Oz.
>
>
> --
>
> ✩ ✩ ✩
> www.ozanyarman.com
>
>
> genewardsmith wrote:
> >
> > --- In tuning@yahoogroups.com, "robert_inventor5"<robertwalker@> wrote:
> >
> >> Many of them completely untested even. As e.g. is the situation at present in cosmology where String Theory is completely untested and doesn't even have any observations that could be made to test it known at present (or if there are any now certainly for many years it had none).
> >
> > The difficulty with presenting this analogy in connection to LucyTuning is that with String Theory *is* a theory. GR was immediately deemed interesting because of its strong theoretical logic, and String Theory has held interest for so long precisely because there is a compelling theory. LucyTuning does not have a theory which passes the test of the most cursory rational scrutiny, and so we need to defend it, if we choose, on Michael's ground, that it sounds better than closely related tunings. So far this claim has received zero evidential support.
> >
> > It's not good enough to claim I can't prove it isn't special. I can't prove that it's false that every time a bell rings, an angel gets his wings, but this doesn't mean that running up and down constantly ringing bells to help out the sad case of the wingless angels would be rational behavior.
> >
> >
>

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:
>
> Many cultures tune up intervals by describing it property as the >emotional quality for instance. While western theory might be precise >it lacks breath of methods,
> such as these, relying on something more closely related to auto >mechanics than poetic nuance.

My personal approach is certainly on the side of emotional quality and association- I never think of even the most basic intervals in numerical terms while making music and have to "think twice" to translate from how I percieve to "normal" descriptions like "that's a fifth" rather than "yellow, squaring off" and such.

But I don't believe there are dividing lines between craft, mechanical realities, and art. I don't have a problem with a genuine "car mechanics" approach, or a genuine "science" approach. So my problem on this list really stems from hand-waving eye-rolling hoodoo stuff that's pretending to be scientific. Like claims that 7:6 is explained by 12-tET or that people can't tune ratios of 11 by ear, or that intervals you can tune up with a few simple steps must be numerology because they're so "complex", woooooo-woooooo! Those are just wacko non-facts located at a candy-coated disjunct from simple mechanical realities I experience every day.

-Cameron Bobro

Hah hah! Good one Cameron.

Oz.

--

✩ ✩ ✩
www.ozanyarman.com

cameron wrote:
>
> --- In tuning@yahoogroups.com, "Brofessor"<kraiggrady@...> wrote:
>> Many cultures tune up intervals by describing it property as the>emotional quality for instance. While western theory might be precise>it lacks breath of methods,
>> such as these, relying on something more closely related to auto>mechanics than poetic nuance.
>
> My personal approach is certainly on the side of emotional quality and association- I never think of even the most basic intervals in numerical terms while making music and have to "think twice" to translate from how I percieve to "normal" descriptions like "that's a fifth" rather than "yellow, squaring off" and such.
>
> But I don't believe there are dividing lines between craft, mechanical realities, and art. I don't have a problem with a genuine "car mechanics" approach, or a genuine "science" approach. So my problem on this list really stems from hand-waving eye-rolling hoodoo stuff that's pretending to be scientific. Like claims that 7:6 is explained by 12-tET or that people can't tune ratios of 11 by ear, or that intervals you can tune up with a few simple steps must be numerology because they're so "complex", woooooo-woooooo! Those are just wacko non-facts located at a candy-coated disjunct from simple mechanical realities I experience every day.
>
> -Cameron Bobro
>
>
>
>

Excellent. I take my hat off to you, Cameron. You invoke in me the concept of `circular disciplines': where one discipline fuels and inspires another discipline.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@> wrote:
> >
> > Many cultures tune up intervals by describing it property as the >emotional quality for instance. While western theory might be precise >it lacks breath of methods,
> > such as these, relying on something more closely related to auto >mechanics than poetic nuance.
>
> My personal approach is certainly on the side of emotional quality and association- I never think of even the most basic intervals in numerical terms while making music and have to "think twice" to translate from how I percieve to "normal" descriptions like "that's a fifth" rather than "yellow, squaring off" and such.
>
> But I don't believe there are dividing lines between craft, mechanical realities, and art. I don't have a problem with a genuine "car mechanics" approach, or a genuine "science" approach. So my problem on this list really stems from hand-waving eye-rolling hoodoo stuff that's pretending to be scientific. Like claims that 7:6 is explained by 12-tET or that people can't tune ratios of 11 by ear, or that intervals you can tune up with a few simple steps must be numerology because they're so "complex", woooooo-woooooo! Those are just wacko non-facts located at a candy-coated disjunct from simple mechanical realities I experience every day.
>
> -Cameron Bobro
>

Me> Love it or hate it, here is my PHI sections scale :-)
>
> The original scale foundation is:
> 0.618^1 + 1 = 1.618 (the period)
> 0.618^2 + 1 = 1.3819
> 0.618^3 + 1 = 1.236
> 0.618^4 + 1 = 1.145
> 0.618^5 + 1 = 1.09
> ...the other part is simply PHI / (the results above) ("reverse logarithmic")
> IE....
> 1.618 / (0.618^2 + 1) = 1.17085
> 1.618 / (0.618^3 + 1) = 1.30906
> 1.618 / (0.618^4 + 1) = 1.4131
> 1.618 / (0.618^5 + 1) = 1.4844

Kraig>"you might try running these through Brun algorithm or Gene's Crunch
Algorythm to see what variations you might get. I think it would spread out the
intervals a bit. just a thought"

Good idea...where can I find simple documentation on these (IE given a
fraction or equation...covert to a "spread out" variation)? I Googled but the
explanations I found IE http://www.uni-salzburg.at/pls/portal/docs/1/1275177.PDF
were a bit above my head. One thing is for sure to me though...the results of
1.145 and 1.17085 along with 1.4131 and 1.3819 are a bit too close for comfort.

Here's a better version of a 46-pitch per octave (here in full 87-note version) scale with a low fifth at 695.454 (88EDO) that is more consistent, sounds better than last attempt.

It's very peaceful, has nice ripple.

!
87 pitches 46per2/1 88EDO
87
!
27.27300
54.54500
81.81800
95.45500
136.36400
163.63600
177.27300
190.90900
231.81800
259.09100
286.36400
313.63600
340.90900
368.18200
395.45400
422.72700
436.36300
463.63600
504.54500
518.18200
545.45400
572.72700
600.00000
627.27200
654.54500
681.81800
695.45400
736.36300
763.63600
777.27200
804.54500
831.81800
859.09100
886.36300
913.63600
940.90900
968.18100
995.45400
1022.72700
1036.36300
1063.63600
1104.54500
1118.18100
1145.45400
1172.72700
1199.99900
1227.27200
1254.54500
1281.81800
1295.45400
1336.36300
1363.63600
1377.27200
1404.54500
1431.81800
1459.09000
1486.36300
1513.63600
1540.90800
1568.18100
1595.45400
1622.72700
1636.36300
1663.63600
1704.54500
1718.18100
1745.45400
1772.72700
1799.99900
1827.27200
1854.54500
1881.81700
1895.45400
1977.27200
2004.54500
2031.81700
2059.09000
2086.36300
2113.63500
2168.18100
2195.45400
2222.72600
2236.36300
2263.63500
2304.54400
2318.18100
2399.99900

Ozan>" Has it escaped the attention of everyone that music is a
social/cultural artform just like all other art forms and is not necessarily
dependant

on a set of cold empirical data that comes out of the laboratory?"

Exactly! That's not to say someone should just be able to say something is
better and let that be that. I have suggested new scale systems be proven with
sound test: both comparing old chords and showing new ones...and then basically
asking people the question "does the new system sound better to you?" That way
you are analyzing/judging a theory in a non-random way and yet letting it stay
an art IE not be bound by, say, a single set of equations.

>"however science certainly does not - at this stage - account for "absolute"
>tastes and pleasures that in fact emerge from and rely solely on a cryptic
>metaphysical world of consciousness"

Yet the "average" absolute taste may help us define, in general, what options
are "more likely" to work in the art of music.

Cameron>"My personal approach is certainly on the side of emotional quality and
association- I never think of even the most basic intervals in numerical terms
while making music and have to "think twice" to translate from how I percieve to
"normal" descriptions like "that's a fifth" rather than "yellow, squaring off"
and such. "

I also compose completely by ear when it comes down to it. My (in progress)
Untwelve entry uses a tuning I made with 4 or so "modes" in it but, to be
honest, as I'm composing it I'm having the best luck by erasing the "mode maps"
from my memory and just finding notes that match my mood. Now some time in the
future I may come back, look at what chord progressions I came up with, and make
a theory about "easy" ways to make modulations work (at least most of the time)
between modes of my scale (or maybe even that the strongest "modes" are not the
ones I found numerically!). But often I find what actually happens when I
compose contradicts what I thought should happen using numerology, and it often
changes my original theories a lot and, I swear, often for the better. I find I
don't really know what my or anyone else's scale really can or can't do until
I've composed with it and done so "by ear".

Michael, I deem words like "average absolute taste" quite dangerous. I also regard every ultra-mega-holistic theory claiming to account for the tonal/modal/etc... basis of all-music-forevermore a grand delusion. One of the fundamental reasons for founding the Alternate Tuning List was - I presume - to show that there is not just one pitch-pathway to effectuate "good music". The list has been very successful in the demonstration of this maxim, I think.

To quote a saying of mine from my own book:

"There is no such thing as an unacceptable interval in music, there is, at most, unacceptable application thereof".

Cordially,
Oz.

--

✩ ✩ ✩
www.ozanyarman.com

Michael wrote:
>
>
> Ozan>"Has it escaped the attention of everyone that music is a
> social/cultural artform just like all other art forms and is not
> necessarily dependant
> on a set of cold empirical data that comes out of the laboratory?"
>
> Exactly! That's not to say someone should just be able to say something
> is better and let that be that. I have suggested new scale systems be
> proven with sound test: both comparing old chords and showing new
> ones...and then basically asking people the question "does the new
> system sound better to you?" That way you are analyzing/judging a theory
> in a non-random way and yet letting it stay an art IE not be bound by,
> say, a single set of equations.
>
>
> >"however science certainly does not - at this stage - account for
> "absolute" tastes and pleasures that in fact emerge from and rely solely
> on a cryptic metaphysical world of consciousness"
>
> Yet the "average" absolute taste may help us define, in general, what
> options are "more likely" to work in the art of music.
>
>

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
> My personal approach is certainly on the side of emotional quality and association- I never > think of even the most basic intervals in numerical terms while making music and have to
> "think twice" to translate from how I percieve to "normal" descriptions like "that's a fifth"
> rather than "yellow, squaring off" and such.

But I thought intervals don't have inherent emotional qualities?

>So my problem on this list really stems from hand-waving eye-rolling hoodoo stuff that's
> pretending to be scientific. Like claims that 7:6 is explained by 12-tET

No one said this.

> or that people can't tune ratios of 11 by ear

No one has suggested that people cannot tune a pitch within the same region as ratios of 11, just that specifically the ratios themselves are not responsible for any psychoacoustic attraction (given typical harmonic timbres). Personally, I think maxima of harmonic entropy are as easy to tune as minima, owing to the local coincidence of multiple relatively-simple ratios. Sort of like how if you clustered a bunch of asteroids together, they could collectively have the same gravitational attraction as one large planet.

>or that intervals you can tune up with a few simple steps must be numerology because they're so "complex"

No one said this, either. Not a single person on this list would argue that you can't tune a complex interval (given that it is the product of some set of simple intervals) by tuning simple intervals in appropriate sequence.

Gosh, Cameron. You sure do love straw men!

-Igs

Ozan>"Michael, I deem words like "average absolute taste" quite dangerous. I
also regard every ultra-mega-holistic theory claiming to account for the
tonal/modal/etc... basis of all-music-forevermore a grand delusion."

I didn't mean "average absolute taste" in the sense of that there is just
one ultimate "taste" like the peak of a mountain (something many people seem to
claim theories like JI and/or 12TET are exclusive peaks and everything else must
revolve around them).

Rather, I believe there may be several separate peaks in "average absolute
taste". For example, one large group of people, on average, may like the
Rolling Stones...another may like the Beatles...yet another likes Brian
Eno...etc. The idea is that of a group of people gravitating toward somethings
over others...not that there is some Holy Grail theory (such as "tonality") that
explains everything else. Such there is a group of people who gravitate toward
tonality, but also a group toward a-tonality...and then you get questions like
in the a-tonal group what type of characteristics do listeners consistently
enjoy?

>"There is no such thing as an unacceptable interval in music, there is, at most,
>unacceptable application thereof".
Not sure I agree completely, I don't think any interval is completely
un-acceptable, but I do thing certain intervals are, in general, more likely to
be deemed acceptable than others. And, meanwhile, the same qualities that make
an interval desirable to one large group can make them undesirable by another.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > My personal approach is certainly on the side of emotional >quality and association- I never > think of even the most basic >intervals in numerical terms while making music and have to
> > "think twice" to translate from how I percieve to "normal" >descriptions like "that's a fifth"
> > rather than "yellow, squaring off" and such.
>
> But I thought intervals don't have inherent emotional qualities?

For the individual, or groups strongly sharing feelings by mutual consent? Of course intervals have emotional/emotive qualities in this way. Dry empirical qualities such as, this tone is measured at more cycles per second than that tone? They have these kinds of qualities, too. Universal emotional/emotive qualities? No.
>
> >So my problem on this list really stems from hand-waving eye-rolling hoodoo stuff that's
> > pretending to be scientific. Like claims that 7:6 is explained by 12-tET
>
> No one said this.

Really?

/tuning/topicId_89711.html#90119?var=0&l=1

Carl, talking to Ozan:

"So I've been looking at your 2009 paper (Weighing Diverse...)
and I'm shocked at how far 12-ET can go to explain the results.
Here are my quick & dirty notes on the histograms:

rast 9/8 5/4 4/3 3/2 2/1
nihavend 9/8--7/6 4/3 3/2--8 10 2/1
kurdilihicazkar 1 2 7/6 4/3 3/2--8--10 2/1
ussak 1.5 7/6 4/3 3/2--7.75 7/4 2/1
huseyni 1.5 7/6 4/3 3/2--8.75 7/4 2/1
hicaz 1.25 5/4--4/3 3/2--8.75 7/4 2/1
saba 1.75 7/6 4.25 4/3 3/2--8 10 2/1
segah 1.25 6/5 4/3--3/2 8.25 10.5 2/1
huzzam 1.25 6/5 4.5 3/2--8.25 10.5

There's a possible tendency to use 1/1 7/6 4/3 for a trichord,
repeated at 3/2."

Other than the 4/3s and 3/2s, I don't see anything there to justify
"how far 12-ET can go to explain the results." 12-tEt doesn't explain these results, which are watered-down interpretations of the actual data to boot, at all!

>
> > or that people can't tune ratios of 11 by ear

> No one has suggested that people cannot tune a pitch within the >same region as ratios of 11, just that specifically the ratios >themselves are not responsible for any psychoacoustic attraction >(given typical harmonic timbres).

Really?

/tuning/topicId_94046.html#94048

Carl to Margo:

"Generally the point is that ratios (dyads) of 11 are not
tunable by ear either harmonically or melodically. "

Just an hour before reading this as I was practicing I had the usual experience of trying to sing a 16:13 cold and once again being pulled by the gravity of 11:9 to an 11:9 (within the slow pitch wobble of the very fretless instrument of course). Concentrating on the "dark green" of 11:9 and the "dusky red" of 16:13, I'm slowly getting to the point where I can sing a middle third cold and not be inexorably pulled by the gravity of 11:9. I have similar experiences with 11:8.

You can cite all the number-magic you want about this, doesn't change my daily experience.

Igliashon wrote:
>Personally, I think maxima of harmonic entropy are as easy to tune >as minima, owing to the local coincidence of multiple >relatively->simple ratios. Sort of like how if you clustered a >bunch of asteroids together, they could collectively have the same >gravitational attraction as one large planet.

Could be, I'm very open to that possibility.

Cameron said:
> >or that intervals you can tune up with a few simple steps must be numerology because they're so "complex"
Igliashon replied:
> No one said this, either. Not a single person on this list would >argue that you can't tune a complex interval (given that it is the >product of some set of simple intervals) by tuning simple intervals >in appropriate sequence.

You miss the point: it's the complex intervals of the ancient and medieval writers which have been accused of being numerology. I merely point out that there turns out to be far far less of this alleged "complexity" when you look at the intervals in context and in the light of fretting methodology. So what happens to the argument that we can disregard an old text because it is just number magic, when the claim that it is number magic is based on a complexity which turns out to be illusory? It sinks.

>
> Gosh, Cameron. You sure do love straw men!
>
> -Igs

I've never loved a straw man- wouldn't he get all moldy later?

Hi Michael. I am curious now just what you find that doesn't sound consonant after your last example. I think that appeggios are not the best way to judge a chord in a tuning, i suggest you try holding it . I don't have a sense of what you consider dissonance, not thatyou have to have one, but i will understand you better, if that is the case.

Once again I will parallel Ozan here (he may have a different take than me on this) in that each interval in every tuning will have certain pushes and pulls that one hopefully is sensitive to.
One would hope that tunings can be something more than just putting old wine in new bottles but a true discovery of unique stresses and pulls.
In the Visual art world new materials always brought with it new applications, we should expect the same.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Ozan>"Michael, I deem words like "average absolute taste" quite dangerous. I
> also regard every ultra-mega-holistic theory claiming to account for the
> tonal/modal/etc... basis of all-music-forevermore a grand delusion."
>
> I didn't mean "average absolute taste" in the sense of that there is just
> one ultimate "taste" like the peak of a mountain (something many people seem to
> claim theories like JI and/or 12TET are exclusive peaks and everything else must
> revolve around them).
>
> Rather, I believe there may be several separate peaks in "average absolute
> taste". For example, one large group of people, on average, may like the
> Rolling Stones...another may like the Beatles...yet another likes Brian
> Eno...etc. The idea is that of a group of people gravitating toward somethings
> over others...not that there is some Holy Grail theory (such as "tonality") that
> explains everything else. Such there is a group of people who gravitate toward
> tonality, but also a group toward a-tonality...and then you get questions like
> in the a-tonal group what type of characteristics do listeners consistently
> enjoy?
>
> >"There is no such thing as an unacceptable interval in music, there is, at most,
> >unacceptable application thereof".
> Not sure I agree completely, I don't think any interval is completely
> un-acceptable, but I do thing certain intervals are, in general, more likely to
> be deemed acceptable than others. And, meanwhile, the same qualities that make
> an interval desirable to one large group can make them undesirable by another.
>

Partch tuned his 11s by ear. There are quite a few strings players just in Los Angeles that do this also

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:

> > No one has suggested that people cannot tune a pitch within the >same region as ratios of 11, just that specifically the ratios >themselves are not responsible for any psychoacoustic attraction >(given typical harmonic timbres).
>
> Really?
>
> /tuning/topicId_94046.html#94048
>

Cameron wrote:

> /tuning/topicId_89711.html#90119?var=0&l=1
[snip]
> Other than the 4/3s and 3/2s, I don't see anything there to
> justify "how far 12-ET can go to explain the results."

The 8 and 10 are 12-ET degrees. There's also the matter
of relative power of these things on the histograms.

> > No one has suggested that people cannot tune a pitch within
> > the same region as ratios of 11, just that specifically the
> > ratios themselves are not responsible for any psychoacoustic
> > attraction (given typical harmonic timbres).
>
> Really?

Yes, really.

> You can cite all the number-magic you want about this, doesn't
> change my daily experience.

Howabout you cite something, which we asked for in the
beginning of this thread: a single example of 11-limit
intervals in a maqam recording. You know, in the vast
collection on youtube, which you suggested we peruse.

-Carl

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:
>
> Partch tuned his 11s by ear.

Yeah, and he used lower identities to do it. -Carl

Kraig>"Hi Michael. I am curious now just what you find that doesn't sound
consonant after your last example"

Last example meaning the short PHI melody example I made yesterday?
Firstly, let me say I agree with Ozan that there is no such thing as a bad
interval IE that any interval no matter how
a-tonal/non-JI/a-periodic/anti-critical-band/high-harmonic-entropy...can be made
"right" given the right context.

Case in point, looking back the PHI section tuning still sounds a bit
dissonant in a way because it's so anti-JI (IE it's very "wolf" fifth is about a
comma off pure). However the context of the scale (at least to my ears) does a
half decent job of tricking the brain into thinking is "stable" in many chords.
In fact, if you shove a perfect fifth in place of the 1.48-ish Wolf fifth, the
pure one actually sounds off...as if it breaks an important albeit relatively
unknown/unexplainable pattern in the scale somehow despite being more Just!
Take the JI version of my scale and the non-JI...and I'm actually fairly
confident you'll find the non-JI one, surprisingly, sounds more stable. I think
my PHI scale is likely not as consonant as 1/4 comma meantone to most, but I
also trust it's a strong example of a bunch of dyads that individually sound
like garbage being able to be fit in a framework well-patterned enough that the
brain can see "an obvious face/form, if a distorted one, formed from the random
pixels of would-be dissonant dyads".

To be honest I'm not sure there is a direct scientific explanation at all:
though Jacques Dudon has mentioned equal beating in recurrent sequences and you
and I both seem to agree that the small range between highest and lowest
possible consonance in the PHI scale makes it easier for chords to cleanly "swap
purposes" (between being used as rest or stress points) in practical musical
use.

All I can say is things like PHI and "chords that numerically shouldn't work
but do" inspire me to seek out new ways to attain some sort of (if not the same
degree of) stability as established things like 1/4 comma meantone. In the same
way I am fascinated with the concept of scales that are, to an extent, chords
and the ideas that "every interval in part gains its purpose for every other
interval and not just from itself". Indeed I believe, as you stated, "new
materials always brought with it new applications". You know what...that last
example I gave of an attempt at a consonant melody in the dyadically "horrid"
13TET was built to rather do the same sort of thing...and as I recall Igs even
was surprised it felt "beatless" despite containing tons of "horribly" beating
dyads (not sure if that was posted in my folder here or on MMM...but it's at one
of those two places).

Granted, some of these applications are more abscure to find and often have
less and less obvious uses than the "mainstream ones" ...but that certainly
doesn't make them anything near useless or "chasing a straw man", as many people
on this list seem to say.

Carl>"How about you cite something, which we asked for in the beginning of this
thread: a single example of 11-limit intervals in a maqam recording."

Counter question: why should we care about this presumably self-imposed
limit? What if tradition showed little of Maqam polyphony or use of 11-limit?
Ozan (and presumably Margo though I have yet to hear her works) have proven
through their own music just how useful such things can be. So maybe 11-limit
JI (or as Margo said, technically Rational Intonation) isn't readily used in
Maqam tradition, boohoo...maybe we should start evolving the tradition a bit by
using it! ;-)

It's funny because when Margo started this post, I recall she made it
remarkably clear that while tetrachords and such (rather played via polyphony or
from one instrument) ARE in Islamic theory even if not widely used in
practice...and indirectly implied, both through her and Ozan's work, that
pushing such use into tradition would not be counter to Maqam theory at all.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> But rather than us sitting here talking about heuristics for whether
> ideas are worth exploring or not, shouldn't it be up to Charles to
> explain WHY 1d waveforms are invalid, and why acoustic equations
> dealing with the propagation of spherical wavefronts should have
> anything at all to do with the VF effect?

And why, even if he is right about waveforms, it in any way supports the idea of defining the fifth in terms (logarithmically) of 1/pi? It's the last point which is really the looniest.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> Has it escaped the attention of everyone that music is a social/cultural
> artform just like all other art forms and is not necessarily dependant
> on a set of cold empirical data that comes out of the laboratory?

An observation which does not in any way support the notion that there some chance a fifth of exactly 600+300/pi cents is much better than other fifths a small fraction of a cent away. That music is an art does not mean theories about it should fail to make any sense.

Thanks for explaining.
BTW i forgot to mention that Buzz Kimball had also done some convincing melodies with 13 ET. i don't think anyone saved it or put it up. Ivor though did the opposite being the "punk rock" spirit he could be at times, writing lullabies to grate on your nerves:)

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Kraig>"Hi Michael. I am curious now just what you find that doesn't sound
> consonant after your last example"
>
> Last example meaning the short PHI melody example I made yesterday?
> Firstly, let me say I agree with Ozan that there is no such thing as a bad
> interval IE that any interval no matter how
> a-tonal/non-JI/a-periodic/anti-critical-band/high-harmonic-entropy...can be made
> "right" given the right context.
>
> Case in point, looking back the PHI section tuning still sounds a bit
> dissonant in a way because it's so anti-JI (IE it's very "wolf" fifth is about a
> comma off pure). However the context of the scale (at least to my ears) does a
> half decent job of tricking the brain into thinking is "stable" in many chords.
> In fact, if you shove a perfect fifth in place of the 1.48-ish Wolf fifth, the
> pure one actually sounds off...as if it breaks an important albeit relatively
> unknown/unexplainable pattern in the scale somehow despite being more Just!
> Take the JI version of my scale and the non-JI...and I'm actually fairly
> confident you'll find the non-JI one, surprisingly, sounds more stable. I think
> my PHI scale is likely not as consonant as 1/4 comma meantone to most, but I
> also trust it's a strong example of a bunch of dyads that individually sound
> like garbage being able to be fit in a framework well-patterned enough that the
> brain can see "an obvious face/form, if a distorted one, formed from the random
> pixels of would-be dissonant dyads".
>
>
> To be honest I'm not sure there is a direct scientific explanation at all:
> though Jacques Dudon has mentioned equal beating in recurrent sequences and you
> and I both seem to agree that the small range between highest and lowest
> possible consonance in the PHI scale makes it easier for chords to cleanly "swap
> purposes" (between being used as rest or stress points) in practical musical
> use.
>
>
> All I can say is things like PHI and "chords that numerically shouldn't work
> but do" inspire me to seek out new ways to attain some sort of (if not the same
> degree of) stability as established things like 1/4 comma meantone. In the same
> way I am fascinated with the concept of scales that are, to an extent, chords
> and the ideas that "every interval in part gains its purpose for every other
> interval and not just from itself". Indeed I believe, as you stated, "new
> materials always brought with it new applications". You know what...that last
> example I gave of an attempt at a consonant melody in the dyadically "horrid"
> 13TET was built to rather do the same sort of thing...and as I recall Igs even
> was surprised it felt "beatless" despite containing tons of "horribly" beating
> dyads (not sure if that was posted in my folder here or on MMM...but it's at one
> of those two places).
>
> Granted, some of these applications are more abscure to find and often have
> less and less obvious uses than the "mainstream ones" ...but that certainly
> doesn't make them anything near useless or "chasing a straw man", as many people
> on this list seem to say.
>

I agree with the sentiment here.
I think as far as anything 'widely used' we have to remember that there are elements of western theory and practice that appeared briefly, say polytonality, yet are still apart of the tradition.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Carl>"How about you cite something, which we asked for in the beginning of this
> thread: a single example of 11-limit intervals in a maqam recording."
>
>
> Counter question: why should we care about this presumably self-imposed
> limit? What if tradition showed little of Maqam polyphony or use of 11-limit?
> Ozan (and presumably Margo though I have yet to hear her works) have proven
> through their own music just how useful such things can be. So maybe 11-limit
> JI (or as Margo said, technically Rational Intonation) isn't readily used in
> Maqam tradition, boohoo...maybe we should start evolving the tradition a bit by
> using it! ;-)
>
> It's funny because when Margo started this post, I recall she made it
> remarkably clear that while tetrachords and such (rather played via polyphony or
> from one instrument) ARE in Islamic theory even if not widely used in
> practice...and indirectly implied, both through her and Ozan's work, that
> pushing such use into tradition would not be counter to Maqam theory at all.
>

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:

> Now that you mention it, though, it is my opinion that the study of tempering and commas is relevant to maqam intonation. Ozan may disagree, even strongly, but I suspect that a lot of the ancient and medieval tuning writings might actually assume the tempering out of certain intervals. I imagine that the Pythagorean interval which is two cents from 6:5 might very well have been meant to be 6:5 (there is a reproduction of an old Pythagoren tanbur fretting scheme presenting this interval at Ozan's site, IIRC).

The two cents to which you refer is the schisma, and so this is schismatic temperament. When you produce chains of pure fifths of 17 or 24 notes to the octave, you get such things all over the place. Schismatic is a microtemperament, so you don't need to flatten the fifth by 1/8 or 1/9 or 1/10 or whatever of a schisma to get good results, and you can call the JI tuning a temperament tuning if that's how it is being used. When I mentioned 171 as a tuning for maqam music, Ozan didn't go for it, but I think he said it was because it involved too many notes.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
> For the individual, or groups strongly sharing feelings by mutual consent? Of course
> intervals have emotional/emotive qualities in this way. Dry empirical qualities such as,
> this tone is measured at more cycles per second than that tone? They have these kinds of > qualities, too. Universal emotional/emotive qualities? No.

Oh come on, you've said yourself several times that minor can sound happy and major can sound sad and vice versa, even to you. Are you retracting that?

> > >Like claims that 7:6 is explained by 12-tET
> >
> > No one said this.
>
> Really?
>
[snip]
> "So I've been looking at your 2009 paper (Weighing Diverse...)
> and I'm shocked at how far 12-ET can go to explain the results.
> Here are my quick & dirty notes on the histograms:
>
> rast 9/8 5/4 4/3 3/2 2/1
> nihavend 9/8--7/6 4/3 3/2--8 10 2/1
> kurdilihicazkar 1 2 7/6 4/3 3/2--8--10 2/1
> ussak 1.5 7/6 4/3 3/2--7.75 7/4 2/1
> huseyni 1.5 7/6 4/3 3/2--8.75 7/4 2/1
> hicaz 1.25 5/4--4/3 3/2--8.75 7/4 2/1
> saba 1.75 7/6 4.25 4/3 3/2--8 10 2/1
> segah 1.25 6/5 4/3--3/2 8.25 10.5 2/1
> huzzam 1.25 6/5 4.5 3/2--8.25 10.5
>
> There's a possible tendency to use 1/1 7/6 4/3 for a trichord,
> repeated at 3/2."
>
> Other than the 4/3s and 3/2s, I don't see anything there to justify
> "how far 12-ET can go to explain the results." 12-tEt doesn't explain these results,
> which are watered-down interpretations of the actual data to boot, at all!

Well, I'm not sure what Carl was really getting at with that, but I'm quite certain he was not suggesting that 7/6 is explained by 12-tET. He certainly didn't make any assertions that 12-tET explained all of it, or even a lot--just that it explained more than he expected it to. Those whole-numbers--1, 2, 8, 10, etc.--are 12-tET semitones, and I believe Carl was probably surprised (as am I) to find actual 12-tET semitones cropping up in maqam music alongside ratios and integer fractions of semitones (the decimal numbers).

> > No one has suggested that people cannot tune a pitch within the same region as
> > ratios of 11, just that specifically the ratios themselves are not responsible for any
> >psychoacoustic attraction (given typical harmonic timbres).
>
> Really?
>
> /tuning/topicId_94046.html#94048
>
> Carl to Margo:
>
> "Generally the point is that ratios (dyads) of 11 are not
> tunable by ear either harmonically or melodically. "

That is a radically different assertion than saying someone can't tune a neutral 3rd or neutral 2nd etc. by ear. We all know that people can and do tune neutral intervals like these by ear all the time, and the only thing anyone has ever debated is the validity of insisting that the intervals being tuned are de-facto ratios of 11 (vs. a fuzzily-defined probability distribution of pitch centered on something like 350 cents or whatever). So yes, neutral thirds et al--totally tunable by ear. Just because ratios of 11 are within the probability distribution of these neutral intervals, does that mean they are tunable by ear?

Igliashon wrote:
> >Personally, I think maxima of harmonic entropy are as easy to tune as minima

Cameron wrote:
> Could be, I'm very open to that possibility.

I wonder what Carl thinks...

> You miss the point: it's the complex intervals of the ancient and medieval writers which > have been accused of being numerology. I merely point out that there turns out to be far > far less of this alleged "complexity" when you look at the intervals in context and in the > light of fretting methodology. So what happens to the argument that we can disregard an > old text because it is just number magic, when the claim that it is number magic is
> based on a complexity which turns out to be illusory? It sinks.

But the complexity *isn't* always illusory. Ratios of 11, for instance, do not pop out of a simple Pythagorean-esque bearing plan. In fact, I'd say the whole "bearing-plan based on simple ratios" is more justification for the use of higher-integer-but-lower-prime-limit ratios in ancient tunings than it is for higher-prime-limit-but-lower-integer ratios. Of course, this assumes fixed-pitch instruments; to suggest that a fretless player or a singer or whatever can follow a bearing-plan of any sort is a little harder to swallow.

Either way, I really think you've misinterpreted Carl's arguments, and the two of you will get nowhere until you actually understand each other.

-Igs

Gene, what you say has nothing to do with what I said.

Oz.

--

✩ ✩ ✩
www.ozanyarman.com

genewardsmith wrote:
>
> --- In tuning@yahoogroups.com, Ozan Yarman<ozanyarman@...> wrote:
>> Has it escaped the attention of everyone that music is a social/cultural
>> artform just like all other art forms and is not necessarily dependant
>> on a set of cold empirical data that comes out of the laboratory?
>
> An observation which does not in any way support the notion that there some chance a fifth of exactly 600+300/pi cents is much better than other fifths a small fraction of a cent away. That music is an art does not mean theories about it should fail to make any sense.
>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Good idea...where can I find simple documentation on these (IE given a
> fraction or equation...covert to a "spread out" variation)? I Googled but the
> explanations I found IE http://www.uni-salzburg.at/pls/portal/docs/1/1275177.PDF
> were a bit above my head. One thing is for sure to me though...the results of
> 1.145 and 1.17085 along with 1.4131 and 1.3819 are a bit too close for comfort.
>

I don't know if there is an irrational interval version of Brun, but Crunch assumes we are working with rational numbers. It would be possible to modify it for regular temperaments, however.

Gene wrote:

> And why, even if he is right about waveforms,
> it in any way supports the idea of defining
> the fifth in terms (logarithmically) of 1/pi? It's
> the last point which is really the looniest.

I dunno, the waveforms are pretty loony.

-Carl

Gene wrote:

> An observation which does not in any way support the notion
> that there some chance a fifth of exactly 600+300/pi cents
> is much better than other fifths a small fraction of a
> cent away. That music is an art does not mean theories about
> it should fail to make any sense.

Exactly. When you get on a mailing list and make falsifiable
claims with numbers and such, you are no longer in the
subjective land of art. I don't come into your practice room
and tell you you're doing it wrong.

-Carl

Igs wrote:

> > > Personally, I think maxima of harmonic entropy are as easy
> > > to tune as minima
> >
> > Could be, I'm very open to that possibility.
>
> I wonder what Carl thinks...

I think they're not as easy to tune, but they may be easier
to tune than intervals that aren't maxima or minima.

-Carl

>"And why, even if he is right about waveforms, it in any way supports the idea
>of defining the fifth in terms (logarithmically) of 1/pi? It's the last point
>which is really the looniest."

The only way to disprove it though, is to show people some "Loony Tunes"
(lol) in Lucytuning and then the same tunes in a favored mean-tone like 1/4
comma and see which ones they like better... Hate to be like this but, in the
end, crazy or not, the question becomes can someone ultimately make "generally
regarded as" more useful music out of it than with competitive tunings?

Kraig>"BTW i forgot to mention that Buzz Kimball had also done some convincing
melodies with 13 ET."
Hehehe...awesome...I want to hear them...if you can post them, more power to
you! :-)

Gene>"I don't know if there is an irrational interval version of Brun, but
Crunch assumes we are working with rational numbers. It would be possible to
modify it for regular temperaments, however."

Still, that (a copy of the "rational only" algorithm) would be greatly
appreciated. By rounding to the nearest 15-odd limit or so fraction I should be
able to get everything within 7 cents or so, I figure...before I toss it into
your algorithm.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> Gene, what you say has nothing to do with what I said.

You responded to a posting about LucyTuning, so I assumed your remarks were in that connection.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"And why, even if he is right about waveforms, it in any way supports the idea
> >of defining the fifth in terms (logarithmically) of 1/pi? It's the last point
> >which is really the looniest."
>
> The only way to disprove it though, is to show people some "Loony Tunes"
> (lol) in Lucytuning and then the same tunes in a favored mean-tone like 1/4
> comma and see which ones they like better...

Since Lucy claims his tuning is better than other tunings such as 88et which are so close to it you can't tell them apart by ear, this wouldn't work.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Still, that (a copy of the "rational only" algorithm) would be greatly
> appreciated. By rounding to the nearest 15-odd limit or so fraction I should be
> able to get everything within 7 cents or so, I figure...before I toss it into
> your algorithm.
>

It's not all that wedded to rationals, that's just what I was thinking of. It's more or less the same as Brun's algorithm in any case.

/tuning-math/message/8999

Me> The only way to disprove it though, is to show people some "Loony Tunes"

> (lol) in Lucytuning and then the same tunes in a favored mean-tone like 1/4
> comma and see which ones they like better...

Gene>"Since Lucy claims his tuning is better than other tunings such as 88et
which are so close to it you can't tell them apart by ear, this wouldn't work."

This seems much the same problem as Ozan's scale has vs. much higher TETs
that approximate his scales almost perfectly. Heck, even my "crazy" PHI
sections scale can be approximated with a few cents by a 50+ TET...almost any
scale can. The difference seems to be can a competitive scale or tuning get the
same quality of feel within an equal or less number of tones (which I figure
would have significant implications to all of; ease of instrument design, ease
of composing with electronically, ease of writing theories for/regarding, and
ease of writing to a 'score' system).

I figure one solution to this "but a high TET can approximate it with
virtual perfection!" issue is to try, say, 19 and 25-tone Lucytuning (it says on
http://lucytune.com/press_room/st_nov_87.html that Lucytuned scale have 19 or 25
parts)...and compare it to other scales of up to 25 tones...and see which of
those sound better to most people in a survey.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> I figure one solution to this "but a high TET can approximate it with
> virtual perfection!" issue is to try, say, 19 and 25-tone Lucytuning (it says on
> http://lucytune.com/press_room/st_nov_87.html that Lucytuned scale have 19 or 25
> parts)...and compare it to other scales of up to 25 tones...and see which of
> those sound better to most people in a survey.
>

My tiny and unscientific sampling of people who've compared 55, 43, 31, and 50 suggests people prefer something sharper than 1/4 comma rather than flatter. 43 sounds pretty good to some people. But it no doubt depends on the style of music to a great extent.

On Wed, Nov 3, 2010 at 5:00 PM, Michael <djtrancendance@...> wrote:
>
> Me> The only way to disprove it though, is to show people some "Loony Tunes"
> > (lol) in Lucytuning and then the same tunes in a favored mean-tone like 1/4
> > comma and see which ones they like better...

A simple understanding of basic acoustics would also be enough to
disprove it. You can't just make a random claim that doesn't make any
acoustical, psychoacoustical, mathematical, etc. sense, provide no
explanation whatsoever as to why this new idea should be true, and
then harp on that your ideas can't be disproven unless someone spends
lots of money to do a huge listening test.

Well, you can, but what's your goal? It certainly isn't to try and
figure out how things work.

-Mike

MikeB>"A simple understanding of basic acoustics would also be enough to
disprove it."

How does Lucytuning translate into direct conflict with basic acoustics?
And even if it did...does that guarantee it will sound bad in an actual
listening scenario?

>"You can't just make a random claim that doesn't make any acoustical,
>psychoacoustical, mathematical, etc. sense, provide no explanation whatsoever as
>to why this new idea should be true, and then harp on that your ideas can't be
>disproven unless someone spends lots of money to do a huge listening test.
>Well, you can, but what's your goal?"

Exactly, given a listening test (and who says it has to be huge and
expensive?), you could prove it at least has a purpose, but (agreed) not "why"
(at least directly).
Remember that Knowsur album posted (I believe to this list along with MMM
that reveled in the acoustically "wrong" tunings of 7 and 14TET making many
people on list say "wow, that actually sounds good, I'm going to have to try
composing in 7 and 14TET again..." and then start several threads trying to
explain why/how 7 and 14TET can work despite "basic acoustics conflicts"?
When you have more people taking an idea seriously, though, the chance of their
working together and finding out "why" (whether it agrees with the at times
bizarre reasons Lucy thinks is why or not) becomes much more realistic to
approach.

And in the case such a test proved people consistantly did not favor
Lucytuning , that would put a "publically-voted" final nail in the coffin and
likely hint to the previously mentioned suspicion that Lucytuning is indeed more
an example of good promotion and/or advertising boosting the appearance of a
theory than anything musically useful.

Yes, thanks- I couldn't remember the name of the comma off-hand.
171 is the equal division that I found over time time to work for what I mostly do, but the only reason I'd use it would be for notation, and I think it's too dang big for that.

Both you and Ozan have mentioned 171, I checked the archives here some time ago.

I suspect that schismatic temperament was implied in a sitar tuning and fretting system I stumbled across on the internet a few years ago (sitar frets are moveable). The "bearing plan" was very Pythagorean, all kinds of fifths bouncing around (check here, check there...) but my understanding was that they were also targeting tones heard "in the drone" which are obviously simple harmonic relations. Maybe you'll agree that that sounds like a very plausible instance of schismatic temperament taking place, maybe even unconsciously.

And I think it's a reasonable possibility in other historical Pythagorean systems.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
>
> > Now that you mention it, though, it is my opinion that the study of tempering and commas is relevant to maqam intonation. Ozan may disagree, even strongly, but I suspect that a lot of the ancient and medieval tuning writings might actually assume the tempering out of certain intervals. I imagine that the Pythagorean interval which is two cents from 6:5 might very well have been meant to be 6:5 (there is a reproduction of an old Pythagoren tanbur fretting scheme presenting this interval at Ozan's site, IIRC).
>
> The two cents to which you refer is the schisma, and so this is schismatic temperament. When you produce chains of pure fifths of 17 or 24 notes to the octave, you get such things all over the place. Schismatic is a microtemperament, so you don't need to flatten the fifth by 1/8 or 1/9 or 1/10 or whatever of a schisma to get good results, and you can call the JI tuning a temperament tuning if that's how it is being used. When I mentioned 171 as a tuning for maqam music, Ozan didn't go for it, but I think he said it was because it involved too many notes.
>

On Wed, Nov 3, 2010 at 5:30 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"A simple understanding of basic acoustics would also be enough to disprove it."
>
>     How does Lucytuning translate into direct conflict with basic acoustics?

All of the spherical wavefront stuff is nonsense. Here's where
spherical wavefront stuff might actually matter: the cochlea is not a
single "point microphone" picking up the wave. I always forget which
way it's laid out, but I think the higher frequencies are further down
the waveguide than the lower ones. And I'm too busy to delve into it
now, but I remember that this had something to do with the asymmetry
in masking, in which lower frequencies mask higher ones more than the
reverse.

None of this has anything to do with VF's or musical consonance or pi.

> And even if it did...does that guarantee it will sound bad in an actual listening scenario?

No, but once you start trying to come up with concrete explanations
for your scales, then you move out of the realm of "art" and into the
realm of "science." And just because a scale sounds good (LucyTuning
is a pretty good meantone that I like a lot) doesn't prove anything
about spherical harmonics or what not.

>      Remember that Knowsur album posted (I believe to this list along with MMM that reveled in the acoustically "wrong" tunings of 7 and 14TET making many people on list say "wow, that actually sounds good, I'm going to have to try composing in 7 and 14TET again..." and then start several threads trying to explain why/how 7 and 14TET can work despite "basic acoustics conflicts"?    When you have more people taking an idea seriously, though, the chance of their working together and finding out "why" (whether it agrees with the at times bizarre reasons Lucy thinks is why or not) becomes much more realistic to approach.

In general, I think you should spend less time debating acoustics and
more time learning acoustics. Everything that you're saying comes out
of the fact that there might be some areas of acoustics that you
haven't studied. If you were to delve into it a bit, you would
probably realize why some of the things that folks around here think
are silly are silly. At least learn the theory first so you can throw
it away later or extend it.

I don't think that there are any 7-tet "acoustics conflicts." I think
that there is a long-standing source of disagreement on this list
about the exact resolution of the ear-brain temporal analysis system,
and how it can resolve harmonics and how strong the VF system is.

Some people tend to think that this resolution is more on the high
side (Cameron), some think it's more on the low side (Carl). There are
some who think it's on the super-high side (the JI folks) and some who
think it's on the super-low side (me, kind of). There are a lot of
people in between.

There is then a second disagreement about how much the brain can adapt
given repeated exposure to "discordant" dyads to eventually resolve
the VF. Some tend to think that the brain's adaptive capacity is high
in this regard (Cameron), some tend to think that it's lower (I think
this is where Carl stands). I'm somewhere in the middle. In general
this is a disagreement about how cognitive factors (such as learning)
and hard-wired psychoacoustical factors interact.

There is then a third disagreement about how dyadic analysis extends
to triadic analysis, and everyone seems to be all over the place with
that. I tend to be more on the extreme side in that I think that the
brain's ability to resolve triads is much less than its ability to
resolve dyads. That is, I don't think that there's any point in
calling something 10:12:15 unless it's actually perceived as pointing
to 1, just like I don't think that there's any point in calling
something 501:400 unless it's actually pointing to 1 - otherwise it's
a mistuned 5/4.

I also think a fourth disagreement is emerging, and one that I'm not
entirely sure that people are aware they're engaged in, that has to do
with what it means to "place" a JI dyad/triad/whatever. For example,
there are generally two things that happen when a JI dyad is played -
some kind of virtual fundamental starts to pop out, and the partials
that are close enough to beat end up beating in some kind of recurring
polyrhythm with one another ("periodicity buzz"). I'm not sure I fully
understand all of the psychoacoustic mechanisms behind the latter.

But when some people refer to "placing" or "being able to identify" a
chunk of the harmonic series, they're referring to the VF part of it
(Carl) and then other people use the same terminology to refer to the
periodicity buzz aspect of it (I think this is what Cameron's doing).
The two are generally lumped together but I'm not entirely sure that
this is the right way to go.

I also think that the recognition of different periodicity buzz
"imprints" is something that's more easily influenced by learning than
the VF aspect of it, but I could be wrong.

The point is that these are all things where there's not like a wealth
of research, so there's lots of disagreements about it. I have some of
my own ideas that are rather extreme compared to the status quo around
here. But none of this has to do with "basic acoustics" and 7-tet is
not in conflict with any of that.

>     And in the case such a test proved people consistantly did not favor Lucytuning , that would put a "publically-voted" final nail in the coffin and likely hint to the previously mentioned suspicion that Lucytuning is indeed more an example of good promotion and/or advertising boosting the appearance of a theory than anything musically useful.

No. Even if Lucytuning sounds great, that still wouldn't say anything
about the underlying theory behind it.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
.
>
> Oh come on, you've said yourself several times that minor can sound happy and major can sound sad and vice versa, even to you. Are you retracting that?

Certainly not. Music is not a montage of isolated and reified "signifiers". A color that we subjectively feel as soft and warm on its own or in most contexts can seem cold and jarring in the right (or wrong) painting.

>
> > > >Like claims that 7:6 is explained by 12-tET
> > >
> > > No one said this.
> >
> > Really?
> >
> [snip]
> > "So I've been looking at your 2009 paper (Weighing Diverse...)
> > and I'm shocked at how far 12-ET can go to explain the results.
> > Here are my quick & dirty notes on the histograms:
> >
> > rast 9/8 5/4 4/3 3/2 2/1
> > nihavend 9/8--7/6 4/3 3/2--8 10 2/1
> > kurdilihicazkar 1 2 7/6 4/3 3/2--8--10 2/1
> > ussak 1.5 7/6 4/3 3/2--7.75 7/4 2/1
> > huseyni 1.5 7/6 4/3 3/2--8.75 7/4 2/1
> > hicaz 1.25 5/4--4/3 3/2--8.75 7/4 2/1
> > saba 1.75 7/6 4.25 4/3 3/2--8 10 2/1
> > segah 1.25 6/5 4/3--3/2 8.25 10.5 2/1
> > huzzam 1.25 6/5 4.5 3/2--8.25 10.5
> >
> > There's a possible tendency to use 1/1 7/6 4/3 for a trichord,
> > repeated at 3/2."
> >
> > Other than the 4/3s and 3/2s, I don't see anything there to justify
> > "how far 12-ET can go to explain the results." 12-tEt doesn't explain these results,
> > which are watered-down interpretations of the actual data to boot, at all!
>
> Well, I'm not sure what Carl was really getting at with that, but I'm quite certain he was not suggesting that 7/6 is explained by 12-tET. He certainly didn't make any assertions that 12-tET explained all of it, or even a lot--just that it explained more than he expected it to. Those whole-numbers--1, 2, 8, 10, etc.--are 12-tET semitones, and I believe Carl was probably surprised (as am I) to find actual 12-tET semitones cropping up in maqam music alongside ratios and integer fractions of semitones (the decimal numbers).

Even the whole tones and semitones aren't explained by 12-tET. They should come as zero suprise to anyone familiar with even the basics
tuning in the Near East- they are the tones and semitones of Pythagorean tuning. 9:8 and the limma, documented for thousands of years. Although I find that he goes off in a strange direction (I doubt he's a practicing musician), Farhat is a very thoughtful author on Persian music, and full of well-done information you can interpret yourself. I agree with him on calling tones and limmas tones and limmas. :-)
>
> > > No one has suggested that people cannot tune a pitch within the same region as
> > > ratios of 11, just that specifically the ratios themselves are not responsible for any
> > >psychoacoustic attraction (given typical harmonic timbres).
> >
> > Really?
> >
> > /tuning/topicId_94046.html#94048
> >
> > Carl to Margo:
> >
> > "Generally the point is that ratios (dyads) of 11 are not
> > tunable by ear either harmonically or melodically. "
>
> That is a radically different assertion than saying someone can't >tune a neutral 3rd or neutral 2nd etc. by ear. We all know that >people can and do tune neutral intervals like these by ear all the >time, and the only thing anyone has ever debated is the validity of >insisting that the intervals being tuned are de-facto ratios of 11 >>(vs. a fuzzily-defined probability distribution of pitch centered on >something like 350 cents or whatever). So yes, neutral thirds et al->-totally tunable by ear. Just because ratios of 11 are within the >probability distribution of these neutral intervals, does that mean >they are tunable by ear?

As I said, you can throw whatever number magic you like around, it's not going to change reality. What magic property do you propose is it that makes me tune to within a couple of cents of 11:9 and 11:8 over and over again, even sometimes when that is NOT exactly where I'm aiming for? The attraction of 11:7 screws with my 14:9 as well, it's causing me a dilemna with alternate clarinet fingerings. I'm going with the Occam's razor explaination of it being
a matter of these intervals sharing the same kind of "gravity" as other simple harmonic relations.

> Either way, I really think you've misinterpreted Carl's arguments, >and the two of you will get nowhere until you actually understand >each other.
>
> -Igs
>

Could be!

-Cameron Bobro

Mike wrote:

> > How does Lucytuning translate into direct conflict
> > with basic acoustics?
>
> All of the spherical wavefront stuff is nonsense. Here's where
> spherical wavefront stuff might actually matter: the cochlea is
> not a single "point microphone" picking up the wave. I always
> forget which way it's laid out, but I think the higher
> frequencies are further down the waveguide than the lower ones.

The wavelength of a 10KHz tone is over an inch -- larger than
your ear-hole. And don't forget about the ear drum. But even
if your cochlea was an open coffee can, so what?

Of course using pi to determine the size of fifth has nothing
to do with any of this.

> And I'm too busy to delve into it now, but I remember that this
> had something to do with the asymmetry in masking, in which lower
> frequencies mask higher ones more than the reverse.

Basilar membrane displacement is not symmetrical around
the center frequencies...

-Carl

On Wed, Nov 3, 2010 at 6:29 PM, Carl Lumma <carl@...> wrote:
>
> >
> > All of the spherical wavefront stuff is nonsense. Here's where
> > spherical wavefront stuff might actually matter: the cochlea is
> > not a single "point microphone" picking up the wave. I always
> > forget which way it's laid out, but I think the higher
> > frequencies are further down the waveguide than the lower ones.
>
> The wavelength of a 10KHz tone is over an inch -- larger than
> your ear-hole. And don't forget about the ear drum. But even
> if your cochlea was an open coffee can, so what?

I said that I don't think that it matters. But the idea is that if the
cochlea was an open coffee can, the wave would end up hitting the
higher frequency hairs at a later time than the lower frequency hairs,
so there'd be phase distortion across the spectrum (and across the
critical band), although it's not significant in real life.

But the point wasn't about its significance, but that if Charles had
taken that direction with his reasoning, it would at least make some
kind of acoustical sense. But that he took it in the direction of VF
placement doesn't make any sense at all

> Basilar membrane displacement is not symmetrical around
> the center frequencies...

Yeah, but weren't we talking about this last month, and didn't we end
up talking about how the traveling wave, as it moves down the cochlea,
causes some particular psychoacoustic effect since it's "traveling?" I
don't think it had anything to do with the cochlear amplification
mechanism. Do you remember what it was? Maybe it was just a random
factoid that I came across in the medical literature that I didn't
post.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Cameron wrote:
>
> > /tuning/topicId_89711.html#90119?var=0&l=1
> [snip]
> > Other than the 4/3s and 3/2s, I don't see anything there to
> > justify "how far 12-ET can go to explain the results."
>
> The 8 and 10 are 12-ET degrees. There's also the matter
> of relative power of these things on the histograms.

You really don't have any idea of the gravity of the conceptual
boo-boo you made calling those things by 12-tET, do you?

>
> > > No one has suggested that people cannot tune a pitch within
> > > the same region as ratios of 11, just that specifically the
> > > ratios themselves are not responsible for any psychoacoustic
> > > attraction (given typical harmonic timbres).
> >
> > Really?
>
> Yes, really.

Okay, I see what you're saying. It's just bunk in my experience. You can wave your midnight chicken and gilt abacus at the crossroads all you want, it's not going to solve the problem that my sweet-sounding 14:9 fingering requires a good deal of lipping down against the aural gravity of 11:7, and me having to use a husky and pale flatter fingering in order to get an accurate 14:9 because my ear is too strongly drawn to 11:7 in the nicer fingering.

> Howabout you cite something, which we asked for in the
> beginning of this thread: a single example of 11-limit
> intervals in a maqam recording. You know, in the vast
> collection on youtube, which you suggested we peruse.

Sure, as soon as I come across something that distinctly sounds
that way to me. Remember that I said that after a certain point, and I think we actually agree to a pretty good extent what that point is, it becomes a matter of choice what you call things. It's unlikely that I could distinguish a 13:12 from "6/7 down from Pythagorean ditone". Should I call it a 243/224? Depends on the context. In Ozan's 79-MOS tuning, I believe the difference is tempered out, and I think this an excellent solution in the daunting task of making a practical quanun tuning. You're making a fool of yourself when you try to paint either of us as number-mystics, for it's plain for all to see that we'e not.

By the way, I'd welcome more genuine number-mystics around here, I think they're groovy even if it's not my bag. Plus there seems to be a
substantial amount of music out there made by number mystics.

-Cameron Bobro

Hi Mike,

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> There is then a third disagreement about how dyadic analysis extends
> to triadic analysis, and everyone seems to be all over the place with
> that. I tend to be more on the extreme side in that I think that the
> brain's ability to resolve triads is much less than its ability to
> resolve dyads. That is, I don't think that there's any point in
> calling something 10:12:15 unless it's actually perceived as pointing
> to 1, just like I don't think that there's any point in calling
> something 501:400 unless it's actually pointing to 1 - otherwise it's
> a mistuned 5/4.

I hear 10:12:15:17 as being more consonant than 1/1:6/5:3/2:12/7.
10:12:15:17 doesn't point to 1, but by mere dyadic analysis it should
sound less consonant than 1/1:6/5:3/2:12/7. So I think there is a
point in calling it 10:12:15:17 even though it doesn't point to 1.

Kalle

On Wed, Nov 3, 2010 at 7:07 PM, Kalle Aho <kalleaho@...> wrote:
>
> I hear 10:12:15:17 as being more consonant than 1/1:6/5:3/2:12/7.
> 10:12:15:17 doesn't point to 1, but by mere dyadic analysis it should
> sound less consonant than 1/1:6/5:3/2:12/7. So I think there is a
> point in calling it 10:12:15:17 even though it doesn't point to 1.
>
> Kalle

A few things -

1) I don't think dyadic analysis matters so much when tetrads are
involved, except to come up with chords that lack roughness
2) You do have a good point in that the intonation can make a huge
difference and that JI numbers can be a good way to specify a specific
intonation. So I concede to you that point
3) But I still don't think that 10:12:15:17 points to 1, and I think
that there might be a more fundamental "minor chord" that 10:12:15:17
and 1/(4:5:6:7) and 16:19:24:27 are just specific intonations of, and
I don't think that this more fundamental underlying minor chord has to
do with JI.
4) Rather I think that it draws some of its emotion from NOT pointing
to a particular 1, but not quite being so discordant that the brain
chills out and labels it a benign noise component of the scene.

-Mike

Mike wrote:

> the idea is that if the cochlea was an open coffee can,
> the wave would end up hitting the higher frequency hairs
> at a later time than the lower frequency hairs, so there'd
> be phase distortion across the spectrum (and across the
> critical band), although it's not significant in real life.

? The wavefront isn't biased with respect to frequency.
Actually it is, depending on the size of the vibrating
object, but that's angular at the source and so the coffee
can still isn't big enough.

But this *does* happen, since it takes time for the wave
to travel down the basilar membrane...

> > Basilar membrane displacement is not symmetrical around
> > the center frequencies...
>
> Yeah, but weren't we talking about this last month, and didn't
> we end up talking about how the traveling wave, as it moves
> down the cochlea, causes some particular psychoacoustic effect
> since it's "traveling?"

I don't remember anything about traveling but masking
(and "pitch shifts") are both related to the asymmetry of
the displacements.

-Carl

Hi Kalle:
> I hear 10:12:15:17 as being more consonant than 1/1:6/5:3/2:12/7.
> 10:12:15:17 doesn't point to 1,

Neither chord points to 1. I agree :17 is more concordant.

-Carl

Just tested 11/9 with the triangle wave test, to distinguish it from
347.0 and from 348.0 (11/9 is 347.407)

There are very clear beats. High pitched but unmistakeable, I don't think I can be fooling myself there, and can easily believe an experienced instrumentalist would be able to tune an exact 11/9 just by tuning until the dyad goes beatless. I'd even call that one easy.

Hardest part would be getting in the region of the desired dyad to start with (plus of course you need an instrument rich in high partials so you can hear the beats, wouldn't be able to tune it, at least in that way, on the recorder).

It's much easier than 81/64.

I'll upload examples so everyone can try when I do the test. Because the 81/64 is subtle - listening again I still think I can probably distinguish it and seems to be by listening to the variation in apparent volume of the difference tone. But would probably help to have an easier one or a couple of easier ones first.

Then you can see how far you get - if you can distinguish an 11/9, and an 81/64. Anyone else got suggestions for a nice one to do the example for? Might be nice to have a third one intermediate in difficulty between those two as it is a bit of a big jump in difficulty from the 11/9 to the 81/64.

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:
>
> Partch tuned his 11s by ear. There are quite a few strings players just in Los Angeles that do this also
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
>
> > > No one has suggested that people cannot tune a pitch within the >same region as ratios of 11, just that specifically the ratios >themselves are not responsible for any psychoacoustic attraction >(given typical harmonic timbres).
> >
> > Really?
> >
> > /tuning/topicId_94046.html#94048
> >
>

On Wed, Nov 3, 2010 at 7:32 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > the idea is that if the cochlea was an open coffee can,
> > the wave would end up hitting the higher frequency hairs
> > at a later time than the lower frequency hairs, so there'd
> > be phase distortion across the spectrum (and across the
> > critical band), although it's not significant in real life.
>
> ? The wavefront isn't biased with respect to frequency.
> Actually it is, depending on the size of the vibrating
> object, but that's angular at the source and so the coffee
> can still isn't big enough.

That isn't what I meant, but for the sake of argument, if the
wavefront were moving through some kind of fluid as in the perilymph
in the cochlea, then the speed of sound would depend on frequency,
yes? Since water is a dispersive medium...

But I was really getting at:

> But this *does* happen, since it takes time for the wave
> to travel down the basilar membrane...

^ was this.

> I don't remember anything about traveling but masking
> (and "pitch shifts") are both related to the asymmetry of
> the displacements.

I don't remember what it was anymore. I'll find it some day. I think
it might have been that the asymmetry of the displacements was caused
in part by the traveling wave or something like that. Or maybe not. I
really don't remember anymore.

-Mike

Hi Robert,

> Just tested 11/9 with the triangle wave test, to distinguish it from
> 347.0 and from 348.0 (11/9 is 347.407)
>
> There are very clear beats. High pitched but unmistakeable,
> I don't think I can be fooling myself there, and can easily
> believe an experienced instrumentalist would be able to tune an
> exact 11/9 just by tuning until the dyad goes beatless.
> I'd even call that one easy.

I take it you mean 347 and 348 have beats while 11/9 does not.
Unfortunately we don't have the ability on real instruments
to make adjustments of 0.4 cents. Also, listening to discrete
sounds is not the same experience as tuning a continuous
oscillator. Lastly, I will say again that almost anything can
be learned with training. That is a very different matter
from doing it (and even thinking of doing it) naively. I do
think it would be a valuable tool to have a basic continuously-
tunable synth with either triangle or sine waves, both upper
and lower tone tunable, and a switch to blind the readout of
cents between them.

-Carl

Mike wrote:

> then the speed of sound would depend on frequency, yes?

Not over the range of human hearing. -Carl

On Wed, Nov 3, 2010 at 8:47 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > then the speed of sound would depend on frequency, yes?
>
> Not over the range of human hearing. -Carl

In water? Do you have a reference? I was looking for an equation
relating the speed of sound in water to frequency but couldn't find
one.

-Mike

MikeB>"but I remember that this had something to do with the asymmetry in
masking, in which lower frequencies mask higher ones more than the reverse."
I remember reading something similar in mp3 "frequency masking"
description...that the analysis works from the bottom frequencies going up and
not the other way around. In addition it takes louder low frequencies to be
audible than higher ones on the frequency curve (perceptual curve of human
hearing). And yes, I'm saying "I know" not "I think" this time around...because
I've been heavily involved in the past in mp3 programming and know a whole lot
of this stuff by heart.

>"None of this has anything to do with VF's or musical consonance or pi."
Agreed IE even if Lucytuning does work...it's likely not for that (false)
reason.

>"And just because a scale sounds good (LucyTuning is a pretty good meantone that
>I like a lot) doesn't prove anything about spherical harmonics or what not."
So Lucytuning doesn't have any impressive scientific explanations...so what?
Neither does my PHI scale, or Igs's or Knowsur's musical ability to make
psychoacoustically lousy tunings quite listenable. I guess my point is...many
things in music can work well without explanation: if we can find explanations,
all the better...but if we can't it doesn't mean the result must be less
musically useful.

>"Everything that you're saying comes out of the fact that there might be some
>areas of acoustics that you
haven't studied. "

First of all, it's simply not true for a large part. For example, yes, I've
heard about the Basilar Membrane, and frequency masking along it long before you
mentioned it (and even mentioned these things several times on list). No, I
have never considered the pattern as a "circle" the way you have or thought of
it as something Charles Lucy might have been confused by and built mis-claims
around...but that certainly doesn't mean I don't know it. In fact I remember
you asking me about a month ago on tuning research "what do you mean by
frequency masking?" when you asked about why noise waves don't sound as
dissonant as they "should".
And if you're going to make huge generalizing statements against me, at least
give specific examples so I get a fair chance to say what I do know.

>"If you were to delve into it a bit, you would probably realize why some of the
>things that folks around here think are silly are silly."

I don't think what Charles was claiming is "not silly"...I just don't get
how you can attack his claim when all the knowledge you seem to have to know
"what he meant" appears nothing more than a guess. Granted, his website is
pretty vague about his theories. Furthermore, again, even if he did, say, mean
to tie Lucytuning to frequency masking (which obviously does not work)...who
cares (it doesn't, alone, mean it sounds bad)?

>"I don't think that there are any 7-tet "acoustics conflicts." I think that
>there is a long-standing source of disagreement on this list about the exact
>resolution of the ear-brain temporal analysis system, and how it can resolve
>harmonics and how strong the VF system is."

In that case, what surprises me is that it seems to imply either the VF
system is not what defines a lot of the sense of "rootedness" in 7TET or that
the system can work differently than it was originally thought to. I still
don't see why you thing Lucytuning is any more "acoustically conflicting" than
7TET...unless you are rating it by its ability to mirror the activity of
ascending frequency masking (something you seem to assume but I've never heard
Charles say IE "by 3D and PI I mean the curve of frequency masking in the
Basilar Membrane").

>"some who think it's on the super-low side (me, kind of)"

Super low side meaning...there are whole lot of frequencies between things
like low-limit JI ratios that act as weak versions of those ratios and imply
similar virtual root tones?

>"I tend to be more on the extreme side in that I think that the brain's ability
>to resolve triads is much less than its ability to resolve dyads."
Agreed, in fact the larger the chord, the less notes seem to matter and the
less obvious the root to me.

>"the partials that are close enough to beat end up beating in some kind of
>recurring
polyrhythm with one another ("periodicity buzz")"

Now this really makes me wonder: I understand periodicity buzz as simply equal
difference tones IE 300hz 400hz 500hz has a constant 100hz periodicity buzz.
I'm guessing the idea revolves around that the oscillation generated by
periodicity buzz itself begins to act as the prominent Virtual Fundamental?.

>"No. Even if Lucytuning sounds great, that still wouldn't say anything about the
>underlying theory behind it."
Never said it would...but I did say (and will say again) that if that did
happen, it might get people thinking seriously about finding out what makes it
click. And I agree: Charles's reasons why it supposedly worse seem vague and
unprovable via acoustics (at least in the detail he describes them in)...but
that doesn't necessarily mean other people can't find a better reason why
Lucytuning works.
And again, if such a test fails...nothing more to be said and a whole lot of
theorists will continue not taking Lucytuning seriously...end of story.

Cameron>"What magic property do you propose is it that makes me tune to within a
couple of cents of 11:9 and 11:8 over and over again, even sometimes when that
is NOT exactly where I'm aiming for? The attraction of 11:7 screws with my 14:9
as well"....

Funny, 11/7, 11/8, and 11/9 are several of my favored 11-limit and 15-limit
ratios that I find easiest on the ear among the 11th limit by far.

In fact, when I think about it, 22/15 (between 10/7 and 3/2) , 18/11 (between
8/5 and 5/3), 11/9 (between 6/5 and 5/4) and 15/11 and 11/8 (between 4/3 and
7/5)...seem to have in common that the are outside fields of attraction of their
neighboring Harmonic Entropy tones. It appears to imply (since it's a constant
pattern among them) that a major reason they may come across clearly as they are
NOT fighting with those tones for tonal identity.

It also begs the question (especially you, Cameron) do you think the above
mentioned ratios (in addition to the ones you mentioned) are substantially
easier to tune than those similar-limit ratios around them (though obviously not
as easy to tune as something much lower complexity like 5/4)?

[This doesn't attempt to keep up with the dialogues of the
last day or so.]

Carl wrote:

> Hi Margo,

>> Please let me express my regrets for any negative part I may
>> have had in a "debate" which is clearly intruding on the
>> positive purposes of the group and creating more heat than
>> light.

> Thanks for saying so, but I didn't feel you had any negative
> part in it. On the contrary, I enjoyed the messages we
> exchanged and thought they were a good example of how such
> things can go. I hope this sense was mutual but if not, it
> certainly wasn't my intention and please contact me offlist if
> you would like to discuss it further.

Great, and I'll confirm that the sense is mutual. In fact, this
looks like a fascinating dialogue, and among other things a
chance to clarify what some of my own positions are or aren't.
Your remarks that follow are invaluable for presenting me an
opportunity to do this, an opportunity which might be very
helpful for the list. It's so easy for me to have "unspoken"
understandings about the meaning of my own words not so obvious
to anyone else.

And I should briefly mention a couple of my technical
limitations: I have no means to access or hear videos, or to do
measurements of frequencies or intervals in cents for a maqam
performance, say. But I'm immensely interested in what you, Ozan,
Cameron, Jacques, or others might find.

>> What are the real issues, not necessarily or solely factual,
>> in question? Well, my own position could be summed up about
>> like this:
>> (1) Medieval Islamic theorists describe tetrachords and
>> modes which are beautiful and can and should be applied to
>> medieval and modern maqamat at least some of the time in some
>> contexts;

> ...Don't see how anyone could disagree with this.

And actually this is about 70% of my point, with a helpful
footnote that I do some rather un-medieval things in my maqam
tunings, with temperament at the top of the list, and the
11:12:13 division (as far as I know) as another.

What both Ozan and I do, in different ways, is to take some
leaves from the medieval book and modify them a bit, or at least
mix in some new ingredients. And for both of us, temperament is
one of those ingredients. The different ways it's used in his
79/80-MOS or my much more modest O3 could be an interesting topic
of comparison.

>> (2) Some of these tunings are closely approximated by
>> current tunings in practical use in various parts of
>> the Near East;

> Seems likely, though the word "closely" can be troublesome.
> The central point I would stress is that we really don't have
> much idea what tunings are currently in use, because of a
> paucity of data. That ought to lead to some humility, which
> would be good for all of us.

What I would predict is that there are far too many variations to
fall neatly into _any_ model, medieval or later, which
recognition may be at least the beginning of humility. Looking at
some measurements of Iranian tunings by Nelly Caron and Dariush
Safvate, and others by Jean During, as well as Hormoz Farhat's
book, I find this variety an inspiration for anyone contemplating
the infinite shadings possible, and of course a daunting obstacle
for anyone who wants a single "master tuning" of any practical
size for a typical acoustical fixed-pitch instrument, as you
suggest below and I agree.

And I see integer ratios as signposts or street numbers, not as
points of unique validity somehow devaluing the territory in
between those signposts. This brings us to a vital point which I
find it prudent to explain before posting summaries of measured
flexible-pitch tunings or instrumental frettings, etc.

An observation of more or less "close" resemblance could lend
itself to any of at least three viewpoints:

VIEWPOINT I: "Isn't it wonderful how medieval tunings
describe interval sizes and shadings close to those of
some tunings used on fixed-pitch instruments or by
flexible-pitch performers today?" Here there's no claim
that the rational values are uniquely salient or
"attractant," only a focus on regions or "neighborhoods"
of the spectrum, leaving open the question of possible
further connections or their lack.

VIEWPOINT 2: "The fact that one or more medieval
theorists describes this rational tetrachord, and this
modern instrument or performance uses or closely
approximates it, indicates that the rational ratios
themselves, not just the general neighborhood or shading,
have some special salience or attractive power."

VIEWPOINT 3: "The correspondence between the medieval
ratios and the modern tuning on a fixed-pitch instrument
shows some common tradition or acoustical logic of the
process of building and playing instruments of the
relevant type."

My own position is to assert Viewpoint 1 and remain open to
evidence one way or the other on Viewpoints 2 and 3, the kinds of
issues raised by Ozan, Cris, and Cameron. Note that my practice
of using certain superparticular or other rational ratios as
intellectually attractive signposts or landmarks in itself
neither affirms nor denies that they may additionally have an
aurally attractive pull for musicians brought up in these
traditions, or a special significance in the vocabulary and
grammar of instrument building, if I may call it that, as a
variation on Cris's etymology of numbers and ratios.

And I must admit that the psychoacoustical theories I would find
most plausible would be those either developed by dastgah and
maqam musicians or at least based on culturally specific
observations of talented performers or listeners brought up in
these traditions who have a native phonology, so to speak.
Objective tests of the ability of people practicing maqam or
dastgah music as a first language to discriminate between shades
of neutral intervals or degrees of contrast between smaller and
larger neutral seconds, for example, might be very interesting.

Further, I find in the Islamic theorists of the Mutazilah Era a
logically attractive lore or discipline focusing on the
gradations and relations of rational ratios, an outlook also
reflected in some portions of _Divisions of the Tetrachord_ by
John Chalmers, that can be embraced while affirming the value of
irrational ratios and divisions also (which John addresses at
length), and leaving open psychoacoustical issues that might not
much affect my artistic outlook, although new knowledge can
always enrich one's perspective.

Having said that, I would emphasize that it's possible to see
resemblances between a medieval rational tuning and a current
intonational practice without necessarily saying that the
specific medieval ratios are precisely represented in, or
"explain," the modern performance.

First, let's consider the oldest description known to me of the
tetrachord that would later be called Rast, al-Farabi's mode of
Zalzal:

1/1 9/8 27/22 4/3
0 204 355 498
9:8 12:11 88:81
204 151 143

Now consider Amine Beyhom's estimate (thesis, Vol. I, at p. 52)
of a typical Lebanese Rast in a "learned" (_savant_) style:

0 200 355 500
200 155 145

When I say that either tuning is "closely approximated" by the
other, I mean simply that they represent similar shades of what
has come to be called Rast. What I'd note is not only the similar
sizes of the neutral thirds, but the subtle difference (around
8-10 cents) between the larger and smaller neutral seconds.

I do not mean to imply that the second tuning is intentionally or
otherwise based on rational ratios, although we might asssociate
200 cents with 9:8. But it's the similar degree of subtle
difference between the two neutral seconds, with the larger
placed first, that catches my attention.

To make my disclaimer more emphatic here, let's consider a
tetrachord that Beyhom measured from a performance in Hijaz by
the Turkish master Kudsi Erguner

<http://www.beyhom.com/download/articles/Beyhom_2007_%20Des_criteres_d_authenticite_filigrane_n5.pdf>:

0 131 368 501
131 237 133

Now I might excitedly, as a self-appointed referee, call "Buzurg"
and cite two possible tetrachords using the ratios specified for
this mode (or actually the lower tetrachord of their pentachordal
schemes) by Safi al-Din al-Urmawi and Qutb al-Din al-Shirazi:

1/1 14/13 16/13 4/3
0 128 359 498
14:13 8:7 13:12
128 231 139

or

1/1 13/12 26/21 4/3
0 139 370 498
13:12 8:7 14:13
128 231 139

Indeed Erguner's tetrachord resembles these in having a small
neutral second, a middle step close to 8:7 (actually a bit
bigger), and another smallish neutral second. Noting this
pleasant kinship, however, isn't to say that Erguner is following
any rational scheme, or is making a distinction between 14:13 and
13:12.

While I can and will celebrate this as an example of a
"Buzurg-type Hijaz," in fact if we are seeking a "close fit,"
36-EDO or 46-EDO would be closer than either rational version of
Buzurg above:

Erguner: 0 131 368 501
131 237 133

36-EDO: 0 133 367 500
133 233 133

46-EDO 0 130 365 496
130 235 130

And I would certainly not conclude from Erguner's performance
that "a Turkish Hijaz of the Buzurg flavor is based on 36-EDO" --
or 46-EDO, for that matter!

Actually, modern Turkish or Syrian theory based on 53 commas
might capture my general category of "Buzurg" as 6-10-6, or here,
using a suggested refinement of Beyhom for models based on 17 or
24 positions per octave, "6- 10+ 6-" to show that each neutral
second is a bit smaller than 6 commas (about 135 cents) while the
middle step is a bit larger than 10 commas (about 226-228 cents)
or even a full 8:7 at 231 cents.

In some cases, we might be able to draw some kind of
"etymological" connection, as Cris Forster has put it, or to draw
some connection between a given fretting scheme and a medieval
theoretical tradition, as Cameron has proposed. But noting
and celebrating some interesting resemblances need not itself
imply either type of connection.

Generally my point in citing and comparing medieval rational
tunings and more or less kindred modern intonations is to
illustrate the variety of Near Eastern tetrachords and shadings,
historical and current.

> However we can say certain things are unlikely. For instance,
> choose a rational number R at random, num(R)*den(R) < 10,000
> and 1 < R < 2. Let's say 55/27. What are the odds it is used
> systematically in maqam music (that is, it is the target of
> some bearing plan, fret placement instruction, vocal training
> regimen, etc, used by more than one musician... that
> musicians/craftsmen have some means of communicating about it,
> not necessarily by name, but in *some* fashion)? Answer: the
> odds are low and we wouldn't believe this unless evidence was
> plainly extant, de novo, of such a bearing plan, fret placement
> instruction, etc. etc.

That's a curious illustration; we're talking about roughly 1232
cents (55/27).

What's likely, or relevant, may depend on the question and on
one's viewpoint. To describe an interval around 370 cents, as on
Cameron's baglama or in my tempered vrsion of a flavor of Turkish
Rast, by association with the rational signpost of 26/21, or a
4/3 less a 14/13, is what some of us find an intuitively
appealing mapping. And, likewise, an interval in this immediate
neighborhood might be associated with 99/80, or 9/8 plus 11/10, a
ratio of around 369 cents occurring in the "Medium Sundered"
tetrachord of Safi al-Din (9:8-11:10-320:297 or 204-165-129
cents).

These conceptual landmarks are useful to some of us -- not
necessarily all of us, as you've made clear! -- in themselves.
Whether fretting schemes might favor these superparticular
patterns more than nearby but distinguishable shadings, and
whether flexible-pitch performers might be especially drawn to
them, are open questions.

>> (3) Just ratios both simple and complex, as well as values
>> in cents, commas, savarts, etc., can be useful in describing
>> and analyzing current Near Eastern practice; and

> I would dispute this beyond the 7-limit. Within the 7-limit
> it's unclear, but plausible, and Weighing Diverse seems to
> support it.

Note that my "useful" may have a minimalistic sense that
rationals can provide an intuitively appealing grid (in the eye
of the beholder!) for mapping and appreciating the continuum of
neutral or Zalzalian seconds or thirds, for example. Such a grid
may or may not itself mark points of salient aural attraction, as
likewise with a grid such as 17-EDO, 24-EDO, or 53-EDO (all of
which have been proposed or used by Near Eastern theorists).

>> (4) Superparticular or other divisions of the medieval
>> theorists, as well as some modern variations, can nicely evoke
>> the state of _tarab_ ("enchantment" or "ecstasy") sought by
>> performances and audiences as an aspect of the maqam
>> tradition.

> I'm not sure how to evaluate this. Beyond the 7-limit I know
> of no property of superparticular intervals that makes them
> special in a melodic context, and even within the 7-limit
> harmonic context, intervals such as 5:3 and 7:4 are on par with
> superparticulars in terms of their stand-out psychoacoustic
> properties.

An ambiguity of my quoted proposition (4), which I'll clarify
now, is whether it means "superparticular and other medieval
divisions alone or especially" or "medieval rational divisions,
among many others." My intended reading is totally nonexclusive,
and thanks for a chance to say so. In other words, "12:13:14 or
128-139 cents is beautiful, and 125-137.5 cents in 96-EDO, or
133.3-133.3 cents in 36-EDO or 63-EDO, might be comparably so."

Whether superparticular divisions such as 12:13:14 or 14:13:12
and 11:12:13 or 13:12:11 have additionally have a special aural
attraction for expert or other performers growing up in a maqam
or dastgah tradition is an empirical question. And I find Cris's
instrumental etymology, which I'll need his book to study in more
detail, quite credible. While Ozan and I have independently been
drawn to the 13:12:11 or 11:12:13 division for certain maqamat or
dastgah-ha, let me prudently note again that I'm not aware of any
medieval sources citing this division.

Also, I don't know if anyone is claiming that superparticulars
and only superparticulars are aurally salient: those of us drawn
to JI/RI have been citing ratios like 13/11, 14/11, and 26/21,
and certainly would recognize 7/4 as well as 16/9 as significant
landmarks. And likewise with 11/9, which Cameron found a clear
aural attractant in certain instrumental timbres (his Spectral
Harmonic Entropy or SHE).

>> Carl, please correct me if I am wrong in seeing your main
>> points as follows:

>> (1) You observe that a 24-EDO model can nicely fit some maqam
>> perforamnces.

> Yes.

And I'd add that Near Eastern theorists such as Vaziri in Iran
have endorsed 24-EDO. I consider it as one point on a continuum.

>> (2) You regard medieval Islamic theory, and likewise the
>> theory of Ptolemy, insofar as it involves superparticular
>> or other rational ratios of medium to high complexity, as
>> having little reference to either the practice of those
>> times or of today -- doubtless allowing an exception for
>> those of us who deliberately study and then set out to
>> implement these tunings.

> I know of no evidence they're connected.

This I see as an open question, which Cris and Cameron may
address further, and the former addresses in detail in his new
book. My own artistic program, which no one else is obliged to
follow (and much less any or all Near Eastern musicians!),
wouldn't depend on the answer.

> I know of strong evidence these theorists would have had no
> alternative but to use rational numbers to express their
> scales.

This is a point that Owen Wright also makes. Cris has commented
that an "equable" division like Ibn Sina's 14;13:12 or 12:13:14
is the way of indicating a 7:6 third derived from two near-equal
steps. While I may like the subtle distinction between 14:13 and
13:12, this doesn't mean a geometric division as in 36-EDO or
63-EDO would be "wrong," or an unequal division like 130-143
cents not necessarily having any clear rational interpretation
(I'm just pulling numbers out of the air for my last example).
One theorist around the 15th or 16th century, as I recall, found
Ibn Sina's 12:13:14:16 (139-128-231 cents) or 28:26:24:21
(128-139-231 cents) less than satisfactory because the two
neutral second steps are too close to identical!

Whether Near Eastern musicians are aurally drawn, or drawn by
instrument designs, to superparticular divisions vis-a-vis
comparably shaded geometric or unequal but not rationally
conceived divisions is an open question, and I'm open to a range
of results, interpretations, and answers.

[On deliberate modern tuning according to medieval ratios]

> Of course I allow that exception.

And that exception is all I really need.

>> (3) You associate concepts such as "11-limit" with a
>> harmonic context where various prime factors are in
>> operation (e.g. 2-3-5-7-11, or possibly 2-3-7-11),
>> rather than simply a melodic system using ratios such
>> as 12:11. If we change "JI" to "RI" (rational
>> intonation), and speak of "ratios of 11," then you
>> might be happier.

> Generally the point is that ratios (dyads) of 11 are not
> tunable by ear either harmonically or melodically. In triads
> like 10:11:12, 4:7:11 and so on, available on dulcimers and the
> like, more can be said of a tendency to gravitate to 11.
> However I have never heard these relationships in recordings,
> and Santoor tuning instructions I have seen have not mentioned
> them. Now, maybe I should just get out more, which is why I
> keep asking for examples. I get accused of insincerity, or
> just ignored, when I do this.

While remaining open to a range of results and conclusions on the
pragmatic question of whether and to what degree melodic
intervals, dyads, or more complex sonorities can be tuned by ear,
I might make two points about intonational politics.

First, tunability or recognizability or reproducibility by ear
might depend a lot on the cultural background and training of the
musicians involved. And the usefulness of a given arithmetic
division or bearing plan for an instrument, as Cameron and Cris
have discussed, might not depend on whether every interval,
simple or complex, can be directly tuned by ear.

Secondly, whether or not rational ratios with an intuitive or
intellectual attraction are tunable by ear or have any special
aural salience, using them as signposts and landmarks can be
tokens of our esteem for the regions of the spectrum in which
they appear. For me, this is true of the territory around 410-420
cents, say, with landmarks such as 33/26 (413 cents) and 14/11
(418 cents), as well as the territory around 360-370 cents cents
with landmarks such as 16/13 (359 cents), 21/17 (366 cents), and
26/21 (370 cents). The ratios are a sign of familiarity and
affection.

And your search for examples, which I often cite to show the
variety of shadings in medieval and modern Near Eastern practice
and theory, and which may or may not point to additional
connections, is laudible. If I had access to video or tools for
analyzing pitch relationships in cents, I might be right in there
with Amine Beyhom, Can Akkoc, Ozan Yarman, you, and others. And I
think what we'll mainly find is variety, variety, variety.

>> (4) You generally find complex integer ratios more
>> confusing that illuminating, and would really prefer
>> simply to see measurements in cents.

> I find that rationals numbers are used in a quasi-religious
> fashion by people purporting to do music theory. That goes far
> outside the maqam realm. If somebody has a religious
> fascination with rational numbers, that's fine by me! Just say
> so from the start, and for heaven's sake don't make objective
> claims about historical or contemporary musical tradition(s),
> supposed health benefits, etc. That's dishonest, disrespectful
> to the practitioners of said tradition(s), offtopic, and likely
> to arouse those with allergies to such things, such as myself.

If you're referring to the commercialization of traditional
cultures and arts, complete with health and asserted other
marketing claims, and sometimes with totally fictional accounts
presented as actual ethnographic data, then we're in agreement
with lots of people in those cultures.

What I hope is that you're referring to a hypothetical case which
happily has not arisen in the list's present colloquies on maqam
and dastgah music and tuning, whatever our differences of view.
Of course, it's possible for honest and respectful analyses to be
theoretically overzealous or simply wrong, and respectful
questioning or outright correction, always I would hope
constructive and polite, is an appropriate response. This
discussion I take to be in that spirit, whatever the merits of
our respective positions.

Similarly, when we were moderating MakeMicroMusic almost a decade
ago, Jon and Jacky and I instituted a guideline that responses to
posted music should always be courteous and constructive. And
when young people share music, it's especially important that any
critical response should honor the effort and share an
encouraging word which may, of course, include friendly
suggestions for improvement. One test: is this the kind of
comment that a friendly coach or mentor might offer, and are we
confident enough of our judgment to offer it in that spirit?

>> (1) The AEU or mostly Pythagorean model (often featuring
>> schismatic 5-limit approximations) for modern Turkish music
>> actuals fits some flavors of perforance in maqamat such as
>> Rast and Segah, but does not represent important flavors >> such as Rast with rast-segah at around 16 commas or in the >> neighborhood of 360 cents (e.g. 16/13), and fails radically >> to account for prevailing intonational style in maqamat such >> as Ushshaq and Huseyni.

> While waiting for Ozan to confirm or deny these details, I can
> say I will hardly be surprised if existing theoretical
> proposals, of whatever vintage, are found wanting.

And I wouldn't be surprised either!

> I will add: there is no guarantee that a single master tuning
> exists for all the maqamat. Of course tunings of arbitrary
> precision, like 1200-ET or 12,000-ET would probably do the job.
> But that would be too easy. Any such master tuning must
> justify itself via some explanatory power, much like a
> scientific theory. It must 'explain' or reveal common features
> of the maqamat, much like Newton's laws of gravitation
> explained a variety of different observations of motion made by
> different people at different times. Otherwise we can be
> perfectly happy knowing a tuning for each maqam, or even at a
> finer level of detail (regional, tetrachordal, etc.) as
> necessary.

Personally I'd far prefer a case-by-case basis, and my very love
of the diversity and many shadings tends to lean in the other
direction from any unifying theory, much less a "master tuning."
Even Ozan's 79/80-MOS of an approximate 159-EDO is meant as a
practical and general solution, but not an all-encompassing one
rendering other tuning systems superfluous.

One virtue of my 24-note maqam temperaments is that no one is
likely to offer one of these as a "master tuning"!

> The master tuning of the West, 12-ET, does in fact have such
> explanatory power over Western music, yet it doesn't go all the
> way. We need the notion of adaptive JI, along with the idea of
> disposing of only those commas assumed to vanish in the score,
> to get the rest of the way. Prior to this list I'm not sure
> this had ever been fully realized. Though people like
> Bosanquet, Groven, Fokker, and Mathieu were definitely on the
> right track.

Certainly we agree that 12-ET/EDO can serve as either a
modification of Pythagorean tuning (possibly its original
application in 15th-century Italy, as suggested by Mark Lindley,
permitting the same lute fret to be used as a diatonic or
chromatic semitone) or as the upper limit of the meantone zone;
and that adaptive JI is an attractive paradigm for 16th-century
vocal music, for example, especially if one wants to avoid comma
drift.

A point worthy of quick mention is that problems involving the
syntonic comma are specific to forms of Western music based on
5-limit consonances starting around the 15th century (and at
least a couple of centuries earlier in some English styles), in
contrast to medieval polyphony based on a Pythagorean outlook.

Another point is that for many people on this list, the Western
composers and styles presenting "the exception that proves the
rule" would be main points of interest: for example Marchettus
and his expressive variations on Pythagorean intonation which
modern performers such as Christopher Page have seen as relevant
to much 13th-14th century French and Italian music; and, of
course, Vicentino, Colonna, and also Gesualdo in the later 16th
and early 17th centuries.

This isn't to miss your point that the "master tuning" concept
can lead to some real insights: for example, my typical 24-note
maqam tunings could be considered variations on a "master tuning"
of 17-EDO. And we agree that maqam music as a whole simply can't
be summed up in this kind of convenient way, using rational
ratios or EDO divisions or anything else we have on hand!

>> Carl, what I mean by "differences in musical orientation"
>> might be illustrated by your response to a piece of
>> Elizabethan music, > _Come, Sirrah Jack, Ho!_ by Thomas
>> Weelkes. From your post, > I might guess that you are more
>> oriented to 18th-19th century > tonality, and are experiencing
>> this composition from around > 1600 from that perspective.

> It's hard to say. My Dad was an early music geek so I grew up
> with such things -- and sang them in high school and college.
> But perhaps my tonal indoctrination runs deeper than I know.

Maybe it's partly training, and partly the proportion of
different influences to which one gravitates.

>> The same music can, and should, evoke different experiences in
>> different people.

> Absolutely.

>> When I heard the piece for the first time around 1976, I'd
>> guess, on an album of the King's Singers, it sounded to me
>> routinely pleasant, without anything standing out.

> I wasn't alive yet in 1976 but I too first heard this
> particular piece on probably that very same King's Singers
> recording. It sounded completely normal until I tried to learn
> the parts.

That's interesting! I wonder how I might react approaching it at
that level. And it's humorous how I envisioned you as being
closer to my age, a healthy reminder for me that there are newer
generations. Maybe my misconception that you were around my age
came from the idea of you as "my fellow Berzerkleyan" -- when I
lived in San Francisco, I often visited Berkeley.

>> <[117]http://www.bestII.com/~mschulter/IntradaFLydian.mp3>
>> <[118]http://www.bestII.com/~mschulter/IntradaFLydian.pdf>

> Thanks for reminding about this piece. Loved it in 2005 as
> much as now.

Glad you like it. I'm not sure if it illustrates similar points
to the ones you were discussing about tonality and modality.

> -Carl

Best,

Margo

On Wed, Nov 3, 2010 at 8:41 PM, Michael <djtrancendance@...> wrote:
>
> >"And just because a scale sounds good (LucyTuning is a pretty good meantone that I like a lot) doesn't prove anything about spherical harmonics or what not."
>   So Lucytuning doesn't have any impressive scientific explanations...so what?  Neither does my PHI scale, or Igs's or Knowsur's musical ability to make psychoacoustically lousy tunings quite listenable.  I guess my point is...many things in music can work well without explanation: if we can find explanations, all the better...but if we can't it doesn't mean the result must be less musically useful.

I specifically said in my last message that I don't think that the
pseudoscience behind the LucyTuning "theory" detracts from its
usefulness.

> >"Everything that you're saying comes out of the fact that there might be some areas of acoustics that you
> haven't studied. "
>
>    First of all, it's simply not true for a large part.  For example, yes, I've heard about the Basilar Membrane, and frequency masking along it long before you mentioned it (and even mentioned these things several times on list).

You asked why spherical propagation patterns are unrelated to the VF
phenomenon, and then started talking about how we can't be sure unless
it's tested. I don't feel a burning need to test stuff like that.

> No, I have never considered the pattern as a "circle" the way you have or thought of it as something Charles Lucy might have been confused by and built mis-claims around...but that certainly doesn't mean I don't know it.  In fact I remember you asking me about a month ago on tuning research "what do you mean by frequency masking?" when you asked about why noise waves don't sound as dissonant as they "should".

I know what frequency masking is. You said that masking would make
noise less dissonant, and I didn't understand why, and I still don't.

>    And if you're going to make huge generalizing statements against me, at least give specific examples so I get a fair chance to say what I do know.

You asked why spherical wave propagation patterns are unrelated to the
VF phenomenon. I assumed you didn't understand enough of the acoustics
to see why they're two entirely different things. If you did, why
would you even think they're connected at all? How could they possibly
be connected? What if we have a plane wave instead of a spherical
wave? Would that change what VF's emerge from a given signal? Why? The
whole thing is just silly.

>     I don't think what Charles was claiming is "not silly"...I just don't get how you can attack his claim when all the knowledge you seem to have to know "what he meant" appears nothing more than a guess.

Because he hasn't offered any explanation and I don't see how you
could possibly connect the two things short of the really tenuous link
that I was discussing in the offshoot with Carl. He isn't even
interested in offering explanations. He is really interested in
patents and stuff like that. If he was just saying "I came up with a
pi-based scale that sounds really cool," that would be one thing.
Nobody would be attacking his subjective experience of it sounding
good based on science. But why start throwing sciencey stuff out there
if you don't want to take it into the realm of scientific discussion?

> Granted, his website is pretty vague about his theories.  Furthermore, again, even if he did, say, mean to tie Lucytuning to frequency masking (which obviously does not work)...who cares (it doesn't, alone, mean it sounds bad)?

Charles cares.

> >"I don't think that there are any 7-tet "acoustics conflicts." I think that there is a long-standing source of disagreement on this list about the exact resolution of the ear-brain temporal analysis system, and how it can resolve harmonics and how strong the VF system is."
>
>    In that case, what surprises me is that it seems to imply either the VF system is not what defines a lot of the sense of "rootedness" in 7TET or that the system can work differently than it was originally thought to.

Originally thought to by whom? I just said that everyone has a
completely different opinion on this. We're all just speculating. Carl
is not the only person on the list and I don't think he's ever claimed
to have all the answers for things that are ongoing fields of
research.

> I still don't see why you thing Lucytuning is any more "acoustically conflicting" than 7TET...unless you are rating it by its ability to mirror the activity of ascending frequency masking (something you seem to assume but I've never heard Charles say IE "by 3D and PI I mean the curve of frequency masking in the Basilar Membrane").

I don't remember ever saying anything like this. I said that the only
possible way I could see "spherical wavefront" or whatever stuff
making any difference at all is through this slight phase distortion
that would result. I don't think that it has anything to do with VF's.

> >"some who think it's on the super-low side (me, kind of)"
>
>      Super low side meaning...there are whole lot of frequencies between things like low-limit JI ratios that act as weak versions of those ratios and imply similar virtual root tones?

I don't understand what you mean by this...

> >"the partials that are close enough to beat end up beating in some kind of recurring
> polyrhythm with one another ("periodicity buzz")"
>
> Now this really makes me wonder: I understand periodicity buzz as simply equal difference tones IE 300hz 400hz 500hz has a constant 100hz periodicity buzz.  I'm guessing the idea revolves around that the oscillation generated by periodicity buzz itself begins to act as the prominent Virtual Fundamental?.

No. I assure you that you aren't hearing anything moving 100 times a
second. That is just way too fast for you to hear it.

>     Never said it would...but I did say (and will say again) that if that did happen, it might get people thinking seriously about finding out what makes it click.  And I agree: Charles's reasons why it supposedly worse seem vague and unprovable via acoustics (at least in the detail he describes them in)...but that doesn't necessarily mean other people can't find a better reason why Lucytuning works.

Sure, here's one reason why it clicks: it tempers out 81/80 and is a
pretty decent meantone with low error. Whee.

>     And again, if such a test fails...nothing more to be said and a whole lot of theorists will continue not taking Lucytuning seriously...end of story.

I don't know of any special properties that LucyTuning has. I'm not
sure a listening test that compares how much people "like it" vs
"liking" 1/4-comma meantone would give out enough useful information
to figure out why. Just my 2 cents.

-Mike

Hi Carl,

Yes that's what I mean.

I don't have much experience of real world tuning recently. But when I had a 'cello I had fine tuning adjustments at the bridge end on every string on the 'cello - which lets you adjust it to much more accuracy than a normal 'cello. That was before I had a computer even and before my interest in alternative tunings, before I knew what a cent was. So I don't know what the accuracy was in cents. But my guess is that probably you could do fractional cents with a tuning method like that. Perhaps members with instruments could say a bit about the tuning accuracy of their instruments.

Sitars are clearly designed for sensitive tuning, and again I'd expect sub cents level tuning accuracy. A google for sitar electronic tuning devices shows quoted accuracy of a tenth of a cent, which may be relevant.

With the 81/64 then the way I'd imagine it happening is that you learn the 3/2 chain of fifths, and get it that way first - but then learn that as a shortcut you can just tune to it directly once you get used to how it sounds, and (assuming I'm not fooling myself) it is noticeably simpler than its fraction of a cent neighbours which have a more "irregular" feel to the beating patterns. Perhaps rather than smoother, a better way to describe it might be, simpler.

With the 11/9, it is so obvious I think by just swooping from a minor to a major third, listening to beats as you go, of course assuming you are able to do sub cent level adjustments and the instrument is rich in harmonics - then I think you would spot it easily as a natural point where beats that were apparent to either side of the tuning vanish.

With Tune Smithy - I could easily implement a dyad with one of the notes continually adjustable. Indeed I think I might have a feature like that already with it adjustable using a controller on the midi keyboard - somewhere in the program, I think in one of the Midi In options windows. It also has triangle wave (also many other wave shapes) in its own internal wave shape player - to high accuracy - pitches accurate to the limit of double precision arithmetic i.e. so decimal value of the interval is accurate to about 14 decimal places. That's what I'll use to make the demo clips. And it would be simple programming to hide the display of the pitches and interval, let the reader adjust one of the notes of the dyad - and then display the interval they have found after they do that.

Only thing is FTS at present is so complex that many of the more advanced features can be hard to find and once found, to learn to use. Also once learnt, easy to forget how it was done if like a year or two later you want to do it again.

But when I do the upgrade to version 4.x hopefully some time next year then I plan to take what I have learned from Bounce Metronome Pro to make it hopefully much easier to use. So - maybe this time next year - depending on whether I have the time to release 4.x by then, I may be able to do this sort of thing rather easily.

Robert

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Robert,
>
> > Just tested 11/9 with the triangle wave test, to distinguish it from
> > 347.0 and from 348.0 (11/9 is 347.407)
> >
> > There are very clear beats. High pitched but unmistakeable,
> > I don't think I can be fooling myself there, and can easily
> > believe an experienced instrumentalist would be able to tune an
> > exact 11/9 just by tuning until the dyad goes beatless.
> > I'd even call that one easy.
>
> I take it you mean 347 and 348 have beats while 11/9 does not.
> Unfortunately we don't have the ability on real instruments
> to make adjustments of 0.4 cents. Also, listening to discrete
> sounds is not the same experience as tuning a continuous
> oscillator. Lastly, I will say again that almost anything can
> be learned with training. That is a very different matter
> from doing it (and even thinking of doing it) naively. I do
> think it would be a valuable tool to have a basic continuously-
> tunable synth with either triangle or sine waves, both upper
> and lower tone tunable, and a switch to blind the readout of
> cents between them.
>
> -Carl
>

MikeB>"You asked why spherical propagation patterns are unrelated to the VF
phenomenon"
No, I asked why you were so sure LucyTuning was "obviously wrong
acoustically". You then changed the focus to VF in your example of "something
wrong acoustically"...and now you appear to be saying saying I asked about VF.
For the record, again, I don't even think Charles Lucy brought up VF as what he
was trying to prove a parallel to in the first place...and if you have directly
evidence he did, please, do tell.

>"You asked why spherical wave propagation patterns are unrelated to the VF
>phenomenon. I assumed you didn't understand enough of the acoustics to see why
>they're two entirely different things."
Argh...I didn't bring up either phenomenon...I simply asked about what you
thought was "obviously wrong acoustically" with LucyTuning and then you
introduced VF and the whole spherical wave pattern idea as if Lucy had mentioned
it clearly and I had read it from his material and confused it. The funny thing
is...you're going around trying to disprove an assumption you think I made based
on two ideas you brought up all the while I haven't said a thing about confusing
(or even mentioning) either of the ideas with respect to LucyTuning or each
other.

And not kidding the idea of a Virtual Fundamental that doesn't exist in dyads
or chords but is pointed to by them has nothing to do with the frequency masking
effect on the Basilar Membrane. Had you simply asked if I knew rather than
randomly assumed I didn't I could have told you that far sooner.

A side note, since the perceptual curve of human hearing is curved
consistently downward at to the 4khz point of maximum sensitivity (about as
high as any standard musical note will reach), it only makes logical sense that
lower frequencies would tend to block out higher ones up to that point. Here's
a graph of the curve I found ->
http://www.ece.uvic.ca/~aupward/p/clip_image010.jpg.

>"I specifically said in my last message that I don't think that the
>pseudoscience behind the LucyTuning "theory" detracts from its usefulness."
Fair enough, agreed...though it didn't seem obvious by the way you switched
to topic to LucyTuning in relation to VF.

>"I know what frequency masking is. You said that masking would make noise less
>dissonant, and I didn't understand why, and I still don't."
It's not exactly on topic so I'll make this short: because frequency peaks
mask those above them and since noise waves have so many nearby peaks many of
them end up masking each other, leaving your mind with much less to analyze than
meets the eye on a spectral analysis graph (IE a lot you can see but not hear).

>"No. I assure you that you aren't hearing anything moving 100 times a second.
>That is just way too fast for you to hear it.
Ok, bad example far as actually being able to hear it with 200 300 400hz...how
about 20 30 40hz (10 times a second IE repeats/has a period at every 1/10th of a
second AKA about the temporal resolution of human hearing)? Any more of this
picky-ness and I just might join it and have a period as well.

On Wed, Nov 3, 2010 at 9:57 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"You asked why spherical propagation patterns are unrelated to the VF phenomenon"
>    No, I asked why you were so sure LucyTuning was "obviously wrong acoustically".  You then changed the focus to VF in your example of "something wrong acoustically"...and now you appear to be saying saying I asked about VF.  For the record, again, I don't even think Charles Lucy brought up VF as what he was trying to prove a parallel to in the first place...and if you have directly evidence he did, please, do tell.

I said that LucyTuning's theory about spherical wavefronts or whatever
is obviously wrong acoustically, and for the exact reason I said.

> >"You asked why spherical wave propagation patterns are unrelated to the VF phenomenon. I assumed you didn't understand enough of the acoustics to see why they're two entirely different things."
>    Argh...I didn't bring up either phenomenon...I simply asked about what you thought was "obviously wrong acoustically" with LucyTuning and then you introduced VF and the whole spherical wave pattern idea as if Lucy had mentioned it clearly and I had read it from his material and confused it.  The funny thing is...you're going around trying to disprove an assumption you think I made based on two ideas you brought up all the while I haven't said a thing about confusing (or even mentioning) either of the ideas with respect to LucyTuning or each other.

He has mentioned it clearly. He's been mentioning it clearly since the
day I joined the list. He always talks about people not being "bold
enough to think outside the box and question whether points of maximum
consonance don't coincide with JI ratios" but rather coincide with the
pi thing because of the spherical wavefronts and so on. If I'm
misunderstanding then feel free to correct me. I don't think I am.

>    And not kidding the idea of a Virtual Fundamental that doesn't exist in dyads or chords but is pointed to by them has nothing to do with the frequency masking effect on the Basilar Membrane.  Had you simply asked if I knew rather than randomly assumed I didn't I could have told you that far sooner.

I never said it did. You missed my point.

>   A side note, since the perceptual curve of human hearing is curved consistently downward at to the 4khz point of maximum sensitivity  (about as high as any standard musical note will reach), it only makes logical sense that lower frequencies would tend to block out higher ones up to that point.  Here's a graph of the curve I found -> http://www.ece.uvic.ca/~aupward/p/clip_image010.jpg.

I'm not sure the two phenomena are related.

> >"I know what frequency masking is. You said that masking would make noise less dissonant, and I didn't understand why, and I still don't."
>    It's not exactly on topic so I'll make this short: because frequency peaks mask those above them and since noise waves have so many nearby peaks many of them end up masking each other, leaving your mind with much less to analyze than meets the eye on a spectral analysis graph (IE a lot you can see but not hear).

Only if the nearby peaks happen to fall within the masking curve. Side
question: So what happens to an impulse?

> >"No. I assure you that you aren't hearing anything moving 100 times a second. That is just way too fast for you to hear it.
>   Ok, bad example far as actually being able to hear it with 200 300 400hz...how about 20 30 40hz (10 times a second IE repeats/has a period at every 1/10th of a second AKA about the temporal resolution of human hearing)?  Any more of this picky-ness and I just might join it and have a period as well.

I think that you're not going to hear periodicity buzz as much as
you're going to hear something sounding like a 10 Hz lowpassed impulse
train. Perhaps the two are related.

-Mike

Hi Robert,

> Sitars are clearly designed for sensitive tuning, and again
> I'd expect sub cents level tuning accuracy. A google for sitar
> electronic tuning devices shows quoted accuracy of a tenth of a
> cent, which may be relevant.

That's just a standard marketing claim. Pianos are designed
for accurate tuning too, and I have the most accurate digital
tuner available for them, which also claims 0.1 cent accuracy.
Through my experience tuning pianos with it, and tuning my
slide guitar with a strobe tuner (also claims 0.1 cent accuracy)
I can say that I am extremely skeptical of anyone claiming
to make adjustments at this level.

> Only thing is FTS at present is so complex that many of the
> more advanced features can be hard to find and once found, to
> learn to use. Also once learnt, easy to forget how it was done
> if like a year or two later you want to do it again.

Yes, I noticed that! :)

> But when I do the upgrade to version 4.x hopefully some time
> next year then I plan to take what I have learned from Bounce
> Metronome Pro to make it hopefully much easier to use. So -
> maybe this time next year - depending on whether I have the
> time to release 4.x by then, I may be able to do this sort of
> thing rather easily.

Bounce Metronome looks awesome - I love your videos on YouTube.

-Carl

Hi Carl,

Okay. Well I can't say much more about this question about accuracy of real world instrument tuning myself right now, but maybe others here can, also may be able to myself in the future too.

The few times I've tried keyboard tuning - with a clavichord - then you could adjust the tuning with the adjustment key crudely - then you could kind of gently nudge it without actually moving it, which might give much more accurate fine tuning. Though the quietness of the instrument meant you had to listen rather carefully!

Anyway didn't do much of that, and attempted just simple things like 3/2s, but when the builders finish my new house, then will be able to get it out of storage and spend more time with it :).

Maybe some time can get myself another 'cello again as well. I often wish I had kept it but at the time had no idea I was going to get so interested in tunings, harmonics and so on and wanted to focus on recorder, plus moving from one place to another rather a lot, and a 'cello is a big thing to keep carting around when you use it rarely.

With your slide guitar - can you buy fine tuning adjustments like the ones you can get for a 'cello?

I'm sure it must be a thing that is highly instrument dependent, may also depend on the make of a particular instrument as well, and on what special technical features it has in its construction to help with fine tuning accurately. I mean - of course - for instruments with fixed pitches that need to be tuned such as open strings and keyboard notes etc.

> > But when I do the upgrade to version 4.x hopefully some time
> > next year then I plan to take what I have learned from Bounce
> > Metronome Pro to make it hopefully much easier to use. So -
> > maybe this time next year - depending on whether I have the
> > time to release 4.x by then, I may be able to do this sort of
> > thing rather easily.
>
> Bounce Metronome looks awesome - I love your videos on YouTube.

Great glad you like it :). Thanks for the encouragement. The general feedback I get is that I'm on the right track with the program design improvements which is encouraging. And look forward to introducing those to FTS as well.

All the features of BM Pro such as the 3D graphics for instance will be available for FTS 4.x as well when I do it. Because I do both programs from the same codebase, just different compile directives.

Thanks,

Robert

Good point, Kraig, just bumping this in case anyone missed it, not much to reply except to say I agree!

Robert

> I have been enjoying and concurring about what you are saying Robert.
I think one difference in the arts is often one comes up with theories afterwards in order to explain phenomenon to themselves.
This is true of quite a few composers i can think of who just write music and "justify " it later.
Being in such a science heavy society, i think many artist feel they have to explain their actions or directions.
Which i think is unfortunate.

MikeB>"I said that LucyTuning's theory about spherical wavefronts or whatever is
obviously wrong acoustically, and for the exact reason I said."
It's right assuming by "spherical" Charles Lucy is talking about the same
phenomenon you are.

>"He always talks about people not being "bold enough to think outside the box
>and question whether points of maximum consonance don't coincide with JI ratios"
So he's mentioning his theory as a replacement for JI. Agreed, that's pretty
nasty if so...equally as annoying as people who think, for example, JI and only
JI explains consonance (indirectly implying only a fool could believe
otherwise).

>"but rather coincide with the pi thing because of the spherical wavefronts and
>so on."
Again, assuming Charles is talking about "spherical wavefronts" in the same
definition and context you are (masking in the Basilar Membrane), he's making a
false claim.

>"I'm not sure the two phenomena"...(perceptual curve and frequency masking
>having more effect from lower masking higher frequencies)..."are related."
Neither am I, I'm just saying it's a bizarre coincidence where, to say the
least, the phenomena seem to follow a correlated curve.

>"Only if the nearby peaks happen to fall within the masking curve."
Which, in a noise wave, is quite often with so many partials clustered so
closely together and degrees phase cancellations often placing peaks and
significantly lower peaks quite near each other.

>"Side question: So what happens to an impulse?"
As in a sudden sound? I figure...the same thing plus temporal masking.
Suddenly your mind hears a burst of noise but (as with the droning noise wave)
some partials cancel out at least a handful of the nearby ones: lots of nearby
mountains and slight valleys with the mountains often masking the valley. Then
temporal masking kicks in and, if the peaks in any way change during the very
short duration of the sound (at least within 10-20ms or so), your mind filters
out any peaks in the current time frame that aren't as loud as those played at
nearby frequencies within the last 10-20ms.

I must say this page -> http://www.ece.uvic.ca/~aupward/p/demos.htm probably
explains the phenomena of temporal and frequency masking much more clearly than
I do. Now if you feed an impulse wave into an mp3 encoder (especially at lower
bit rates)...it will take out many the temporal and frequency masked areas
automatically...so analyzing its results after encoding will likely give you
some idea of the frequencies that actually end up "registering" to your ear.

>"I think that you're not going to hear periodicity buzz as much as you're going
>to hear something sounding like a 10 Hz lowpassed impulse train. Perhaps the two
>are related."
Perhaps...my ears hear periodicity buzz as a sort of constant mechanical
vibration over the entire waveform. Personal preference: it's why I like using
instruments with some modulation built into them to keep the periodicity buzz
from dominating with its mechanical sound over the feel of the overtones.

On Wed, Nov 3, 2010 at 10:49 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"I said that LucyTuning's theory about spherical wavefronts or whatever is obviously wrong acoustically, and for the exact reason I said."
>    It's right assuming by "spherical" Charles Lucy is talking about the same phenomenon you are.

I don't need to assume anything, because I was there when he said it.
Why don't you go search through the archives and find it yourself? He
talks, more specifically, about the analysis of 1d waveforms being
invalid because sound propagates in 3 dimensions.

> >"He always talks about people not being "bold enough to think outside the box and question whether points of maximum consonance don't coincide with JI ratios"
>   So he's mentioning his theory as a replacement for JI.  Agreed, that's pretty nasty if so...equally as annoying as people who think, for example, JI and only JI explains consonance (indirectly implying only a fool could believe otherwise).

I don't think anyone would disagree with this.

> >"but rather coincide with the pi thing because of the spherical wavefronts and so on."
>    Again, assuming Charles is talking about "spherical wavefronts" in the same definition and context you are (masking in the Basilar Membrane), he's making a false claim.

Rather than tell me I'm making assumptions, why don't you just look up
some old LucyTuning argument threads?

> >"Only if the nearby peaks happen to fall within the masking curve."
>   Which, in a noise wave, is quite often with so many partials clustered so closely together and degrees phase cancellations often placing peaks and significantly lower peaks quite near each other.

I don't understand what you mean by degrees phase cancellations here...

> >"Side question: So what happens to an impulse?"
>    As in a sudden sound?  I figure...the same thing plus temporal masking.
>   Suddenly your mind hears a burst of noise but (as with the droning noise wave) some partials cancel out at least a handful of the nearby ones: lots of nearby mountains and slight valleys with the mountains often masking the valley.  Then temporal masking kicks in and, if the peaks in any way change during the very short duration of the sound (at least within 10-20ms or so), your mind filters out any peaks in the current time frame that aren't as loud as those played at nearby frequencies within the last 10-20ms.

I don't mean a noise burst, I mean an impulse. Like a Dirac delta. You
know, the thing they use to compute the "impulse response" of a
filter. There is only one peak. If we're in the digital realm, use a
Kroenecker delta instead.

The Fourier transform of an impulse is 1 all across the spectrum.

>   I must say this page -> http://www.ece.uvic.ca/~aupward/p/demos.htm probably explains the phenomena of temporal and frequency masking much more clearly than I do.  Now if you feed an impulse wave into an mp3 encoder (especially at lower bit rates)...it will take out many the temporal and frequency masked areas automatically...so analyzing its results after encoding will likely give you some idea of the frequencies that actually end up "registering" to your ear.

I'm not really sure how an MP3 codec would alter an impulse. I assume
it would deal only with temporal masking.

> >"I think that you're not going to hear periodicity buzz as much as you're going to hear something sounding like a 10 Hz lowpassed impulse train. Perhaps the two are related."
>   Perhaps...my ears hear periodicity buzz as a sort of constant mechanical vibration over the entire waveform.  Personal preference: it's why I like using instruments with some modulation built into them to keep the periodicity buzz from dominating with its mechanical sound over the feel of the overtones.

But I don't think that hearing the periodicity buzz has anything to do
with VF placement, and I think you can hear periodicity buzz for more
intervals than clearly produce a VF.

-Mike

Hi Robert,

> The few times I've tried keyboard tuning - with a clavichord -
> then you could adjust the tuning with the adjustment key
> crudely - then you could kind of gently nudge it without actually
> moving it, which might give much more accurate fine tuning.
> Though the quietness of the instrument meant you had to listen
> rather carefully!

I owned a clavichord in the late '90s -- never an instrument I
associated with intonation accuracy. But it did, as all
pinblock instruments I've tuned, have had this 'nudge the hammer
without moving it' possibility. On a piano, a lot of it is to
do with getting tensions on either side of the bridge
to equalize.

For reference, the elimination a slow, phasing beat with a
period of 4 seconds between a pair of faint partials at 4 KHz
represents a tenth of a cent. It's about 40 times smaller
than the melodic just noticeable difference.

> With your slide guitar - can you buy fine tuning adjustments
> like the ones you can get for a 'cello?

I've never played a cello but those I've seen have not
seemed paragons of intonation accuracy either. I suspect
my slide guitar (open tuning... there are 28 strings) is
capable of more accuracy than most cellos.

-Carl

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
> Remember that I said that after a certain point, and I think we actually agree to a pretty good extent what that point is, it becomes a matter of choice what you call things. It's unlikely that I could distinguish a 13:12 from "6/7 down from Pythagorean ditone". Should I call it a 243/224? Depends on the context. In Ozan's 79-MOS tuning, I believe the difference is tempered out, and I think this an excellent solution in the daunting task of making a practical quanun tuning.

729/728 is not tempered out by 159et, but it is by 171et. I'd be interested in a list of commas which you think help provide excellent solutions to the daunting task of making practical quanun tuning.

For what it's worth, 171 tempers out 32805/32768 in the 5-limit; 65625/65536, 2401/2400 and 4375/4374 in the 7-limit; 243/242, 441/440, and 540/539 in the 11-limit; 364/363, 625/624, and 729/728 in the 13-limit.

Hello Margo~
The implication that JI ratios have no special attraction is possibly proven otherwise by the history of piano tuning. Regardless of the system, these intervals have served as the bedrock point of departure in order to put forth all those imaginative approaches we have seen for centuries. The just intervals have been tuned and the only way some tuning have even been tuned is by tricks with counting beats and comparing it to clocks.
This is quite removed from the process in which we deal with intervals in music.

That there are other intervals of great musical expressiveness is proven in countless examples around the world.
Still JI intervals will always hold a unique place.

Partch could tune his 43 tone scale by ear, on instruments that often have extremely short durations. Some of these it was years before i actually heard some of the chords going on in his 'Delusion of the Fury'. Most people are so used to these not being tuned they hear it as percussion and little more.

On the other hand I don't know of anyone who can get even marginally close to 11 or 13 ET or even 22 by ear.

It would be unfair if i did not mention recurrent sequences of all having a special perceptible property that can be used to tune by paying attention to difference tones.

These are only two "acoustical phenomenon' that can be used to tune by ear.
I make no assumption that they are the only ones.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> [This doesn't attempt to keep up with the dialogues of the
> last day or so.]
>
> Carl wrote:
>
> > Hi Margo,
>
> >> Please let me express my regrets for any negative part I may
> >> have had in a "debate" which is clearly intruding on the
> >> positive purposes of the group and creating more heat than
> >> light.
>
> > Thanks for saying so, but I didn't feel you had any negative
> > part in it. On the contrary, I enjoyed the messages we
> > exchanged and thought they were a good example of how such
> > things can go. I hope this sense was mutual but if not, it
> > certainly wasn't my intention and please contact me offlist if
> > you would like to discuss it further.
>
> Great, and I'll confirm that the sense is mutual. In fact, this
> looks like a fascinating dialogue, and among other things a
> chance to clarify what some of my own positions are or aren't.
> Your remarks that follow are invaluable for presenting me an
> opportunity to do this, an opportunity which might be very
> helpful for the list. It's so easy for me to have "unspoken"
> understandings about the meaning of my own words not so obvious
> to anyone else.
>
> And I should briefly mention a couple of my technical
> limitations: I have no means to access or hear videos, or to do
> measurements of frequencies or intervals in cents for a maqam
> performance, say. But I'm immensely interested in what you, Ozan,
> Cameron, Jacques, or others might find.
>
> >> What are the real issues, not necessarily or solely factual,
> >> in question? Well, my own position could be summed up about
> >> like this:
> >> (1) Medieval Islamic theorists describe tetrachords and
> >> modes which are beautiful and can and should be applied to
> >> medieval and modern maqamat at least some of the time in some
> >> contexts;
>
> > ...Don't see how anyone could disagree with this.
>
> And actually this is about 70% of my point, with a helpful
> footnote that I do some rather un-medieval things in my maqam
> tunings, with temperament at the top of the list, and the
> 11:12:13 division (as far as I know) as another.
>
> What both Ozan and I do, in different ways, is to take some
> leaves from the medieval book and modify them a bit, or at least
> mix in some new ingredients. And for both of us, temperament is
> one of those ingredients. The different ways it's used in his
> 79/80-MOS or my much more modest O3 could be an interesting topic
> of comparison.
>
> >> (2) Some of these tunings are closely approximated by
> >> current tunings in practical use in various parts of
> >> the Near East;
>
> > Seems likely, though the word "closely" can be troublesome.
> > The central point I would stress is that we really don't have
> > much idea what tunings are currently in use, because of a
> > paucity of data. That ought to lead to some humility, which
> > would be good for all of us.
>
> What I would predict is that there are far too many variations to
> fall neatly into _any_ model, medieval or later, which
> recognition may be at least the beginning of humility. Looking at
> some measurements of Iranian tunings by Nelly Caron and Dariush
> Safvate, and others by Jean During, as well as Hormoz Farhat's
> book, I find this variety an inspiration for anyone contemplating
> the infinite shadings possible, and of course a daunting obstacle
> for anyone who wants a single "master tuning" of any practical
> size for a typical acoustical fixed-pitch instrument, as you
> suggest below and I agree.
>
> And I see integer ratios as signposts or street numbers, not as
> points of unique validity somehow devaluing the territory in
> between those signposts. This brings us to a vital point which I
> find it prudent to explain before posting summaries of measured
> flexible-pitch tunings or instrumental frettings, etc.
>
> An observation of more or less "close" resemblance could lend
> itself to any of at least three viewpoints:
>
> VIEWPOINT I: "Isn't it wonderful how medieval tunings
> describe interval sizes and shadings close to those of
> some tunings used on fixed-pitch instruments or by
> flexible-pitch performers today?" Here there's no claim
> that the rational values are uniquely salient or
> "attractant," only a focus on regions or "neighborhoods"
> of the spectrum, leaving open the question of possible
> further connections or their lack.
>
> VIEWPOINT 2: "The fact that one or more medieval
> theorists describes this rational tetrachord, and this
> modern instrument or performance uses or closely
> approximates it, indicates that the rational ratios
> themselves, not just the general neighborhood or shading,
> have some special salience or attractive power."
>
> VIEWPOINT 3: "The correspondence between the medieval
> ratios and the modern tuning on a fixed-pitch instrument
> shows some common tradition or acoustical logic of the
> process of building and playing instruments of the
> relevant type."
>
> My own position is to assert Viewpoint 1 and remain open to
> evidence one way or the other on Viewpoints 2 and 3, the kinds of
> issues raised by Ozan, Cris, and Cameron. Note that my practice
> of using certain superparticular or other rational ratios as
> intellectually attractive signposts or landmarks in itself
> neither affirms nor denies that they may additionally have an
> aurally attractive pull for musicians brought up in these
> traditions, or a special significance in the vocabulary and
> grammar of instrument building, if I may call it that, as a
> variation on Cris's etymology of numbers and ratios.
>
> And I must admit that the psychoacoustical theories I would find
> most plausible would be those either developed by dastgah and
> maqam musicians or at least based on culturally specific
> observations of talented performers or listeners brought up in
> these traditions who have a native phonology, so to speak.
> Objective tests of the ability of people practicing maqam or
> dastgah music as a first language to discriminate between shades
> of neutral intervals or degrees of contrast between smaller and
> larger neutral seconds, for example, might be very interesting.
>
> Further, I find in the Islamic theorists of the Mutazilah Era a
> logically attractive lore or discipline focusing on the
> gradations and relations of rational ratios, an outlook also
> reflected in some portions of _Divisions of the Tetrachord_ by
> John Chalmers, that can be embraced while affirming the value of
> irrational ratios and divisions also (which John addresses at
> length), and leaving open psychoacoustical issues that might not
> much affect my artistic outlook, although new knowledge can
> always enrich one's perspective.
>
> Having said that, I would emphasize that it's possible to see
> resemblances between a medieval rational tuning and a current
> intonational practice without necessarily saying that the
> specific medieval ratios are precisely represented in, or
> "explain," the modern performance.
>
> First, let's consider the oldest description known to me of the
> tetrachord that would later be called Rast, al-Farabi's mode of
> Zalzal:
>
> 1/1 9/8 27/22 4/3
> 0 204 355 498
> 9:8 12:11 88:81
> 204 151 143
>
> Now consider Amine Beyhom's estimate (thesis, Vol. I, at p. 52)
> of a typical Lebanese Rast in a "learned" (_savant_) style:
>
> 0 200 355 500
> 200 155 145
>
> When I say that either tuning is "closely approximated" by the
> other, I mean simply that they represent similar shades of what
> has come to be called Rast. What I'd note is not only the similar
> sizes of the neutral thirds, but the subtle difference (around
> 8-10 cents) between the larger and smaller neutral seconds.
>
> I do not mean to imply that the second tuning is intentionally or
> otherwise based on rational ratios, although we might asssociate
> 200 cents with 9:8. But it's the similar degree of subtle
> difference between the two neutral seconds, with the larger
> placed first, that catches my attention.
>
> To make my disclaimer more emphatic here, let's consider a
> tetrachord that Beyhom measured from a performance in Hijaz by
> the Turkish master Kudsi Erguner
>
> <http://www.beyhom.com/download/articles/Beyhom_2007_%20Des_criteres_d_authenticite_filigrane_n5.pdf>:
>
> 0 131 368 501
> 131 237 133
>
> Now I might excitedly, as a self-appointed referee, call "Buzurg"
> and cite two possible tetrachords using the ratios specified for
> this mode (or actually the lower tetrachord of their pentachordal
> schemes) by Safi al-Din al-Urmawi and Qutb al-Din al-Shirazi:
>
> 1/1 14/13 16/13 4/3
> 0 128 359 498
> 14:13 8:7 13:12
> 128 231 139
>
> or
>
> 1/1 13/12 26/21 4/3
> 0 139 370 498
> 13:12 8:7 14:13
> 128 231 139
>
> Indeed Erguner's tetrachord resembles these in having a small
> neutral second, a middle step close to 8:7 (actually a bit
> bigger), and another smallish neutral second. Noting this
> pleasant kinship, however, isn't to say that Erguner is following
> any rational scheme, or is making a distinction between 14:13 and
> 13:12.
>
> While I can and will celebrate this as an example of a
> "Buzurg-type Hijaz," in fact if we are seeking a "close fit,"
> 36-EDO or 46-EDO would be closer than either rational version of
> Buzurg above:
>
> Erguner: 0 131 368 501
> 131 237 133
>
> 36-EDO: 0 133 367 500
> 133 233 133
>
> 46-EDO 0 130 365 496
> 130 235 130
>
> And I would certainly not conclude from Erguner's performance
> that "a Turkish Hijaz of the Buzurg flavor is based on 36-EDO" --
> or 46-EDO, for that matter!
>
> Actually, modern Turkish or Syrian theory based on 53 commas
> might capture my general category of "Buzurg" as 6-10-6, or here,
> using a suggested refinement of Beyhom for models based on 17 or
> 24 positions per octave, "6- 10+ 6-" to show that each neutral
> second is a bit smaller than 6 commas (about 135 cents) while the
> middle step is a bit larger than 10 commas (about 226-228 cents)
> or even a full 8:7 at 231 cents.
>
> In some cases, we might be able to draw some kind of
> "etymological" connection, as Cris Forster has put it, or to draw
> some connection between a given fretting scheme and a medieval
> theoretical tradition, as Cameron has proposed. But noting
> and celebrating some interesting resemblances need not itself
> imply either type of connection.
>
> Generally my point in citing and comparing medieval rational
> tunings and more or less kindred modern intonations is to
> illustrate the variety of Near Eastern tetrachords and shadings,
> historical and current.
>
> > However we can say certain things are unlikely. For instance,
> > choose a rational number R at random, num(R)*den(R) < 10,000
> > and 1 < R < 2. Let's say 55/27. What are the odds it is used
> > systematically in maqam music (that is, it is the target of
> > some bearing plan, fret placement instruction, vocal training
> > regimen, etc, used by more than one musician... that
> > musicians/craftsmen have some means of communicating about it,
> > not necessarily by name, but in *some* fashion)? Answer: the
> > odds are low and we wouldn't believe this unless evidence was
> > plainly extant, de novo, of such a bearing plan, fret placement
> > instruction, etc. etc.
>
> That's a curious illustration; we're talking about roughly 1232
> cents (55/27).
>
> What's likely, or relevant, may depend on the question and on
> one's viewpoint. To describe an interval around 370 cents, as on
> Cameron's baglama or in my tempered vrsion of a flavor of Turkish
> Rast, by association with the rational signpost of 26/21, or a
> 4/3 less a 14/13, is what some of us find an intuitively
> appealing mapping. And, likewise, an interval in this immediate
> neighborhood might be associated with 99/80, or 9/8 plus 11/10, a
> ratio of around 369 cents occurring in the "Medium Sundered"
> tetrachord of Safi al-Din (9:8-11:10-320:297 or 204-165-129
> cents).
>
> These conceptual landmarks are useful to some of us -- not
> necessarily all of us, as you've made clear! -- in themselves.
> Whether fretting schemes might favor these superparticular
> patterns more than nearby but distinguishable shadings, and
> whether flexible-pitch performers might be especially drawn to
> them, are open questions.
>
> >> (3) Just ratios both simple and complex, as well as values
> >> in cents, commas, savarts, etc., can be useful in describing
> >> and analyzing current Near Eastern practice; and
>
> > I would dispute this beyond the 7-limit. Within the 7-limit
> > it's unclear, but plausible, and Weighing Diverse seems to
> > support it.
>
> Note that my "useful" may have a minimalistic sense that
> rationals can provide an intuitively appealing grid (in the eye
> of the beholder!) for mapping and appreciating the continuum of
> neutral or Zalzalian seconds or thirds, for example. Such a grid
> may or may not itself mark points of salient aural attraction, as
> likewise with a grid such as 17-EDO, 24-EDO, or 53-EDO (all of
> which have been proposed or used by Near Eastern theorists).
>
> >> (4) Superparticular or other divisions of the medieval
> >> theorists, as well as some modern variations, can nicely evoke
> >> the state of _tarab_ ("enchantment" or "ecstasy") sought by
> >> performances and audiences as an aspect of the maqam
> >> tradition.
>
> > I'm not sure how to evaluate this. Beyond the 7-limit I know
> > of no property of superparticular intervals that makes them
> > special in a melodic context, and even within the 7-limit
> > harmonic context, intervals such as 5:3 and 7:4 are on par with
> > superparticulars in terms of their stand-out psychoacoustic
> > properties.
>
> An ambiguity of my quoted proposition (4), which I'll clarify
> now, is whether it means "superparticular and other medieval
> divisions alone or especially" or "medieval rational divisions,
> among many others." My intended reading is totally nonexclusive,
> and thanks for a chance to say so. In other words, "12:13:14 or
> 128-139 cents is beautiful, and 125-137.5 cents in 96-EDO, or
> 133.3-133.3 cents in 36-EDO or 63-EDO, might be comparably so."
>
> Whether superparticular divisions such as 12:13:14 or 14:13:12
> and 11:12:13 or 13:12:11 have additionally have a special aural
> attraction for expert or other performers growing up in a maqam
> or dastgah tradition is an empirical question. And I find Cris's
> instrumental etymology, which I'll need his book to study in more
> detail, quite credible. While Ozan and I have independently been
> drawn to the 13:12:11 or 11:12:13 division for certain maqamat or
> dastgah-ha, let me prudently note again that I'm not aware of any
> medieval sources citing this division.
>
> Also, I don't know if anyone is claiming that superparticulars
> and only superparticulars are aurally salient: those of us drawn
> to JI/RI have been citing ratios like 13/11, 14/11, and 26/21,
> and certainly would recognize 7/4 as well as 16/9 as significant
> landmarks. And likewise with 11/9, which Cameron found a clear
> aural attractant in certain instrumental timbres (his Spectral
> Harmonic Entropy or SHE).
>
> >> Carl, please correct me if I am wrong in seeing your main
> >> points as follows:
>
> >> (1) You observe that a 24-EDO model can nicely fit some maqam
> >> perforamnces.
>
> > Yes.
>
> And I'd add that Near Eastern theorists such as Vaziri in Iran
> have endorsed 24-EDO. I consider it as one point on a continuum.
>
> >> (2) You regard medieval Islamic theory, and likewise the
> >> theory of Ptolemy, insofar as it involves superparticular
> >> or other rational ratios of medium to high complexity, as
> >> having little reference to either the practice of those
> >> times or of today -- doubtless allowing an exception for
> >> those of us who deliberately study and then set out to
> >> implement these tunings.
>
> > I know of no evidence they're connected.
>
> This I see as an open question, which Cris and Cameron may
> address further, and the former addresses in detail in his new
> book. My own artistic program, which no one else is obliged to
> follow (and much less any or all Near Eastern musicians!),
> wouldn't depend on the answer.
>
> > I know of strong evidence these theorists would have had no
> > alternative but to use rational numbers to express their
> > scales.
>
> This is a point that Owen Wright also makes. Cris has commented
> that an "equable" division like Ibn Sina's 14;13:12 or 12:13:14
> is the way of indicating a 7:6 third derived from two near-equal
> steps. While I may like the subtle distinction between 14:13 and
> 13:12, this doesn't mean a geometric division as in 36-EDO or
> 63-EDO would be "wrong," or an unequal division like 130-143
> cents not necessarily having any clear rational interpretation
> (I'm just pulling numbers out of the air for my last example).
> One theorist around the 15th or 16th century, as I recall, found
> Ibn Sina's 12:13:14:16 (139-128-231 cents) or 28:26:24:21
> (128-139-231 cents) less than satisfactory because the two
> neutral second steps are too close to identical!
>
> Whether Near Eastern musicians are aurally drawn, or drawn by
> instrument designs, to superparticular divisions vis-a-vis
> comparably shaded geometric or unequal but not rationally
> conceived divisions is an open question, and I'm open to a range
> of results, interpretations, and answers.
>
> [On deliberate modern tuning according to medieval ratios]
>
> > Of course I allow that exception.
>
> And that exception is all I really need.
>
> >> (3) You associate concepts such as "11-limit" with a
> >> harmonic context where various prime factors are in
> >> operation (e.g. 2-3-5-7-11, or possibly 2-3-7-11),
> >> rather than simply a melodic system using ratios such
> >> as 12:11. If we change "JI" to "RI" (rational
> >> intonation), and speak of "ratios of 11," then you
> >> might be happier.
>
> > Generally the point is that ratios (dyads) of 11 are not
> > tunable by ear either harmonically or melodically. In triads
> > like 10:11:12, 4:7:11 and so on, available on dulcimers and the
> > like, more can be said of a tendency to gravitate to 11.
> > However I have never heard these relationships in recordings,
> > and Santoor tuning instructions I have seen have not mentioned
> > them. Now, maybe I should just get out more, which is why I
> > keep asking for examples. I get accused of insincerity, or
> > just ignored, when I do this.
>
> While remaining open to a range of results and conclusions on the
> pragmatic question of whether and to what degree melodic
> intervals, dyads, or more complex sonorities can be tuned by ear,
> I might make two points about intonational politics.
>
> First, tunability or recognizability or reproducibility by ear
> might depend a lot on the cultural background and training of the
> musicians involved. And the usefulness of a given arithmetic
> division or bearing plan for an instrument, as Cameron and Cris
> have discussed, might not depend on whether every interval,
> simple or complex, can be directly tuned by ear.
>
> Secondly, whether or not rational ratios with an intuitive or
> intellectual attraction are tunable by ear or have any special
> aural salience, using them as signposts and landmarks can be
> tokens of our esteem for the regions of the spectrum in which
> they appear. For me, this is true of the territory around 410-420
> cents, say, with landmarks such as 33/26 (413 cents) and 14/11
> (418 cents), as well as the territory around 360-370 cents cents
> with landmarks such as 16/13 (359 cents), 21/17 (366 cents), and
> 26/21 (370 cents). The ratios are a sign of familiarity and
> affection.
>
> And your search for examples, which I often cite to show the
> variety of shadings in medieval and modern Near Eastern practice
> and theory, and which may or may not point to additional
> connections, is laudible. If I had access to video or tools for
> analyzing pitch relationships in cents, I might be right in there
> with Amine Beyhom, Can Akkoc, Ozan Yarman, you, and others. And I
> think what we'll mainly find is variety, variety, variety.
>
> >> (4) You generally find complex integer ratios more
> >> confusing that illuminating, and would really prefer
> >> simply to see measurements in cents.
>
> > I find that rationals numbers are used in a quasi-religious
> > fashion by people purporting to do music theory. That goes far
> > outside the maqam realm. If somebody has a religious
> > fascination with rational numbers, that's fine by me! Just say
> > so from the start, and for heaven's sake don't make objective
> > claims about historical or contemporary musical tradition(s),
> > supposed health benefits, etc. That's dishonest, disrespectful
> > to the practitioners of said tradition(s), offtopic, and likely
> > to arouse those with allergies to such things, such as myself.
>
> If you're referring to the commercialization of traditional
> cultures and arts, complete with health and asserted other
> marketing claims, and sometimes with totally fictional accounts
> presented as actual ethnographic data, then we're in agreement
> with lots of people in those cultures.
>
> What I hope is that you're referring to a hypothetical case which
> happily has not arisen in the list's present colloquies on maqam
> and dastgah music and tuning, whatever our differences of view.
> Of course, it's possible for honest and respectful analyses to be
> theoretically overzealous or simply wrong, and respectful
> questioning or outright correction, always I would hope
> constructive and polite, is an appropriate response. This
> discussion I take to be in that spirit, whatever the merits of
> our respective positions.
>
> Similarly, when we were moderating MakeMicroMusic almost a decade
> ago, Jon and Jacky and I instituted a guideline that responses to
> posted music should always be courteous and constructive. And
> when young people share music, it's especially important that any
> critical response should honor the effort and share an
> encouraging word which may, of course, include friendly
> suggestions for improvement. One test: is this the kind of
> comment that a friendly coach or mentor might offer, and are we
> confident enough of our judgment to offer it in that spirit?
>
> >> (1) The AEU or mostly Pythagorean model (often featuring
> >> schismatic 5-limit approximations) for modern Turkish music
> >> actuals fits some flavors of perforance in maqamat such as
> >> Rast and Segah, but does not represent important flavors
> >> such as Rast with rast-segah at around 16 commas or in the
> >> neighborhood of 360 cents (e.g. 16/13), and fails radically
> >> to account for prevailing intonational style in maqamat such
> >> as Ushshaq and Huseyni.
>
> > While waiting for Ozan to confirm or deny these details, I can
> > say I will hardly be surprised if existing theoretical
> > proposals, of whatever vintage, are found wanting.
>
> And I wouldn't be surprised either!
>
> > I will add: there is no guarantee that a single master tuning
> > exists for all the maqamat. Of course tunings of arbitrary
> > precision, like 1200-ET or 12,000-ET would probably do the job.
> > But that would be too easy. Any such master tuning must
> > justify itself via some explanatory power, much like a
> > scientific theory. It must 'explain' or reveal common features
> > of the maqamat, much like Newton's laws of gravitation
> > explained a variety of different observations of motion made by
> > different people at different times. Otherwise we can be
> > perfectly happy knowing a tuning for each maqam, or even at a
> > finer level of detail (regional, tetrachordal, etc.) as
> > necessary.
>
> Personally I'd far prefer a case-by-case basis, and my very love
> of the diversity and many shadings tends to lean in the other
> direction from any unifying theory, much less a "master tuning."
> Even Ozan's 79/80-MOS of an approximate 159-EDO is meant as a
> practical and general solution, but not an all-encompassing one
> rendering other tuning systems superfluous.
>
> One virtue of my 24-note maqam temperaments is that no one is
> likely to offer one of these as a "master tuning"!
>
> > The master tuning of the West, 12-ET, does in fact have such
> > explanatory power over Western music, yet it doesn't go all the
> > way. We need the notion of adaptive JI, along with the idea of
> > disposing of only those commas assumed to vanish in the score,
> > to get the rest of the way. Prior to this list I'm not sure
> > this had ever been fully realized. Though people like
> > Bosanquet, Groven, Fokker, and Mathieu were definitely on the
> > right track.
>
> Certainly we agree that 12-ET/EDO can serve as either a
> modification of Pythagorean tuning (possibly its original
> application in 15th-century Italy, as suggested by Mark Lindley,
> permitting the same lute fret to be used as a diatonic or
> chromatic semitone) or as the upper limit of the meantone zone;
> and that adaptive JI is an attractive paradigm for 16th-century
> vocal music, for example, especially if one wants to avoid comma
> drift.
>
> A point worthy of quick mention is that problems involving the
> syntonic comma are specific to forms of Western music based on
> 5-limit consonances starting around the 15th century (and at
> least a couple of centuries earlier in some English styles), in
> contrast to medieval polyphony based on a Pythagorean outlook.
>
> Another point is that for many people on this list, the Western
> composers and styles presenting "the exception that proves the
> rule" would be main points of interest: for example Marchettus
> and his expressive variations on Pythagorean intonation which
> modern performers such as Christopher Page have seen as relevant
> to much 13th-14th century French and Italian music; and, of
> course, Vicentino, Colonna, and also Gesualdo in the later 16th
> and early 17th centuries.
>
> This isn't to miss your point that the "master tuning" concept
> can lead to some real insights: for example, my typical 24-note
> maqam tunings could be considered variations on a "master tuning"
> of 17-EDO. And we agree that maqam music as a whole simply can't
> be summed up in this kind of convenient way, using rational
> ratios or EDO divisions or anything else we have on hand!
>
> >> Carl, what I mean by "differences in musical orientation"
> >> might be illustrated by your response to a piece of
> >> Elizabethan music, > _Come, Sirrah Jack, Ho!_ by Thomas
> >> Weelkes. From your post, > I might guess that you are more
> >> oriented to 18th-19th century > tonality, and are experiencing
> >> this composition from around > 1600 from that perspective.
>
> > It's hard to say. My Dad was an early music geek so I grew up
> > with such things -- and sang them in high school and college.
> > But perhaps my tonal indoctrination runs deeper than I know.
>
> Maybe it's partly training, and partly the proportion of
> different influences to which one gravitates.
>
> >> The same music can, and should, evoke different experiences in
> >> different people.
>
> > Absolutely.
>
> >> When I heard the piece for the first time around 1976, I'd
> >> guess, on an album of the King's Singers, it sounded to me
> >> routinely pleasant, without anything standing out.
>
> > I wasn't alive yet in 1976 but I too first heard this
> > particular piece on probably that very same King's Singers
> > recording. It sounded completely normal until I tried to learn
> > the parts.
>
> That's interesting! I wonder how I might react approaching it at
> that level. And it's humorous how I envisioned you as being
> closer to my age, a healthy reminder for me that there are newer
> generations. Maybe my misconception that you were around my age
> came from the idea of you as "my fellow Berzerkleyan" -- when I
> lived in San Francisco, I often visited Berkeley.
>
> >> <[117]http://www.bestII.com/~mschulter/IntradaFLydian.mp3>
> >> <[118]http://www.bestII.com/~mschulter/IntradaFLydian.pdf>
>
> > Thanks for reminding about this piece. Loved it in 2005 as
> > much as now.
>
> Glad you like it. I'm not sure if it illustrates similar points
> to the ones you were discussing about tonality and modality.
>
> > -Carl
>
> Best,
>
> Margo
>

Hi Carl,

With the 'cello what I found was that you had to get the tension balanced between the open string and the parts of the string between the tailpiece and the bridge and between the peg and the nut. Because if the tension is higher in the open string, as you play then the string gets gradually flatter, or if it is lower in the open string, as you play it will get gradually sharper.

You can do that by pressing lightly to either side of the bridge, if I remember properly, until the tension evens out, and ditto for the nut.

So - first you need to adjust the nut end of course with the peg, until approximately in tune. Then even out the tension. Then you can do the fine tuning adjustment, which doesn't have that same issue of putting the tension out of balance.

Oh, and it's important to make sure the bridge is completely flat on the body and steady as well.

Another subtlety was that as you adjust the tuning of one of the strings it can cause small changes in the tension of the others. Increasing the tension of one string can slightly decrease the tension of the other three. Maybe that's because it causes the bridge to tilt very slightly, or shift slightly not sure really what it was now.

And - theoretically at least I think that might also affect the balance of the tension in the three parts of each string i.e. the balance between open string and the bit at either end beyond the bridge and the head though I can't remember whether it did or not.

So you could spend a long time just tuning the 'cello to get it right.

Surely depends on make of 'cello of course, how sensitive it is to those kinds of things.

But - that's memories from maybe two decades ago now, may be hazy.

Anyway details probably not important, anyone with a 'cello will discover them for themselves - but just that there were lots of subtleties and things to learn before you could do accurate really fine tuning adjustments of the instrument and expect that is true of many instruments.

With the clavichord, of course the pitch of the string varies if you press the key down hard. Though - if one can learn to do that cleanly so the pitch doesn't vary noticeably at start and end of the note, maybe that could even be a plus, letting one to dynamically adjust the pitches of notes in real time as you play. I don't know, it is something to find out and explore.

Yes indeed we are talking about adjustments much less than the normal just noticeable melodic acuity - although that is highly variable between musicians - I find that for myself, it varies quite a bit depending on how much "training" I have had recently, if I've been doing something that requires me to listen out for it then my acuity increases temporarily. If you had to do that over a long period of time then I'm pretty sure you would train yourself and it would increase probably permanently to a new base level.

But anyway - aim is to get a smooth sounding j.i. chord presumably, and so long as you can hear these beats then they will be something you would hear in any played chords sustained for more than a fraction of a second. It should be a noticeable point in the pitch spectrum for the player - assuming capability of doing the adjustments physically and suitable instrument timbre - and in some contexts at least I think listeners would hear it too, you'd be able to say something like "your 11/9 was slightly out - I could hear the beats" though whether you'd be able to say whether the upper note was flat or sharp, I don't know.

Would depend on the instrument timbre as well of course, if it had detuned partials e.g. string under high tension the point presumably would be slightly different, you would call it an 11/9 still probably but it would be a smidgen sharper - or whatever - than usual.

Robert

--- In tuning@...m, "Carl Lumma" <carl@...> wrote:
>
> Hi Robert,
>
> > The few times I've tried keyboard tuning - with a clavichord -
> > then you could adjust the tuning with the adjustment key
> > crudely - then you could kind of gently nudge it without actually
> > moving it, which might give much more accurate fine tuning.
> > Though the quietness of the instrument meant you had to listen
> > rather carefully!
>
> I owned a clavichord in the late '90s -- never an instrument I
> associated with intonation accuracy. But it did, as all
> pinblock instruments I've tuned, have had this 'nudge the hammer
> without moving it' possibility. On a piano, a lot of it is to
> do with getting tensions on either side of the bridge
> to equalize.
>
> For reference, the elimination a slow, phasing beat with a
> period of 4 seconds between a pair of faint partials at 4 KHz
> represents a tenth of a cent. It's about 40 times smaller
> than the melodic just noticeable difference.
>
> > With your slide guitar - can you buy fine tuning adjustments
> > like the ones you can get for a 'cello?
>
> I've never played a cello but those I've seen have not
> seemed paragons of intonation accuracy either. I suspect
> my slide guitar (open tuning... there are 28 strings) is
> capable of more accuracy than most cellos.
>
> -Carl
>

Hi Carl,

Realise, the fine tuning adjustment would also put the tension out of balance actually. At the nut end it does because it tightens or loosens the portion of string between peg and nut more than it does the rest of the string.

For the fine tuning adjustment would work the other way, tighten or loosen the open string between bridge and nut slightly more than the other portions of the string.

So you'd probably need to even out the tension slightly from time to time during the fine tuning adjustments as well.

So long ago I can't remember whether I did that or not. I think the thing that particularly made it a long process (though enjoyable) was the tendency of all the other strings to adjust in pitch slightly when you adjust the tuning of one of them so you needed to go round all the strings several times in recursive process until you got it right to your satisfaction. When you hit it spot on then the 'cello seems to "sing out" more which is rewarding :). And when you play any of the open strings you hear ringing harmonics from the other strings, also when you play harmonics on one of the strings you hear the harmonics on other strings, if I remember right, long time ago though.

But I remember I went to a wonderful concert by Mitislav Rostropovitch playing the Bach 'cello suites - and he had fine tuning adjustments on all his strings, so obviously felt it worthwhile to fine tune his 'cello carefully :).

Robert

Yes I agree- more than agree, because my personal experience is that the simple proportions in the audible harmonic spectrum exert very strong gravities. Melodically as well- last night I sang an ascending 7:6 two cents flat and a 5:4 one cent sharp (according to Adobe Audition pitch analysis, that's some kind of averaging window of course), not on purpose, wasn't even aiming for these intervals, but by feeling the vibe of that JI... thing. I couldn't sing with such accuracy "on purpose" if my life depended on it- it's just going with the flow of a strong natural phenomenon.

In a room with a good amount of echo, it must be said.

Here's something that had a profound effect on my perception of perception: the teacher passes around two seemingly identical tiny stainless steel ball bearings. Noone in the class could see any difference in size. Well there's a positivistic indication that the difference between the two is imperceptible, right? Wrong- except for one guy with heavily calloused hands, and one who wouldn't even give it a try for whatever reason, everyone in the class could FEEL the difference with their eyes closed and distinguish the larger and smaller, checked against micrometer. (seems that precisely this ability was taken advantage of during WWII, in the employment of blind people in factories- obviously Braille comes to mind as well).

As far as "scientific" perception tests, it seems I can match intervals by ear PERFECTLY! Yeah right. In typically fastiduous but fundamentally clueless fashion, the test I took at a science fair in Germany a few years ago was conducted by putting two different tones into headphones, one in each ear. A very large (super smooth and high quality, nice!) knob changed the frequency of one pitch, the machines tracking the process of course. The test was to tune the pitches to unison.

Well, unlike the informal test with the ball bearings, which revealed profound truths about human perception, this "scientific" test was a joke: having done plenty of headphone mixing, I immediately percieved that the stereo image of the tones in this test would collapse when the tones were matched. So I just tuned out the stereo and voila. Pfffft.

Just (haha!) some observations.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:
>
> Hello Margo~
> The implication that JI ratios have no special attraction is possibly proven otherwise by the history of piano tuning. Regardless of the system, these intervals have served as the bedrock point of departure in order to put forth all those imaginative approaches we have seen for centuries. The just intervals have been tuned and the only way some tuning have even been tuned is by tricks with counting beats and comparing it to clocks.
> This is quite removed from the process in which we deal with intervals in music.
>
> That there are other intervals of great musical expressiveness is proven in countless examples around the world.
> Still JI intervals will always hold a unique place.
>
> Partch could tune his 43 tone scale by ear, on instruments that often have extremely short durations. Some of these it was years before i actually heard some of the chords going on in his 'Delusion of the Fury'. Most people are so used to these not being tuned they hear it as percussion and little more.
>
> On the other hand I don't know of anyone who can get even marginally close to 11 or 13 ET or even 22 by ear.
>
> It would be unfair if i did not mention recurrent sequences of all having a special perceptible property that can be used to tune by paying attention to difference tones.
>
> These are only two "acoustical phenomenon' that can be used to tune by ear.
> I make no assumption that they are the only ones.
>
>
>
>
>
>
> --- In tuning@yahoogroups.com, Margo Schulter <mschulter@> wrote:
> >
> > [This doesn't attempt to keep up with the dialogues of the
> > last day or so.]
> >
> > Carl wrote:
> >
> > > Hi Margo,
> >
> > >> Please let me express my regrets for any negative part I may
> > >> have had in a "debate" which is clearly intruding on the
> > >> positive purposes of the group and creating more heat than
> > >> light.
> >
> > > Thanks for saying so, but I didn't feel you had any negative
> > > part in it. On the contrary, I enjoyed the messages we
> > > exchanged and thought they were a good example of how such
> > > things can go. I hope this sense was mutual but if not, it
> > > certainly wasn't my intention and please contact me offlist if
> > > you would like to discuss it further.
> >
> > Great, and I'll confirm that the sense is mutual. In fact, this
> > looks like a fascinating dialogue, and among other things a
> > chance to clarify what some of my own positions are or aren't.
> > Your remarks that follow are invaluable for presenting me an
> > opportunity to do this, an opportunity which might be very
> > helpful for the list. It's so easy for me to have "unspoken"
> > understandings about the meaning of my own words not so obvious
> > to anyone else.
> >
> > And I should briefly mention a couple of my technical
> > limitations: I have no means to access or hear videos, or to do
> > measurements of frequencies or intervals in cents for a maqam
> > performance, say. But I'm immensely interested in what you, Ozan,
> > Cameron, Jacques, or others might find.
> >
> > >> What are the real issues, not necessarily or solely factual,
> > >> in question? Well, my own position could be summed up about
> > >> like this:
> > >> (1) Medieval Islamic theorists describe tetrachords and
> > >> modes which are beautiful and can and should be applied to
> > >> medieval and modern maqamat at least some of the time in some
> > >> contexts;
> >
> > > ...Don't see how anyone could disagree with this.
> >
> > And actually this is about 70% of my point, with a helpful
> > footnote that I do some rather un-medieval things in my maqam
> > tunings, with temperament at the top of the list, and the
> > 11:12:13 division (as far as I know) as another.
> >
> > What both Ozan and I do, in different ways, is to take some
> > leaves from the medieval book and modify them a bit, or at least
> > mix in some new ingredients. And for both of us, temperament is
> > one of those ingredients. The different ways it's used in his
> > 79/80-MOS or my much more modest O3 could be an interesting topic
> > of comparison.
> >
> > >> (2) Some of these tunings are closely approximated by
> > >> current tunings in practical use in various parts of
> > >> the Near East;
> >
> > > Seems likely, though the word "closely" can be troublesome.
> > > The central point I would stress is that we really don't have
> > > much idea what tunings are currently in use, because of a
> > > paucity of data. That ought to lead to some humility, which
> > > would be good for all of us.
> >
> > What I would predict is that there are far too many variations to
> > fall neatly into _any_ model, medieval or later, which
> > recognition may be at least the beginning of humility. Looking at
> > some measurements of Iranian tunings by Nelly Caron and Dariush
> > Safvate, and others by Jean During, as well as Hormoz Farhat's
> > book, I find this variety an inspiration for anyone contemplating
> > the infinite shadings possible, and of course a daunting obstacle
> > for anyone who wants a single "master tuning" of any practical
> > size for a typical acoustical fixed-pitch instrument, as you
> > suggest below and I agree.
> >
> > And I see integer ratios as signposts or street numbers, not as
> > points of unique validity somehow devaluing the territory in
> > between those signposts. This brings us to a vital point which I
> > find it prudent to explain before posting summaries of measured
> > flexible-pitch tunings or instrumental frettings, etc.
> >
> > An observation of more or less "close" resemblance could lend
> > itself to any of at least three viewpoints:
> >
> > VIEWPOINT I: "Isn't it wonderful how medieval tunings
> > describe interval sizes and shadings close to those of
> > some tunings used on fixed-pitch instruments or by
> > flexible-pitch performers today?" Here there's no claim
> > that the rational values are uniquely salient or
> > "attractant," only a focus on regions or "neighborhoods"
> > of the spectrum, leaving open the question of possible
> > further connections or their lack.
> >
> > VIEWPOINT 2: "The fact that one or more medieval
> > theorists describes this rational tetrachord, and this
> > modern instrument or performance uses or closely
> > approximates it, indicates that the rational ratios
> > themselves, not just the general neighborhood or shading,
> > have some special salience or attractive power."
> >
> > VIEWPOINT 3: "The correspondence between the medieval
> > ratios and the modern tuning on a fixed-pitch instrument
> > shows some common tradition or acoustical logic of the
> > process of building and playing instruments of the
> > relevant type."
> >
> > My own position is to assert Viewpoint 1 and remain open to
> > evidence one way or the other on Viewpoints 2 and 3, the kinds of
> > issues raised by Ozan, Cris, and Cameron. Note that my practice
> > of using certain superparticular or other rational ratios as
> > intellectually attractive signposts or landmarks in itself
> > neither affirms nor denies that they may additionally have an
> > aurally attractive pull for musicians brought up in these
> > traditions, or a special significance in the vocabulary and
> > grammar of instrument building, if I may call it that, as a
> > variation on Cris's etymology of numbers and ratios.
> >
> > And I must admit that the psychoacoustical theories I would find
> > most plausible would be those either developed by dastgah and
> > maqam musicians or at least based on culturally specific
> > observations of talented performers or listeners brought up in
> > these traditions who have a native phonology, so to speak.
> > Objective tests of the ability of people practicing maqam or
> > dastgah music as a first language to discriminate between shades
> > of neutral intervals or degrees of contrast between smaller and
> > larger neutral seconds, for example, might be very interesting.
> >
> > Further, I find in the Islamic theorists of the Mutazilah Era a
> > logically attractive lore or discipline focusing on the
> > gradations and relations of rational ratios, an outlook also
> > reflected in some portions of _Divisions of the Tetrachord_ by
> > John Chalmers, that can be embraced while affirming the value of
> > irrational ratios and divisions also (which John addresses at
> > length), and leaving open psychoacoustical issues that might not
> > much affect my artistic outlook, although new knowledge can
> > always enrich one's perspective.
> >
> > Having said that, I would emphasize that it's possible to see
> > resemblances between a medieval rational tuning and a current
> > intonational practice without necessarily saying that the
> > specific medieval ratios are precisely represented in, or
> > "explain," the modern performance.
> >
> > First, let's consider the oldest description known to me of the
> > tetrachord that would later be called Rast, al-Farabi's mode of
> > Zalzal:
> >
> > 1/1 9/8 27/22 4/3
> > 0 204 355 498
> > 9:8 12:11 88:81
> > 204 151 143
> >
> > Now consider Amine Beyhom's estimate (thesis, Vol. I, at p. 52)
> > of a typical Lebanese Rast in a "learned" (_savant_) style:
> >
> > 0 200 355 500
> > 200 155 145
> >
> > When I say that either tuning is "closely approximated" by the
> > other, I mean simply that they represent similar shades of what
> > has come to be called Rast. What I'd note is not only the similar
> > sizes of the neutral thirds, but the subtle difference (around
> > 8-10 cents) between the larger and smaller neutral seconds.
> >
> > I do not mean to imply that the second tuning is intentionally or
> > otherwise based on rational ratios, although we might asssociate
> > 200 cents with 9:8. But it's the similar degree of subtle
> > difference between the two neutral seconds, with the larger
> > placed first, that catches my attention.
> >
> > To make my disclaimer more emphatic here, let's consider a
> > tetrachord that Beyhom measured from a performance in Hijaz by
> > the Turkish master Kudsi Erguner
> >
> > <http://www.beyhom.com/download/articles/Beyhom_2007_%20Des_criteres_d_authenticite_filigrane_n5.pdf>:
> >
> > 0 131 368 501
> > 131 237 133
> >
> > Now I might excitedly, as a self-appointed referee, call "Buzurg"
> > and cite two possible tetrachords using the ratios specified for
> > this mode (or actually the lower tetrachord of their pentachordal
> > schemes) by Safi al-Din al-Urmawi and Qutb al-Din al-Shirazi:
> >
> > 1/1 14/13 16/13 4/3
> > 0 128 359 498
> > 14:13 8:7 13:12
> > 128 231 139
> >
> > or
> >
> > 1/1 13/12 26/21 4/3
> > 0 139 370 498
> > 13:12 8:7 14:13
> > 128 231 139
> >
> > Indeed Erguner's tetrachord resembles these in having a small
> > neutral second, a middle step close to 8:7 (actually a bit
> > bigger), and another smallish neutral second. Noting this
> > pleasant kinship, however, isn't to say that Erguner is following
> > any rational scheme, or is making a distinction between 14:13 and
> > 13:12.
> >
> > While I can and will celebrate this as an example of a
> > "Buzurg-type Hijaz," in fact if we are seeking a "close fit,"
> > 36-EDO or 46-EDO would be closer than either rational version of
> > Buzurg above:
> >
> > Erguner: 0 131 368 501
> > 131 237 133
> >
> > 36-EDO: 0 133 367 500
> > 133 233 133
> >
> > 46-EDO 0 130 365 496
> > 130 235 130
> >
> > And I would certainly not conclude from Erguner's performance
> > that "a Turkish Hijaz of the Buzurg flavor is based on 36-EDO" --
> > or 46-EDO, for that matter!
> >
> > Actually, modern Turkish or Syrian theory based on 53 commas
> > might capture my general category of "Buzurg" as 6-10-6, or here,
> > using a suggested refinement of Beyhom for models based on 17 or
> > 24 positions per octave, "6- 10+ 6-" to show that each neutral
> > second is a bit smaller than 6 commas (about 135 cents) while the
> > middle step is a bit larger than 10 commas (about 226-228 cents)
> > or even a full 8:7 at 231 cents.
> >
> > In some cases, we might be able to draw some kind of
> > "etymological" connection, as Cris Forster has put it, or to draw
> > some connection between a given fretting scheme and a medieval
> > theoretical tradition, as Cameron has proposed. But noting
> > and celebrating some interesting resemblances need not itself
> > imply either type of connection.
> >
> > Generally my point in citing and comparing medieval rational
> > tunings and more or less kindred modern intonations is to
> > illustrate the variety of Near Eastern tetrachords and shadings,
> > historical and current.
> >
> > > However we can say certain things are unlikely. For instance,
> > > choose a rational number R at random, num(R)*den(R) < 10,000
> > > and 1 < R < 2. Let's say 55/27. What are the odds it is used
> > > systematically in maqam music (that is, it is the target of
> > > some bearing plan, fret placement instruction, vocal training
> > > regimen, etc, used by more than one musician... that
> > > musicians/craftsmen have some means of communicating about it,
> > > not necessarily by name, but in *some* fashion)? Answer: the
> > > odds are low and we wouldn't believe this unless evidence was
> > > plainly extant, de novo, of such a bearing plan, fret placement
> > > instruction, etc. etc.
> >
> > That's a curious illustration; we're talking about roughly 1232
> > cents (55/27).
> >
> > What's likely, or relevant, may depend on the question and on
> > one's viewpoint. To describe an interval around 370 cents, as on
> > Cameron's baglama or in my tempered vrsion of a flavor of Turkish
> > Rast, by association with the rational signpost of 26/21, or a
> > 4/3 less a 14/13, is what some of us find an intuitively
> > appealing mapping. And, likewise, an interval in this immediate
> > neighborhood might be associated with 99/80, or 9/8 plus 11/10, a
> > ratio of around 369 cents occurring in the "Medium Sundered"
> > tetrachord of Safi al-Din (9:8-11:10-320:297 or 204-165-129
> > cents).
> >
> > These conceptual landmarks are useful to some of us -- not
> > necessarily all of us, as you've made clear! -- in themselves.
> > Whether fretting schemes might favor these superparticular
> > patterns more than nearby but distinguishable shadings, and
> > whether flexible-pitch performers might be especially drawn to
> > them, are open questions.
> >
> > >> (3) Just ratios both simple and complex, as well as values
> > >> in cents, commas, savarts, etc., can be useful in describing
> > >> and analyzing current Near Eastern practice; and
> >
> > > I would dispute this beyond the 7-limit. Within the 7-limit
> > > it's unclear, but plausible, and Weighing Diverse seems to
> > > support it.
> >
> > Note that my "useful" may have a minimalistic sense that
> > rationals can provide an intuitively appealing grid (in the eye
> > of the beholder!) for mapping and appreciating the continuum of
> > neutral or Zalzalian seconds or thirds, for example. Such a grid
> > may or may not itself mark points of salient aural attraction, as
> > likewise with a grid such as 17-EDO, 24-EDO, or 53-EDO (all of
> > which have been proposed or used by Near Eastern theorists).
> >
> > >> (4) Superparticular or other divisions of the medieval
> > >> theorists, as well as some modern variations, can nicely evoke
> > >> the state of _tarab_ ("enchantment" or "ecstasy") sought by
> > >> performances and audiences as an aspect of the maqam
> > >> tradition.
> >
> > > I'm not sure how to evaluate this. Beyond the 7-limit I know
> > > of no property of superparticular intervals that makes them
> > > special in a melodic context, and even within the 7-limit
> > > harmonic context, intervals such as 5:3 and 7:4 are on par with
> > > superparticulars in terms of their stand-out psychoacoustic
> > > properties.
> >
> > An ambiguity of my quoted proposition (4), which I'll clarify
> > now, is whether it means "superparticular and other medieval
> > divisions alone or especially" or "medieval rational divisions,
> > among many others." My intended reading is totally nonexclusive,
> > and thanks for a chance to say so. In other words, "12:13:14 or
> > 128-139 cents is beautiful, and 125-137.5 cents in 96-EDO, or
> > 133.3-133.3 cents in 36-EDO or 63-EDO, might be comparably so."
> >
> > Whether superparticular divisions such as 12:13:14 or 14:13:12
> > and 11:12:13 or 13:12:11 have additionally have a special aural
> > attraction for expert or other performers growing up in a maqam
> > or dastgah tradition is an empirical question. And I find Cris's
> > instrumental etymology, which I'll need his book to study in more
> > detail, quite credible. While Ozan and I have independently been
> > drawn to the 13:12:11 or 11:12:13 division for certain maqamat or
> > dastgah-ha, let me prudently note again that I'm not aware of any
> > medieval sources citing this division.
> >
> > Also, I don't know if anyone is claiming that superparticulars
> > and only superparticulars are aurally salient: those of us drawn
> > to JI/RI have been citing ratios like 13/11, 14/11, and 26/21,
> > and certainly would recognize 7/4 as well as 16/9 as significant
> > landmarks. And likewise with 11/9, which Cameron found a clear
> > aural attractant in certain instrumental timbres (his Spectral
> > Harmonic Entropy or SHE).
> >
> > >> Carl, please correct me if I am wrong in seeing your main
> > >> points as follows:
> >
> > >> (1) You observe that a 24-EDO model can nicely fit some maqam
> > >> perforamnces.
> >
> > > Yes.
> >
> > And I'd add that Near Eastern theorists such as Vaziri in Iran
> > have endorsed 24-EDO. I consider it as one point on a continuum.
> >
> > >> (2) You regard medieval Islamic theory, and likewise the
> > >> theory of Ptolemy, insofar as it involves superparticular
> > >> or other rational ratios of medium to high complexity, as
> > >> having little reference to either the practice of those
> > >> times or of today -- doubtless allowing an exception for
> > >> those of us who deliberately study and then set out to
> > >> implement these tunings.
> >
> > > I know of no evidence they're connected.
> >
> > This I see as an open question, which Cris and Cameron may
> > address further, and the former addresses in detail in his new
> > book. My own artistic program, which no one else is obliged to
> > follow (and much less any or all Near Eastern musicians!),
> > wouldn't depend on the answer.
> >
> > > I know of strong evidence these theorists would have had no
> > > alternative but to use rational numbers to express their
> > > scales.
> >
> > This is a point that Owen Wright also makes. Cris has commented
> > that an "equable" division like Ibn Sina's 14;13:12 or 12:13:14
> > is the way of indicating a 7:6 third derived from two near-equal
> > steps. While I may like the subtle distinction between 14:13 and
> > 13:12, this doesn't mean a geometric division as in 36-EDO or
> > 63-EDO would be "wrong," or an unequal division like 130-143
> > cents not necessarily having any clear rational interpretation
> > (I'm just pulling numbers out of the air for my last example).
> > One theorist around the 15th or 16th century, as I recall, found
> > Ibn Sina's 12:13:14:16 (139-128-231 cents) or 28:26:24:21
> > (128-139-231 cents) less than satisfactory because the two
> > neutral second steps are too close to identical!
> >
> > Whether Near Eastern musicians are aurally drawn, or drawn by
> > instrument designs, to superparticular divisions vis-a-vis
> > comparably shaded geometric or unequal but not rationally
> > conceived divisions is an open question, and I'm open to a range
> > of results, interpretations, and answers.
> >
> > [On deliberate modern tuning according to medieval ratios]
> >
> > > Of course I allow that exception.
> >
> > And that exception is all I really need.
> >
> > >> (3) You associate concepts such as "11-limit" with a
> > >> harmonic context where various prime factors are in
> > >> operation (e.g. 2-3-5-7-11, or possibly 2-3-7-11),
> > >> rather than simply a melodic system using ratios such
> > >> as 12:11. If we change "JI" to "RI" (rational
> > >> intonation), and speak of "ratios of 11," then you
> > >> might be happier.
> >
> > > Generally the point is that ratios (dyads) of 11 are not
> > > tunable by ear either harmonically or melodically. In triads
> > > like 10:11:12, 4:7:11 and so on, available on dulcimers and the
> > > like, more can be said of a tendency to gravitate to 11.
> > > However I have never heard these relationships in recordings,
> > > and Santoor tuning instructions I have seen have not mentioned
> > > them. Now, maybe I should just get out more, which is why I
> > > keep asking for examples. I get accused of insincerity, or
> > > just ignored, when I do this.
> >
> > While remaining open to a range of results and conclusions on the
> > pragmatic question of whether and to what degree melodic
> > intervals, dyads, or more complex sonorities can be tuned by ear,
> > I might make two points about intonational politics.
> >
> > First, tunability or recognizability or reproducibility by ear
> > might depend a lot on the cultural background and training of the
> > musicians involved. And the usefulness of a given arithmetic
> > division or bearing plan for an instrument, as Cameron and Cris
> > have discussed, might not depend on whether every interval,
> > simple or complex, can be directly tuned by ear.
> >
> > Secondly, whether or not rational ratios with an intuitive or
> > intellectual attraction are tunable by ear or have any special
> > aural salience, using them as signposts and landmarks can be
> > tokens of our esteem for the regions of the spectrum in which
> > they appear. For me, this is true of the territory around 410-420
> > cents, say, with landmarks such as 33/26 (413 cents) and 14/11
> > (418 cents), as well as the territory around 360-370 cents cents
> > with landmarks such as 16/13 (359 cents), 21/17 (366 cents), and
> > 26/21 (370 cents). The ratios are a sign of familiarity and
> > affection.
> >
> > And your search for examples, which I often cite to show the
> > variety of shadings in medieval and modern Near Eastern practice
> > and theory, and which may or may not point to additional
> > connections, is laudible. If I had access to video or tools for
> > analyzing pitch relationships in cents, I might be right in there
> > with Amine Beyhom, Can Akkoc, Ozan Yarman, you, and others. And I
> > think what we'll mainly find is variety, variety, variety.
> >
> > >> (4) You generally find complex integer ratios more
> > >> confusing that illuminating, and would really prefer
> > >> simply to see measurements in cents.
> >
> > > I find that rationals numbers are used in a quasi-religious
> > > fashion by people purporting to do music theory. That goes far
> > > outside the maqam realm. If somebody has a religious
> > > fascination with rational numbers, that's fine by me! Just say
> > > so from the start, and for heaven's sake don't make objective
> > > claims about historical or contemporary musical tradition(s),
> > > supposed health benefits, etc. That's dishonest, disrespectful
> > > to the practitioners of said tradition(s), offtopic, and likely
> > > to arouse those with allergies to such things, such as myself.
> >
> > If you're referring to the commercialization of traditional
> > cultures and arts, complete with health and asserted other
> > marketing claims, and sometimes with totally fictional accounts
> > presented as actual ethnographic data, then we're in agreement
> > with lots of people in those cultures.
> >
> > What I hope is that you're referring to a hypothetical case which
> > happily has not arisen in the list's present colloquies on maqam
> > and dastgah music and tuning, whatever our differences of view.
> > Of course, it's possible for honest and respectful analyses to be
> > theoretically overzealous or simply wrong, and respectful
> > questioning or outright correction, always I would hope
> > constructive and polite, is an appropriate response. This
> > discussion I take to be in that spirit, whatever the merits of
> > our respective positions.
> >
> > Similarly, when we were moderating MakeMicroMusic almost a decade
> > ago, Jon and Jacky and I instituted a guideline that responses to
> > posted music should always be courteous and constructive. And
> > when young people share music, it's especially important that any
> > critical response should honor the effort and share an
> > encouraging word which may, of course, include friendly
> > suggestions for improvement. One test: is this the kind of
> > comment that a friendly coach or mentor might offer, and are we
> > confident enough of our judgment to offer it in that spirit?
> >
> > >> (1) The AEU or mostly Pythagorean model (often featuring
> > >> schismatic 5-limit approximations) for modern Turkish music
> > >> actuals fits some flavors of perforance in maqamat such as
> > >> Rast and Segah, but does not represent important flavors
> > >> such as Rast with rast-segah at around 16 commas or in the
> > >> neighborhood of 360 cents (e.g. 16/13), and fails radically
> > >> to account for prevailing intonational style in maqamat such
> > >> as Ushshaq and Huseyni.
> >
> > > While waiting for Ozan to confirm or deny these details, I can
> > > say I will hardly be surprised if existing theoretical
> > > proposals, of whatever vintage, are found wanting.
> >
> > And I wouldn't be surprised either!
> >
> > > I will add: there is no guarantee that a single master tuning
> > > exists for all the maqamat. Of course tunings of arbitrary
> > > precision, like 1200-ET or 12,000-ET would probably do the job.
> > > But that would be too easy. Any such master tuning must
> > > justify itself via some explanatory power, much like a
> > > scientific theory. It must 'explain' or reveal common features
> > > of the maqamat, much like Newton's laws of gravitation
> > > explained a variety of different observations of motion made by
> > > different people at different times. Otherwise we can be
> > > perfectly happy knowing a tuning for each maqam, or even at a
> > > finer level of detail (regional, tetrachordal, etc.) as
> > > necessary.
> >
> > Personally I'd far prefer a case-by-case basis, and my very love
> > of the diversity and many shadings tends to lean in the other
> > direction from any unifying theory, much less a "master tuning."
> > Even Ozan's 79/80-MOS of an approximate 159-EDO is meant as a
> > practical and general solution, but not an all-encompassing one
> > rendering other tuning systems superfluous.
> >
> > One virtue of my 24-note maqam temperaments is that no one is
> > likely to offer one of these as a "master tuning"!
> >
> > > The master tuning of the West, 12-ET, does in fact have such
> > > explanatory power over Western music, yet it doesn't go all the
> > > way. We need the notion of adaptive JI, along with the idea of
> > > disposing of only those commas assumed to vanish in the score,
> > > to get the rest of the way. Prior to this list I'm not sure
> > > this had ever been fully realized. Though people like
> > > Bosanquet, Groven, Fokker, and Mathieu were definitely on the
> > > right track.
> >
> > Certainly we agree that 12-ET/EDO can serve as either a
> > modification of Pythagorean tuning (possibly its original
> > application in 15th-century Italy, as suggested by Mark Lindley,
> > permitting the same lute fret to be used as a diatonic or
> > chromatic semitone) or as the upper limit of the meantone zone;
> > and that adaptive JI is an attractive paradigm for 16th-century
> > vocal music, for example, especially if one wants to avoid comma
> > drift.
> >
> > A point worthy of quick mention is that problems involving the
> > syntonic comma are specific to forms of Western music based on
> > 5-limit consonances starting around the 15th century (and at
> > least a couple of centuries earlier in some English styles), in
> > contrast to medieval polyphony based on a Pythagorean outlook.
> >
> > Another point is that for many people on this list, the Western
> > composers and styles presenting "the exception that proves the
> > rule" would be main points of interest: for example Marchettus
> > and his expressive variations on Pythagorean intonation which
> > modern performers such as Christopher Page have seen as relevant
> > to much 13th-14th century French and Italian music; and, of
> > course, Vicentino, Colonna, and also Gesualdo in the later 16th
> > and early 17th centuries.
> >
> > This isn't to miss your point that the "master tuning" concept
> > can lead to some real insights: for example, my typical 24-note
> > maqam tunings could be considered variations on a "master tuning"
> > of 17-EDO. And we agree that maqam music as a whole simply can't
> > be summed up in this kind of convenient way, using rational
> > ratios or EDO divisions or anything else we have on hand!
> >
> > >> Carl, what I mean by "differences in musical orientation"
> > >> might be illustrated by your response to a piece of
> > >> Elizabethan music, > _Come, Sirrah Jack, Ho!_ by Thomas
> > >> Weelkes. From your post, > I might guess that you are more
> > >> oriented to 18th-19th century > tonality, and are experiencing
> > >> this composition from around > 1600 from that perspective.
> >
> > > It's hard to say. My Dad was an early music geek so I grew up
> > > with such things -- and sang them in high school and college.
> > > But perhaps my tonal indoctrination runs deeper than I know.
> >
> > Maybe it's partly training, and partly the proportion of
> > different influences to which one gravitates.
> >
> > >> The same music can, and should, evoke different experiences in
> > >> different people.
> >
> > > Absolutely.
> >
> > >> When I heard the piece for the first time around 1976, I'd
> > >> guess, on an album of the King's Singers, it sounded to me
> > >> routinely pleasant, without anything standing out.
> >
> > > I wasn't alive yet in 1976 but I too first heard this
> > > particular piece on probably that very same King's Singers
> > > recording. It sounded completely normal until I tried to learn
> > > the parts.
> >
> > That's interesting! I wonder how I might react approaching it at
> > that level. And it's humorous how I envisioned you as being
> > closer to my age, a healthy reminder for me that there are newer
> > generations. Maybe my misconception that you were around my age
> > came from the idea of you as "my fellow Berzerkleyan" -- when I
> > lived in San Francisco, I often visited Berkeley.
> >
> > >> <[117]http://www.bestII.com/~mschulter/IntradaFLydian.mp3>
> > >> <[118]http://www.bestII.com/~mschulter/IntradaFLydian.pdf>
> >
> > > Thanks for reminding about this piece. Loved it in 2005 as
> > > much as now.
> >
> > Glad you like it. I'm not sure if it illustrates similar points
> > to the ones you were discussing about tonality and modality.
> >
> > > -Carl
> >
> > Best,
> >
> > Margo
> >
>

That would be a question to put to Ozan, not me. I'm sure he and I wouldn't agree on many things, but my opinion in based on acoustic perceptions in my reality, while his is specifically maqam-oriented and of course infinitely more informed than mine in that area.

As far as tuning, in practical and implementable manner, of tetrachordal music intended to both incorporate ancient tunings as well as be used in polyphonic music- certainly related to what Ozan is doing, which is why I'd even dare to speak on the subject- I do have a great deal to say.

It's clear from simply listening to various maqam musics that the Pythagorean skeletal structures and the simplest of intervals are not sacrosanct- the melodic step is very powerful. Farhat is very big on this. For the creating of a practical system of non-infinite scope- like tuning a qanun- this surely creates a serious problem. If it's true that microtonal inflections along the lines of, say, a "fourth" at 515 cents (remembered from tuning up to jam along with a video on YouTube) are essential characteristics, the magnitude of the problem of where to temper is clearly immense.

I don't face this problem personally, as I simply use pure, or plainly altered. This (using either pure or plainly altered) is, in my opinion, the only real option in a limited system that is not attempting to shoulder a huge burden. So, concretely: if we assume the ancient preference for superparticulars, we might come up with a very lovely sounding tetrachord of, in step sizes, 11/10, 9/8, 14/13 (in any order). This in my opinion belongs in a rational system, not a tempered system, as we're looking at a comma of 2080:2079 generated at the 4:3. In a tempered system, temper it out.

What about the 1287/1280 comma at 4:3 were we to use the also lovely combination of 13/12, 11/10 and 9/8 to make our tetrachord? That's already almost 9.5 cents. At 12/11, 11/10, 9/8 we've got a concrete comma. At almost a syntonic comma wide, I suspect that it may be one of the very commas that grates against 24-tET approximation.

I just tried to present a how of thinking of it here- first you have to choose the tetrachords you want, then temper. Maqam music has the additional problem of there being being little melodies played in characteristic intonations, not just tetrachords, trichords and pentachords.

Notice that my argument with Carl probably actually originates in the statement "choose the tetrachords you want".

I think it's just spouting new-agey fog to go on and on about the unfixed nature of pitches in maqam music. "No shit Sherlock- but how in the hell am I going to tune this string to "about 125-140 cents, maybe..""? Let the unfixed pitches be played by instruments of... unfixed pitch. In the meantime we've got to choose SOMETHING for our fixed pitch instruments (and notation!). After you choose the something, you can temper away.

I assume you've read Ozan's thesis, it's well worth it if you haven't.

-Cameron Bobro

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
> > Remember that I said that after a certain point, and I think we actually agree to a pretty good extent what that point is, it becomes a matter of choice what you call things. It's unlikely that I could distinguish a 13:12 from "6/7 down from Pythagorean ditone". Should I call it a 243/224? Depends on the context. In Ozan's 79-MOS tuning, I believe the difference is tempered out, and I think this an excellent solution in the daunting task of making a practical quanun tuning.
>
> 729/728 is not tempered out by 159et, but it is by 171et. I'd be interested in a list of commas which you think help provide excellent solutions to the daunting task of making practical quanun tuning.
>
> For what it's worth, 171 tempers out 32805/32768 in the 5-limit; 65625/65536, 2401/2400 and 4375/4374 in the 7-limit; 243/242, 441/440, and 540/539 in the 11-limit; 364/363, 625/624, and 729/728 in the 13-limit.
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@> wrote:
> >
> > Partch tuned his 11s by ear.
>
> Yeah, and he used lower identities to do it. -Carl
>

This is garbage.

I can tune 11s by ear all day long. And 13s. And 17s. And 19s. And some 23s. Ocassionally, I think I may have gotten some 29s and 31s. Last week, I think I got a 37 ; it awaits confirmation.

If Carl Lumma is really so ignorant of basic microtonality ( and I would call tuning 11s by ear basic ), he should most certainly be replaced as moderator. I think the source of many flame wars can be clearly identified.

> > Partch tuned his 11s by ear.
>
> Yeah, and he used lower identities to do it. -Carl
>

Chris John>"This is garbage. I can tune 11s by ear all day long. And 13s. And
17s. And 19s. And some 23s. Ocassionally, I think I may have gotten some 29s and
31s. Last week, I think I got a 37 ; it awaits confirmation."

Argh...yet another example of Carl's "do it my way or be ignorant" attitude
toward alternative tuning theories not based on theories he favors.

Yes, the ears seem to gravitate toward very low (IE 9 or less) limit ratios
so far as consonance on the average.
Yes, there does seem a tendency for ratios of low entropy to be easy to tune.
Yes, Maqam music in practice does often get near Pythagorean ratios.
Yes, many ratios that are easily tunable are also highly concordant

But, perhaps more importantly...
NO, these general observations do not compromise anything near what is
possible in micro-tonality. Easy example: Cameron, myself, Ozan, Jacques Dudon,
Margo, Igs, now Chris, and several others finding uses for 11-limit in high
consonance and sometimes often "even" high-tune-ably. Yet whenever someone
tries to explain why, Carl typically pops up and says "you're just wrong and
that's the end of it, stop pretending you are doing 'real' research" or even
(metaphorically) "you're worshopping false idols". :-D

So maybe there's one paper in the past Carl finds that says such things are
impossible...does that make them impossible and/or imply the listed people above
must have problems with hearing or "practicing pseudoscience"?
Absolutely not! It means that no more than the type of scholarly papers that
say 12TET is the basis of all music mean microtonality is "invalid". If we
stopped the endless fighting about what is/isn't science and instead focused on
patterns in what we hear, I swear, we would not only avoid tons of flame wars,
but be a whole lot more productive...no, NOT as "scientists", but as musicians.
The fact we have very strong mathematicians like Robert (even) favoring the idea
of open-mindedness toward ideas without intense "academically correct"
mathematical proof behind them also seems to say a lot. So does that Igs gave
up trying to define ET in terms of JI or Harmonic Entropy because of too many
exceptions...and went for the idea of simply listing chords that work well
musically in each tuning.

The days of "a few theories limit all attempts at new not-so-related
theories" that Carl seems to back up are finally coming to an end!

To future of this list evolving, to me, seems an obvious challenge of what
can many of us find we agree on BY EAR and only then deciding what "can never be
done".

I figure...If anyone, say, proposes a chord theory and no one agrees it
sounds good, it will be ignored and dropped...but if at least a handful of
people think it sounds good those people may well work together to develop
theories on why the chords sound good or how and where they can be used
musically. The result often won't be papers full of theories or impressive
graphs, but instead sets of chords and scales and perhaps suggestions on
musical/emotional uses for them that prove very useful to significant numbers of
musicians...and why would that, devoid of "science" or not, be anything to be
ashamed of?

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:

> I just tried to present a how of thinking of it here- first you have to choose the tetrachords you want, then temper.

There are a lot to choose from. Below I give all the tetrachords with superparicular steps which come within 8 cents of 4/3 without nailing it exactly and have numerators for the steps less than or equal to 27; there are 44 of them. I give the comma, and the three numerators.

[225/224, [6, 15, 25]]
[225/224, [8, 9, 25]]
[225/224, [9, 10, 15]]
[230/231, [8, 10, 23]]
[231/230, [7, 11, 24]]
[252/253, [7, 12, 24]]
[255/256, [6, 17, 25]]
[255/256, [7, 15, 17]]
[255/256, [9, 10, 17]]
[273/272, [7, 13, 18]]
[276/275, [6, 16, 23]]
[324/323, [6, 18, 20]]
[324/325, [6, 16, 27]]
[351/350, [6, 15, 26]]
[351/350, [8, 9, 26]]
[351/352, [9, 12, 13]]
[384/385, [8, 12, 16]]
[385/384, [7, 11, 25]]
[399/400, [6, 19, 21]]
[400/399, [8, 10, 20]]
[440/441, [8, 10, 22]]
[441/440, [7, 12, 21]]
[441/442, [7, 14, 18]]
[455/456, [7, 13, 20]]
[459/460, [6, 17, 24]]
[483/484, [7, 12, 23]]
[540/539, [8, 12, 15]]
[561/560, [6, 17, 22]]
[561/560, [8, 11, 17]]
[576/575, [6, 16, 24]]
[594/595, [6, 18, 22]]
[594/595, [8, 11, 18]]
[624/625, [6, 16, 26]]
[729/728, [6, 15, 27]]
[729/728, [8, 9, 27]]
[833/832, [7, 14, 17]]
[1001/1000, [7, 11, 26]]
[1701/1700, [6, 18, 21]]
[1729/1728, [7, 13, 19]]
[1863/1870, [6, 18, 23]]
[2079/2080, [7, 11, 27]]
[2079/2080, [9, 11, 14]]
[3213/3200, [6, 17, 21]]
[3519/3520, [6, 17, 23]]

Thanks Gene for the list. I assume we add a demominator which is -1 of the far right bracketed intervals.

If we assume that the smallest melodic interval might be in the range of 45/44 i think you could expand this list more by allowing for that.
Unless there is some objection.

Musically these could be used as less stable tetrachords or variations in free JI tone space where one might not want to allow the music to resolve or to add a tenser variation to material one might want to start or return to.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
>
> > I just tried to present a how of thinking of it here- first you have to choose the tetrachords you want, then temper.
>
> There are a lot to choose from. Below I give all the tetrachords with superparicular steps which come within 8 cents of 4/3 without nailing it exactly and have numerators for the steps less than or equal to 27; there are 44 of them. I give the comma, and the three numerators.
>
> [225/224, [6, 15, 25]]
> [225/224, [8, 9, 25]]
> [225/224, [9, 10, 15]]
> [230/231, [8, 10, 23]]
> [231/230, [7, 11, 24]]
> [252/253, [7, 12, 24]]
> [255/256, [6, 17, 25]]
> [255/256, [7, 15, 17]]
> [255/256, [9, 10, 17]]
> [273/272, [7, 13, 18]]
> [276/275, [6, 16, 23]]
> [324/323, [6, 18, 20]]
> [324/325, [6, 16, 27]]
> [351/350, [6, 15, 26]]
> [351/350, [8, 9, 26]]
> [351/352, [9, 12, 13]]
> [384/385, [8, 12, 16]]
> [385/384, [7, 11, 25]]
> [399/400, [6, 19, 21]]
> [400/399, [8, 10, 20]]
> [440/441, [8, 10, 22]]
> [441/440, [7, 12, 21]]
> [441/442, [7, 14, 18]]
> [455/456, [7, 13, 20]]
> [459/460, [6, 17, 24]]
> [483/484, [7, 12, 23]]
> [540/539, [8, 12, 15]]
> [561/560, [6, 17, 22]]
> [561/560, [8, 11, 17]]
> [576/575, [6, 16, 24]]
> [594/595, [6, 18, 22]]
> [594/595, [8, 11, 18]]
> [624/625, [6, 16, 26]]
> [729/728, [6, 15, 27]]
> [729/728, [8, 9, 27]]
> [833/832, [7, 14, 17]]
> [1001/1000, [7, 11, 26]]
> [1701/1700, [6, 18, 21]]
> [1729/1728, [7, 13, 19]]
> [1863/1870, [6, 18, 23]]
> [2079/2080, [7, 11, 27]]
> [2079/2080, [9, 11, 14]]
> [3213/3200, [6, 17, 21]]
> [3519/3520, [6, 17, 23]]
>

Gene, that is awesome, thanks!

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cameron" <misterbobro@> wrote:
>
> > I just tried to present a how of thinking of it here- first you have to choose the tetrachords you want, then temper.
>
> There are a lot to choose from. Below I give all the tetrachords with superparicular steps which come within 8 cents of 4/3 without nailing it exactly and have numerators for the steps less than or equal to 27; there are 44 of them. I give the comma, and the three numerators.
>
> [225/224, [6, 15, 25]]
> [225/224, [8, 9, 25]]
> [225/224, [9, 10, 15]]
> [230/231, [8, 10, 23]]
> [231/230, [7, 11, 24]]
> [252/253, [7, 12, 24]]
> [255/256, [6, 17, 25]]
> [255/256, [7, 15, 17]]
> [255/256, [9, 10, 17]]
> [273/272, [7, 13, 18]]
> [276/275, [6, 16, 23]]
> [324/323, [6, 18, 20]]
> [324/325, [6, 16, 27]]
> [351/350, [6, 15, 26]]
> [351/350, [8, 9, 26]]
> [351/352, [9, 12, 13]]
> [384/385, [8, 12, 16]]
> [385/384, [7, 11, 25]]
> [399/400, [6, 19, 21]]
> [400/399, [8, 10, 20]]
> [440/441, [8, 10, 22]]
> [441/440, [7, 12, 21]]
> [441/442, [7, 14, 18]]
> [455/456, [7, 13, 20]]
> [459/460, [6, 17, 24]]
> [483/484, [7, 12, 23]]
> [540/539, [8, 12, 15]]
> [561/560, [6, 17, 22]]
> [561/560, [8, 11, 17]]
> [576/575, [6, 16, 24]]
> [594/595, [6, 18, 22]]
> [594/595, [8, 11, 18]]
> [624/625, [6, 16, 26]]
> [729/728, [6, 15, 27]]
> [729/728, [8, 9, 27]]
> [833/832, [7, 14, 17]]
> [1001/1000, [7, 11, 26]]
> [1701/1700, [6, 18, 21]]
> [1729/1728, [7, 13, 19]]
> [1863/1870, [6, 18, 23]]
> [2079/2080, [7, 11, 27]]
> [2079/2080, [9, 11, 14]]
> [3213/3200, [6, 17, 21]]
> [3519/3520, [6, 17, 23]]
>

Christopher wrote:

> This is garbage.

Nice to meet you too.

> I can tune 11s by ear all day long. And 13s. And 17s.
> And 19s. And some 23s. Ocassionally, I think I may have
> gotten some 9s and 31s. Last week, I think I got a 37;
> it awaits confirmation.

Thanks for chiming in. Can you describe your process?

-Carl

Michale wrote:

> Argh...yet another example of Carl's "do it my way or be
> ignorant" attitude

Ok Michael, put a sock in it. Or shall I make my last act
as moderator banning you?

-Carl

--- In tuning@yahoogroups.com, "Brofessor" <kraiggrady@...> wrote:

> If we assume that the smallest melodic interval might be in the range of 45/44 i think you could expand this list more by allowing for that.
> Unless there is some objection.

Here you go--I limited the prime limit to 23.

[221/220, [5, 26, 34]]
[221/220, [6, 13, 34]]
[224/225, [6, 16, 28]]
[225/224, [5, 22, 45]]
[225/224, [5, 25, 36]]
[225/224, [5, 29, 30]]
[225/224, [6, 15, 25]]
[225/224, [8, 9, 25]]
[225/224, [9, 10, 15]]
[230/231, [8, 10, 23]]
[231/230, [7, 11, 24]]
[243/242, [6, 12, 45]]
[252/253, [7, 12, 24]]
[255/256, [5, 33, 34]]
[255/256, [6, 17, 25]]
[255/256, [7, 15, 17]]
[255/256, [9, 10, 17]]
[273/272, [5, 26, 35]]
[273/272, [6, 13, 35]]
[273/272, [7, 13, 18]]
[276/275, [6, 16, 23]]
[300/299, [5, 24, 40]]
[324/323, [6, 18, 20]]
[324/325, [6, 14, 36]]
[324/325, [6, 16, 27]]
[350/351, [5, 28, 40]]
[350/351, [7, 10, 40]]
[351/350, [5, 26, 36]]
[351/350, [6, 13, 36]]
[351/350, [6, 15, 26]]
[351/350, [8, 9, 26]]
[351/352, [5, 26, 45]]
[351/352, [6, 13, 45]]
[351/352, [9, 12, 13]]
[384/385, [8, 12, 16]]
[385/384, [5, 28, 33]]
[385/384, [7, 10, 33]]
[385/384, [7, 11, 25]]
[399/400, [6, 19, 21]]
[400/399, [8, 10, 20]]
[440/441, [8, 10, 22]]
[441/440, [7, 12, 21]]
[441/442, [6, 14, 35]]
[441/442, [7, 14, 18]]
[455/456, [5, 28, 39]]
[455/456, [7, 10, 39]]
[455/456, [7, 13, 20]]
[459/460, [6, 17, 24]]
[483/484, [7, 12, 23]]
[539/540, [7, 11, 28]]
[540/539, [8, 12, 15]]
[561/560, [6, 17, 22]]
[561/560, [8, 11, 17]]
[576/575, [6, 16, 24]]
[594/595, [6, 18, 22]]
[594/595, [8, 11, 18]]
[595/594, [5, 28, 34]]
[595/594, [7, 10, 34]]
[624/625, [6, 16, 26]]
[625/624, [5, 25, 40]]
[675/676, [5, 27, 40]]
[714/715, [6, 14, 34]]
[729/728, [5, 27, 36]]
[729/728, [6, 15, 27]]
[729/728, [8, 9, 27]]
[833/832, [7, 14, 17]]
[1001/1000, [7, 11, 26]]
[1215/1216, [5, 27, 39]]
[1225/1224, [5, 28, 35]]
[1225/1224, [7, 10, 35]]
[1521/1520, [5, 26, 39]]
[1521/1520, [6, 13, 39]]
[1701/1700, [6, 18, 21]]
[1729/1728, [7, 13, 19]]
[1755/1748, [5, 24, 39]]
[1863/1870, [6, 18, 23]]
[2025/2024, [5, 24, 45]]
[2079/2080, [6, 14, 33]]
[2079/2080, [7, 11, 27]]
[2079/2080, [9, 11, 14]]
[2295/2288, [5, 27, 34]]
[3213/3200, [6, 17, 21]]
[3519/3520, [6, 17, 23]]
[4875/4864, [5, 25, 39]]
[5625/5632, [5, 25, 45]]
[13365/13312, [5, 27, 33]]
[14175/14144, [5, 27, 35]]
[15525/15488, [5, 23, 45]]
[18225/18304, [5, 27, 45]]

Hi Robert,

> You can do that by pressing lightly to either side of the
> bridge, if I remember properly, until the tension evens out,
> and ditto for the nut.

On a piano, you play the note vigorously, and lift the
tension on and off the pin. Also, sometimes tuners will tune
an instrument twice, to make sure it's reach equilibrium.

Regarding the cello, of course we're talking about open
string tunings. One doesn't have tenth-cent accuracy in
fingering. And that was really my point... the overall
accuracy of most musical instruments is far below 0.1 cents.
Even synthesizers often don't deliver such accuracy.
When this claim was made for Kyma, it was a big deal.

-Carl

> Hello Margo~

Hello, Kraig, and thanks to you and Cameron for fine replies to
my post.

> The implication that JI ratios have no special attraction is
> possibly proven otherwise by the history of piano
> tuning. Regardless of the system, these intervals have served
> as the bedrock point of departure in order to put forth all
> those imaginative approaches we have seen for centuries. The
> just intervals have been tuned and the only way some tuning
> have even been tuned is by tricks with counting beats and
> comparing it to clocks.

> This is quite removed from the process in which we deal with
> intervals in music.

I should clarify that while the main point of my reply to Carl
was that the validity of my music and use of near-just versions
of medieval Islamic and other ratios such as 14/13 or 13/8
doesn't depend on the question of tunabllity by ear, that doesn't
mean that I don't lean in your direction. The fact that I tune by
synthesizer table makes me a bit caution in getting into this
question, but even my imperfect hearing and digital musicmaking
have taught me that these intervals and regions are significant.

Over the years, how high up the harmonic series one is "supposed"
to be able to hear seems like a fashion statement subject to
rising and falling trends, like hemlines. Thus one theory I
recall from around a decade ago was that "recognizable" ratios or
the like have ratios not greater than a*b=104. That "rule" of
"harmonic entropy" was evidently devised at a time when 13/8 was
in.

Other times 13/8 may be "out," or even ratios of 11. I recall a
discussion maybe a decade ago about whether I should really be
describing 14/11 and 13/11 in rational terms.

And still other times, people involved in the "regular mapping"
approach have told me that it's possible to tune by ear at least
up to 17:13, although adding that the fact that an interval is so
tunable or "recognizable" doesn't mean that it necessarily will
seem more consonant than surrounding intervals of the same
region.

What I know is that I can hear a difference between 14/13 and
13/12, which so nicely complement each other, as in Ibn Sina's
tetrachord of 28:26:24:21 or, Ozan has suggested, 12:13:14:16.
And George Secor taught me to take ratios of 11 and 13 very
seriously.

The real comedy is that we have vanguard research here into all
kinds of commas and three-digit and four-digit EDO's, but
something like 14/13 or 26/21 becomes an exemplar of
"psychoacoustically unfounded theory."

> That there are other intervals of great musical expressiveness
> is proven in countless examples around the world.

Yes, of course, with gamelan and "equable heptaonic" tunings of
many shadings in Southeast Asia and Africa as one example.

> Still JI intervals will always hold a unique place.

That;s how I feel, and I have a certain mixed feeling about
tempering, often by not more than 2-3 cents, in order to get a
chain of regular or near-regular fifths -- in O3, for example, at
either 1 or 2 binary millioctaves wide (i.e. 1024-EDO). One main
effect of the tempering is to get an apotome just shy of 14/13,
and a diminished fourth, e.g. B-Eb, at a virtually just 26/21
(370 cents), or sometimes Safi al-Din's 99/80 (369 cents).

And in something like Erv's 1-3-7-9-11-13 eikosony, I do get the
just ratios as occurately as 1024-EDO will permit. And I know he
hasn't been doctrinaire: he's done metaslendro, metameantone, and
lots of systems both just and tempered.

> Partch could tune his 43 tone scale by ear, on instruments that
> often have extremely short durations. Some of these it was
> years before i actually heard some of the chords going on in
> his 'Delusion of the Fury'. Most people are so used to these
> not being tuned they hear it as percussion and little more.

In one book on Partch in my local University library I saw a
diagram of a diamond going up to 17, if I remember correctly,
including 17/14, one of my favorites, and neat for Turkish Maqam
Segah.

> On the other hand I don't know of anyone who can get even marginally close to
> 11 or 13 ET or even 22 by ear.

I'm recalling a post where you humorously suggested that 22 could
be taken as a series of 32:31 steps. That was a reaction to the
trend of viewpoint JI in term of some EDO.

> It would be unfair if i did not mention recurrent sequences of all having a
> special perceptible property that can be used to tune by paying attention to
> difference tones.

Maybe it would be a good exercise for me to see if I can become
aware of and learn to recognize some of the difference tones that
might arise in O3. Would 4:6:7 be a good place to start: at one
location, A-E-F#*, it's around 0-703.1-960.0 cents? Or maybe
something like 6:9:11, A-E-G* at 0-703.1-1048.8 cents?

If I can learn to recognize different tones, and the temperament
is accurate enough, maybe I could experience some "near-just
phenomena" and feel more confident in these discussions.

Cameron wrote in response to Kraig:

> Yes I agree- more than agree, because my personal experience
> is that the simple proportions in the audible harmonic
> spectrum exert very strong gravities. Melodically as well-
> last night I sang an ascending 7:6 two cents flat and a 5:4
> one cent sharp (according to Adobe Audition pitch analysis,
> that's some kind of averaging window of course), not on
> purpose, wasn't even aiming for these intervals, but by
> feeling the vibe of that JI... thing. I couldn't sing with
> such accuracy "on purpose" if my life depended on it- it's
> just going with the flow of a strong natural phenomenon.

Hi, Cameron.

Thanks for adding your experience, and also your comments about
11/9 and the importance of instrument-specific SHE.

One question: do you find yourself singing at or near
superparticular ratios for neutral or Zalzalian seconds like
14:13, 13:12, 12:11, and 11:10 (about which you posted in an
article I'm answering next)? I see no reason these shouldn't be
recognizable with practice and a bit of stylistic familiarity,
which you have. There's an example in Ozan's thesis that looks
like 14:13:12 to him and me alike, and I've heard that this
division or 12:13:14 occurs in some other world musics.

Your baglama posts have really got me mobilized, and I really
enjoyed your remark about being drawn to 11/7. This is my usual
regular minor sixth, with my maqam tunings tending to support
both 14/9 and 11/7 in some locations, and one or the other in
lots more, although my 14/9's are notorious for getting tempered
to 273/176's or the like about four or five cents narrower!

My musical abilities, however imperfect, do permit me to
appreciate that Rast with a 16/13 and with a 26/21 are different
flavors, and I like both. A few months ago, Ozan was talking
about 370 cents as a historically prevant tuning of perde segah
in Rast, and your baglama seems to have hit the spot.

One point about ratios: I've been told that luthiers still use
the 16th-century "Rule of 18" to fret acoustically near-equal
semitones, using a ratio of 18:17 which, when fretting physics
comes into play, actually yields a more accurate 100 cents than
the "logarithmically correct" spacing.

Why not a "Rule of 14" for the baglama or the like: for example,
place the 4/3 fret in usual Pythagorean fashion, and then place
the fret the third of Rast (perde segah) so as to add another
13th part in length, producing an interval of 14:13, or of 26/21
from the 1/1?

I can easily see this kind of thing being handed down. Safi
al-Din al-Urmawi's "Medium Sundered" tetrachord of
9/8-11/10-320/297 (which leads to my next intended post) shows
another method for placing an almost identical segah fret.
Tune a 9/8 in usual Pythagorean fashion (as your six-year-old sun
might say, two soldierlies up and an octave down), and then place
a fret spaced from this by 1/11 of the remaining length. We could
call this a "Rule of 11."

The temperament issues you raise I'll get into with my next post,
where I'll also ask some questions about the rest of the baglama
tuning whose lowest tetrachord you've posted -- but hopefully
questions that won't require more measures, and might be
approached largely on the basis of which fourths or fifths are
pure or notably otherwise, etc.

[Later note: having found that addressing your temperament
questions produced a long post in itself, I will try to get to
those baglama questions tomorrow.]

With many thanks,

Margo

[Dear Cameron: In what follows I address some temeperament
questions and some of the tetrachords you discuss, as well as a
couple of others that might illustrate some related comma
questions. I apologize for the length! And while your baglama
does come up, another post focusing on your instrument itself
should follow soon.]

Cameron wrote:

> As far as tuning, in practical and implementable manner, of
> tetrachordal music intended to both incorporate ancient
> tunings as well as be used in polyphonic music- certainly
> related to what Ozan is doing, which is why I'd even dare to
> speak on the subject- I do have a great deal to say.

Dear Cameron,

Please let me emphasize that I can't speak for Ozan, but can say
that one of the lesson's I've learned from him is that
"maqam-based polyphony" can mean different things to different
people. And the kind of tuning or temperament system will reflect
both the medieval Islamic and more recent tetrachords in use, and
the logic of a given polyphonic style. That can mean creative
compromises in various directions -- and often dramatically
different ones for different people and styles.

Thus for Ozan, "polyphony" often means a desire for thirds at or
close to 5/4 -- or ideally a tad lower, by the schisma of Safi
al-Din al-Urmawi and the 24-note Pythgorean model of AEU, or
maybe around 382 cents, as suggested in one of his posts. Since
Ozan also wants an optional meantone path to that Rast third near
5/4, he uses a 79/80-MOS very close to 159-EDO, with some fifths
tempered by 1/3 Holderian comma or 1/159 octave while others
remain literally pure (by minute modifications to 159-EDO) or
virtually pure. There are both schismatic and meantone paths to
that 5/4 region, and the temperament of some fifths by over 7
cents (a bit more than in 19-EDO) is the necessary and logical
compromise to achieve that goal.

For me, "polyphony" means adopting 13th-14th century European
techniques to a maqam context rich with its Zalzalian steps and
intervals. In 13th-14th century music of Continental Europe,
based mostly on Pythagorean intonation, fifths and fourths are
the stable consonances, with thirds and sixths more or less
relatively concordant but complex and unstable, seeking
resolution to unisons, fifths, or octaves, for example. So
neutral thirds at various ratios fit in nicely. And something
like 26/21 is especially dilectable, because 370 cents is like a
"Zalzalian ditone" with the same kind of pleasant complexity as
14/11 at 418 cents, for example.

These are two different worlds. In Ozan's, 5/4 and 6/5 are needed
both as fitting one side of current Turkish maqam practice which
might be traced back at least to the 17-note Pythagorean
"Systematist" theory of the 13th century (and I believe Cris
shows to further back than that), and to meet the needs of his
polyphonic style using 5-limit consonances.

In mine, the emphasis is on ratios of 2-3-7-11-13, and any
occurrences of 5/4 or 6/5 approximations are more or less
incidental, rather than a basic or intended feature of a
neomedieval system. The rules of counterpoint can apply to
general categories of intervals: for example, "a major, minor, or
Zalzalian third often tends to contract to a unison or expand to
a fifth."

Furthermore, Ozan for his purposes needs an option for a
circulating 12-note chromatic scale to permit compatibility with
Western music based on a 12-note well-temperament or 12-EDO, one
of the design principles of his 79/80-MOS. What I need is
compatibility with 13th-14th century European style based on
Pythagoran intonation, of which I see a single 12-note keyboard
in O3 as a gentle modification, with an Eb-G# chain of fifths
tempered in 1024-EDO at an average of around 703.871 cents.

And temperament is an essential ingredient for both of us. Thus
on Ozan's 79/80-tone qanun, we have a suggested Rast (following
his thesis, p. 118(, of 0-196-392-498 cents, with the major third
being formed from two meantone steps of 196 cents. As he notes,
it is possible to spell this tetrachord simply C-D-E-F.

While temperament gets Ozan his meantone path to a near-5/4, it
gets me my "neo-Systematist" path to neutral or Zalzalian
intervals found within a single 12-note keyboard, for example in
a Rast tetrachord like B-C#-Eb-E at 0-207-369-496 cents or
207-162-127 cents. Note that on a Pythagorean keyboard, this same
spelling would result in a schismatic tetrachord of 0-204-384-498
cents, or 204-180-114 cents. These "schismatic" mappings thus
generate on each of the two 12-note keyboards the smallest and
largest neutral intervals, for example steps near 14:13 and
11:10, while combining notes from the two keyboards (spaced at
57.422 cents) produces central neutral intervals like steps near
13:12 and 12:11.

Here I don't want to get too enmeshed in the mechanics of the
79/80-MOS, on which Ozan is of course the expert, and O3, but to
give some idea of how polyphonic styles can vary and influence
tuning systems to move in different directions while still
sharing common themes like a desire for accurate representations
of superparticular middle seconds.

> It's clear from simply listening to various maqam musics that
> the Pythagorean skeletal structures and the simplest of
> intervals are not sacrosanct- the melodic step is very
> powerful. Farhat is very big on this. For the creating of a
> practical system of non-infinite scope- like tuning a qanun-
> this surely creates a serious problem. If it's true that
> microtonal inflections along the lines of, say, a "fourth" at
> 515 cents (remembered from tuning up to jam along with a video
> on YouTube) are essential characteristics, the magnitude of the
> problem of where to temper is clearly immense.

If circulation isn't a consideration, which it certainly isn't in
traditional Iranian music or Farhat's 17-note tar tuning, then
"odd" fourths and fifths can be a strength. For example, in the
24-note O3 temperament, we have a location where the closest
available fourth is 485 cents -- almost identical, as I learned
in a book by Nelly Caron and Dariouche Safvate, to a 484-cent
fourth used in a traditional tuning of a beautiful dastgah or
avaz (a satellite dastgah to the principal seven) known as the
Old Bayat-e Tork. They give 0-204-346-484-704-908-980-1200
cents.

More generally, the Iranian taste for septimal or near-septimal
intervals means that we're not going to get a tidy 17-note
circulating system on tar. Caron and Safvate, on the basis of
measuring one or more instruments, give a Shur tetrachord at
0-136-276-500 cents or 136-140-224 cents. A large tone that close
to 8:7 means that we can expect at least one notably narrow
fourth of the kind found in the "Old Tork" above.

In O3, we have 24 positions and 22 of them with usual fifths at
703.1 or 704.3 cents -- the "odd" two at G#-Eb* (an asterisk
showing a note on the upper keyboard) with a 714.8-cent fifth,
and G#*-E at 726.6 cents, or close to 32/21. And there are a
number of locations with a choice between 4/3 or 21/16, something
George Secor has taught me to relish, and nice for doing
different interpretations of Maqam `Iraq (some Syrians favor a
fourth at 21 commas or around 475 cents, realized at 472 or 473
cents in this temperament).

For Ozan, it _is_ vital to circulate, and he's made some
intricate and delicate compromises to do so while supporting lots
of neutral or Zalzalian flavors, among many other things.

> I don't face this problem personally, as I simply use pure, or
> plainly altered. This (using either pure or plainly altered)
> is, in my opinion, the only real option in a limited system
> that is not attempting to shoulder a huge burden.

Yes, and the "limited system" concept certainly applies to O3
with only 24 notes. Not being concerned with either circulation
or the syntonic comma simplifies lots of things, and means a
gentle degree of temperament is all that's needed.

> So, concretely: if we assume the ancient preference for
> superparticulars, we might come up with a very lovely sounding
> tetrachord of, in step sizes, 11/10, 9/8, 14/13 (in any
> order). This in my opinion belongs in a rational system, not a
> tempered system, as we're looking at a comma of 2080:2079
> generated at the 4:3. In a tempered system, temper it out.

In fact you've just brought up the topic of one of my favorite
tetrachords, so nicely illustrated on your baglama, and which
I've been discussing in some of my Ethno Extras articles. This is
Safi al-Din al-Urmawi's "Medium Sundered" which slightly enlarges
the 14/13 to make a full 4/3: 9/8-11/10-320/297 or 204-165-129
cents.

A JI solution might be to "temper by ratios" by keeping all
steps superparticular, 9/8-11/10-14/13, and letting that fourth
be narrow by a 2080:2079, less than a cent. But I guess that the
idea of a tetrachord at a just 4:3 led Safi al-Din to stretch the
14:13 by that amount instead.

On your baglama at 202-168-128 cents, a slightly enlarged 11/10
takes up the slack for the minutely narrow 9/8 as well as the
virtually just 14/13 -- two cents for the first, and another cent
for the second, placing it at 168 rather than 165 cents. If the
9/8 were precisely just, we might similarly stretch 11/10 by
exactly 2080:2079, getting 208/189 and a tuning of 204-166-128
cents.

Now let's see what happens in O3 for a similar tetrachord. Giving
Safi al-Din his due, we'll start with the tempered tetrachord
closest to his 9/8-11/10-320/297. Then we'll see what happens in
the almost identical tetrachord closest in its third size to your
baglama.

Safi al-Din: 1/1 9/8 99/80 4/3
0.0 203.9 368.9 498.0
9:8 11:10 320:297
203.9 165.0 129.1

O3: B C# Eb E
0.0 207.4 369.1 495.7
207.4 161.7 126.6

While the tempered neutral third at 369.1 cents is almost
identical to Safi al-Din's 99/80, the tone B-C# more than
compensates for the 2080:2079 comma in the JI version by its
wideness of about 3.5 cents in comparison to 9/8. The fourth,
tempered at about 2.3 cents narrow, is impure by an amount almost
three times that of the comma. And in the process, 11/10 gets
compressed to 161.7 cents, or by about 3.3 cents, just a tad more
than the 3.24 cents set as a maximum for the impurity of the
ratios supported in his 29-HTT (secor29htt.scl in the Scala
archive).

If we focus specifically on the interval from the neutral third
to the fourth, Eb-E in the tempered version, we find that the
third at 369.1 cents is a virtually just 99/80, but that the
narrowing of the fourth by some 2.3 cents more than accounts for
the 2080:2079 comma, indeed so much so that the remaining 14/13
step, for from needing a bit of widening as in Safi al-Din, is
actually narrow by about 1.7 cents (126.6 vs. 128.3 cents).

Now let's look at a trivially different tempered tetrachord
closer to your baglama's slightly larger neutral third, which
I'll call a virtually just 26/21, likewise taking your fourth as
a just 4/3:

Cameron's baglama: 0 202 370 498
202 168 128

O3: F# G# Bb B
0 208.6 370.3 496.9
208.6 161.7 126.6

Here the two upper melodic steps of the tempered tetrachord are
identical to those of the last, but the major second at 208.6
cents, and the fourth at 496.9 cents, are 1/1024 octave larger.
Your baglama and O3 may be about equally far in their central
steps from a just 11/10 at 165 cents, albeit in opposite
directions, Here, with the tempered third at a virtually just
26/21, the remaining step would be a just 14/13 -- except that
the fourth is narrow, this time by about 1.2 cents.

> What about the 1287/1280 comma at 4:3 were we to use the also
> lovely combination of 13/12, 11/10 and 9/8 to make our
> tetrachord? That's already almost 9.5 cents.

Humorously, with O3, I can give the answer that the steps aren't
so arranged that it's possible to combine these ratios all in a
single tetrachord, so the question doesn't arise <grin>. What O3
does have with 9/8 and 13/12 that might go a step further is this
tetrachord in the manner of one school of Aleppo for Maqam `Iraq:

Eb E F# G*
0 126.6 334.0 472.3
126.6 207.4 138.3

My point here, leaving aside the fine points of this tetrachord
(apart from noting that the Syrian 6-9-6 commas would be around
135-340-475 cents, with my 126.6-cent step rather smaller),
is that altered fourths and fifths sometimes go with the
territory. But let's get back to 13/12, 11/10, and 9/8, and see
how Ozan's 79-MOS might handle this. Suppose we want to keep all
three superparticular steps as close as possible to just. If we
start on step 13 of his scale (Scala archives, 79-159.scl), his
tempered or meantone major second step in Maqam Rast known as
perde dugah, we can do the following:

JI: 1/1 13/12 143/120 429/320
0 138.6 303.6 507.4
13/12 11/10 9/8
138.6 165.0 203.9

yarmans: 0 9 20 33L
79-MOS: 0 135.8 301.9 505.7
135.8 166.0 203.8
9 11 13L

You'll see that Ozan's meantone fourth at 505.7 cents, or 1/3
Holderian comma wide, absorbs most of the burden of that
1287/1280 comma, with the narrowing of 13/12 by not quite 3 cents
taking up the rest of the comma, and also compensating for the
tempering of 11/10 at about a cent wide. The numbers of yarmans,
or 79-MOS steps normally at 2/3 Holderian comma (2/159 octave) or
just over 15 cents, may help clarify the process. In the 79-MOS,
there is one "large" step at a full comma or about 1/53 octave,
and the notations "33L" for the fourth and "13L" for the 9/8 step
that concludes the tetrachord show an interval including this
large or full-comma tuning step.

Another solution would be to trim the 9/8 by 1/3 comma, and let
the fourth remain precisely or virtually pure. For example,
starting on Ozan's 1/1 or perde rast:

JI: 1/1 13/12 143/120 429/320
0 138.6 303.6 507.4
13/12 11/10 9/8
138.6 165.0 203.9

yarmans: 0 9 20 33
79-MOS: 0 135.8 301.9 498.1
135.8 166.0 196.2
9 11 13

This time the upper major second gets narrowed by the lion's
share of the comma instead of the fourth being widened by a
comparable amount, and all the intervals are built from regular
tuning steps of 2/3 Holderian comma or around 15 cents.

> At 12/11, 11/10, 9/8 we've got a concrete comma. At almost a
> syntonic comma wide, I suspect that it may be one of the very
> commas that grates against 24-tET approximation.

Here my first reaction is that 12/11 plus 11/10 should be
precisely a 6/5, and that plus 9/8 precisely a 27/20, so that we
are indeed a syntonic comma wide. Change the 9/8 to a 10/9, and
we have a 4/3, as well as Ptolemy's Equable Diatonic that Cris
was recently discussing, at 12:11:10:9.

But this might invite the consideration of one more case where
the comma involved using only superparticular ratios must somehow
be accounted for, and a temperament stays fairly close to one JI
solution. Let's consider a tetrachord which could be used in
Persian Shur, Arab Bayyati, or Turkish Arazbar, for example:

JI: 1/1 13/12 13/11 4/3
0 138.6 289.2 498.0
13:12 12:11 44:39
138.6 150.6 208.8

O3: F# G* A B
0 138.3 289.5 496.9
138.3 151.2 207.4

In the just version, we have a 13:12:11 division of a 13/11 minor
third, so that reaching a pure 4/3 requires a major second wider
than 9/8 by a 352:351 at some 4.9 cents, in other words a 44/39,
thus, on monochord, 52:48:44:39.

In O3, the 13/12 and 12/11 steps are virtually just, so the
352:351 gets handled essentially in two ways. First, the tone at
207.4 cents is about 3.5 cents wide of 9/8, and not too far from
44/39. Secondly, the fourth is narrow by not quite 1.2 cents. As
it happens, the 13/11 is at this location a tad wide at 289.5
cents compared to a just 289.2, helping with the comma also. At
some other locations, where 13/11 is not quite a cent narrow of
just at 288.3 cents, a wider major second at 208.6 cents (almost
precisely 44/39), or narrower fourth at 495.7 cents, is there to
compensate.

So we have commas of less than a cent, like the 2080:2079 as with
the beautiful Rast tetrachord made famous by your baglama (Safi
al-Din didn't call it Rast, but it wonderfully fits that maqam);
commas of around 4-5 cents like the 352:351; and the "biggies"
like your 1207:1280 example approaching 9.5 cents, and yet more
so the 81:80 at 21.5 cents or the 64/63 at 27.3 cents.

With the larger commas, I take a "JI-ish" perspective: let them
stand. For me, the 64:63 is the main one I deal with regularly.
In O3, some small ones like the 352:351 are tempered out, while
the 2080:2079 might in a sense be "observed" (e.g. 369.1 cents as
Safi al-Din's 99/80, and 370.3 cents as your baglama's 26/21),
hopefully while keeping a "quasi-rational" structure for the most
part intact.

And large commas can be invaluable, not only for yielding
"special effects" intervals like 21/16 when we want them, but for
permitting more choices: a smaller or larger neutral second to
start this tetrachord, or a 7/4 or a 16/9? Jacques and I both
seem to devise 17-note sets or subsets, for Persian music for
example, and then throw in a couple of extra notes to add comma
alternatives.

Please forgive me if this is too long: a lot of this stuff about
maqam tetrachords and tempering may not have been presented so
systematically before, and, of course, what I've written about
Ozan's 79/80-MOS is very much subject to his correction or
amendment!

Most appreciatively,

Margo
mschulter@...

Margo- I'm delighted to be reading this! Unfortunately I don't have time at the moment to reply in the detail I'd like to, as it is organizing and financing time around here, and for a non-beaurocratic person such as myself organizing a half dozen concerts is more difficult than giving two dozen concerts. However if I can work in another all-night recording session this weekend I'll be able to reply in quality (there's some kind of right-left brain unhinging, or reconnecting, or something, benefit to reviewing recorded stuff while thinking about something else, I catch different things that way).

-Cameron Bobro

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> [Dear Cameron: In what follows I address some temeperament
> questions and some of the tetrachords you discuss, as well as a
> couple of others that might illustrate some related comma
> questions. I apologize for the length! And while your baglama
> does come up, another post focusing on your instrument itself
> should follow soon.]
>
> Cameron wrote:
>
> > As far as tuning, in practical and implementable manner, of
> > tetrachordal music intended to both incorporate ancient
> > tunings as well as be used in polyphonic music- certainly
> > related to what Ozan is doing, which is why I'd even dare to
> > speak on the subject- I do have a great deal to say.
>
> Dear Cameron,
>
> Please let me emphasize that I can't speak for Ozan, but can say
> that one of the lesson's I've learned from him is that
> "maqam-based polyphony" can mean different things to different
> people. And the kind of tuning or temperament system will reflect
> both the medieval Islamic and more recent tetrachords in use, and
> the logic of a given polyphonic style. That can mean creative
> compromises in various directions -- and often dramatically
> different ones for different people and styles.
>
> Thus for Ozan, "polyphony" often means a desire for thirds at or
> close to 5/4 -- or ideally a tad lower, by the schisma of Safi
> al-Din al-Urmawi and the 24-note Pythgorean model of AEU, or
> maybe around 382 cents, as suggested in one of his posts. Since
> Ozan also wants an optional meantone path to that Rast third near
> 5/4, he uses a 79/80-MOS very close to 159-EDO, with some fifths
> tempered by 1/3 Holderian comma or 1/159 octave while others
> remain literally pure (by minute modifications to 159-EDO) or
> virtually pure. There are both schismatic and meantone paths to
> that 5/4 region, and the temperament of some fifths by over 7
> cents (a bit more than in 19-EDO) is the necessary and logical
> compromise to achieve that goal.
>
> For me, "polyphony" means adopting 13th-14th century European
> techniques to a maqam context rich with its Zalzalian steps and
> intervals. In 13th-14th century music of Continental Europe,
> based mostly on Pythagorean intonation, fifths and fourths are
> the stable consonances, with thirds and sixths more or less
> relatively concordant but complex and unstable, seeking
> resolution to unisons, fifths, or octaves, for example. So
> neutral thirds at various ratios fit in nicely. And something
> like 26/21 is especially dilectable, because 370 cents is like a
> "Zalzalian ditone" with the same kind of pleasant complexity as
> 14/11 at 418 cents, for example.
>
> These are two different worlds. In Ozan's, 5/4 and 6/5 are needed
> both as fitting one side of current Turkish maqam practice which
> might be traced back at least to the 17-note Pythagorean
> "Systematist" theory of the 13th century (and I believe Cris
> shows to further back than that), and to meet the needs of his
> polyphonic style using 5-limit consonances.
>
> In mine, the emphasis is on ratios of 2-3-7-11-13, and any
> occurrences of 5/4 or 6/5 approximations are more or less
> incidental, rather than a basic or intended feature of a
> neomedieval system. The rules of counterpoint can apply to
> general categories of intervals: for example, "a major, minor, or
> Zalzalian third often tends to contract to a unison or expand to
> a fifth."
>
> Furthermore, Ozan for his purposes needs an option for a
> circulating 12-note chromatic scale to permit compatibility with
> Western music based on a 12-note well-temperament or 12-EDO, one
> of the design principles of his 79/80-MOS. What I need is
> compatibility with 13th-14th century European style based on
> Pythagoran intonation, of which I see a single 12-note keyboard
> in O3 as a gentle modification, with an Eb-G# chain of fifths
> tempered in 1024-EDO at an average of around 703.871 cents.
>
> And temperament is an essential ingredient for both of us. Thus
> on Ozan's 79/80-tone qanun, we have a suggested Rast (following
> his thesis, p. 118(, of 0-196-392-498 cents, with the major third
> being formed from two meantone steps of 196 cents. As he notes,
> it is possible to spell this tetrachord simply C-D-E-F.
>
> While temperament gets Ozan his meantone path to a near-5/4, it
> gets me my "neo-Systematist" path to neutral or Zalzalian
> intervals found within a single 12-note keyboard, for example in
> a Rast tetrachord like B-C#-Eb-E at 0-207-369-496 cents or
> 207-162-127 cents. Note that on a Pythagorean keyboard, this same
> spelling would result in a schismatic tetrachord of 0-204-384-498
> cents, or 204-180-114 cents. These "schismatic" mappings thus
> generate on each of the two 12-note keyboards the smallest and
> largest neutral intervals, for example steps near 14:13 and
> 11:10, while combining notes from the two keyboards (spaced at
> 57.422 cents) produces central neutral intervals like steps near
> 13:12 and 12:11.
>
> Here I don't want to get too enmeshed in the mechanics of the
> 79/80-MOS, on which Ozan is of course the expert, and O3, but to
> give some idea of how polyphonic styles can vary and influence
> tuning systems to move in different directions while still
> sharing common themes like a desire for accurate representations
> of superparticular middle seconds.
>
> > It's clear from simply listening to various maqam musics that
> > the Pythagorean skeletal structures and the simplest of
> > intervals are not sacrosanct- the melodic step is very
> > powerful. Farhat is very big on this. For the creating of a
> > practical system of non-infinite scope- like tuning a qanun-
> > this surely creates a serious problem. If it's true that
> > microtonal inflections along the lines of, say, a "fourth" at
> > 515 cents (remembered from tuning up to jam along with a video
> > on YouTube) are essential characteristics, the magnitude of the
> > problem of where to temper is clearly immense.
>
> If circulation isn't a consideration, which it certainly isn't in
> traditional Iranian music or Farhat's 17-note tar tuning, then
> "odd" fourths and fifths can be a strength. For example, in the
> 24-note O3 temperament, we have a location where the closest
> available fourth is 485 cents -- almost identical, as I learned
> in a book by Nelly Caron and Dariouche Safvate, to a 484-cent
> fourth used in a traditional tuning of a beautiful dastgah or
> avaz (a satellite dastgah to the principal seven) known as the
> Old Bayat-e Tork. They give 0-204-346-484-704-908-980-1200
> cents.
>
> More generally, the Iranian taste for septimal or near-septimal
> intervals means that we're not going to get a tidy 17-note
> circulating system on tar. Caron and Safvate, on the basis of
> measuring one or more instruments, give a Shur tetrachord at
> 0-136-276-500 cents or 136-140-224 cents. A large tone that close
> to 8:7 means that we can expect at least one notably narrow
> fourth of the kind found in the "Old Tork" above.
>
> In O3, we have 24 positions and 22 of them with usual fifths at
> 703.1 or 704.3 cents -- the "odd" two at G#-Eb* (an asterisk
> showing a note on the upper keyboard) with a 714.8-cent fifth,
> and G#*-E at 726.6 cents, or close to 32/21. And there are a
> number of locations with a choice between 4/3 or 21/16, something
> George Secor has taught me to relish, and nice for doing
> different interpretations of Maqam `Iraq (some Syrians favor a
> fourth at 21 commas or around 475 cents, realized at 472 or 473
> cents in this temperament).
>
> For Ozan, it _is_ vital to circulate, and he's made some
> intricate and delicate compromises to do so while supporting lots
> of neutral or Zalzalian flavors, among many other things.
>
> > I don't face this problem personally, as I simply use pure, or
> > plainly altered. This (using either pure or plainly altered)
> > is, in my opinion, the only real option in a limited system
> > that is not attempting to shoulder a huge burden.
>
> Yes, and the "limited system" concept certainly applies to O3
> with only 24 notes. Not being concerned with either circulation
> or the syntonic comma simplifies lots of things, and means a
> gentle degree of temperament is all that's needed.
>
> > So, concretely: if we assume the ancient preference for
> > superparticulars, we might come up with a very lovely sounding
> > tetrachord of, in step sizes, 11/10, 9/8, 14/13 (in any
> > order). This in my opinion belongs in a rational system, not a
> > tempered system, as we're looking at a comma of 2080:2079
> > generated at the 4:3. In a tempered system, temper it out.
>
> In fact you've just brought up the topic of one of my favorite
> tetrachords, so nicely illustrated on your baglama, and which
> I've been discussing in some of my Ethno Extras articles. This is
> Safi al-Din al-Urmawi's "Medium Sundered" which slightly enlarges
> the 14/13 to make a full 4/3: 9/8-11/10-320/297 or 204-165-129
> cents.
>
> A JI solution might be to "temper by ratios" by keeping all
> steps superparticular, 9/8-11/10-14/13, and letting that fourth
> be narrow by a 2080:2079, less than a cent. But I guess that the
> idea of a tetrachord at a just 4:3 led Safi al-Din to stretch the
> 14:13 by that amount instead.
>
> On your baglama at 202-168-128 cents, a slightly enlarged 11/10
> takes up the slack for the minutely narrow 9/8 as well as the
> virtually just 14/13 -- two cents for the first, and another cent
> for the second, placing it at 168 rather than 165 cents. If the
> 9/8 were precisely just, we might similarly stretch 11/10 by
> exactly 2080:2079, getting 208/189 and a tuning of 204-166-128
> cents.
>
> Now let's see what happens in O3 for a similar tetrachord. Giving
> Safi al-Din his due, we'll start with the tempered tetrachord
> closest to his 9/8-11/10-320/297. Then we'll see what happens in
> the almost identical tetrachord closest in its third size to your
> baglama.
>
> Safi al-Din: 1/1 9/8 99/80 4/3
> 0.0 203.9 368.9 498.0
> 9:8 11:10 320:297
> 203.9 165.0 129.1
>
> O3: B C# Eb E
> 0.0 207.4 369.1 495.7
> 207.4 161.7 126.6
>
> While the tempered neutral third at 369.1 cents is almost
> identical to Safi al-Din's 99/80, the tone B-C# more than
> compensates for the 2080:2079 comma in the JI version by its
> wideness of about 3.5 cents in comparison to 9/8. The fourth,
> tempered at about 2.3 cents narrow, is impure by an amount almost
> three times that of the comma. And in the process, 11/10 gets
> compressed to 161.7 cents, or by about 3.3 cents, just a tad more
> than the 3.24 cents set as a maximum for the impurity of the
> ratios supported in his 29-HTT (secor29htt.scl in the Scala
> archive).
>
> If we focus specifically on the interval from the neutral third
> to the fourth, Eb-E in the tempered version, we find that the
> third at 369.1 cents is a virtually just 99/80, but that the
> narrowing of the fourth by some 2.3 cents more than accounts for
> the 2080:2079 comma, indeed so much so that the remaining 14/13
> step, for from needing a bit of widening as in Safi al-Din, is
> actually narrow by about 1.7 cents (126.6 vs. 128.3 cents).
>
> Now let's look at a trivially different tempered tetrachord
> closer to your baglama's slightly larger neutral third, which
> I'll call a virtually just 26/21, likewise taking your fourth as
> a just 4/3:
>
> Cameron's baglama: 0 202 370 498
> 202 168 128
>
> O3: F# G# Bb B
> 0 208.6 370.3 496.9
> 208.6 161.7 126.6
>
> Here the two upper melodic steps of the tempered tetrachord are
> identical to those of the last, but the major second at 208.6
> cents, and the fourth at 496.9 cents, are 1/1024 octave larger.
> Your baglama and O3 may be about equally far in their central
> steps from a just 11/10 at 165 cents, albeit in opposite
> directions, Here, with the tempered third at a virtually just
> 26/21, the remaining step would be a just 14/13 -- except that
> the fourth is narrow, this time by about 1.2 cents.
>
> > What about the 1287/1280 comma at 4:3 were we to use the also
> > lovely combination of 13/12, 11/10 and 9/8 to make our
> > tetrachord? That's already almost 9.5 cents.
>
> Humorously, with O3, I can give the answer that the steps aren't
> so arranged that it's possible to combine these ratios all in a
> single tetrachord, so the question doesn't arise <grin>. What O3
> does have with 9/8 and 13/12 that might go a step further is this
> tetrachord in the manner of one school of Aleppo for Maqam `Iraq:
>
> Eb E F# G*
> 0 126.6 334.0 472.3
> 126.6 207.4 138.3
>
> My point here, leaving aside the fine points of this tetrachord
> (apart from noting that the Syrian 6-9-6 commas would be around
> 135-340-475 cents, with my 126.6-cent step rather smaller),
> is that altered fourths and fifths sometimes go with the
> territory. But let's get back to 13/12, 11/10, and 9/8, and see
> how Ozan's 79-MOS might handle this. Suppose we want to keep all
> three superparticular steps as close as possible to just. If we
> start on step 13 of his scale (Scala archives, 79-159.scl), his
> tempered or meantone major second step in Maqam Rast known as
> perde dugah, we can do the following:
>
> JI: 1/1 13/12 143/120 429/320
> 0 138.6 303.6 507.4
> 13/12 11/10 9/8
> 138.6 165.0 203.9
>
> yarmans: 0 9 20 33L
> 79-MOS: 0 135.8 301.9 505.7
> 135.8 166.0 203.8
> 9 11 13L
>
> You'll see that Ozan's meantone fourth at 505.7 cents, or 1/3
> Holderian comma wide, absorbs most of the burden of that
> 1287/1280 comma, with the narrowing of 13/12 by not quite 3 cents
> taking up the rest of the comma, and also compensating for the
> tempering of 11/10 at about a cent wide. The numbers of yarmans,
> or 79-MOS steps normally at 2/3 Holderian comma (2/159 octave) or
> just over 15 cents, may help clarify the process. In the 79-MOS,
> there is one "large" step at a full comma or about 1/53 octave,
> and the notations "33L" for the fourth and "13L" for the 9/8 step
> that concludes the tetrachord show an interval including this
> large or full-comma tuning step.
>
> Another solution would be to trim the 9/8 by 1/3 comma, and let
> the fourth remain precisely or virtually pure. For example,
> starting on Ozan's 1/1 or perde rast:
>
> JI: 1/1 13/12 143/120 429/320
> 0 138.6 303.6 507.4
> 13/12 11/10 9/8
> 138.6 165.0 203.9
>
> yarmans: 0 9 20 33
> 79-MOS: 0 135.8 301.9 498.1
> 135.8 166.0 196.2
> 9 11 13
>
> This time the upper major second gets narrowed by the lion's
> share of the comma instead of the fourth being widened by a
> comparable amount, and all the intervals are built from regular
> tuning steps of 2/3 Holderian comma or around 15 cents.
>
> > At 12/11, 11/10, 9/8 we've got a concrete comma. At almost a
> > syntonic comma wide, I suspect that it may be one of the very
> > commas that grates against 24-tET approximation.
>
> Here my first reaction is that 12/11 plus 11/10 should be
> precisely a 6/5, and that plus 9/8 precisely a 27/20, so that we
> are indeed a syntonic comma wide. Change the 9/8 to a 10/9, and
> we have a 4/3, as well as Ptolemy's Equable Diatonic that Cris
> was recently discussing, at 12:11:10:9.
>
> But this might invite the consideration of one more case where
> the comma involved using only superparticular ratios must somehow
> be accounted for, and a temperament stays fairly close to one JI
> solution. Let's consider a tetrachord which could be used in
> Persian Shur, Arab Bayyati, or Turkish Arazbar, for example:
>
> JI: 1/1 13/12 13/11 4/3
> 0 138.6 289.2 498.0
> 13:12 12:11 44:39
> 138.6 150.6 208.8
>
> O3: F# G* A B
> 0 138.3 289.5 496.9
> 138.3 151.2 207.4
>
> In the just version, we have a 13:12:11 division of a 13/11 minor
> third, so that reaching a pure 4/3 requires a major second wider
> than 9/8 by a 352:351 at some 4.9 cents, in other words a 44/39,
> thus, on monochord, 52:48:44:39.
>
> In O3, the 13/12 and 12/11 steps are virtually just, so the
> 352:351 gets handled essentially in two ways. First, the tone at
> 207.4 cents is about 3.5 cents wide of 9/8, and not too far from
> 44/39. Secondly, the fourth is narrow by not quite 1.2 cents. As
> it happens, the 13/11 is at this location a tad wide at 289.5
> cents compared to a just 289.2, helping with the comma also. At
> some other locations, where 13/11 is not quite a cent narrow of
> just at 288.3 cents, a wider major second at 208.6 cents (almost
> precisely 44/39), or narrower fourth at 495.7 cents, is there to
> compensate.
>
> So we have commas of less than a cent, like the 2080:2079 as with
> the beautiful Rast tetrachord made famous by your baglama (Safi
> al-Din didn't call it Rast, but it wonderfully fits that maqam);
> commas of around 4-5 cents like the 352:351; and the "biggies"
> like your 1207:1280 example approaching 9.5 cents, and yet more
> so the 81:80 at 21.5 cents or the 64/63 at 27.3 cents.
>
> With the larger commas, I take a "JI-ish" perspective: let them
> stand. For me, the 64:63 is the main one I deal with regularly.
> In O3, some small ones like the 352:351 are tempered out, while
> the 2080:2079 might in a sense be "observed" (e.g. 369.1 cents as
> Safi al-Din's 99/80, and 370.3 cents as your baglama's 26/21),
> hopefully while keeping a "quasi-rational" structure for the most
> part intact.
>
> And large commas can be invaluable, not only for yielding
> "special effects" intervals like 21/16 when we want them, but for
> permitting more choices: a smaller or larger neutral second to
> start this tetrachord, or a 7/4 or a 16/9? Jacques and I both
> seem to devise 17-note sets or subsets, for Persian music for
> example, and then throw in a couple of extra notes to add comma
> alternatives.
>
> Please forgive me if this is too long: a lot of this stuff about
> maqam tetrachords and tempering may not have been presented so
> systematically before, and, of course, what I've written about
> Ozan's 79/80-MOS is very much subject to his correction or
> amendment!
>
> Most appreciatively,
>
> Margo
> mschulter@...
>

Hi Carl,

Thanks, that's interesting, about how pianos are tuned. Does seem to be a related thing.

With the 'cello then I only tuned the open strings to 3/2s. Though - you also then have the harmonics as well, when you play harmonics which you can do on two strings at once.

Not sure when you'd play an 11/9 on the open strings. Though I suppose you might specify an 11/9 interval of the strings, e.g. tune top string down to say F half sharp instead of A for a microtonal piece for scordatura 'cello, similar idea to the Bach 'cello suite 5 (A tuned down to G). That might be a fun idea for a 'cello playing microtonal composer to explore :).

As for resolution while playing the notes with the fingers - well I can't speak from experience. Certainly can be quite accurate I imagine - not just sliding the finger, can just roll it slightly to micro adjust the pitch similar to the nudging of a tuning peg, but not sure how accurate you can get. I suppose there will be some limit or other,

It would be interesting to hear from 'cello players if you can eliminate beats on an 11/9 dyad on long held notes played without vibrato.

Snapping into a chord like that directly at start of a note would presumably be more challenging.

You'd expect it to be easier on a 'cello than on say a violin as the strings are so long. Probably double bass would be even better for accurate pitching of dyads. Also the lower the pitch, the slower the beats, and so less accuracy of placement needed to get a chord that sounds beatless to the ears. And the lower the pitch then the lower the pitch of the partials which may help make them a bit more obvious perhaps.

Just a few thoughts, as I don't have a 'cello to hand to try it out on.

Robert

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Robert,
>
> > You can do that by pressing lightly to either side of the
> > bridge, if I remember properly, until the tension evens out,
> > and ditto for the nut.
>
> On a piano, you play the note vigorously, and lift the
> tension on and off the pin. Also, sometimes tuners will tune
> an instrument twice, to make sure it's reach equilibrium.
>
> Regarding the cello, of course we're talking about open
> string tunings. One doesn't have tenth-cent accuracy in
> fingering. And that was really my point... the overall
> accuracy of most musical instruments is far below 0.1 cents.
> Even synthesizers often don't deliver such accuracy.
> When this claim was made for Kyma, it was a big deal.
>
> -Carl
>

Thank you Margo,
I think I understand more just where you thinking fits in the middle of all of this.
Looking at others post and the subject at large about the audible or not, there is no reason we might all experience a little of both even if we all fall into a different place.
When this happens in a cultural level maybe these are the tones that become "movable". With the Greeks this might be everything but the 6-8-9-12 and with the great torchbearers of this knowledge, the Persians and other Mideast musicians we might be seeing this in the various thirds of which the neutral one as well the second of this nature. These places will always allow others to explore this and i am enriched by your explorations of this areas as well as others on this list.
Your work has posed unique questions that i don't think is touch upon by anyone else and in so doing given new meaning to the struggles in a period of music that is often just thought of as a prelude to what was to follow.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> > Hello Margo~
>
> Hello, Kraig, and thanks to you and Cameron for fine replies to
> my post.
>
> > The implication that JI ratios have no special attraction is
> > possibly proven otherwise by the history of piano
> > tuning. Regardless of the system, these intervals have served
> > as the bedrock point of departure in order to put forth all
> > those imaginative approaches we have seen for centuries. The
> > just intervals have been tuned and the only way some tuning
> > have even been tuned is by tricks with counting beats and
> > comparing it to clocks.
>
> > This is quite removed from the process in which we deal with
> > intervals in music.
>
> I should clarify that while the main point of my reply to Carl
> was that the validity of my music and use of near-just versions
> of medieval Islamic and other ratios such as 14/13 or 13/8
> doesn't depend on the question of tunabllity by ear, that doesn't
> mean that I don't lean in your direction. The fact that I tune by
> synthesizer table makes me a bit caution in getting into this
> question, but even my imperfect hearing and digital musicmaking
> have taught me that these intervals and regions are significant.
>
> Over the years, how high up the harmonic series one is "supposed"
> to be able to hear seems like a fashion statement subject to
> rising and falling trends, like hemlines. Thus one theory I
> recall from around a decade ago was that "recognizable" ratios or
> the like have ratios not greater than a*b=104. That "rule" of
> "harmonic entropy" was evidently devised at a time when 13/8 was
> in.
>
> Other times 13/8 may be "out," or even ratios of 11. I recall a
> discussion maybe a decade ago about whether I should really be
> describing 14/11 and 13/11 in rational terms.
>
> And still other times, people involved in the "regular mapping"
> approach have told me that it's possible to tune by ear at least
> up to 17:13, although adding that the fact that an interval is so
> tunable or "recognizable" doesn't mean that it necessarily will
> seem more consonant than surrounding intervals of the same
> region.
>
> What I know is that I can hear a difference between 14/13 and
> 13/12, which so nicely complement each other, as in Ibn Sina's
> tetrachord of 28:26:24:21 or, Ozan has suggested, 12:13:14:16.
> And George Secor taught me to take ratios of 11 and 13 very
> seriously.
>
> The real comedy is that we have vanguard research here into all
> kinds of commas and three-digit and four-digit EDO's, but
> something like 14/13 or 26/21 becomes an exemplar of
> "psychoacoustically unfounded theory."
>
> > That there are other intervals of great musical expressiveness
> > is proven in countless examples around the world.
>
> Yes, of course, with gamelan and "equable heptaonic" tunings of
> many shadings in Southeast Asia and Africa as one example.
>
> > Still JI intervals will always hold a unique place.
>
> That;s how I feel, and I have a certain mixed feeling about
> tempering, often by not more than 2-3 cents, in order to get a
> chain of regular or near-regular fifths -- in O3, for example, at
> either 1 or 2 binary millioctaves wide (i.e. 1024-EDO). One main
> effect of the tempering is to get an apotome just shy of 14/13,
> and a diminished fourth, e.g. B-Eb, at a virtually just 26/21
> (370 cents), or sometimes Safi al-Din's 99/80 (369 cents).
>
> And in something like Erv's 1-3-7-9-11-13 eikosony, I do get the
> just ratios as occurately as 1024-EDO will permit. And I know he
> hasn't been doctrinaire: he's done metaslendro, metameantone, and
> lots of systems both just and tempered.
>
> > Partch could tune his 43 tone scale by ear, on instruments that
> > often have extremely short durations. Some of these it was
> > years before i actually heard some of the chords going on in
> > his 'Delusion of the Fury'. Most people are so used to these
> > not being tuned they hear it as percussion and little more.
>
> In one book on Partch in my local University library I saw a
> diagram of a diamond going up to 17, if I remember correctly,
> including 17/14, one of my favorites, and neat for Turkish Maqam
> Segah.
>
> > On the other hand I don't know of anyone who can get even marginally close to
> > 11 or 13 ET or even 22 by ear.
>
> I'm recalling a post where you humorously suggested that 22 could
> be taken as a series of 32:31 steps. That was a reaction to the
> trend of viewpoint JI in term of some EDO.
>
> > It would be unfair if i did not mention recurrent sequences of all having a
> > special perceptible property that can be used to tune by paying attention to
> > difference tones.
>
> Maybe it would be a good exercise for me to see if I can become
> aware of and learn to recognize some of the difference tones that
> might arise in O3. Would 4:6:7 be a good place to start: at one
> location, A-E-F#*, it's around 0-703.1-960.0 cents? Or maybe
> something like 6:9:11, A-E-G* at 0-703.1-1048.8 cents?
>
> If I can learn to recognize different tones, and the temperament
> is accurate enough, maybe I could experience some "near-just
> phenomena" and feel more confident in these discussions.
>
> Cameron wrote in response to Kraig:
>
> > Yes I agree- more than agree, because my personal experience
> > is that the simple proportions in the audible harmonic
> > spectrum exert very strong gravities. Melodically as well-
> > last night I sang an ascending 7:6 two cents flat and a 5:4
> > one cent sharp (according to Adobe Audition pitch analysis,
> > that's some kind of averaging window of course), not on
> > purpose, wasn't even aiming for these intervals, but by
> > feeling the vibe of that JI... thing. I couldn't sing with
> > such accuracy "on purpose" if my life depended on it- it's
> > just going with the flow of a strong natural phenomenon.
>
> Hi, Cameron.
>
> Thanks for adding your experience, and also your comments about
> 11/9 and the importance of instrument-specific SHE.
>
> One question: do you find yourself singing at or near
> superparticular ratios for neutral or Zalzalian seconds like
> 14:13, 13:12, 12:11, and 11:10 (about which you posted in an
> article I'm answering next)? I see no reason these shouldn't be
> recognizable with practice and a bit of stylistic familiarity,
> which you have. There's an example in Ozan's thesis that looks
> like 14:13:12 to him and me alike, and I've heard that this
> division or 12:13:14 occurs in some other world musics.
>
> Your baglama posts have really got me mobilized, and I really
> enjoyed your remark about being drawn to 11/7. This is my usual
> regular minor sixth, with my maqam tunings tending to support
> both 14/9 and 11/7 in some locations, and one or the other in
> lots more, although my 14/9's are notorious for getting tempered
> to 273/176's or the like about four or five cents narrower!
>
> My musical abilities, however imperfect, do permit me to
> appreciate that Rast with a 16/13 and with a 26/21 are different
> flavors, and I like both. A few months ago, Ozan was talking
> about 370 cents as a historically prevant tuning of perde segah
> in Rast, and your baglama seems to have hit the spot.
>
> One point about ratios: I've been told that luthiers still use
> the 16th-century "Rule of 18" to fret acoustically near-equal
> semitones, using a ratio of 18:17 which, when fretting physics
> comes into play, actually yields a more accurate 100 cents than
> the "logarithmically correct" spacing.
>
> Why not a "Rule of 14" for the baglama or the like: for example,
> place the 4/3 fret in usual Pythagorean fashion, and then place
> the fret the third of Rast (perde segah) so as to add another
> 13th part in length, producing an interval of 14:13, or of 26/21
> from the 1/1?
>
> I can easily see this kind of thing being handed down. Safi
> al-Din al-Urmawi's "Medium Sundered" tetrachord of
> 9/8-11/10-320/297 (which leads to my next intended post) shows
> another method for placing an almost identical segah fret.
> Tune a 9/8 in usual Pythagorean fashion (as your six-year-old sun
> might say, two soldierlies up and an octave down), and then place
> a fret spaced from this by 1/11 of the remaining length. We could
> call this a "Rule of 11."
>
> The temperament issues you raise I'll get into with my next post,
> where I'll also ask some questions about the rest of the baglama
> tuning whose lowest tetrachord you've posted -- but hopefully
> questions that won't require more measures, and might be
> approached largely on the basis of which fourths or fifths are
> pure or notably otherwise, etc.
>
> [Later note: having found that addressing your temperament
> questions produced a long post in itself, I will try to get to
> those baglama questions tomorrow.]
>
> With many thanks,
>
> Margo
>

Hi Margo,

Just a few quick notes...

> >> (2) Some of these tunings are closely approximated by
> >> current tunings in practical use in various parts of
> >> the Near East;
>
> > Seems likely, though the word "closely" can be troublesome.
> > The central point I would stress is that we really don't have
> > much idea what tunings are currently in use, because of a
> > paucity of data. That ought to lead to some humility, which
> > would be good for all of us.
[snip]
> To make my disclaimer more emphatic here, let's consider a
> tetrachord that Beyhom measured from a performance in Hijaz by
> the Turkish master Kudsi Erguner
>
> http://bit.ly/dA5cU8
>
> 0 131 368 501
> 131 237 133

What an awesome-looking paper. You must read French better
than you let on! It's too bad, but I can't participate because
of the language barrier.

> > However we can say certain things are unlikely. For instance,
> > choose a rational number R at random, num(R)*den(R) < 10,000
> > and 1 < R < 2. Let's say 55/27. What are the odds it is used
> > systematically in maqam music (that is, it is the target of
> > some bearing plan, fret placement instruction, vocal training
> > regimen, etc, used by more than one musician... that
> > musicians/craftsmen have some means of communicating about it,
> > not necessarily by name, but in *some* fashion)? Answer: the
> > odds are low and we wouldn't believe this unless evidence was
> > plainly extant, de novo, of such a bearing plan, fret placement
> > instruction, etc. etc.
[snip]
> These conceptual landmarks are useful to some of us -- not
> necessarily all of us, as you've made clear! -- in themselves.
> Whether fretting schemes might favor these superparticular
> patterns more than nearby but distinguishable shadings, and
> whether flexible-pitch performers might be especially drawn to
> them, are open questions.

They're open in the sense that there's no data contradicting
them, but closed in the sense that there is no particular
reason to suspect they might be true... unless there is.
For instance, Al-Farabi's instructions which Cameron recently
linked to certainly point to 27/22 as a target of a lute
fretting. So that's the kind of thing I was asking for, and
getting yelled at for asking for. It's also in contrast to
what we saw in some sources, where pitch-tracking data were
fit to rationals, apparently arbitrarily (or at least without
explanation).

> Whether superparticular divisions such as 12:13:14 or 14:13:12
> and 11:12:13 or 13:12:11 have additionally have a special aural
> attraction for expert or other performers growing up in a maqam
> or dastgah tradition is an empirical question.

As I remarked, such triads, when played in the proper (rather
high) register can sound special. But I haven't heard them in
maqam music. Like I said, maybe I need to get out more, but if
people are so sure they're there I would have expected links
offered straight away.

> This is a point that Owen Wright also makes. Cris has commented
> that an "equable" division like Ibn Sina's 14:13:12 or 12:13:14
> is the way of indicating a 7:6 third derived from two near-equal
> steps.

They are equal in terms of distance on the fretboard, so it's
entirely possible such a division would arise even if it's
never played as a triad. Of course that supposes the 7:6 is
tuned with some accuracy to start with, which again, I've never
heard stand out in maqam music.

> Whether Near Eastern musicians are aurally drawn, or drawn by
> instrument designs, to superparticular divisions vis-a-vis
> comparably shaded geometric or unequal but not rationally
> conceived divisions is an open question, and I'm open to a
> range of results, interpretations, and answers.

I'm open to a range of them too. However let's not paper
over the fact that some folks are engaged in number games,
and probably have been for a long time.

> First, tunability or recognizability or reproducibility by ear
> might depend a lot on the cultural background and training of
> the musicians involved.

Is there any evidence maqam musicians train to hear harmonics
like 11? I mean, it just flies in the face of everything I know
about the practice of maqam music (not that I know very much).

> If you're referring to the commercialization of traditional
> cultures and arts, complete with health and asserted other
> marketing claims, and sometimes with totally fictional accounts
> presented as actual ethnographic data, then we're in agreement
> with lots of people in those cultures.

To me it's no better than the proverbial late colonial-era
musician reporting that X musical tradition uses a cheap
imitation of 12-ET, so often maligned by the very people who...

> What I hope is that you're referring to a hypothetical case which
> happily has not arisen in the list's present colloquies on maqam
> and dastgah music and tuning, whatever our differences of view.

I will refrain from mentioning names at this time.

> Of course, it's possible for honest and respectful analyses to
> be theoretically overzealous or simply wrong, and respectful
> questioning or outright correction, always I would hope
> constructive and polite, is an appropriate response. This
> discussion I take to be in that spirit, whatever the merits of
> our respective positions.

The archives tell the story of who escalated where.
But I'm no angel when provoked and I should work harder
at that.

> Certainly we agree that 12-ET/EDO can serve as either a
> modification of Pythagorean tuning (possibly its original
> application in 15th-century Italy, as suggested by Mark Lindley,
> permitting the same lute fret to be used as a diatonic or
> chromatic semitone) or as the upper limit of the meantone zone;
> and that adaptive JI is an attractive paradigm for 16th-century
> vocal music, for example, especially if one wants to avoid comma
> drift.

I agree. Though if one really wants the edginess of
Pythagorean (e.g. on the organ), 12ET will tend to disappoint.

> A point worthy of quick mention is that problems involving the
> syntonic comma are specific to forms of Western music based on
> 5-limit consonances starting around the 15th century (and at
> least a couple of centuries earlier in some English styles), in
> contrast to medieval polyphony based on a Pythagorean outlook.

Yes, of course.

> Another point is that for many people on this list, the Western
> composers and styles presenting "the exception that proves the
> rule" would be main points of interest: for example Marchettus
> and his expressive variations on Pythagorean intonation which
> modern performers such as Christopher Page have seen as relevant
> to much 13th-14th century French and Italian music; and, of
> course, Vicentino, Colonna, and also Gesualdo in the later 16th
> and early 17th centuries.

Musica reservata certainly is an exception. I assume you've
heard the latest stuff being done by Jon Wild, etc? (Sorry,
but I can't remember if you were involved in the thread
regarding the recent BBC radio documentary...)

You may not know, but over the years I've made extensive use of
your excellent reviews of recordings. That was back when one
purchased CDs! and such decisions were always taken carefully.

> > I wasn't alive yet in 1976 but I too first heard this
> > particular piece on probably that very same King's Singers
> > recording. It sounded completely normal until I tried
> > to learn the parts.
>
> That's interesting! I wonder how I might react approaching it at
> that level. And it's humorous how I envisioned you as being
> closer to my age, a healthy reminder for me that there are newer
> generations. Maybe my misconception that you were around my age
> came from the idea of you as "my fellow Berzerkleyan" -- when I
> lived in San Francisco, I often visited Berkeley.

You're in the Sacremento area now? Alas, I'm no longer in
Berkeley, having moved to the San Jose area in 2006. As much
as I dislike some aspects of the suburban life here, it has
some considerable advantages in the raising children dept.

But yeah, I found myself always singing the F#, as it were.
I could do with a much better dose of modal intelligence.
I am always in awe of jazz artists in this respect. Say,
have you heard the recordings the Orlando consort did with
that jazz group... Perfect Houseplants?

> Glad you like it. I'm not sure if it illustrates similar points
> to the ones you were discussing about tonality and modality.

When my sore throat recovers I'll attempt to sing it and
let you know!

-Carl

I also concur.

On Wed, Nov 3, 2010 at 10:41 PM, robert_inventor5
<robertwalker@...> wrote:
>
>
>
> Good point, Kraig, just bumping this in case anyone missed it, not much to reply except to say I agree!
>
> Robert
>
> > I have been enjoying and concurring about what you are saying Robert.
> I think one difference in the arts is often one comes up with theories afterwards in order to explain phenomenon to themselves.
> This is true of quite a few composers i can think of who just write music and "justify " it later.
> Being in such a science heavy society, i think many artist feel they have to explain their actions or directions.
> Which i think is unfortunate.

> Hi Margo,

> Just a few quick notes...

Hi, Carl.

To keep this a bit briefer, I'll snip a bit of our last rounds
of comments quoted in your message. If it seems helpful, I'll sum
up previous comments or topical contexts in brackets.

> [snip]

[Quote from a paper by Amine Beyhom showing measurements in cents
for the Turkish master Kudsi Erguner's performance of Hijaz in a
flavor rather resembling, but not neatly matching, either of a
couple of medieval JI/RI tunings of the lower fourth of a Buzurg
pentachord, e.g. 14:13-8:7-13:12 (128-231-139 cents):

> [182]http://bit.ly/dA5cU8
>
>> 0 131 368 501
>> 131 237 133

> What an awesome-looking paper. You must read French better
> than you let on! It's too bad, but I can't participate because
> of the language barrier.

Here my intention in quoting Beyhom's reported values in cents
and giving some his context, as imperfectly as I may be
comprehending and translating his French, was to make his data
and observations more accessible.

[On ratios, for example for superparticular neutral or middle
seconds, that appear in medieval Islamic theory]

[snip]
> These conceptual landmarks are useful to some of us -- not
> necessarily all of us, as you've made clear! -- in themselves.
> Whether fretting schemes might favor these superparticular
> patterns more than nearby but distinguishable shadings, and
> whether flexible-pitch performers might be especially drawn to
> them, are open questions.

> They're open in the sense that there's no data contradicting
> them, but closed in the sense that there is no particular
> reason to suspect they might be true... unless there is.

Actually I'd say that's pretty open.

In one recent post, Ozan interestingly took the view that we
should regard such ratios for of all as "RI" or rational
intonation landmarks which might or might not serve as special
points of "attraction" to performers. That seems to me intuitive,
pragmatic, and wise.

And whatever devotion Ozan or I may have to certain
superparticular ratios or divisions, this doesn't stop either of
us from noting nuances that a doctrinaire "Superparticulars
Rule!" theorist would prefer to avoid.

For example, Ozan makes it clear that when segah, the third step
of Maqam Rast, is in a Turkish style meant to be in its high
position close to 5/4, it should actually be a bit shy of 5/4,
and indeed a bit lower than the schismatic Pythagorean equivalent
at 8192/6561 or 384 cents, with 382 cents as one "sweet spot."
Indeed, I might guess that one special allure of 41-EDO in a
Turkish context is that the schismatic major third at 380.49
cents is in this "sweet zone" a bit narrow of 5/4.

>> For instance, Al-Farabi's instructions which Cameron recently
>> linked to certainly point to 27/22 as a target of a lute
>> fretting. So that's the kind of thing I was asking for, and
>> getting yelled at for asking for. It's also in contrast to
>> what we saw in some sources, where pitch-tracking data were
>> fit to rationals, apparently arbitrarily (or at least without
>> explanation).

Certainly I see no advantage in the yelling, and it might just be
an advantage for me _not_ to be a moderator, so that I can
advocate for a respectful dialogue from the vantage point of an
NGO rather than an official representative of a government, so to
speak.

>> Whether superparticular divisions such as 12:13:14 or 14:13:12
>> and 11:12:13 or 13:12:11 have additionally have a special
>> aural > attraction for expert or other performers growing up
>> in a maqam > or dastgah tradition is an empirical question.

> As I remarked, such triads, when played in the proper (rather
> high) register can sound special. But I haven't heard them in
> maqam music. Like I said, maybe I need to get out more, but if
> people are so sure they're there I would have expected links
> offered straight away.

One very important point: by "triad," do you mean three notes
played simultaneously at 12:13:14 or 11:12:13, for example --
something I'd call an isoharmonic tone cluster, maybe? If so, I
must admit that over the better part of nine years in exploring
these _melodic_ divisions and some tempered variations, it had
never occurred to me to assume that all three notes would be
played at once.

Rather, I would think of something like Ibn Sina's 12:13:14:16
(if that's his original tetrachord, as suggested by Ozan) as
above all a _melodic_ division, meant to be enjoyed in monophonic
music. I wouldn't assume any kind of harmony, although a drone,
for example, might bring out the vertical attraction of 7/6 or
4/3; and Ibn Sina describes a technique, called a _tarqib_ or
"mixture," of sometimes playing two simultaneous notes at a
consonant interval such as a 4:3 fourth or 3:2 fifth, a bit as in
improvised medieval European organum or diaphony. (More often, I
should note, the term _tarqib_ in maqam theory refers to a
"mixed" or "composite" maqam seen to be derived from two or more
simpler maqamat.)

In fact, in learning or exploring a maqam, I find it helpful to
start in and often return to a monophonic framework, even though
polyphony is indeed of great interest to me. When superparticular
steps like 14:13, 13:12, 12:11, and 11:10 are discussed, I think
of them in a traditional maqam/dastgah context as above all
melodic.

In 21st-century "Zalzalian polyphony," a division like 12:13:14
can also take on a vertical or harmonic aspect -- but not, at
least in my practice so far, that of a simultaneous triad. Rather
we have in such a new practice -- and not necessarily in any
medieval or current Near Eastern practice!! -- progressions like
this, using numbers of harmonics and then ratio notations:

14 13 7/6 13/12
12 13 or 1/1 13/12

Here the two voices start at a 7/6 minor third, with one voice
ascending by 13:12 and the other descending by 14:13 so as to
resolve to a unison. And we can get a subtly different melodic
and contrapuntal quality by having the same vertical intervals
and melodic steps, but with 14:13 ascending and 13:12 descending:

7/6 14/13
1/1 14/13

And lest things take on too much of a "purist" or "rationals
only!" atmosphere, please let me rush to add that I do temper,
for example in O3 versions of these progressions:

B* 264.8 Bb* 138.2 G* 264.8 F# 126.6
A 0 Bb* 138.2 or F 0 F# 126.6

That said, I would emphasize my understanding that medieval
divisions like 14:13:12, and likewise Ptolemy's earlier Equable
Diatonic at 12:11:10:9, are above all melodic phenomena, although
they may have very interesting polyphonic and contrapuntal
ramifications in a modern context that I see as quite apart from
the traditional Near Eastern styles that we're discussing.

>> This is a point that Owen Wright also makes. Cris has
>> commented that an "equable" division like Ibn Sina's 14:13:12
>> or 12:13:14 is the way of indicating a 7:6 third derived from
>> two near-equal steps.

> They are equal in terms of distance on the fretboard, so it's
> entirely possible such a division would arise even if it's
> never played as a triad. Of course that supposes the 7:6 is
> tuned with some accuracy to start with, which again, I've never
> heard stand out in maqam music.

Just to make it clear, because I realize that lots of people may
be oriented to chordal genres of music and music theory to the
degree that misunderstandings are very easy: I might expect to
hear something like 12:13:14 or 14:13:12 often played as a
melodic figure in a relevant medieval or later Near Eastern
context, but not as a simultaneous triad. In fact, what I have in
mind is a basically monophonic setting where fine distinctions of
melodic tuning may be appreciated without the distractions of
vertical events such as those I sometimes use in my maqam
improvisations.

As to 7:6, I'd say there's very strong evidence that the general
region is vital to Turkish and Persian styles, at least, but the
precise ratio may be a moot question. As we've discussed,
variability and nuance make any assertion of a precise rational
ratio a hazardous undertaking -- and likewise for any EDO model.

For example, Karl Signell found that the tuning of a theoretical
12-comma step on Necdet Yasar's tanbur was in the range of
270-273 cents, which I would say is close to 7/6 (267 cents), but
actually in the slightly higher range of the advertised 12-comma
interval, which Cris Forster calls a "triple limma," about 271
cents in a Pythagorean context (15 fourths down, or thrice
256/243 at 90.225 cents), and 271.70 cents in 53-EDO.

This is in Signell's classic _Makam: Modal Practice in Turkish
Art Music_, Appendix A. I should note that Signell takes a
special interest in intervals, especially neutral or middle
ones, that don't fit in with the Turkish AEU scheme -- although
the triple limma at 12 commas happens to be one that does.

And Beyhom measures a Turkish performance of another flavor of
Hijaz at 130-265-90 cents. Here the central interval of 265 cents
is just narrow of 7/6, and 6 or 7 cents so of a triple limma or
literal 12 commas (Pythagorean or 53-EDO).

Thus these flexible-pitch performances and tanbur tunings are
certainly in the "ballpark" of 7/6, but not always necessarily
aimed at precisely that ratio, and sometimes in fact consistently
aimed at the slightly higher goal of 12 commas. Those of us who
might aim for 7/6 aren't "wrong," but we aren't uniquely right,
either.

>> Whether Near Eastern musicians are aurally drawn, or drawn by
>> instrument designs, to superparticular divisions vis-a-vis >
>> comparably shaded geometric or unequal but not rationally >
>> conceived divisions is an open question, and I'm open to a >
>> range of results, interpretations, and answers.

> I'm open to a range of them too. However let's not paper over
> the fact that some folks are engaged in number games, and
> probably have been for a long time.

Who on the tuning list, at least among people who get into
analyses or theories of some kind, _isn't_ involved in "numbers
games" of one kind or another? Can we really do the regular
mapping paradigm or harmonic entropy without numbers?

In fact, I'd say that music is one of the four disciplines of the
quadrivium, along with arithmetic, geometry, and astronomy. We're
dealing with "multitudes" (i.e. integer ratios), and also
"magnitudes" (e.g. logarithmic measures such as cents).

When Ozan records his analysis of a performance in Maqam Ushshaq
as using a measured tetrachord of around 123-137-228 cents, and
he and I agree that "12:13:14:16" is an approximate although not
precise evocation of this tuning, then we're playing at the game
of seeking connections and seeking to understand, with this RI
model as one possible viewpoint.

>> First, tunability or recognizability or reproducibility by ear
>> might depend a lot on the cultural background and training of
>> the musicians involved.

> Is there any evidence maqam musicians train to hear harmonics
> like 11? I mean, it just flies in the face of everything I
> know about the practice of maqam music (not that I know very
> much).

My own initial hypothesis might not focus on tuning by audible
harmonics, but rather on superparticular frettings like 12:11,
which might influence as well as be influenced by the fine
melodic taste of flexible-pitch performers in a primarily
monophonic context.

What I'd predict is that we may find very fine degrees of melodic
pitch discrimination in a range of world musics, fine shadings
and nuances which make sense in purely melodic terms, whether or
whatever degree they may coincide with superparticular steps like
11:10, 12:11, 13:12, 14:13, and so forth.

As to tuning by audible harmonics, I'd want to check out the
practices of traditional musicians very carefully before drawing
conclusions. The fact that Jean During seems to recommend using
the audible 13th harmonic in tuning a small Persian neutral sixth
at 13/8 doesn't necessarily mean that traditional Persian or
other Iranian musicians necessarily prefer 13/8 or tune it in
this fashion, although its favored position in Ibn Sina's `oud
tuning would make me ask if there might be any connection. My
guess is that a small Persian neutral sixth might typically have
a range of something like 830-845 cents, which would include Ibn
Sina's ratio of 13/8 (841 cents), and also 21/13 (830 cents)
found in a mode based on his tetrachord of 12:13:14:16 or
28:26:24:21 (the second reading shown in avicenna_diat.scl in the
Scala scale archive, with Ozan favoring the first).

The fact that these classic ratios are included within the range,
however, doesn't mean that they're uniquely favored in modern
Iranian music. Finding out what kind of distribution of sizes for
neutral sixths might occur in practice, and also whether
traditional musicians do sometimes use audible harmonics in
tuning, would be very worthwhile.

>> If you're referring to the commercialization of traditional
>> cultures and arts, complete with health and asserted other
>> marketing claims, and sometimes with totally fictional
>> accounts presented as actual ethnographic data, then we're in
>> agreement with lots of people in those cultures.

> To me it's no better than the proverbial late colonial-era
> musician reporting that X musical tradition uses a cheap
> imitation of 12-ET, so often maligned by the very people who...

Yes, if someone were taking, or rather inventing, some extraneous
scale or "ancient spiritual tradition" and using it to market
"Mystical Anatolian Chimes" supposedly based on "the wisdom of
the ancient Greek, Chaldean, Egyptian, and Hebrew sages as still
practiced today in Turkey, the path to instantly improved
physical health and spiritual enlightenment."

But I don't see anyone on this list doing that, people oriented
to JI/RI or others.

>> What I hope is that you're referring to a hypothetical case
>> which happily has not arisen in the list's present colloquies
>> on maqam and dastgah music and tuning, whatever our
>> differences of view.

> I will refrain from mentioning names at this time.

Happily, I haven't seen the type of cultural exploitation you're
describing -- not on this list, that is.

What I do see is mostly the antithesis, whether people exploring
Near Eastern music (including some Near Eastern musicians) are
focusing on JI/RI concepts of the medieval theorists, or on other
kinds of approaches.

>> Of course, it's possible for honest and respectful analyses to
>> be theoretically overzealous or simply wrong, and respectful >
>> questioning or outright correction, always I would hope >
>> constructive and polite, is an appropriate response. This >
>> discussion I take to be in that spirit, whatever the merits of
>> > our respective positions.

> The archives tell the story of who escalated where. But I'm no
> angel when provoked and I should work harder at that.

Certainly I hope that we'll all strive to follow "the better
angels of our nature," and agree that you have undoubtedly been
the target of uncivil, unwarranted, and totally counterproductive
personal attacks. That's a cycle of escalation I want to help
break, definitively if possible.

And likewise, it may promote de-escalation, rhetorical and
otherwise, to reach a mutual understanding that people here,
however much we differ on the theory and sometimes on an accurate
reading of relevant facts, are acting in good faith and respect
for the traditions being explored and analyzed, however aptly or
otherwise.

As I suspect Ozan or Amine Beyhom or Karl Signell would quickly
agree, almost everything in this area of empirical measurements
remains to be done! But I'd see it as an honorable, culturally
respectful, endeavor, and that includes the use of medieval or
other Near Eastern theory, not some arbitrary imposition of
outsiders but an ornament of the tradition itself.

[On 12-EDO as a substitute for Pythagorean when playing in
medieval European styles]

> I agree. Though if one really wants the edginess of
> Pythagorean (e.g. on the organ), 12ET will tend to disappoint.

It's curious that I tend, in tuning systems mean for medieval
European as well as maqam/dastgah music, to temper about the same
amount as in 12-EDO, but in the "more interesting direction"!
And this, too, is a distortion of the original Pythagorean
framework, however "gentle" I would like to envision it.

Where it would get into obvious problems is with early
15th-century music, where near-5-limit schismatic thirds for
sonorities involving written sharps (played as Pythagorean flats,
e.g. written A-C# realized as A-Db at 384 cents) are a basic
feature of the intended performance, with keyboard tunings like
Gb-B or maybe Db-F# promoting that ideal. Neither my choice of an
Eb-G# range, nor my deliberate temperament to get things like
diminished fourths at 370 cents and augmented seconds at 334
cents -- in contrast to 384 and 318 cents -- is a formula for
success with the Faenza Codex or Buxheim Organ Book; or for
Dufay's music very likely presuming a similar kind of tuning (as
Mark Lindley has persuasively argued).

For 14th-century Italian music, say, where an augmented or
diminished interval is evidently meant to be a moment of striking
color rather than of notably smooth consonance, having a
momentary F-C# at 830 cents rather than 816 cents might be fine,
and in fact it's exactly what could have happened in a Marchettan
type of style where sharps tend to be sung rather higher than
Pythagorean.

[On "exceptions that prove the rule" as to 12-EDO as an
approximation of medieval-Romantic European styles]

> Musica reservata certainly is an exception. I assume you've
> heard the latest stuff being done by Jon Wild, etc? (Sorry,
> but I can't remember if you were involved in the thread
> regarding the recent BBC radio documentary...)

Yes, I've heard one incredible performance of a madrigal or the
like by Vicentino, and would be very interested in learning about
the BBC documentary.

> You may not know, but over the years I've made extensive use of
> your excellent reviews of recordings. That was back when one
> purchased CDs! and such decisions were always taken carefully.

Giving credit where credit is due, I'd want to make it very clear
that those reviews are by Todd McComb and others at
www.medieval.org, the site of the Medieval Music and Arts
Foundation which he edits. While I've contributed some articles
on theory there, I don't recall contributing any CD reviews, but
agree that these reviews and other discography material are an
absolutely invaluable resource!

So while I'm flattered to be associated with the site, and would
warmly agree that the record and CD reviews are among its most
valuable offerings, I'd want to emphasize that the credit goes to
others. And you've given me a good reminder that I've been out of
touch with some of the folks responsible for the reviews, and
should try to remedy this.

And you also reminded me of Joseph Spencer and his program which
I heard around the beginning of the 1990's on KPFA (easier to get
in Sacramento then than now, as far as I know). I'm not sure if I
ever visited The Musical Offering, but those programs were
something else again!

> You're in the Sacramento area now? Alas, I'm no longer in
> Berkeley, having moved to the San Jose area in 2006. As much
> as I dislike some aspects of the suburban life here, it has
> some considerable advantages in the raising children dept.

My move to Sacramento was in 1984, and I was very fortunate to
find an apartment building near California State University,
Sacramento (CSUS) with a very reasonable library. At the time I
playfully called it my "rustification," and have been quite happy
since with this location.

> But yeah, I found myself always singing the F#, as it were. I
> could do with a much better dose of modal intelligence. I am
> always in awe of jazz artists in this respect. Say, have you
> heard the recordings the Orlando consort did with that jazz
> group... Perfect Houseplants?

This I'll need to hear. One of my favorite jazz albums is _Kinda
Blue_ by Miles Davis.

>> Glad you like it. I'm not sure if it illustrates similar points
>> to the ones you were discussing about tonality and modality.

> When my sore throat recovers I'll attempt to sing it and let
> you know!

That should be interesting -- and I hope that you're better
soon.

> -Carl

Best,

Margo

On Sun, 7 Nov 2010, Margo Schulter wrote:

> When Ozan records his analysis of a performance in Maqam Ushshaq
> as using a measured tetrachord of around 123-137-228 cents, and
> he and I agree that "12:13:14:16" is an approximate although not
> precise evocation of this tuning, then we're playing at the game
> of seeking connections and seeking to understand, with this RI
> model as one possible viewpoint.

Please let me quickly correct my use of 12:13:14:16 where I
obviously meant 28:26:24:21, or 1/1-14/13-7/6-4/3 (0-128-267-498
cents), which Ozan got correctly in his thesis, p. 29. While
my mistake might seem a relatively small point, I absolutely
want to clarify that he stated the correct ratios, and I goofed
it up in my post, absolutely not his responsibility, of course!

And one might add that 96-EDO, for example, could actually
provide a more accurate model at 125-137.5-225 cents, which like
the flexible-pitch tuning studied by Ozan, but unlike Ibn Sina's
rational tuning, has a notably narrow fourth (489 cents or so
in the actual performance, if I'm correct, and 487.5 cents in
96-EDO, in contrast to Ibn Sina's just 4/3 at 498 cents).

Thus one needn't conclude that the actual performance "is based
on" either Ibn Sina's ratios or 96-EDO, although these provide
possible grids.

But the fact that Ibn Sina's 11th-century tetrachord (evidently
distinct from the 17-note `oud tuning that Cris Forster has been
discussing) is not too far from such a modern perforamnce
indicates that this beautiful historical tuning is well worth
using and celebrating as one possible shading in this general
neighborhood that also includes the performance measured and
analyzed by Ozan, one of the high points of his thesis.

Best,

Margo

please see the middle of this page

http://en.wikipedia.org/wiki/Sound

or go to a library and find a CRC handbook of chemistry and physics for much
more information.

Chris

On Wed, Nov 3, 2010 at 8:49 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> On Wed, Nov 3, 2010 at 8:47 PM, Carl Lumma <carl@...<carl%40lumma.org>>
> wrote:
> >
> > Mike wrote:
> >
> > > then the speed of sound would depend on frequency, yes?
> >
> > Not over the range of human hearing. -Carl
>
> In water? Do you have a reference? I was looking for an equation
> relating the speed of sound in water to frequency but couldn't find
> one.
>
> -Mike
>
>

On Mon, Nov 8, 2010 at 6:29 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> please see the middle of this page
>
> http://en.wikipedia.org/wiki/Sound
>
> or go to a library and find a CRC handbook of chemistry and physics for much more information.

Hi Chris,

I'm confused. I don't see anything on this page talking about the
dispersive nature of water as a sound medium, or describing how c
would change over the range of human hearing. Maybe you replied to the
wrong comment? We were just picking nits with this little tangent of
the discussion anyway.

-Mike

I thought that you wanted an equation for the speed of sound. And I see I
missed there.

Here are the equations

http://en.wikipedia.org/wiki/Speed_of_sound

Sounds like what you are after is an acoustic prism.

the pertaining portion is

In a *non-dispersive medium* sound speed is independent of sound frequency,
so the speeds of energy transport and sound propagation are the same. For
audible sounds air is a non-dispersive medium. But air does contain a small
amount of CO2 which *is* a dispersive medium, and it introduces dispersion
to air at ultrasonic <http://en.wikipedia.org/wiki/Ultrasound> frequencies
(> 28 kHz <http://en.wikipedia.org/wiki/KHz>).[3]<http://en.wikipedia.org/wiki/Speed_of_sound#cite_note-2>

In a *dispersive medium* sound speed is a function of sound frequency,
through the dispersion
relation<http://en.wikipedia.org/wiki/Dispersion_relation>.
The spatial and temporal distribution of a propagating disturbance will
continually change. Each frequency component propagates at its own phase
velocity <http://en.wikipedia.org/wiki/Phase_velocity>, while the energy of
the disturbance propagates at the group
velocity<http://en.wikipedia.org/wiki/Group_velocity>.
The same phenomenon occurs with light waves; see optical
dispersion<http://en.wikipedia.org/wiki/Dispersion_%28optics%29#Group_and_phase_velocity>for
a description.

which leads to here:

http://en.wikipedia.org/wiki/Dispersion_relation

Chris

On Mon, Nov 8, 2010 at 6:59 AM, Mike Battaglia <battaglia01@gmail.com>wrote:

>
>
> On Mon, Nov 8, 2010 at 6:29 AM, Chris Vaisvil <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
> wrote:
> >
> > please see the middle of this page
> >
> > http://en.wikipedia.org/wiki/Sound
> >
> > or go to a library and find a CRC handbook of chemistry and physics for
> much more information.
>
> Hi Chris,
>
> I'm confused. I don't see anything on this page talking about the
> dispersive nature of water as a sound medium, or describing how c
> would change over the range of human hearing. Maybe you replied to the
> wrong comment? We were just picking nits with this little tangent of
> the discussion anyway.
>
> -Mike
>
>

On Mon, Nov 8, 2010 at 7:56 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> In a dispersive medium sound speed is a function of sound frequency, through the dispersion relation. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at its own phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves; see optical dispersion for a description.
>
> which leads to here:
>
> http://en.wikipedia.org/wiki/Dispersion_relation

I saw this but gave up trying to understand it after a bit. I'll have
to try again. Thanks for the reference.

Looks like for shallow water, which I would assume applies in the
cochlea, group velocity is equal to phase velocity, so it won't be
dispersive. For deep water, where the water depth is twice the
wavelength, group velocity is 1/2 of phase velocity, which I can't
figure out what that means from a signal processing standpoint how
matter how hard I try

-Mike

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

> For example, Ozan makes it clear that when segah, the third step
> of Maqam Rast, is in a Turkish style meant to be in its high
> position close to 5/4, it should actually be a bit shy of 5/4,
> and indeed a bit lower than the schismatic Pythagorean equivalent
> at 8192/6561 or 384 cents, with 382 cents as one "sweet spot."
> Indeed, I might guess that one special allure of 41-EDO in a
> Turkish context is that the schismatic major third at 380.49
> cents is in this "sweet zone" a bit narrow of 5/4.

Are there any other "sweet spots" a bit off from a small integer ratio one can point to?

> For example, Karl Signell found that the tuning of a theoretical
> 12-comma step on Necdet Yasar's tanbur was in the range of
> 270-273 cents, which I would say is close to 7/6 (267 cents), but
> actually in the slightly higher range of the advertised 12-comma
> interval, which Cris Forster calls a "triple limma," about 271
> cents in a Pythagorean context (15 fourths down, or thrice
> 256/243 at 90.225 cents), and 271.70 cents in 53-EDO.

This might be one such.

> And Beyhom measures a Turkish performance of another flavor of
> Hijaz at 130-265-90 cents. Here the central interval of 265 cents
> is just narrow of 7/6, and 6 or 7 cents so of a triple limma or
> literal 12 commas (Pythagorean or 53-EDO).

Or this.

I *think* I have a handle on this.

The group velocity is equal to the ADSR envelope of the sound where as the
phase velocity are the individual frequencies that make up that sound.

For instance:

Lets say you use an audiophone to inject 1 second of a default saw wave
setting from your synth at the bottom of the ocean.

The attack, decay, sustain, release (ADSR) will define how loud the sound
is (group velocity)
Since this is a saw wave http://en.wikipedia.org/wiki/Sawtooth_wave
each of the harmonics will be affected by the phase velocity and travel
differently (in a way I don't understand right now).

Maybe John Chalmers can weigh in - he is a more advanced scientist then I.

Chris

On Mon, Nov 8, 2010 at 8:18 AM, Mike Battaglia <battaglia01@...>wrote:

>
>
> On Mon, Nov 8, 2010 at 7:56 AM, Chris Vaisvil <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
> wrote:
> >
> > In a dispersive medium sound speed is a function of sound frequency,
> through the dispersion relation. The spatial and temporal distribution of a
> propagating disturbance will continually change. Each frequency component
> propagates at its own phase velocity, while the energy of the disturbance
> propagates at the group velocity. The same phenomenon occurs with light
> waves; see optical dispersion for a description.
> >
> > which leads to here:
> >
> > http://en.wikipedia.org/wiki/Dispersion_relation
>
> I saw this but gave up trying to understand it after a bit. I'll have
> to try again. Thanks for the reference.
>
> Looks like for shallow water, which I would assume applies in the
> cochlea, group velocity is equal to phase velocity, so it won't be
> dispersive. For deep water, where the water depth is twice the
> wavelength, group velocity is 1/2 of phase velocity, which I can't
> figure out what that means from a signal processing standpoint how
> matter how hard I try
>
> -Mike
>
>

Dear Margo,

First I must say that my interest in temperament really extends only to notational issues. Regardless of what kind of music, I feel that notation should only define pitch to the point at which you'd prefer to have the perfomer make their own choice.

Obviously for music which has as part of its very essence extreme precision in pitch is going to need extreme precision in notation- or something that effects extreme precision.

But, it is precisely such music which rarely presents a problem in notation, for such music is often electronically synthesized, in which case specification of pitch to microscopic precision is downright trivial, and the "score" is often computer code anyway, such that "reading the score" and producing the music are the same act. And, the score of acoustic music which has as a prequisite radical precision of pitch definition often assumes, in practice, the actual instruments upon which it is performed. This is similar to the tradition of the gamelan- and of the pianoforte in "atonal" music for that matter. An example of this would be acoustic pieces and repertoires with very specific pitch requirements such as proportionate beating.

In general though, I feel that notation should leave room for intonational interpretation. If specific intonation or purpose-built tuning is desired, then pitch references- electronic, monochord, marimba- should be included with the score. But the score itself should only have very specific pitch indications when necessary.

Where the line of "specific" pitch is drawn is surely a matter of an agreement, not, in real life, necessarily amicable or bilateral, between composer and performers.

Of course, temperament, or the deliberate acceptance of small commas, is necessary if the approach is to create new chord progressions by tempering out, or tempering out in effect, unusual commas. It is not necessary for circulation- unless your standard of circulation requires literal or near-literal transpositions of specific pitch combinations.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> [Dear Cameron: In what follows I address some temeperament
> questions and some of the tetrachords you discuss, as well as a
> couple of others that might illustrate some related comma
> questions. I apologize for the length! And while your baglama
> does come up, another post focusing on your instrument itself
> should follow soon.]
>
> Cameron wrote:
>
> > As far as tuning, in practical and implementable manner, of
> > tetrachordal music intended to both incorporate ancient
> > tunings as well as be used in polyphonic music- certainly
> > related to what Ozan is doing, which is why I'd even dare to
> > speak on the subject- I do have a great deal to say.
>
> Dear Cameron,
>
> Please let me emphasize that I can't speak for Ozan, but can say
> that one of the lesson's I've learned from him is that
> "maqam-based polyphony" can mean different things to different
> people. And the kind of tuning or temperament system will reflect
> both the medieval Islamic and more recent tetrachords in use, and
> the logic of a given polyphonic style. That can mean creative
> compromises in various directions -- and often dramatically
> different ones for different people and styles.

>
> Thus for Ozan, "polyphony" often means a desire for thirds at or
> close to 5/4 -- or ideally a tad lower, by the schisma of Safi
> al-Din al-Urmawi and the 24-note Pythgorean model of AEU, or
> maybe around 382 cents, as suggested in one of his posts. Since
> Ozan also wants an optional meantone path to that Rast third near
> 5/4, he uses a 79/80-MOS very close to 159-EDO, with some fifths
> tempered by 1/3 Holderian comma or 1/159 octave while others
> remain literally pure (by minute modifications to 159-EDO) or
> virtually pure. There are both schismatic and meantone paths to
> that 5/4 region, and the temperament of some fifths by over 7
> cents (a bit more than in 19-EDO) is the necessary and logical
> compromise to achieve that goal.
>
> For me, "polyphony" means adopting 13th-14th century European
> techniques to a maqam context rich with its Zalzalian steps and
> intervals. In 13th-14th century music of Continental Europe,
> based mostly on Pythagorean intonation, fifths and fourths are
> the stable consonances, with thirds and sixths more or less
> relatively concordant but complex and unstable, seeking
> resolution to unisons, fifths, or octaves, for example. So
> neutral thirds at various ratios fit in nicely. And something
> like 26/21 is especially dilectable, because 370 cents is like a
> "Zalzalian ditone" with the same kind of pleasant complexity as
> 14/11 at 418 cents, for example.

>
> These are two different worlds. In Ozan's, 5/4 and 6/5 are needed
> both as fitting one side of current Turkish maqam practice which
> might be traced back at least to the 17-note Pythagorean
> "Systematist" theory of the 13th century (and I believe Cris
> shows to further back than that), and to meet the needs of his
> polyphonic style using 5-limit consonances.
>
> In mine, the emphasis is on ratios of 2-3-7-11-13, and any
> occurrences of 5/4 or 6/5 approximations are more or less
> incidental, rather than a basic or intended feature of a
> neomedieval system. The rules of counterpoint can apply to
> general categories of intervals: for example, "a major, minor, or
> Zalzalian third often tends to contract to a unison or expand to
> a fifth."

My principal tuning is based on ratios of 2-3-7-13, with a handful of inevitable incidental near-11 ratios occuring. By near-11, an example would be that of a 16/13 above 4/3 differind from a 12/11 above 3/2 by a touch less than 5 cents. If there is indeed a pull exerted by successive superparticular intervals, it would be reasonable to assume that I'd sharp the Ad when going F-G-Ad, and reasonable, given my thoughts on tempering for notation, to temper out the 352/351 between 128/117 and 12711 (128/117 being the ratio of illusory "complexity" which arises between G and Ad when Ad is a 16/13 above F, F and G being Pythagorean here of course).

>
> Furthermore, Ozan for his purposes needs an option for a
> circulating 12-note chromatic scale to permit compatibility with
> Western music based on a 12-note well-temperament or 12-EDO, one
> of the design principles of his 79/80-MOS. What I need is
> compatibility with 13th-14th century European style based on
> Pythagoran intonation, of which I see a single 12-note keyboard
> in O3 as a gentle modification, with an Eb-G# chain of fifths
> tempered in 1024-EDO at an average of around 703.871 cents.

I believe that we discussed this long ago- the slightly sharp fifths are to my ears "more real than real", given the concept of a fifth as bright or "soldierly". Of course they are wrong when the concept of a fifth is a soft meantone-style interval. With instruments of flexible pitch, I would speculate that the fifth is also often modified minutely depending on context- mellow here, pure there, brilliant elsewhere.

Well I'll have to comment further at a later date!

-Cameron Bobro

>
> And temperament is an essential ingredient for both of us. Thus
> on Ozan's 79/80-tone qanun, we have a suggested Rast (following
> his thesis, p. 118(, of 0-196-392-498 cents, with the major third
> being formed from two meantone steps of 196 cents. As he notes,
> it is possible to spell this tetrachord simply C-D-E-F.
>
> While temperament gets Ozan his meantone path to a near-5/4, it
> gets me my "neo-Systematist" path to neutral or Zalzalian
> intervals found within a single 12-note keyboard, for example in
> a Rast tetrachord like B-C#-Eb-E at 0-207-369-496 cents or
> 207-162-127 cents. Note that on a Pythagorean keyboard, this same
> spelling would result in a schismatic tetrachord of 0-204-384-498
> cents, or 204-180-114 cents. These "schismatic" mappings thus
> generate on each of the two 12-note keyboards the smallest and
> largest neutral intervals, for example steps near 14:13 and
> 11:10, while combining notes from the two keyboards (spaced at
> 57.422 cents) produces central neutral intervals like steps near
> 13:12 and 12:11.
>
> Here I don't want to get too enmeshed in the mechanics of the
> 79/80-MOS, on which Ozan is of course the expert, and O3, but to
> give some idea of how polyphonic styles can vary and influence
> tuning systems to move in different directions while still
> sharing common themes like a desire for accurate representations
> of superparticular middle seconds.
>
> > It's clear from simply listening to various maqam musics that
> > the Pythagorean skeletal structures and the simplest of
> > intervals are not sacrosanct- the melodic step is very
> > powerful. Farhat is very big on this. For the creating of a
> > practical system of non-infinite scope- like tuning a qanun-
> > this surely creates a serious problem. If it's true that
> > microtonal inflections along the lines of, say, a "fourth" at
> > 515 cents (remembered from tuning up to jam along with a video
> > on YouTube) are essential characteristics, the magnitude of the
> > problem of where to temper is clearly immense.
>
> If circulation isn't a consideration, which it certainly isn't in
> traditional Iranian music or Farhat's 17-note tar tuning, then
> "odd" fourths and fifths can be a strength. For example, in the
> 24-note O3 temperament, we have a location where the closest
> available fourth is 485 cents -- almost identical, as I learned
> in a book by Nelly Caron and Dariouche Safvate, to a 484-cent
> fourth used in a traditional tuning of a beautiful dastgah or
> avaz (a satellite dastgah to the principal seven) known as the
> Old Bayat-e Tork. They give 0-204-346-484-704-908-980-1200
> cents.
>
> More generally, the Iranian taste for septimal or near-septimal
> intervals means that we're not going to get a tidy 17-note
> circulating system on tar. Caron and Safvate, on the basis of
> measuring one or more instruments, give a Shur tetrachord at
> 0-136-276-500 cents or 136-140-224 cents. A large tone that close
> to 8:7 means that we can expect at least one notably narrow
> fourth of the kind found in the "Old Tork" above.
>
> In O3, we have 24 positions and 22 of them with usual fifths at
> 703.1 or 704.3 cents -- the "odd" two at G#-Eb* (an asterisk
> showing a note on the upper keyboard) with a 714.8-cent fifth,
> and G#*-E at 726.6 cents, or close to 32/21. And there are a
> number of locations with a choice between 4/3 or 21/16, something
> George Secor has taught me to relish, and nice for doing
> different interpretations of Maqam `Iraq (some Syrians favor a
> fourth at 21 commas or around 475 cents, realized at 472 or 473
> cents in this temperament).
>
> For Ozan, it _is_ vital to circulate, and he's made some
> intricate and delicate compromises to do so while supporting lots
> of neutral or Zalzalian flavors, among many other things.
>
> > I don't face this problem personally, as I simply use pure, or
> > plainly altered. This (using either pure or plainly altered)
> > is, in my opinion, the only real option in a limited system
> > that is not attempting to shoulder a huge burden.
>
> Yes, and the "limited system" concept certainly applies to O3
> with only 24 notes. Not being concerned with either circulation
> or the syntonic comma simplifies lots of things, and means a
> gentle degree of temperament is all that's needed.
>
> > So, concretely: if we assume the ancient preference for
> > superparticulars, we might come up with a very lovely sounding
> > tetrachord of, in step sizes, 11/10, 9/8, 14/13 (in any
> > order). This in my opinion belongs in a rational system, not a
> > tempered system, as we're looking at a comma of 2080:2079
> > generated at the 4:3. In a tempered system, temper it out.
>
> In fact you've just brought up the topic of one of my favorite
> tetrachords, so nicely illustrated on your baglama, and which
> I've been discussing in some of my Ethno Extras articles. This is
> Safi al-Din al-Urmawi's "Medium Sundered" which slightly enlarges
> the 14/13 to make a full 4/3: 9/8-11/10-320/297 or 204-165-129
> cents.
>
> A JI solution might be to "temper by ratios" by keeping all
> steps superparticular, 9/8-11/10-14/13, and letting that fourth
> be narrow by a 2080:2079, less than a cent. But I guess that the
> idea of a tetrachord at a just 4:3 led Safi al-Din to stretch the
> 14:13 by that amount instead.
>
> On your baglama at 202-168-128 cents, a slightly enlarged 11/10
> takes up the slack for the minutely narrow 9/8 as well as the
> virtually just 14/13 -- two cents for the first, and another cent
> for the second, placing it at 168 rather than 165 cents. If the
> 9/8 were precisely just, we might similarly stretch 11/10 by
> exactly 2080:2079, getting 208/189 and a tuning of 204-166-128
> cents.
>
> Now let's see what happens in O3 for a similar tetrachord. Giving
> Safi al-Din his due, we'll start with the tempered tetrachord
> closest to his 9/8-11/10-320/297. Then we'll see what happens in
> the almost identical tetrachord closest in its third size to your
> baglama.
>
> Safi al-Din: 1/1 9/8 99/80 4/3
> 0.0 203.9 368.9 498.0
> 9:8 11:10 320:297
> 203.9 165.0 129.1
>
> O3: B C# Eb E
> 0.0 207.4 369.1 495.7
> 207.4 161.7 126.6
>
> While the tempered neutral third at 369.1 cents is almost
> identical to Safi al-Din's 99/80, the tone B-C# more than
> compensates for the 2080:2079 comma in the JI version by its
> wideness of about 3.5 cents in comparison to 9/8. The fourth,
> tempered at about 2.3 cents narrow, is impure by an amount almost
> three times that of the comma. And in the process, 11/10 gets
> compressed to 161.7 cents, or by about 3.3 cents, just a tad more
> than the 3.24 cents set as a maximum for the impurity of the
> ratios supported in his 29-HTT (secor29htt.scl in the Scala
> archive).
>
> If we focus specifically on the interval from the neutral third
> to the fourth, Eb-E in the tempered version, we find that the
> third at 369.1 cents is a virtually just 99/80, but that the
> narrowing of the fourth by some 2.3 cents more than accounts for
> the 2080:2079 comma, indeed so much so that the remaining 14/13
> step, for from needing a bit of widening as in Safi al-Din, is
> actually narrow by about 1.7 cents (126.6 vs. 128.3 cents).
>
> Now let's look at a trivially different tempered tetrachord
> closer to your baglama's slightly larger neutral third, which
> I'll call a virtually just 26/21, likewise taking your fourth as
> a just 4/3:
>
> Cameron's baglama: 0 202 370 498
> 202 168 128
>
> O3: F# G# Bb B
> 0 208.6 370.3 496.9
> 208.6 161.7 126.6
>
> Here the two upper melodic steps of the tempered tetrachord are
> identical to those of the last, but the major second at 208.6
> cents, and the fourth at 496.9 cents, are 1/1024 octave larger.
> Your baglama and O3 may be about equally far in their central
> steps from a just 11/10 at 165 cents, albeit in opposite
> directions, Here, with the tempered third at a virtually just
> 26/21, the remaining step would be a just 14/13 -- except that
> the fourth is narrow, this time by about 1.2 cents.
>
> > What about the 1287/1280 comma at 4:3 were we to use the also
> > lovely combination of 13/12, 11/10 and 9/8 to make our
> > tetrachord? That's already almost 9.5 cents.
>
> Humorously, with O3, I can give the answer that the steps aren't
> so arranged that it's possible to combine these ratios all in a
> single tetrachord, so the question doesn't arise <grin>. What O3
> does have with 9/8 and 13/12 that might go a step further is this
> tetrachord in the manner of one school of Aleppo for Maqam `Iraq:
>
> Eb E F# G*
> 0 126.6 334.0 472.3
> 126.6 207.4 138.3
>
> My point here, leaving aside the fine points of this tetrachord
> (apart from noting that the Syrian 6-9-6 commas would be around
> 135-340-475 cents, with my 126.6-cent step rather smaller),
> is that altered fourths and fifths sometimes go with the
> territory. But let's get back to 13/12, 11/10, and 9/8, and see
> how Ozan's 79-MOS might handle this. Suppose we want to keep all
> three superparticular steps as close as possible to just. If we
> start on step 13 of his scale (Scala archives, 79-159.scl), his
> tempered or meantone major second step in Maqam Rast known as
> perde dugah, we can do the following:
>
> JI: 1/1 13/12 143/120 429/320
> 0 138.6 303.6 507.4
> 13/12 11/10 9/8
> 138.6 165.0 203.9
>
> yarmans: 0 9 20 33L
> 79-MOS: 0 135.8 301.9 505.7
> 135.8 166.0 203.8
> 9 11 13L
>
> You'll see that Ozan's meantone fourth at 505.7 cents, or 1/3
> Holderian comma wide, absorbs most of the burden of that
> 1287/1280 comma, with the narrowing of 13/12 by not quite 3 cents
> taking up the rest of the comma, and also compensating for the
> tempering of 11/10 at about a cent wide. The numbers of yarmans,
> or 79-MOS steps normally at 2/3 Holderian comma (2/159 octave) or
> just over 15 cents, may help clarify the process. In the 79-MOS,
> there is one "large" step at a full comma or about 1/53 octave,
> and the notations "33L" for the fourth and "13L" for the 9/8 step
> that concludes the tetrachord show an interval including this
> large or full-comma tuning step.
>
> Another solution would be to trim the 9/8 by 1/3 comma, and let
> the fourth remain precisely or virtually pure. For example,
> starting on Ozan's 1/1 or perde rast:
>
> JI: 1/1 13/12 143/120 429/320
> 0 138.6 303.6 507.4
> 13/12 11/10 9/8
> 138.6 165.0 203.9
>
> yarmans: 0 9 20 33
> 79-MOS: 0 135.8 301.9 498.1
> 135.8 166.0 196.2
> 9 11 13
>
> This time the upper major second gets narrowed by the lion's
> share of the comma instead of the fourth being widened by a
> comparable amount, and all the intervals are built from regular
> tuning steps of 2/3 Holderian comma or around 15 cents.
>
> > At 12/11, 11/10, 9/8 we've got a concrete comma. At almost a
> > syntonic comma wide, I suspect that it may be one of the very
> > commas that grates against 24-tET approximation.
>
> Here my first reaction is that 12/11 plus 11/10 should be
> precisely a 6/5, and that plus 9/8 precisely a 27/20, so that we
> are indeed a syntonic comma wide. Change the 9/8 to a 10/9, and
> we have a 4/3, as well as Ptolemy's Equable Diatonic that Cris
> was recently discussing, at 12:11:10:9.
>
> But this might invite the consideration of one more case where
> the comma involved using only superparticular ratios must somehow
> be accounted for, and a temperament stays fairly close to one JI
> solution. Let's consider a tetrachord which could be used in
> Persian Shur, Arab Bayyati, or Turkish Arazbar, for example:
>
> JI: 1/1 13/12 13/11 4/3
> 0 138.6 289.2 498.0
> 13:12 12:11 44:39
> 138.6 150.6 208.8
>
> O3: F# G* A B
> 0 138.3 289.5 496.9
> 138.3 151.2 207.4
>
> In the just version, we have a 13:12:11 division of a 13/11 minor
> third, so that reaching a pure 4/3 requires a major second wider
> than 9/8 by a 352:351 at some 4.9 cents, in other words a 44/39,
> thus, on monochord, 52:48:44:39.
>
> In O3, the 13/12 and 12/11 steps are virtually just, so the
> 352:351 gets handled essentially in two ways. First, the tone at
> 207.4 cents is about 3.5 cents wide of 9/8, and not too far from
> 44/39. Secondly, the fourth is narrow by not quite 1.2 cents. As
> it happens, the 13/11 is at this location a tad wide at 289.5
> cents compared to a just 289.2, helping with the comma also. At
> some other locations, where 13/11 is not quite a cent narrow of
> just at 288.3 cents, a wider major second at 208.6 cents (almost
> precisely 44/39), or narrower fourth at 495.7 cents, is there to
> compensate.
>
> So we have commas of less than a cent, like the 2080:2079 as with
> the beautiful Rast tetrachord made famous by your baglama (Safi
> al-Din didn't call it Rast, but it wonderfully fits that maqam);
> commas of around 4-5 cents like the 352:351; and the "biggies"
> like your 1207:1280 example approaching 9.5 cents, and yet more
> so the 81:80 at 21.5 cents or the 64/63 at 27.3 cents.
>
> With the larger commas, I take a "JI-ish" perspective: let them
> stand. For me, the 64:63 is the main one I deal with regularly.
> In O3, some small ones like the 352:351 are tempered out, while
> the 2080:2079 might in a sense be "observed" (e.g. 369.1 cents as
> Safi al-Din's 99/80, and 370.3 cents as your baglama's 26/21),
> hopefully while keeping a "quasi-rational" structure for the most
> part intact.
>
> And large commas can be invaluable, not only for yielding
> "special effects" intervals like 21/16 when we want them, but for
> permitting more choices: a smaller or larger neutral second to
> start this tetrachord, or a 7/4 or a 16/9? Jacques and I both
> seem to devise 17-note sets or subsets, for Persian music for
> example, and then throw in a couple of extra notes to add comma
> alternatives.
>
> Please forgive me if this is too long: a lot of this stuff about
> maqam tetrachords and tempering may not have been presented so
> systematically before, and, of course, what I've written about
> Ozan's 79/80-MOS is very much subject to his correction or
> amendment!
>
> Most appreciatively,
>
> Margo
> mschulter@...
>

While notation can be based on the harmonic identity, it is also possible to define it by its melodic position in a scale.
This is mainly the method used in generalized keyboard mappings where what is a sharp in one system need not be the same in the other. Bosanquet is the one who defined this method. It makes playing the scale on the keyboard extremely efficient.
As far as traditional instruments, in the end i think Reinhardt was correct in that one will end up notating by cent deviation from 12 ET as traditional instrument will have to rely on tuning devices.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
>
> Dear Margo,
>
> First I must say that my interest in temperament really extends only to notational issues. Regardless of what kind of music, I feel that notation should only define pitch to the point at which you'd prefer to have the performer make their own choice.
>
> Obviously for music which has as part of its very essence extreme precision in pitch is going to need extreme precision in notation- or something that effects extreme precision.
>
> But, it is precisely such music which rarely presents a problem in notation, for such music is often electronically synthesized, in which case specification of pitch to microscopic precision is downright trivial, and the "score" is often computer code anyway, such that "reading the score" and producing the music are the same act. And, the score of acoustic music which has as a prequisite radical precision of pitch definition often assumes, in practice, the actual instruments upon which it is performed. This is similar to the tradition of the gamelan- and of the pianoforte in "atonal" music for that matter. An example of this would be acoustic pieces and repertoires with very specific pitch requirements such as proportionate beating.
>
> In general though, I feel that notation should leave room for intonational interpretation. If specific intonation or purpose-built tuning is desired, then pitch references- electronic, monochord, marimba- should be included with the score. But the score itself should only have very specific pitch indications when necessary.
>
> Where the line of "specific" pitch is drawn is surely a matter of an agreement, not, in real life, necessarily amicable or bilateral, between composer and performers.
>
> Of course, temperament, or the deliberate acceptance of small commas, is necessary if the approach is to create new chord progressions by tempering out, or tempering out in effect, unusual commas. It is not necessary for circulation- unless your standard of circulation requires literal or near-literal transpositions of specific pitch combinations.
>
> --- In tuning@yahoogroups.com, Margo Schulter <mschulter@> wrote:
> >
> > [Dear Cameron: In what follows I address some temeperament
> > questions and some of the tetrachords you discuss, as well as a
> > couple of others that might illustrate some related comma
> > questions. I apologize for the length! And while your baglama
> > does come up, another post focusing on your instrument itself
> > should follow soon.]
> >
> > Cameron wrote:
> >
> > > As far as tuning, in practical and implementable manner, of
> > > tetrachordal music intended to both incorporate ancient
> > > tunings as well as be used in polyphonic music- certainly
> > > related to what Ozan is doing, which is why I'd even dare to
> > > speak on the subject- I do have a great deal to say.
> >
> > Dear Cameron,
> >
> > Please let me emphasize that I can't speak for Ozan, but can say
> > that one of the lesson's I've learned from him is that
> > "maqam-based polyphony" can mean different things to different
> > people. And the kind of tuning or temperament system will reflect
> > both the medieval Islamic and more recent tetrachords in use, and
> > the logic of a given polyphonic style. That can mean creative
> > compromises in various directions -- and often dramatically
> > different ones for different people and styles.
>
> >
> > Thus for Ozan, "polyphony" often means a desire for thirds at or
> > close to 5/4 -- or ideally a tad lower, by the schisma of Safi
> > al-Din al-Urmawi and the 24-note Pythgorean model of AEU, or
> > maybe around 382 cents, as suggested in one of his posts. Since
> > Ozan also wants an optional meantone path to that Rast third near
> > 5/4, he uses a 79/80-MOS very close to 159-EDO, with some fifths
> > tempered by 1/3 Holderian comma or 1/159 octave while others
> > remain literally pure (by minute modifications to 159-EDO) or
> > virtually pure. There are both schismatic and meantone paths to
> > that 5/4 region, and the temperament of some fifths by over 7
> > cents (a bit more than in 19-EDO) is the necessary and logical
> > compromise to achieve that goal.
> >
> > For me, "polyphony" means adopting 13th-14th century European
> > techniques to a maqam context rich with its Zalzalian steps and
> > intervals. In 13th-14th century music of Continental Europe,
> > based mostly on Pythagorean intonation, fifths and fourths are
> > the stable consonances, with thirds and sixths more or less
> > relatively concordant but complex and unstable, seeking
> > resolution to unisons, fifths, or octaves, for example. So
> > neutral thirds at various ratios fit in nicely. And something
> > like 26/21 is especially dilectable, because 370 cents is like a
> > "Zalzalian ditone" with the same kind of pleasant complexity as
> > 14/11 at 418 cents, for example.
>
>
> >
> > These are two different worlds. In Ozan's, 5/4 and 6/5 are needed
> > both as fitting one side of current Turkish maqam practice which
> > might be traced back at least to the 17-note Pythagorean
> > "Systematist" theory of the 13th century (and I believe Cris
> > shows to further back than that), and to meet the needs of his
> > polyphonic style using 5-limit consonances.
> >
> > In mine, the emphasis is on ratios of 2-3-7-11-13, and any
> > occurrences of 5/4 or 6/5 approximations are more or less
> > incidental, rather than a basic or intended feature of a
> > neomedieval system. The rules of counterpoint can apply to
> > general categories of intervals: for example, "a major, minor, or
> > Zalzalian third often tends to contract to a unison or expand to
> > a fifth."
>
> My principal tuning is based on ratios of 2-3-7-13, with a handful of inevitable incidental near-11 ratios occuring. By near-11, an example would be that of a 16/13 above 4/3 differind from a 12/11 above 3/2 by a touch less than 5 cents. If there is indeed a pull exerted by successive superparticular intervals, it would be reasonable to assume that I'd sharp the Ad when going F-G-Ad, and reasonable, given my thoughts on tempering for notation, to temper out the 352/351 between 128/117 and 12711 (128/117 being the ratio of illusory "complexity" which arises between G and Ad when Ad is a 16/13 above F, F and G being Pythagorean here of course).
>
> >
> > Furthermore, Ozan for his purposes needs an option for a
> > circulating 12-note chromatic scale to permit compatibility with
> > Western music based on a 12-note well-temperament or 12-EDO, one
> > of the design principles of his 79/80-MOS. What I need is
> > compatibility with 13th-14th century European style based on
> > Pythagoran intonation, of which I see a single 12-note keyboard
> > in O3 as a gentle modification, with an Eb-G# chain of fifths
> > tempered in 1024-EDO at an average of around 703.871 cents.
>
> I believe that we discussed this long ago- the slightly sharp fifths are to my ears "more real than real", given the concept of a fifth as bright or "soldierly". Of course they are wrong when the concept of a fifth is a soft meantone-style interval. With instruments of flexible pitch, I would speculate that the fifth is also often modified minutely depending on context- mellow here, pure there, brilliant elsewhere.
>
> Well I'll have to comment further at a later date!
>
> -Cameron Bobro
>
> >
> > And temperament is an essential ingredient for both of us. Thus
> > on Ozan's 79/80-tone qanun, we have a suggested Rast (following
> > his thesis, p. 118(, of 0-196-392-498 cents, with the major third
> > being formed from two meantone steps of 196 cents. As he notes,
> > it is possible to spell this tetrachord simply C-D-E-F.
> >
> > While temperament gets Ozan his meantone path to a near-5/4, it
> > gets me my "neo-Systematist" path to neutral or Zalzalian
> > intervals found within a single 12-note keyboard, for example in
> > a Rast tetrachord like B-C#-Eb-E at 0-207-369-496 cents or
> > 207-162-127 cents. Note that on a Pythagorean keyboard, this same
> > spelling would result in a schismatic tetrachord of 0-204-384-498
> > cents, or 204-180-114 cents. These "schismatic" mappings thus
> > generate on each of the two 12-note keyboards the smallest and
> > largest neutral intervals, for example steps near 14:13 and
> > 11:10, while combining notes from the two keyboards (spaced at
> > 57.422 cents) produces central neutral intervals like steps near
> > 13:12 and 12:11.
> >
> > Here I don't want to get too enmeshed in the mechanics of the
> > 79/80-MOS, on which Ozan is of course the expert, and O3, but to
> > give some idea of how polyphonic styles can vary and influence
> > tuning systems to move in different directions while still
> > sharing common themes like a desire for accurate representations
> > of superparticular middle seconds.
> >
> > > It's clear from simply listening to various maqam musics that
> > > the Pythagorean skeletal structures and the simplest of
> > > intervals are not sacrosanct- the melodic step is very
> > > powerful. Farhat is very big on this. For the creating of a
> > > practical system of non-infinite scope- like tuning a qanun-
> > > this surely creates a serious problem. If it's true that
> > > microtonal inflections along the lines of, say, a "fourth" at
> > > 515 cents (remembered from tuning up to jam along with a video
> > > on YouTube) are essential characteristics, the magnitude of the
> > > problem of where to temper is clearly immense.
> >
> > If circulation isn't a consideration, which it certainly isn't in
> > traditional Iranian music or Farhat's 17-note tar tuning, then
> > "odd" fourths and fifths can be a strength. For example, in the
> > 24-note O3 temperament, we have a location where the closest
> > available fourth is 485 cents -- almost identical, as I learned
> > in a book by Nelly Caron and Dariouche Safvate, to a 484-cent
> > fourth used in a traditional tuning of a beautiful dastgah or
> > avaz (a satellite dastgah to the principal seven) known as the
> > Old Bayat-e Tork. They give 0-204-346-484-704-908-980-1200
> > cents.
> >
> > More generally, the Iranian taste for septimal or near-septimal
> > intervals means that we're not going to get a tidy 17-note
> > circulating system on tar. Caron and Safvate, on the basis of
> > measuring one or more instruments, give a Shur tetrachord at
> > 0-136-276-500 cents or 136-140-224 cents. A large tone that close
> > to 8:7 means that we can expect at least one notably narrow
> > fourth of the kind found in the "Old Tork" above.
> >
> > In O3, we have 24 positions and 22 of them with usual fifths at
> > 703.1 or 704.3 cents -- the "odd" two at G#-Eb* (an asterisk
> > showing a note on the upper keyboard) with a 714.8-cent fifth,
> > and G#*-E at 726.6 cents, or close to 32/21. And there are a
> > number of locations with a choice between 4/3 or 21/16, something
> > George Secor has taught me to relish, and nice for doing
> > different interpretations of Maqam `Iraq (some Syrians favor a
> > fourth at 21 commas or around 475 cents, realized at 472 or 473
> > cents in this temperament).
> >
> > For Ozan, it _is_ vital to circulate, and he's made some
> > intricate and delicate compromises to do so while supporting lots
> > of neutral or Zalzalian flavors, among many other things.
> >
> > > I don't face this problem personally, as I simply use pure, or
> > > plainly altered. This (using either pure or plainly altered)
> > > is, in my opinion, the only real option in a limited system
> > > that is not attempting to shoulder a huge burden.
> >
> > Yes, and the "limited system" concept certainly applies to O3
> > with only 24 notes. Not being concerned with either circulation
> > or the syntonic comma simplifies lots of things, and means a
> > gentle degree of temperament is all that's needed.
> >
> > > So, concretely: if we assume the ancient preference for
> > > superparticulars, we might come up with a very lovely sounding
> > > tetrachord of, in step sizes, 11/10, 9/8, 14/13 (in any
> > > order). This in my opinion belongs in a rational system, not a
> > > tempered system, as we're looking at a comma of 2080:2079
> > > generated at the 4:3. In a tempered system, temper it out.
> >
> > In fact you've just brought up the topic of one of my favorite
> > tetrachords, so nicely illustrated on your baglama, and which
> > I've been discussing in some of my Ethno Extras articles. This is
> > Safi al-Din al-Urmawi's "Medium Sundered" which slightly enlarges
> > the 14/13 to make a full 4/3: 9/8-11/10-320/297 or 204-165-129
> > cents.
> >
> > A JI solution might be to "temper by ratios" by keeping all
> > steps superparticular, 9/8-11/10-14/13, and letting that fourth
> > be narrow by a 2080:2079, less than a cent. But I guess that the
> > idea of a tetrachord at a just 4:3 led Safi al-Din to stretch the
> > 14:13 by that amount instead.
> >
> > On your baglama at 202-168-128 cents, a slightly enlarged 11/10
> > takes up the slack for the minutely narrow 9/8 as well as the
> > virtually just 14/13 -- two cents for the first, and another cent
> > for the second, placing it at 168 rather than 165 cents. If the
> > 9/8 were precisely just, we might similarly stretch 11/10 by
> > exactly 2080:2079, getting 208/189 and a tuning of 204-166-128
> > cents.
> >
> > Now let's see what happens in O3 for a similar tetrachord. Giving
> > Safi al-Din his due, we'll start with the tempered tetrachord
> > closest to his 9/8-11/10-320/297. Then we'll see what happens in
> > the almost identical tetrachord closest in its third size to your
> > baglama.
> >
> > Safi al-Din: 1/1 9/8 99/80 4/3
> > 0.0 203.9 368.9 498.0
> > 9:8 11:10 320:297
> > 203.9 165.0 129.1
> >
> > O3: B C# Eb E
> > 0.0 207.4 369.1 495.7
> > 207.4 161.7 126.6
> >
> > While the tempered neutral third at 369.1 cents is almost
> > identical to Safi al-Din's 99/80, the tone B-C# more than
> > compensates for the 2080:2079 comma in the JI version by its
> > wideness of about 3.5 cents in comparison to 9/8. The fourth,
> > tempered at about 2.3 cents narrow, is impure by an amount almost
> > three times that of the comma. And in the process, 11/10 gets
> > compressed to 161.7 cents, or by about 3.3 cents, just a tad more
> > than the 3.24 cents set as a maximum for the impurity of the
> > ratios supported in his 29-HTT (secor29htt.scl in the Scala
> > archive).
> >
> > If we focus specifically on the interval from the neutral third
> > to the fourth, Eb-E in the tempered version, we find that the
> > third at 369.1 cents is a virtually just 99/80, but that the
> > narrowing of the fourth by some 2.3 cents more than accounts for
> > the 2080:2079 comma, indeed so much so that the remaining 14/13
> > step, for from needing a bit of widening as in Safi al-Din, is
> > actually narrow by about 1.7 cents (126.6 vs. 128.3 cents).
> >
> > Now let's look at a trivially different tempered tetrachord
> > closer to your baglama's slightly larger neutral third, which
> > I'll call a virtually just 26/21, likewise taking your fourth as
> > a just 4/3:
> >
> > Cameron's baglama: 0 202 370 498
> > 202 168 128
> >
> > O3: F# G# Bb B
> > 0 208.6 370.3 496.9
> > 208.6 161.7 126.6
> >
> > Here the two upper melodic steps of the tempered tetrachord are
> > identical to those of the last, but the major second at 208.6
> > cents, and the fourth at 496.9 cents, are 1/1024 octave larger.
> > Your baglama and O3 may be about equally far in their central
> > steps from a just 11/10 at 165 cents, albeit in opposite
> > directions, Here, with the tempered third at a virtually just
> > 26/21, the remaining step would be a just 14/13 -- except that
> > the fourth is narrow, this time by about 1.2 cents.
> >
> > > What about the 1287/1280 comma at 4:3 were we to use the also
> > > lovely combination of 13/12, 11/10 and 9/8 to make our
> > > tetrachord? That's already almost 9.5 cents.
> >
> > Humorously, with O3, I can give the answer that the steps aren't
> > so arranged that it's possible to combine these ratios all in a
> > single tetrachord, so the question doesn't arise <grin>. What O3
> > does have with 9/8 and 13/12 that might go a step further is this
> > tetrachord in the manner of one school of Aleppo for Maqam `Iraq:
> >
> > Eb E F# G*
> > 0 126.6 334.0 472.3
> > 126.6 207.4 138.3
> >
> > My point here, leaving aside the fine points of this tetrachord
> > (apart from noting that the Syrian 6-9-6 commas would be around
> > 135-340-475 cents, with my 126.6-cent step rather smaller),
> > is that altered fourths and fifths sometimes go with the
> > territory. But let's get back to 13/12, 11/10, and 9/8, and see
> > how Ozan's 79-MOS might handle this. Suppose we want to keep all
> > three superparticular steps as close as possible to just. If we
> > start on step 13 of his scale (Scala archives, 79-159.scl), his
> > tempered or meantone major second step in Maqam Rast known as
> > perde dugah, we can do the following:
> >
> > JI: 1/1 13/12 143/120 429/320
> > 0 138.6 303.6 507.4
> > 13/12 11/10 9/8
> > 138.6 165.0 203.9
> >
> > yarmans: 0 9 20 33L
> > 79-MOS: 0 135.8 301.9 505.7
> > 135.8 166.0 203.8
> > 9 11 13L
> >
> > You'll see that Ozan's meantone fourth at 505.7 cents, or 1/3
> > Holderian comma wide, absorbs most of the burden of that
> > 1287/1280 comma, with the narrowing of 13/12 by not quite 3 cents
> > taking up the rest of the comma, and also compensating for the
> > tempering of 11/10 at about a cent wide. The numbers of yarmans,
> > or 79-MOS steps normally at 2/3 Holderian comma (2/159 octave) or
> > just over 15 cents, may help clarify the process. In the 79-MOS,
> > there is one "large" step at a full comma or about 1/53 octave,
> > and the notations "33L" for the fourth and "13L" for the 9/8 step
> > that concludes the tetrachord show an interval including this
> > large or full-comma tuning step.
> >
> > Another solution would be to trim the 9/8 by 1/3 comma, and let
> > the fourth remain precisely or virtually pure. For example,
> > starting on Ozan's 1/1 or perde rast:
> >
> > JI: 1/1 13/12 143/120 429/320
> > 0 138.6 303.6 507.4
> > 13/12 11/10 9/8
> > 138.6 165.0 203.9
> >
> > yarmans: 0 9 20 33
> > 79-MOS: 0 135.8 301.9 498.1
> > 135.8 166.0 196.2
> > 9 11 13
> >
> > This time the upper major second gets narrowed by the lion's
> > share of the comma instead of the fourth being widened by a
> > comparable amount, and all the intervals are built from regular
> > tuning steps of 2/3 Holderian comma or around 15 cents.
> >
> > > At 12/11, 11/10, 9/8 we've got a concrete comma. At almost a
> > > syntonic comma wide, I suspect that it may be one of the very
> > > commas that grates against 24-tET approximation.
> >
> > Here my first reaction is that 12/11 plus 11/10 should be
> > precisely a 6/5, and that plus 9/8 precisely a 27/20, so that we
> > are indeed a syntonic comma wide. Change the 9/8 to a 10/9, and
> > we have a 4/3, as well as Ptolemy's Equable Diatonic that Cris
> > was recently discussing, at 12:11:10:9.
> >
> > But this might invite the consideration of one more case where
> > the comma involved using only superparticular ratios must somehow
> > be accounted for, and a temperament stays fairly close to one JI
> > solution. Let's consider a tetrachord which could be used in
> > Persian Shur, Arab Bayyati, or Turkish Arazbar, for example:
> >
> > JI: 1/1 13/12 13/11 4/3
> > 0 138.6 289.2 498.0
> > 13:12 12:11 44:39
> > 138.6 150.6 208.8
> >
> > O3: F# G* A B
> > 0 138.3 289.5 496.9
> > 138.3 151.2 207.4
> >
> > In the just version, we have a 13:12:11 division of a 13/11 minor
> > third, so that reaching a pure 4/3 requires a major second wider
> > than 9/8 by a 352:351 at some 4.9 cents, in other words a 44/39,
> > thus, on monochord, 52:48:44:39.
> >
> > In O3, the 13/12 and 12/11 steps are virtually just, so the
> > 352:351 gets handled essentially in two ways. First, the tone at
> > 207.4 cents is about 3.5 cents wide of 9/8, and not too far from
> > 44/39. Secondly, the fourth is narrow by not quite 1.2 cents. As
> > it happens, the 13/11 is at this location a tad wide at 289.5
> > cents compared to a just 289.2, helping with the comma also. At
> > some other locations, where 13/11 is not quite a cent narrow of
> > just at 288.3 cents, a wider major second at 208.6 cents (almost
> > precisely 44/39), or narrower fourth at 495.7 cents, is there to
> > compensate.
> >
> > So we have commas of less than a cent, like the 2080:2079 as with
> > the beautiful Rast tetrachord made famous by your baglama (Safi
> > al-Din didn't call it Rast, but it wonderfully fits that maqam);
> > commas of around 4-5 cents like the 352:351; and the "biggies"
> > like your 1207:1280 example approaching 9.5 cents, and yet more
> > so the 81:80 at 21.5 cents or the 64/63 at 27.3 cents.
> >
> > With the larger commas, I take a "JI-ish" perspective: let them
> > stand. For me, the 64:63 is the main one I deal with regularly.
> > In O3, some small ones like the 352:351 are tempered out, while
> > the 2080:2079 might in a sense be "observed" (e.g. 369.1 cents as
> > Safi al-Din's 99/80, and 370.3 cents as your baglama's 26/21),
> > hopefully while keeping a "quasi-rational" structure for the most
> > part intact.
> >
> > And large commas can be invaluable, not only for yielding
> > "special effects" intervals like 21/16 when we want them, but for
> > permitting more choices: a smaller or larger neutral second to
> > start this tetrachord, or a 7/4 or a 16/9? Jacques and I both
> > seem to devise 17-note sets or subsets, for Persian music for
> > example, and then throw in a couple of extra notes to add comma
> > alternatives.
> >
> > Please forgive me if this is too long: a lot of this stuff about
> > maqam tetrachords and tempering may not have been presented so
> > systematically before, and, of course, what I've written about
> > Ozan's 79/80-MOS is very much subject to his correction or
> > amendment!
> >
> > Most appreciatively,
> >
> > Margo
> > mschulter@
> >
>