Re: [tuning] Digest Number 3539

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

>
> Ah! Now we have a problem. Would you count tuning one's major thirds
> ever closer to the rational ideal of 504:635 as an example of the
> process of just intonation. These are theoretically only 0.0006 of a
> cent from the major thirds of 12-equal and in practice utterly
> indistinguishable from them.
>

Yes, if the composer wants 504:635 and not a 12tet major third, why not?

> If not, then wouldn't it be better to say "to some just or pure ideal"
> or "to some beatless ideal", rather than "to some rational [number]
> ideal"?
>
>

No, "pure" or "beatless" are problematic given the real spectra of
many real instruments, loudspeakers, etc..

>
> This is good. So primarly Just Intonation is something you _do_ when
> tuning one pitch against another, to the best of your ability at a
> particular time and place. So degrees of sucess must be admitted, and
> therefore degrees of justness.
>

Yes, the particular "time and place-ness" of the exercise is part of
the identity of a given music. For Greeks or Byzantines, the accuracy
of "beatless" tuning for auloi or lyres was good enough, while we
certainly are not faced with the same restrictions.

> From there we go to describing certain intervals (in the abstract),
> that are close to certain sizes, as just intervals or JI intervals,
> and from there we can describe certain scales (in the abstract) as JI
> scales because their pitches are fully connected, with more than
> merely linear connectivity, by just intervals.
>
> > and distances us productively away from the viewpoint that
> > would hold that a given temperament is "the same as" Just
> > Intonation.
>
> One doesn't need to invoke the purely mathematical concept of rational
> number (with its attendant problems of inaudibility and
> immeasurability) in order to distance oneself from this viewpoint.

I suppose that you could characterize mine as a "constructive" approach.

I
> assume you saw that I did so in a recent discussion with Gene Ward
Smith.
>

> That makes perfect sense. However there is no more reason that a
> sufficiently gentle temperament should prevent such a JI orientation
> than do the normal small random inaccuracies of actual instrument
tunings.
>
> I agree there can be a sharp line between rational and tempered
> orientations to composition, but there is no sharp line between
> rational and tempered in the actual tuning of most instruments or in
> our ability to distinguish them by listening or measurement.
>

I think that we differ on how we assess the role of intention in
musical performance. I think that if a player goes into a performance
with the idea that a given approximation will be good enough, then
that performance will probably be robbed of the opportunity to do
better than the approximation.

In general, I find that contemporary scientific approaches to musical
perception are rather limiting, if not pessimistic, about our capacity
for detail and range. Isn't it in fact more interesting to approach a
musical idea with the question of "how can I make this idea audible?"
than with the conclusion that it is not possible?

Daniel Wolf

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@s...> wrote:

> I think that we differ on how we assess the role of intention in
> musical performance. I think that if a player goes into a performance
> with the idea that a given approximation will be good enough, then
> that performance will probably be robbed of the opportunity to do
> better than the approximation.

That no longer makes sense with nanotempering. If someone was trying
to perform something in ennealimmal or 7-limit breed, you'd have to
instruct them to get as close as they could to just intonation.

> In general, I find that contemporary scientific approaches to musical
> perception are rather limiting, if not pessimistic, about our capacity
> for detail and range. Isn't it in fact more interesting to approach a
> musical idea with the question of "how can I make this idea audible?"
> than with the conclusion that it is not possible?

After a while you can prove it cannot be possible. Obviously Dave's
example of two notes differing by 10^(-100) cent is not possible, so
asking how you can make it audible is merely silly. So your comment
above still has to be taken in practical terms, if you plan on taking
it seriously.

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> >
> > Ah! Now we have a problem. Would you count tuning one's major thirds
> > ever closer to the rational ideal of 504:635 as an example of the
> > process of just intonation. These are theoretically only 0.0006 of a
> > cent from the major thirds of 12-equal and in practice utterly
> > indistinguishable from them.
> >
>
> Yes, if the composer wants 504:635 and not a 12tet major third, why not?
>

So are you saying that something audibly-indistinguishable from
12-equal can be called JI if the composer consider all its intervals
to be based on rational numbers?

I wrote more on the problems of such a position in
/tuning/topicId_58865.html#58883
and
/tuning/topicId_58865.html#58890

Lest anyone think that these messages were prescient in anticipating
Daniel Wolf's points, or that Daniel has ignored them, I should point
out that I received Daniel's message by email _before_ I wrote them
and then asked Daniel to post his message to the list so I could
address it here. Thanks Dan.

> > If not, then wouldn't it be better to say "to some just or pure
ideal"
> > or "to some beatless ideal", rather than "to some rational [number]
> > ideal"?
> >
> >
>
> No, "pure" or "beatless" are problematic given the real spectra of
> many real instruments, loudspeakers, etc..

Yes. My definition needs to say that just intervals are intervals
_of_a_size_ that is tunable by ear so as to approach beatlessness,
when an unadorned harmonically-rich timbre is used (no vibrato, chorus
etc). It doesn't mean that it has to be tunable by ear with every
actual timbre or instrument that is used.

I also understand that more complex ratios become tunable by ear in
the context of larger otonalities (harmonic series segments) than
would be tunable by ear as bare dyads. I'm happy to allow tuning by
ear in the context of any sonority that the scale can provide.

> > This is good. So primarly Just Intonation is something you _do_ when
> > tuning one pitch against another, to the best of your ability at a
> > particular time and place. So degrees of sucess must be admitted, and
> > therefore degrees of justness.
> >
>
> Yes, the particular "time and place-ness" of the exercise is part of
> the identity of a given music. For Greeks or Byzantines, the accuracy
> of "beatless" tuning for auloi or lyres was good enough, while we
> certainly are not faced with the same restrictions.

But from a listener's point of view, we are still faced with the same
limitations on our ears and brains.

You will notice that in the above messages I have cast this as a sort
of "consumer's rights" issue, like how much beef has to be in a
suasage before the producer can call it a beef sausage. :-) Now I know
that at this point in time this is somewhat ridiculous since producers
of JI music need all the help they can get and consumers should be
grateful for whatever they get. But the definition of JI may
eventually become a real consumer's rights issue, and even now, I hope
you will agree that the JI listener has a valid point of view on this.

By the way, the one thing I've "composed", and which has had 3 public
"performances" (two in the USA and one in Australia), is in just
intonation.
http://dkeenan.com/Music/StereoDekany.htm

From a listener's point of view, there is a special audible quality of
certain intervals and chords (close to simple ratios) that we need a
name for. Historically it has been called "justness" or "just
intonation", but now, for some reason that I am still trying to
fathom, some people (and it ain't the mathematicians) want
"justness"/"just intonation" to be a purely mathematical property that
is completely inaudible.

The thing is, we already have a name for that mathematical property -
"rationality" (not to be confused with the mental faculty of the same
name).

If "just" is to be redefined as merely a synonym for "rational", then
what are we to call that special audible property of certain sonorities?

> I suppose that you could characterize mine as a "constructive" approach.
>

Right. You want a word for how the scale is constructed or for its
structure in general, while I want a word for how it _sounds_. I'm
arguing that you already have such a word - "rational", so you don't
need to steal mine - "just".

> I think that we differ on how we assess the role of intention in
> musical performance. I think that if a player goes into a performance
> with the idea that a given approximation will be good enough, then
> that performance will probably be robbed of the opportunity to do
> better than the approximation.

So how close an approximation _will_ be good enough? If a performer
goes in with the idea that it has to be within 0.001 cents to be good
enough, then that's as good as her going in with the idea that it has
to be spot-on, because
(a) no performer is that good, and
(b) no listener is that discriminating.

>
> In general, I find that contemporary scientific approaches to musical
> perception are rather limiting, if not pessimistic, about our capacity
> for detail and range. Isn't it in fact more interesting to approach a
> musical idea with the question of "how can I make this idea audible?"
> than with the conclusion that it is not possible?

But we know that short of turbo-charged cochlear implants or
genetically-engineered super-ears, connected to more than the usual
number of neurons, there are certain things that will never be audible
to the great bulk of any audience.

I understand you are afraid that people will start allowing too-large
deviations and still calling it JI. Do you really think that the best
way to prevent that is to cling to a definition that allows something
that's audibly-indistinguishable from 12-equal to be called JI.

Wouldn't it be better to try to nail down the conditions that give
rise to the _sound_ of JI. Now I agree this won't be easy and will
only be a gradual process. I liken it to agreeing on names for
colours, or (a beter analogy) agreeing on what constitutes a
"saturated" colour. It may requires the combined efforts of many
experts over many years, but we might already be able to make a start
on what intervals are definitely just and what are definitely not (in
any context), even though there will always be grey areas in between.

Is there any context in which a 75 cent interval could be considered just?

-- Dave Keenan

Once again Dave, your definition of JI excludes all those pieces by LaMonte Young based on high harmonics produced by machine. Perhaps you should call him up an tell him he doesn't do JI
Why might not a JI composer want beats at times. perhaps you can tell Kyle Gann that his music isn't in JI because he uses such beating intervals.
What about the organ parts in some of Harry Partch's music. I guess this isn't JI either. since he is making beats
Where does any JI say anything about beatless intervals? the question is ambiguity.
there is nothing in using ratios that requires the use or desire or no beats, at least for the last hundred years
And one again why should we not apply the same standard to ET, that is is only tunable by Machine.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> Once again Dave, your definition of JI excludes all those pieces by
> LaMonte Young based on high harmonics produced by machine. Perhaps you
> should call him up an tell him he doesn't do JI

Hi Kraig,

Why would I want to do that?

If you tell me his stuff _sounds_ like JI to you, then I'll take your
word for it (unfortunately I'm never likely to get to hear the dream
house). But I'm not necessarily going to accept that it's JI if you're
saying that purely because it's based on ratios.

A ratio can be any size. Simple ratios sound just. Some moderately
complex ratios sound just in some contexts, some don't, some you can't
really say, or it depends very much on the context. Some very complex
ratios sound just because they are very close to simpler ones. So
merely knowing something is in ratios, doesn't tell you anything about
how it sounds.

My definition is incomplete, and may always be. I'm happy to modify it
if necessary to accomodate LaMonte Young's stuff. Did you read what I
wrote about higher harmonics being perceivable as Just when they are
supported by a lot of others?

But let's say I find someone who claims to be using a JI scale, and
when I tune up its ratios myself and listen under the most favourable
conditions, I can't hear a single just interval or just chord of any
kind, but maybe their music still really blows me (and a lot of other
people) away. If so, why should they worry if I tell them it isn't JI?

Try this scale. Does it sound like JI to you? Or will you say it is JI
without even listening, simply because it is expressed as ratios?

Mystery scale
7
!
202/181
153/124
175/128
199/130
261/154
211/112
194/93

No true octave and 1/1 is implied as usual for Scala .scl files.

> Why might not a JI composer want beats at times. perhaps you can tell
> Kyle Gann that his music isn't in JI because he uses such beating
intervals.
> What about the organ parts in some of Harry Partch's music. I guess
this
> isn't JI either. since he is making beats

You must have missed where I said no one expects every interval in a
JI piece (or a JI scale) to be Just or beatless. That would be ridiculous.

> Where does any JI say anything about beatless intervals?

See my third paragraph below.

> the question is ambiguity.

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

> there is nothing in using ratios that requires the use or desire or
> no beats, at least for the last hundred years

That's right. There is nothing in using _ratios_ that implies
beatlessness. And there is nothing that requires every interval in a
JI scale to be a just interval. But a JI scale has to have _some_ just
intervals. In fact I think a JI scale ought to be fully connected by
them, with better than linear connectivity, to qualify (this avoids
having to say that 19-ET is JI due to its chain of just minor thirds).

And if a JI scale has more than about 6 notes then it can't help but
contain many non-just intervals. You could still call these "JI scale
intervals", but that doesn't make them Just intervals.

And a just interval doesn't have to be beatless, it only has to be
close enough to a simple enough ratio that at least with _some_
harmonic timbre, in _some_ chordal context, you can hear that the
beating of _some_ harmonics is slow enough so as to give rise to that
distinctive Just sound.

I don't know when a significant number of people started saying that
the justness of an interval wasn't any quality you can hear, but
instead a purely mathematical property. Maybe it was a hundred years
ago, but maybe it only started around when the first digital
synthesizers became available. In any case, there was an awful lot of
time before a hundred years ago, when the justness of an interval
meant something you could actually _hear_. I see no reason to give
that up.

> And one again why should we not apply the same standard to ET, that
> is is only tunable by Machine.

Because
(a) ET usn't the opposite of JI, non-JI is. Some JI scales are subsets
of large ETs. Some ETs are JI.
(b) Some non-JI scales are tunable by ear, for example 19-ET can be
tuned as a chain of just minor thirds (5:6).
(c) Many non-JI scales, including many ETs, are tunable by ear by
counting beats or by using temporary reference frequencies outside the
scale, or various other tricks of the trade.

I say again, "tunable by ear" is not my sole criterion for justness.
It was just a snappy phrase to contrast against "tuned to ratios".
What I really want to base my definition on is that special sound that
just intervals have (particularly when sustained in harmonic timbres,
or even with sine-waves if they are loud enough), which is related to
non-beating or minimally-beating harmonic partials and sum and
difference tones. But I don't insist that the intervals have to always
be sustained or always be in those timbres.

I hope that has set your mind at rest somewhat.

Can you set my mind at rest by telling me that scale I gave above
isn't JI, and/or that 12-equal (or something indistinguishable from it
by even the most discriminating listener or measurement) doesn't
become JI simply by being expressed in ratios?

-- Dave Keenan

I think the `beatlessness` Dave formulates depends rather on the tonic of the scale being `in tune via simple integer relationships` with the other pitches of the scale next to `modular replicas` of the same `justness` distributed here and there. The rest of the `unjust intervals` are `just` (only) by-products of this highly rational arrangment in reference to the starting tone.

The distinction between ET and JI is therefore only a matter of qualitative distinction and pre-defined purpose in a piece of music. For all I know, pianos tuned to Well Temperament can be considered just as much as a strict JI in 5 limit is. Thusly, Maqams can be expressed both from a high-limit JI perspective, and a ET perspective.

Wasn't Monz trying to point out a while ago that Schonberg himself was conceiving of 12ET pitches as just?

Cordially,
Ozan

----- Original Message -----
From: Kraig Grady
To: tuning@yahoogroups.com
Sent: 06 Haziran 2005 Pazartesi 13:58
Subject: [tuning] Definitions of JI (was: Digest Number 3539)

Once again Dave, your definition of JI excludes all those pieces by
LaMonte Young based on high harmonics produced by machine. Perhaps you
should call him up an tell him he doesn't do JI
Why might not a JI composer want beats at times. perhaps you can tell
Kyle Gann that his music isn't in JI because he uses such beating intervals.
What about the organ parts in some of Harry Partch's music. I guess this
isn't JI either. since he is making beats
Where does any JI say anything about beatless intervals? the question is
ambiguity.
there is nothing in using ratios that requires the use or desire or no
beats, at least for the last hundred years
And one again why should we not apply the same standard to ET, that
is is only tunable by Machine.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I think the `beatlessness` Dave formulates depends rather on the
tonic of the scale being `in tune via simple integer relationships`
with the other pitches of the scale next to `modular replicas` of the
same `justness` distributed here and there. The rest of the `unjust
intervals` are `just` (only) by-products of this highly rational
arrangment in reference to the starting tone.
>

You've got pretty much the right idea, however my condition is weaker
even than that. I don't require everything to be audibly just with
respect to a tonic, but only that every pitch be reachable from every
other pitch by some chain of audibly just intervals. So some pitches
need not be reachable from the tonic in a single audibly just leap,
but might need other pitches of the scale as stepping stones. But I
suggest that it isn't enough for them to be linked into a single chain
(or loop under octave-equivalence) of audibly just intervals. There
needs to be a few more audibly just connections than that.

> The distinction between ET and JI is therefore only a matter of
qualitative distinction and pre-defined purpose in a piece of music.
For all I know, pianos tuned to Well Temperament can be considered
just as much as a strict JI in 5 limit is. Thusly, Maqams can be
expressed both from a high-limit JI perspective, and a ET perspective.
>

You could also say a high-limit _rational_ perspective.

> Wasn't Monz trying to point out a while ago that Schonberg himself
was conceiving of 12ET pitches as just?
>

Yes. But that isn't because it can be approximated closely by complex
ratios, but because he could hear its very poor approximations to
simple ratios. Monz is saying he conceived (and presumably perceived)
12ET as an approximation to (simple ratio) JI (in other words a
temperament), but not one that was so close that it actually sounded just.

-- Dave Keenan

In that case, we are almost in complete alignment as to the reservation of the term "rational" in order to express fractions that are not bound to any JI conception in the first place, and "just" to express only those `simple integer relationships` that are highly correlated to a cycle of pure JI intervals, with the intent of producing near-beatless tones of unique pitch quality.

This definition neatly sums up the intricate construction of Maqam scales, all of which I'm more certain than ever should be explained in terms of as high as 29-limit JI.

It is with great excitement that I wish to proclaim that I determined (after several days of trial and error) 43tET to be an excellent basic choice in both the JI approximation and the proper notation of Maqam Music in general. It appears that nothing other than dense meantone ETs with a generator of ~698 cents suffice for the job. This means that East and West may musically converge without perceptual barriers at long last. For a better representation, 67tET (which I notice is not claimed or used by anyone yet according to `Monzopedia`) is even better with a 43tET mapping. In fact, I believe I'm on the verge of solving the intonational/notational problems caused by the Yekta-Arel-Ezgi school by utilizing only the quarter-tone (Tartini) accidentals proposed by George Secor.

I will on short notice extirpate the mandals of my Qanun fixed at 70tET, and re-infix them according to 67tET, the pitches of which can be beautifully interpretted in terms of 43tET constricted to quarter-tone symbology.

Cordially,
Ozan

----- Original Message -----
From: Dave Keenan
To: tuning@yahoogroups.com
Sent: 06 Haziran 2005 Pazartesi 19:15
Subject: [tuning] Re: Definitions of JI (was: Digest Number 3539)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I think the `beatlessness` Dave formulates depends rather on the
tonic of the scale being `in tune via simple integer relationships`
with the other pitches of the scale next to `modular replicas` of the
same `justness` distributed here and there. The rest of the `unjust
intervals` are `just` (only) by-products of this highly rational
arrangment in reference to the starting tone.
>

You've got pretty much the right idea, however my condition is weaker
even than that. I don't require everything to be audibly just with
respect to a tonic, but only that every pitch be reachable from every
other pitch by some chain of audibly just intervals. So some pitches
need not be reachable from the tonic in a single audibly just leap,
but might need other pitches of the scale as stepping stones. But I
suggest that it isn't enough for them to be linked into a single chain
(or loop under octave-equivalence) of audibly just intervals. There
needs to be a few more audibly just connections than that.

> The distinction between ET and JI is therefore only a matter of
qualitative distinction and pre-defined purpose in a piece of music.
For all I know, pianos tuned to Well Temperament can be considered
just as much as a strict JI in 5 limit is. Thusly, Maqams can be
expressed both from a high-limit JI perspective, and a ET perspective.
>

You could also say a high-limit _rational_ perspective.

> Wasn't Monz trying to point out a while ago that Schonberg himself
was conceiving of 12ET pitches as just?
>

Yes. But that isn't because it can be approximated closely by complex
ratios, but because he could hear its very poor approximations to
simple ratios. Monz is saying he conceived (and presumably perceived)
12ET as an approximation to (simple ratio) JI (in other words a
temperament), but not one that was so close that it actually sounded just.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Wouldn't it be better to try to nail down the conditions that give
> rise to the _sound_ of JI.

There first comes a point where a side-by-side produces a discernable
difference, but it is not immediately apparent which one is just.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> And a just interval doesn't have to be beatless, it only has to be
> close enough to a simple enough ratio that at least with _some_
> harmonic timbre, in _some_ chordal context, you can hear that the
> beating of _some_ harmonics is slow enough so as to give rise to that
> distinctive Just sound.

Here's Kyle Gann's description of that sound. I think it is a
distinctive sound, and I think ennealimmal tempering has it also,
which means under Dave's definition I should call it just.

``I've had interesting experiences playing just-intonation music for
non-music-major students. Sometimes they will identify an
equal-tempered chord as "happy, upbeat," and the same chord in just
intonation as "sad, gloomy." Of course, this is the first time they've
ever heard anything but equal temperament, and they're far more
familiar with the first sound than the second. But I think they
correctly hit on the point that equal temperament chords do have a
kind of active buzz to them, a level of harmonic excitement and
intensity. By contrast, just-intonation chords are much calmer, more
passive; you literally have to slow down to listen to them. (As Terry
Riley says, Western music is fast because it's not in tune.) It makes
sense that American teenagers would identify tranquil, purely
consonant harmony as moody and depressing. Listening from the other
side, I've learned to hear equal temperament music as a kind of aural
caffeine, overly busy and nervous-making. If you're used to getting
that kind of buzz from music, you feel the lack of it as a deprivation
when it's not there. But do we need it? Most cultures use music for
meditation, and ours may be the only culture that doesn't. With our
tuning, we can't.''

I've described just chords as having a granite-slab quality, of
steadiness and a kind of purity. Also interesting is the nearly-just
sound, but since 768-et--certainly nearly just, you might say very
nearly just--won't do for Kraig, clearly this isn't what some people
are looking for. Personally I think there is something to be said for
the view that slightly detuned chords, as you get from microtempering
which is not nanotempering, are musically more interesting for most
purposes than JI.

> I don't know when a significant number of people started saying that
> the justness of an interval wasn't any quality you can hear, but
> instead a purely mathematical property.

I don't know, but if someone does it seems to me that material should
be added to the Wikipedia article on Just Intonation, which adopts a
purely modern, JI network type definition. I think formerly only
5-limit JI was considered "just", come to that.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Wasn't Monz trying to point out a while ago that Schonberg himself
was conceiving of 12ET pitches as just?

I've just being reading Schoenberg's Harmonielehre, and there is a
hell of a lot about tuning and tuning history Schoenberg didn't know.
By no means was he an expert. But I don't recall this claim; rather,
he tries to relate the chromatic scale to the overtone series, but not
very exactly.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:

> It is with great excitement that I wish to proclaim that I
determined (after several days of trial and error) 43tET to be an
excellent basic choice in both the JI approximation and the proper
notation of Maqam Music in general.

This is extemely interesting; it suggests you can notate Maquam music
very nicely using Western-style sharps and flats. 43-et is a good
compromise between the advocates of 55 and 31, and since it is almost
precisely the same as 1/5-comma, has excellent historical credentials
also.

``It appears that nothing other than dense meantone ETs with a
generator of ~698 cents suffice for the job.''

So what's a dense meantone et?

``This means that East and West may musically converge without
perceptual barriers at long last. For a better representation, 67tET
(which I notice is not claimed or used by anyone yet according to
`Monzopedia`) is even better with a 43tET mapping.''

Now it gets confusing. That is a good enough 5-limit meantone, but in
the 7-limit one might want to use a different version of septimal
meantone, with an otonal tetrad given by C:E:G:G### rather than
C:E:G:A#. Is this the mapping you'd use? You also skipped over 55; how
does that work for Maquam music?

``In fact, I believe I'm on the verge of solving the
intonational/notational problems caused by the Yekta-Arel-Ezgi school
by utilizing only the quarter-tone (Tartini) accidentals proposed by
George Secor.''

Evidently you don't need quarter-tone accidentals at all.

By the way, you might take a look at 103-et; this tuning can be used
as a very mild meantone (very roughly 1/7 comma vs the 1/6 comma of
67) but is also a miracle system. If it worked for Maquam music, as it
seems it might, you'd get a common meantone-miracle relationship to
Maquam music, which could concievably be useful.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > Wouldn't it be better to try to nail down the conditions that give
> > rise to the _sound_ of JI.
>
> There first comes a point where a side-by-side produces a discernable
> difference, but it is not immediately apparent which one is just.

We can let the grey area be as wide as you like. There must surely
still be some regions where we can all agree that this special sound
is absent (under even the most favourable conditions) and others where
we can all agree it is present.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> > I don't know when a significant number of people started saying that
> > the justness of an interval wasn't any quality you can hear, but
> > instead a purely mathematical property.
>
> I don't know, but if someone does it seems to me that material should
> be added to the Wikipedia article on Just Intonation, which adopts a
> purely modern, JI network type definition.

You mean "if someone does [think it is a quality you can hear]"?

Yes I noticed it says simply JI = rational. The other point of view
ought to be represented too. But there's no point adding this if
someone is just going to take umbrage and immediately delete it. I
hope that through this discussion, folks will have enough
understanding of the other point of view, that this will not happen.

Thanks for the Kyle Gann quote. If we used something based on that,
who could argue?

> I think formerly only
> 5-limit JI was considered "just", come to that.

Yes. That's true. But I don't want to limit it in that way. Who can
deny that there is also a subminor seventh (augmented sixth) that has
that Just sound.

I aim to sail between the Scylla of too low a limit and the Charybdis
of "any ratio will do". Maybe we don't know exactly where the limit of
the audibility of justness in ratios ends. But I think we can safely
say that if some ratio involving 4-digit numbers sounds just, then it
is purely due to its proximity to a much simpler ratio.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> You mean "if someone does [think it is a quality you can hear]"?

No, if someone does know enough to explain the history of the term, it
would be a valuable addition to this article.

> Yes I noticed it says simply JI = rational. The other point of view
> ought to be represented too. But there's no point adding this if
> someone is just going to take umbrage and immediately delete it. I
> hope that through this discussion, folks will have enough
> understanding of the other point of view, that this will not happen.

You can't simply unilaterally delete things and have it stand if the
point being made can be supported. People like Hyathinth, with no dog
in this fight, would quickly become a part of the picture, and you
could get NPOV discussions and the whole bit.

> Yes I noticed it says simply JI = rational.

I agree that the two should not "equal" each other. Music can
sound "Just"; it cannot sound "Rational". As far as I can see, the
term "Just" is an adjective to describe the sound of an interval or
chord. The trouble began when it was realized that these Just-
sounding chords were representative of simple integer frequency
ratios: people started reasoning that any chord or interval that
represents simple integer frequency ratios should be called "Just".
Let me put this reasoning into standard form to illustrate its
invalidity:

Premise A: chord X has a certain audible quality which we call
Justness.
Premise B: chord X represents simple integer frequency ratios.
Conclusion: all chords that represent simple integer frequency ratios
will have the quality of Justness.

The conclusion does not at all follow from the premises.

I personally think that the term "Just Intonation" should be replaced
with "Rational Intonation", seeing as how in even the simplest "JI"
systems not all the intervals are uniformly Just in their sound
quality. I've yet to see a JI system without a wolf. And rather
than trying to set some sort of "threshold" as to how many wolf
intervals are allowable in a Just Intonation (which is impractical
and will likely never be agreed upon), why not just get rid of the
troublesome misnomer and stick with something that can consistently
describe these tuning systems?

I challenge anyone to give me a practical reason why the term "Just
Intonation" should not simply be replaced with "Rational
Intonation". What would be lost? What would be compromised? What
effect would it have on the music?

-Igs

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > You mean "if someone does [think it is a quality you can hear]"?
>
> No, if someone does know enough to explain the history of the term, it
> would be a valuable addition to this article.
>
> > Yes I noticed it says simply JI = rational. The other point of view
> > ought to be represented too. But there's no point adding this if
> > someone is just going to take umbrage and immediately delete it. I
> > hope that through this discussion, folks will have enough
> > understanding of the other point of view, that this will not happen.
>
> You can't simply unilaterally delete things and have it stand if the
> point being made can be supported. People like Hyathinth, with no dog
> in this fight, would quickly become a part of the picture, and you
> could get NPOV discussions and the whole bit.

OK. Well there's the Shorter Oxford Dictionary entry. They don't even
mention ratios.

"/Mus./ in /just interval/ etc.: Harmonically pure; sounding perfectly
in tune 1811."

That "1811" means that this is the year of the oldest known english
language document that uses the word in this way.

Now the Oxford Dictionary isn't static, they list both older and newer
usages of words with the years that they were first used. So clearly
they did not consider there was any such new usage at the time my
tattered old copy of the Shorter Oxford was last revised (1933).

If someone has access to the lastest edition (maybe of the full
Oxford) it would be good to check, and maybe find out what that 1811
document was. Of course entries in any other old or new dictionaries,
particularly musical specialist ones would be good to know about too.

Kraig likes Helmholtz, "On the sensations of tone". What did Helmholtz
assume was meant by "just intonation". Can anyone quote him?

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Kraig likes Helmholtz, "On the sensations of tone". What did Helmholtz
> assume was meant by "just intonation". Can anyone quote him?

Helmholtz thought shismatic tempering was just: "Now, since the
interval of 886/885 [by which he means 32805/32768] is itself on the
limits of of sensible difference of pitch, the eighth part of this
interval cannot be taken into account at all...". Helmholtz called
this chapter "Harmonium in Just Intonation", referring to one tuned,
or attempted to be tuned, in 1/8 schisma schismatic. I'd say Helmholtz
is firmly in your camp. He would probably agree that 171-et was just
intonation, and certainly that
612-et was. He also say the error of the fifth of 53-et is "quite
inappreciable", which underlines the point.

1/8 schisma schismatic has fifths a mere 1/8 schisma, or about 1/4
cent, flat, and makes major thirds exact 5/4s. Hence Helmholtz is
suggesting that if you get within 1/4 cent, it should count as JI.
That would agree with my suggestion that ennealimmal counts as JI in
the 7-limit.

Dave Keenan wrote:

> OK. Well there's the Shorter Oxford Dictionary entry. They don't even
> mention ratios.
> > "/Mus./ in /just interval/ etc.: Harmonically pure; sounding perfectly
> in tune 1811."
> > That "1811" means that this is the year of the oldest known english
> language document that uses the word in this way.
> > Now the Oxford Dictionary isn't static, they list both older and newer
> usages of words with the years that they were first used. So clearly
> they did not consider there was any such new usage at the time my
> tattered old copy of the Shorter Oxford was last revised (1933).
> > If someone has access to the lastest edition (maybe of the full
> Oxford) it would be good to check, and maybe find out what that 1811
> document was. Of course entries in any other old or new dictionaries,
> particularly musical specialist ones would be good to know about too.

New Shorter Oxford, 1993:

/Mus./ Set or tuned according to the exact vibration intervals or the notes; non-tempered, natural. Esp. in /just intonation,/ M19.

That's "middle to the 19th century".

klaus

> > Kraig likes Helmholtz, "On the sensations of tone". What did Helmholtz
> assume was meant by "just intonation". Can anyone quote him?

I that case, I retract my statement. Tuning is hard science not to be trifled with.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 07 Haziran 2005 Salı 5:13
Subject: [tuning] Re: Definitions of JI (was: Digest Number 3539)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Wasn't Monz trying to point out a while ago that Schonberg himself
was conceiving of 12ET pitches as just?

I've just being reading Schoenberg's Harmonielehre, and there is a
hell of a lot about tuning and tuning history Schoenberg didn't know.
By no means was he an expert. But I don't recall this claim; rather,
he tries to relate the chromatic scale to the overtone series, but not
very exactly.

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
> Dave Keenan wrote:
>
> > OK. Well there's the Shorter Oxford Dictionary entry. They don't even
> > mention ratios.
> >
> > "/Mus./ in /just interval/ etc.: Harmonically pure; sounding perfectly
> > in tune 1811."
> >
> > That "1811" means that this is the year of the oldest known english
> > language document that uses the word in this way.
...
> New Shorter Oxford, 1993:
>
> /Mus./ Set or tuned according to the exact vibration intervals or the
> notes; non-tempered, natural. Esp. in /just intonation,/ M19.
>
> That's "middle to the 19th century".

Thanks Klaus. Should that be "_of_ the notes"?

And "middle _of_ the 19th century"?

I'm feeling a warm glow after reading all the latest posts in this
thread. Here we have people with diametrically opposed views all
really trying to understand each others positions. I'm sure some of us
are feeling frustrated, but no one has flamed out.

Gee I love you guys. :-)

But I gotta stop this, and get some other things done.

-- Dave Keenan

Kraig,

While we're feeling this warm glow of camaraderie (or I am at least),
what would make it perfect is to have you retract some of the bad
things you said about Paul Erlich in that "Count Chocula?" thread
earlier this year. I happen to know he's still really hurting from
them, and really wants to be friends again.

Apart from your definition of JI (which seems Apollonian) I see Paul
as Apollo and you as Dionysius. Polar opposites in many ways, but
still brothers.

I know that you were just protecting Erv. But I think you know by now
that you shot the wrong guy. Paul already publically retracted (in the
same thread) the things he said that got you (understandably) riled.
In fact I think he retracted them twice.

C'mon Kraig. Please.

-- Dave Keenan

I publicly apologize for having some grave misunderstandings about Paul's actions

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> I publicly apologize for having some grave misunderstandings about
> Paul's actions

What a man! Kraig, you've really made my day, and I expect Paul's.

You've made me realise that I owe someone an apology too.

Gene, I'm sorry for losing my temper at you all those months back,
particularly over such a trivial thing as colons in interval ratios.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Gene, I'm sorry for losing my temper at you all those months back,
> particularly over such a trivial thing as colons in interval ratios.

I'm sorry for being such a grouch too. Of course the trouble with
bringing this stuff up is that we may have forgotten about it. I was
afraid during the Count Chocula business I might have to actually put
someone (not you, Kraig!) on moderated status, but it all blew over
and I'd forgotten all about it. Anyway, I apologize to Paul for our
lack of communication over the moats.

Dave Keenan wrote:

> Thanks Klaus. Should that be "_of_ the notes"?

This is standard with me. or = of

> > And "middle _of_ the 19th century"?

but the one with to is a new one.

klaus

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
> wrote:
> [OY:]
> > It is with great excitement that I wish to proclaim that I
> determined (after several days of trial and error) 43tET to be an
> excellent basic choice in both the JI approximation and the proper
> notation of Maqam Music in general.
> [GWS:]
> This is extemely interesting; it suggests you can notate Maquam
music
> very nicely using Western-style sharps and flats. 43-et is a good
> compromise between the advocates of 55 and 31, and since it is
almost
> precisely the same as 1/5-comma, has excellent historical
credentials
> also.
> ... [OY:]
> ``It appears that nothing other than dense meantone ETs with a
> generator of ~698 cents suffice for the job.''
> [GWS:]
> So what's a dense meantone et?
> [OY:]
> ``This means that East and West may musically converge without
> perceptual barriers at long last. For a better representation, 67tET
> (which I notice is not claimed or used by anyone yet according to
> `Monzopedia`) is even better with a 43tET mapping.''
> [GWS:]
> Now it gets confusing. That is a good enough 5-limit meantone, but
in
> the 7-limit one might want to use a different version of septimal
> meantone, with an otonal tetrad given by C:E:G:G### rather than
> C:E:G:A#. Is this the mapping you'd use? You also skipped over 55;
how
> does that work for Maquam music?
> [OY:]
> ``In fact, I believe I'm on the verge of solving the
> intonational/notational problems caused by the Yekta-Arel-Ezgi
school
> by utilizing only the quarter-tone (Tartini) accidentals proposed by
> George Secor.''
> [GWS:]
> Evidently you don't need quarter-tone accidentals at all.

Ozan, some of this sounds so outrageous to me that I'm wondering if
you posted this just to see if I'm still around (I've been here only
sporadically -- very, very busy lately with more things than I
expected).

I'm sure you've noticed that you can't use a 5-comma symbol to notate
43-ET, since you mention "utilizing *only* the quarter-tone
accidentals". While an 11-diesis (or quartertone) symbol could be
used, it would be very confusing to do so, since that's 2/3 of an
apotome in 43-ET, and the apotome-less-11-diesis (a larger interval
in JI) would be 1/3 of an apotome in 43-ET.

The most logical choice for the single degree of 43-ET is the 7-
comma, something we didn't need for the 41-ET notation (for which I
still owe you a reply). If you're basing your Maqam notation on 43-
ET (something I don't quite understand), then you'll need to start
all over with some different symbols.

Sorry, but I can't stick around right now, but just wanted to let you
know that I'm peeking in occasionally.

Best,

--George

Hi again dear George, I'm glad you noticed my having mentioned you. Yes, you are right in every aspect about the notation issue, but you realize, don't you, that my main concern is divorcing the meanings attributed to certain symbols at will for convenient purposes whenever such will do the job. However, it is indeed outrageous for me to do so as you say. Thus, perhaps you can help me. My main concern is achieving a meantone notation (sharps & flats reversed, E closer to 5/4) of sufficient tone resolution while being able to transpose this system equally everywhere. Maybe I should just give up thinking in terms of cycle of fifths and adopt a puritan JI approach? But then, so many pitches out of the pitch continuum have to be specified for the Ney alone.

For one thing, a Zarlino diatonical gamut with the 6th alterating by a syntonic comma is the Rast scale, and MUST be notated as C-D-E-F-G-A-B-C without any accidentals whatsoever.

If I do so, however, and choose any one of 41, 53 or 65 ETs with a near-pure fifth, I must use your 5-comma flat for the 3rd and 7th degrees, and for the 6th degree when the occasion demands it. HOWEVER, I must avoid this at all costs. Rast scale for all instruments must be notated as I delineated above.

The only way without sacrificing transposition over every key and without requiring hundreds of ratios is by meantone temperaments above 43tET. However, then I am troubled by being unable to make the distinction between Rast and Suz-i Dilara, 5-limit major and 3-limit major.

Help!

Cordially,
Ozan

----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 0:37
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
> wrote:
> [OY:]
> > It is with great excitement that I wish to proclaim that I
> determined (after several days of trial and error) 43tET to be an
> excellent basic choice in both the JI approximation and the proper
> notation of Maqam Music in general.
> [GWS:]
> This is extemely interesting; it suggests you can notate Maquam
music
> very nicely using Western-style sharps and flats. 43-et is a good
> compromise between the advocates of 55 and 31, and since it is
almost
> precisely the same as 1/5-comma, has excellent historical
credentials
> also.
> ... [OY:]
> ``It appears that nothing other than dense meantone ETs with a
> generator of ~698 cents suffice for the job.''
> [GWS:]
> So what's a dense meantone et?
> [OY:]
> ``This means that East and West may musically converge without
> perceptual barriers at long last. For a better representation, 67tET
> (which I notice is not claimed or used by anyone yet according to
> `Monzopedia`) is even better with a 43tET mapping.''
> [GWS:]
> Now it gets confusing. That is a good enough 5-limit meantone, but
in
> the 7-limit one might want to use a different version of septimal
> meantone, with an otonal tetrad given by C:E:G:G### rather than
> C:E:G:A#. Is this the mapping you'd use? You also skipped over 55;
how
> does that work for Maquam music?
> [OY:]
> ``In fact, I believe I'm on the verge of solving the
> intonational/notational problems caused by the Yekta-Arel-Ezgi
school
> by utilizing only the quarter-tone (Tartini) accidentals proposed by
> George Secor.''
> [GWS:]
> Evidently you don't need quarter-tone accidentals at all.

Ozan, some of this sounds so outrageous to me that I'm wondering if
you posted this just to see if I'm still around (I've been here only
sporadically -- very, very busy lately with more things than I
expected).

I'm sure you've noticed that you can't use a 5-comma symbol to notate
43-ET, since you mention "utilizing *only* the quarter-tone
accidentals". While an 11-diesis (or quartertone) symbol could be
used, it would be very confusing to do so, since that's 2/3 of an
apotome in 43-ET, and the apotome-less-11-diesis (a larger interval
in JI) would be 1/3 of an apotome in 43-ET.

The most logical choice for the single degree of 43-ET is the 7-
comma, something we didn't need for the 41-ET notation (for which I
still owe you a reply). If you're basing your Maqam notation on 43-
ET (something I don't quite understand), then you'll need to start
all over with some different symbols.

Sorry, but I can't stick around right now, but just wanted to let you
know that I'm peeking in occasionally.

Best,

--George

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> For one thing, a Zarlino diatonical gamut with the 6th alterating by
a syntonic comma is the Rast scale, and MUST be notated as
C-D-E-F-G-A-B-C without any accidentals whatsoever.

This is just a diatonic gamut with the sixth not altered by anything.
If it is required that you have this in your system of scales, a
tuning system which can handle meantone does make sense, which makes
24-et rather marginal, and bodes ill for 53 or 65.

> If I do so, however, and choose any one of 41, 53 or 65 ETs with a
near-pure fifth, I must use your 5-comma flat for the 3rd and 7th
degrees, and for the 6th degree when the occasion demands it.

It's not really the same scale when you use the commas, but that might
not matter if you are not going to use harmony.

HOWEVER, I must avoid this at all costs. Rast scale for all
instruments must be notated as I delineated above.

But you must avoid it at all costs--then, back to 43 or 55!

> The only way without sacrificing transposition over every key and
without requiring hundreds of ratios is by meantone temperaments above
43tET. However, then I am troubled by being unable to make the
distinction between Rast and Suz-i Dilara, 5-limit major and 3-limit
major.

If you need both meantone and Pythagorean fifths in a single equal
temperament, and if 12-et won't do, you have to go with something like
270, because you must have two different fifths.

hi Gene and Ozan,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> If you need both meantone and Pythagorean fifths in
> a single equal temperament, and if 12-et won't do, you
> have to go with something like 270, because you must
> have two different fifths.

By my calculations, 92-edo is the first cardinality which
gives you two different 5ths, one resembling the pythagorean
3/2 ratio and the other a ~1/3-comma meantone 5th.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> hi Gene and Ozan,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > If you need both meantone and Pythagorean fifths in
> > a single equal temperament, and if 12-et won't do, you
> > have to go with something like 270, because you must
> > have two different fifths.
>
>
> By my calculations, 92-edo is the first cardinality which
> gives you two different 5ths, one resembling the pythagorean
> 3/2 ratio and the other a ~1/3-comma meantone 5th.

I clicked "send" too soon on that one. I meant to
add the ~cents values for the two 92-edo 5ths:
704.3478261 and 691.3043478.

Also, i see that there are lower cardinality EDOs
which do get somewhat close to the two targets.
73-edo has ~706.8493151 and ~690.4109589 cents,
so it looks like the lowest cardinality which
could possibly qualify.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> hi Gene and Ozan,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > If you need both meantone and Pythagorean fifths in
> > a single equal temperament, and if 12-et won't do, you
> > have to go with something like 270, because you must
> > have two different fifths.
>
>
> By my calculations, 92-edo is the first cardinality which
> gives you two different 5ths, one resembling the pythagorean
> 3/2 ratio and the other a ~1/3-comma meantone 5th.

But it won't do for his purposes. The first et which bas a fifth
flatter than its best fifth lying between 25/43 and 32/55 is 184, but
270 has a more accurate fifth and does all those other things besides.
To get a reall good fifth, you could try 306, but then you are
half-way to 612. I'd say 270 looks like his best bet overall, but he's
rejected the whole approach as excessively complicated.

Goodness, no! 270tET notation is all wrong. I need the sharps and flats reversed as in the meantone notation of 43tET, with the Rast scale composed of:

1/1 9/8 5/4 4/3 3/2 27/16 15/8 2/1

where the 6th degree=huseyni may be 5/3 at times.

All these pitches MUST be naturally indicated on the staff, because Rast is the mother of all maqams.

Furthermore, I require that the 3rd and 7th degrees be flattened a notch (possibly with the already known - but semiologically revised - quarter-tone accidentals) whenever needed. (I hope George understands why I cannot sacrifice current understanding in favor of a rock-hard symbology)

In 270tET, the pitches of the C major scale are closer to Suz-i Dilara, or the Pythagorean major scale:

1/1 9/8 81/64 4/3 3/2 27/16 243/128 2/1

whose third and seventh degrees should be expressed for the Neys with diamand noteheads to indicate the half-open blowing of the fourth degree=Chargah. For other instruments, I do not even wish to consider adding any accidental before the notes.

The difference then is a slight change within the range of a quarter-tone, being the change of perdes from Segah (3rd) to Buselik, and from Evdj (7th) to Mahur.

Thusly:

1. The system must have ALL diatonic major scales fixed at default Rast intervals, expressed solely by standart Western accidentals through all tones.

2. The fifths of the scale must be so narrowed as to result in a notation akin to 43tET.

3. The system must be sufficiently expressed using ONLY the quarter-tone accidentals whose meanings may be re-specified accordingly. That is to ensure transition from the old concept to the new.

Cordially,
Ozan
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 10:22
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> hi Gene and Ozan,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > If you need both meantone and Pythagorean fifths in
> > a single equal temperament, and if 12-et won't do, you
> > have to go with something like 270, because you must
> > have two different fifths.
>
>
> By my calculations, 92-edo is the first cardinality which
> gives you two different 5ths, one resembling the pythagorean
> 3/2 ratio and the other a ~1/3-comma meantone 5th.

But it won't do for his purposes. The first et which bas a fifth
flatter than its best fifth lying between 25/43 and 32/55 is 184, but
270 has a more accurate fifth and does all those other things besides.
To get a reall good fifth, you could try 306, but then you are
half-way to 612. I'd say 270 looks like his best bet overall, but he's
rejected the whole approach as excessively complicated.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Goodness, no! 270tET notation is all wrong. I need the sharps and
flats reversed as in the meantone notation of 43tET, with the Rast
scale composed of:
>
> 1/1 9/8 5/4 4/3 3/2 27/16 15/8 2/1
>
> where the 6th degree=huseyni may be 5/3 at times.

If you take 157 steps out of 270, you get something very close to
25/43--only 1/10 of a cent sharper, which isn't really audible. So
there is no question 270 can handle the meantone aspect. However, you
say sometimes you want a 27/16, and sometimes you want a 5/3, which
means you are not *in* a meantone system and the whole meantone thing
may be a complete red herring. This is a difference of a comma, and
meantone simply erases it. It does not and cannot distinguish between
rast and huseyni as you have defined them; however 53 *can*.

> All these pitches MUST be naturally indicated on the staff, because
Rast is the mother of all maqams.

53 is a combination of schismatic and kleismic tempering, and the
schismatic part means that notating on a staff is very natural for it.
However, you get a Pythagorean sound, unless you use Fb in place of E,
etc. The flat is *lower* than the sharp; this is *not* a meantone
system but it is not clear at this point you want one.

> Furthermore, I require that the 3rd and 7th degrees be flattened a
notch (possibly with the already known - but semiologically revised -
quarter-tone accidentals) whenever needed.

If you know how large a "notch" is, the step size of your equal
division must be at least a "notch". If a notch is about a comma, then
certainly 55 can flatten its version of 27/16 by a comma. However, if
it does that you don't get its version of 5/3, or anything very close.
You get the 55-et version of 3375/2048 instead, if we stick to the
5-limit. This is the 55 version of 128/125 lower than 27/16, or
equivalently the 55 version of 2048/2025 lower than 5/3; this all gets
identified in 55 or any meantone system, because (128/125)/(2048/2025)
= 81/80, and (27/16)/(5/3) = 81/80. Meantone is incapable of making
these distinctions, but shismatic can.

(I hope George understands why I cannot sacrifice current
understanding in favor of a rock-hard symbology)
>
> In 270tET, the pitches of the C major scale are closer to Suz-i
Dilara, or the Pythagorean major scale:
>
> 1/1 9/8 81/64 4/3 3/2 27/16 243/128 2/1

That's assuming you use 158 steps for a fifth, not 157. If you use 157
you definately get the diatonic major scale, which is rast if I
understand this business right. You *cannot* get both the diatonic
major and the Pythagorean scales without going to soemthing like 270.
If you want an equal temperament which supports both, 270 does. If you
want something smaller which still does, it now depends on how flat
you will allow your meantone fifth to be, and how sharp your
Pythagorean fifth. How flat can the fifth of rast be allowed to be?

> 1. The system must have ALL diatonic major scales fixed at default
Rast intervals, expressed solely by standart Western accidentals
through all tones.

What's a default rast interval?

> 2. The fifths of the scale must be so narrowed as to result in a
notation akin to 43tET.

270 certainly does that; it is *very* close to 43.

> 3. The system must be sufficiently expressed using ONLY the
quarter-tone accidentals whose meanings may be re-specified
accordingly. That is to ensure transition from the old concept to the new.

270 can be expressed in staff notation without quatertones, though it
would be a huge mess. Hence, it certainly can be expressed *with*
quartertones. 11 steps of 270 gives a 48.889 cent quarter tone, its
version of 36/35, which is 48.770 cents. This is often a good size of
quartertone to use if you are thinking in septimal and not just
5-limit terms.

In any case, given your requirements it seems you *must*, whether you
like it or not, use some system like 270, in which case why not 270
itself?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Hi again dear George, I'm glad you noticed my having mentioned you.

I only have time now to look over the subject lines and to search for
my own name in recent messages -- which is how I found yours.

> Yes, you are right in every aspect about the notation issue, but
you realize, don't you, that my main concern is divorcing the
meanings attributed to certain symbols at will for convenient
purposes whenever such will do the job. However, it is indeed
outrageous for me to do so as you say.

Perhaps it was a bit harsh of me to use the word "outrageous". I've
been going with too little sleep lately, and I had only a few minutes
before leaving when I posted that message and didn't even take time
to think of putting a "winkie" ;-) after that statement -- until
after I had sent the message and gone out the door. (Haste and
fatigue are not conducive to civility.)

Anyway, I've taken a few minutes to think over what you've said in
your response, and I've concluded that perhaps it would not be
necessary to abandon a correct notational syntax in order to achieve
your objectives.

> Thus, perhaps you can help me. My main concern is achieving a
meantone notation (sharps & flats reversed, E closer to 5/4)

By "sharps and flats reversed," I assume that you mean that
neighboring pairs of sharps and flats, such as F# and Gb, will have
the sharped nominal lower in pitch than the flatted one -- the
reverse of a Pythagorean sequence.

> of sufficient tone resolution while being able to transpose this
system equally everywhere.

If you mean "sufficient resolution" of pitch for Maquam music, then I
would say that 43 is probably your best choice, since it's comparable
to 41. You would be a better judge about whether that amount of
resolution is sufficient.

> ...
> If I do so, however, and choose any one of 41, 53 or 65 ETs with a
near-pure fifth, I must use your 5-comma flat for the 3rd and 7th
degrees, and for the 6th degree when the occasion demands it.
HOWEVER, I must avoid this at all costs. Rast scale for all
instruments must be notated as I delineated above.

You said that you wished to use the Tartini accidentals. A
symantically proper way to employ the Tartini "semisharp" symbol
would be as the 11M diesis (medium-size 11 diesis, 32:33, ~53 cents)
for 2 degrees of 43, which (at ~55 cents) is in very good agreement
for melodic purposes. The single-degree symbol of 43 would then be
the 11L diesis (apotome-minus-11M), which does not have a counterpart
in the Tartini scheme of things, unless you were to combine a sharp
with a backwards ("semi-") flat -- but I believe you would more
likely want a single symbol instead.

It would be reasonable to have the 11M and 11L symbols similar in
physical size (as they are in Sagittal), because their rational sizes
are not very different (53 vs. 60 cents). Several months ago I took
the time to experiment with some symbols (both upward and downward)
for 11L that could have been used to expand the 41-tone Tartini-plus
symbols that we were working on for use in 53-ET. They're similar in
appearance to the 11L Sagittal symbols, but in a style closer to the
Tartini set. If you're interested in seeing them, I could make a
figure showing a proposed 43-tone symbol sequence.

Best,

--George

Ah, that was the pure version. Here is the optimized version:

0: 0.000 cents 0.000 0 0 commas C
46: 695.955 cents -6.000 -184 G
13: 700.728 cents -7.227 -222 D
59: 695.955 cents -13.227 -406 A
26: 700.728 cents -14.454 -444 E
72: 695.955 cents -20.454 -628 B
39: 700.728 cents -21.681 -665 F#
6: 700.728 cents -22.908 -703 C#
52: 695.955 cents -28.908 -887 G#
19: 700.728 cents -30.135 -925 D#
65: 695.955 cents -36.135 -1109 A#
32: 700.728 cents -37.362 -1147 E#
78: 695.955 cents -43.362 -1331 B#
45: 700.728 cents -44.589 -1368 G\
12: 700.728 cents -45.817 -1406 -49/23 synt. commas D\
58: 695.955 cents -51.817 -1590 A\
25: 700.728 cents -53.044 -1628 E\
71: 695.955 cents -59.044 -1812 B\
38: 700.728 cents -60.271 -1850 F#\
5: 700.728 cents -61.498 -1887 C#\
51: 695.955 cents -67.498 -2072 G#\
18: 700.728 cents -68.725 -2109 D#\
64: 695.955 cents -74.725 -2293 A#\
31: 700.728 cents -75.952 -2331 F\\
77: 695.955 cents -81.952 -2515 C\\
44: 700.728 cents -83.179 -2553 G\\
11: 700.728 cents -84.406 -2590 D\\
57: 695.955 cents -90.406 -2775 A\\
24: 700.728 cents -91.633 -2812 E\\
70: 695.955 cents -97.633 -2996 B\\
37: 700.728 cents -98.860 -3034 F)
4: 700.728 cents -100.087 -3072 C)
50: 695.955 cents -106.087 -3256 G)
17: 700.728 cents -107.314 -3294 D)
63: 695.955 cents -113.314 -3478 A)
30: 700.728 cents -114.541 -3515 -83/17 Pyth. commas Fv
76: 695.955 cents -120.541 -3699 Cv
43: 700.728 cents -121.768 -3737 -109/21 Pyth. commas Gv
10: 700.728 cents -122.995 -3775 Dv
56: 695.955 cents -128.995 -3959 Av
23: 700.728 cents -130.223 -3997 Ev
69: 695.955 cents -136.223 -4181 Bv
36: 700.728 cents -137.450 -4218 F^
3: 700.728 cents -138.677 -4256 C^
49: 695.955 cents -144.677 -4440 G^
16: 700.728 cents -145.904 -4478 D^
62: 695.955 cents -151.904 -4662 A^
29: 700.728 cents -153.131 -4700 F(
75: 695.955 cents -159.131 -4884 C(
42: 700.728 cents -160.358 -4921 G(
9: 700.728 cents -161.585 -4959 D(
55: 695.955 cents -167.585 -5143 A(
22: 700.728 cents -168.812 -5181 E(
68: 695.955 cents -174.812 -5365 B(
35: 700.728 cents -176.039 -5403 F//
2: 700.728 cents -177.266 -5440 C//
48: 695.955 cents -183.266 -5625 G//
15: 700.728 cents -184.493 -5662 D//
61: 695.955 cents -190.493 -5846 A//
28: 700.728 cents -191.720 -5884 E//
74: 695.955 cents -197.720 -6068 B//
41: 700.728 cents -198.947 -6106 Gb/
8: 700.728 cents -200.174 -6143 -121/13 synt. commas Db/
54: 695.955 cents -206.174 -6328 Ab/
21: 700.728 cents -207.401 -6365 Eb/
67: 695.955 cents -213.401 -6549 Bb/
34: 700.728 cents -214.629 -6587 F/
1: 700.728 cents -215.856 -6625 C/
47: 695.955 cents -221.856 -6809 -196/19 synt. commas G/
14: 700.728 cents -223.083 -6847 D/
60: 695.955 cents -229.083 -7031 A/
27: 700.728 cents -230.310 -7068 Fb
73: 695.955 cents -236.310 -7252 Cb
40: 700.728 cents -237.537 -7290 Gb
7: 700.728 cents -238.764 -7328 Db
53: 695.955 cents -244.764 -7512 Ab
20: 700.728 cents -245.991 -7550 Eb
66: 695.955 cents -251.991 -7734 Bb
33: 700.728 cents -253.218 -7771 F
79: 700.728 cents -254.445 -7809 C
Average absolute difference: 131.1892 cents
Root mean square difference: 151.2604 cents
Maximum absolute difference: 254.4451 cents
Maximum formal fifth difference: 6.0000 cents

Now what is the EDO cardinality that this gamut is a sub-set of?

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 22:34
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Goodness, no! 270tET notation is all wrong. I need the sharps and
flats reversed as in the meantone notation of 43tET, with the Rast
scale composed of:
>
> 1/1 9/8 5/4 4/3 3/2 27/16 15/8 2/1
>
> where the 6th degree=huseyni may be 5/3 at times.

If you take 157 steps out of 270, you get something very close to
25/43--only 1/10 of a cent sharper, which isn't really audible. So
there is no question 270 can handle the meantone aspect. However, you
say sometimes you want a 27/16, and sometimes you want a 5/3, which
means you are not *in* a meantone system and the whole meantone thing
may be a complete red herring. This is a difference of a comma, and
meantone simply erases it. It does not and cannot distinguish between
rast and huseyni as you have defined them; however 53 *can*.

Yuck! I don't want 53. It's completely against Maqam Music intervals and notation. The misconception is based on thinking in terms of pure fifths. However, that gives us a Pythagorean notation where the apotome sharp ascends the apotome flat. That cannot be the case in Maqam Music. That Arel-Ezgi distorted the correct symbology to cram everything inside awkwardly is proof enough that this system cannot be a basis for expressing Maqams.

I know that meantone merges 5-limit JI with pythagorean. But still, the system I propose embodies both of these in a sense, where one can re-specify 3-limit JI through adjacent tones.

> All these pitches MUST be naturally indicated on the staff, because
Rast is the mother of all maqams.

53 is a combination of schismatic and kleismic tempering, and the
schismatic part means that notating on a staff is very natural for it.
However, you get a Pythagorean sound, unless you use Fb in place of E,
etc. The flat is *lower* than the sharp; this is *not* a meantone
system but it is not clear at this point you want one.

No no no! Impossible. I want a meantone notation with 5-limit JI sounds for the natural keys approximated very closely by meantone pitches. I believe, the 79-tone system I proposed is good enough for it where I also get special tone colors. Should I call it a well-temperament then?

> Furthermore, I require that the 3rd and 7th degrees be flattened a
notch (possibly with the already known - but semiologically revised -
quarter-tone accidentals) whenever needed.

If you know how large a "notch" is, the step size of your equal
division must be at least a "notch". If a notch is about a comma, then
certainly 55 can flatten its version of 27/16 by a comma. However, if
it does that you don't get its version of 5/3, or anything very close.
You get the 55-et version of 3375/2048 instead, if we stick to the
5-limit. This is the 55 version of 128/125 lower than 27/16, or
equivalently the 55 version of 2048/2025 lower than 5/3; this all gets
identified in 55 or any meantone system, because (128/125)/(2048/2025)
= 81/80, and (27/16)/(5/3) = 81/80. Meantone is incapable of making
these distinctions, but shismatic can.

Precisely. The notch must be half a comma at most. 79 is the lowest cardinality whose ET gives me meantone notation with ALMOST correct pitches, which I tweaked a little in order to achieve a super-pythagorean version of Suz-i Dilara. I am aware that 5/3 and 27/16 are compacted into one pitch, but still, alternate ratios can come to the rescue as you very well demonstrated. All in all, the theory and practice will not be an exact match, but a fine-granularity approximation at best.

(I hope George understands why I cannot sacrifice current
understanding in favor of a rock-hard symbology)
>
> In 270tET, the pitches of the C major scale are closer to Suz-i
Dilara, or the Pythagorean major scale:
>
> 1/1 9/8 81/64 4/3 3/2 27/16 243/128 2/1

That's assuming you use 158 steps for a fifth, not 157. If you use 157
you definately get the diatonic major scale, which is rast if I
understand this business right. You *cannot* get both the diatonic
major and the Pythagorean scales without going to soemthing like 270.

How about Zarlino major and super-Pythagorean major together then? You must understand that no one can handle 270 mandals per octave! That number has to be doubled due to the diatonical ascent of the gamut of the Qanun. 79 is indeed pushing the barrier to its limit.

If you want an equal temperament which supports both, 270 does. If you
want something smaller which still does, it now depends on how flat
you will allow your meantone fifth to be, and how sharp your
Pythagorean fifth. How flat can the fifth of rast be allowed to be?

No less than 697 cents. Preferably somewhere around 698.

> 1. The system must have ALL diatonic major scales fixed at default
Rast intervals, expressed solely by standart Western accidentals
through all tones.

What's a default rast interval?

The default Zarlino diatonical gamut intervals that I gave previously.

> 2. The fifths of the scale must be so narrowed as to result in a
notation akin to 43tET.

270 certainly does that; it is *very* close to 43.

Not to mention extremely crowded. I do not need to modulate everywhere, just the 30 keys common to Western Music practice.

> 3. The system must be sufficiently expressed using ONLY the
quarter-tone accidentals whose meanings may be re-specified
accordingly. That is to ensure transition from the old concept to the new.

270 can be expressed in staff notation without quatertones, though it
would be a huge mess. Hence, it certainly can be expressed *with*
quartertones. 11 steps of 270 gives a 48.889 cent quarter tone, its
version of 36/35, which is 48.770 cents. This is often a good size of
quartertone to use if you are thinking in septimal and not just
5-limit terms.

For gosh sakes, 270 is gargantuan, nobody can play it with the Qanun. Forget it will you?

In any case, given your requirements it seems you *must*, whether you
like it or not, use some system like 270, in which case why not 270
itself?

For practical reasons, is it not obvious?

Cordially,
Ozan

----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 22:47
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Hi again dear George, I'm glad you noticed my having mentioned you.

I only have time now to look over the subject lines and to search for
my own name in recent messages -- which is how I found yours.

> Yes, you are right in every aspect about the notation issue, but
you realize, don't you, that my main concern is divorcing the
meanings attributed to certain symbols at will for convenient
purposes whenever such will do the job. However, it is indeed
outrageous for me to do so as you say.

Perhaps it was a bit harsh of me to use the word "outrageous". I've
been going with too little sleep lately, and I had only a few minutes
before leaving when I posted that message and didn't even take time
to think of putting a "winkie" ;-) after that statement -- until
after I had sent the message and gone out the door. (Haste and
fatigue are not conducive to civility.)

Understandably so dear George, it's quite alright.

Anyway, I've taken a few minutes to think over what you've said in
your response, and I've concluded that perhaps it would not be
necessary to abandon a correct notational syntax in order to achieve
your objectives.

If indeed our joint collaboration produces dazzling results, who would be happier than myself?

> Thus, perhaps you can help me. My main concern is achieving a
meantone notation (sharps & flats reversed, E closer to 5/4)

By "sharps and flats reversed," I assume that you mean that
neighboring pairs of sharps and flats, such as F# and Gb, will have
the sharped nominal lower in pitch than the flatted one -- the
reverse of a Pythagorean sequence.

Exactly.

> of sufficient tone resolution while being able to transpose this
system equally everywhere.

If you mean "sufficient resolution" of pitch for Maquam music, then I
would say that 43 is probably your best choice, since it's comparable
to 41. You would be a better judge about whether that amount of
resolution is sufficient.

But dear George, the issue is not a crude approximation when it comes to affixing the mandals of a Qanun. I assure you, 43tET cannot hope to suffice any more than 41. 55 or 67 don't cut it either. I had to go all the way up to 79, and even then, I have to be content with a wolf of 711 cents, which I am hoping to conceal with timbral articulations. Do you think it feasible to sound a super-pythagorean C major within this modified 79tET that I've been proposing?

> ...
> If I do so, however, and choose any one of 41, 53 or 65 ETs with a
near-pure fifth, I must use your 5-comma flat for the 3rd and 7th
degrees, and for the 6th degree when the occasion demands it.
HOWEVER, I must avoid this at all costs. Rast scale for all
instruments must be notated as I delineated above.

You said that you wished to use the Tartini accidentals. A
symantically proper way to employ the Tartini "semisharp" symbol
would be as the 11M diesis (medium-size 11 diesis, 32:33, ~53 cents)
for 2 degrees of 43, which (at ~55 cents) is in very good agreement
for melodic purposes. The single-degree symbol of 43 would then be
the 11L diesis (apotome-minus-11M), which does not have a counterpart
in the Tartini scheme of things, unless you were to combine a sharp
with a backwards ("semi-") flat -- but I believe you would more
likely want a single symbol instead.

Certainly! I do not dispute for a moment that your semiology is perfectly well thought of. However, you must understand that Maqam Music has been expressed for centuries through only 17 perdes which stood for at least half a dozen ratios each.

It would be reasonable to have the 11M and 11L symbols similar in
physical size (as they are in Sagittal), because their rational sizes
are not very different (53 vs. 60 cents). Several months ago I took
the time to experiment with some symbols (both upward and downward)
for 11L that could have been used to expand the 41-tone Tartini-plus
symbols that we were working on for use in 53-ET. They're similar in
appearance to the 11L Sagittal symbols, but in a style closer to the
Tartini set. If you're interested in seeing them, I could make a
figure showing a proposed 43-tone symbol sequence.

Do please show them to me.

Best,

--George

Cordially,
Ozan

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> 53 is a combination of schismatic and kleismic tempering,
> and the schismatic part means that notating on a staff is
> very natural for it.

Can you explain why that is so?

-monz

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Ah, that was the pure version. Here is the optimized version:

Optimized how? What is the target for your optimization?

> No no no! Impossible. I want a meantone notation with 5-limit JI
sounds for the natural keys approximated very closely by meantone
pitches. I believe, the 79-tone system I proposed is good enough for
it where I also get special tone colors. Should I call it a
well-temperament then?

> For gosh sakes, 270 is gargantuan, nobody can play it with the
Qanun. Forget it will you?

Yet you in effect introduced 159 in an effort to notate maqams. I
don't see what playing it with the Qanun has to do with anything if
you are using it to define scales with, and given the nature of the
problem as you've described it, you are stuck with triple digits if
you want an et.

> For practical reasons, is it not obvious?

Nope. I don't see any problem; no one is suggesting someone needs to
build an instrument with 270 notes to the octave--or 159 for that
matter. If you require two sizes of fifths and an equal temperament,
the problem one which requires this kind of solution, especially if
flat fifths such as 1/3 comma are not going to do for you.

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> hi Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
>
> > 53 is a combination of schismatic and kleismic tempering,
> > and the schismatic part means that notating on a staff is
> > very natural for it.
>
>
> Can you explain why that is so?

Because schismatic tenpering uses the fifth as a generator.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 7:04
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Ah, that was the pure version. Here is the optimized version:

Optimized how? What is the target for your optimization?

In the latest 79 MOS from 159tET example I gave, in your terms, I have made sure that the meantone fifth was equally away from pure as the super-pythagorean.

> No no no! Impossible. I want a meantone notation with 5-limit JI
sounds for the natural keys approximated very closely by meantone
pitches. I believe, the 79-tone system I proposed is good enough for
it where I also get special tone colors. Should I call it a
well-temperament then?

> For gosh sakes, 270 is gargantuan, nobody can play it with the
Qanun. Forget it will you?

Yet you in effect introduced 159 in an effort to notate maqams. I
don't see what playing it with the Qanun has to do with anything if
you are using it to define scales with, and given the nature of the
problem as you've described it, you are stuck with triple digits if
you want an et.

159 is for me then, no one in their right of mind will incline to accept it around these parts. But maybe they will lend an ear if I demonstrate them this 79 MOS ouf of 159? Who knows...

> For practical reasons, is it not obvious?

Nope. I don't see any problem; no one is suggesting someone needs to
build an instrument with 270 notes to the octave--or 159 for that
matter. If you require two sizes of fifths and an equal temperament,
the problem one which requires this kind of solution, especially if
flat fifths such as 1/3 comma are not going to do for you.

Ah, I see where you are getting at. No, 270 is still gargantuan, 159 may work in its stead.

But I want to implement a solution where the 55tET conceptualization of 9 commas per whole tone take root within such huge systems. It appears several pitches must be assigned single comma numbers to do so. Any suggestions?

Cordially,
Ozan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> But I want to implement a solution where the 55tET conceptualization
of 9 commas per whole tone take root within such huge systems. It
appears several pitches must be assigned single comma numbers to do
so. Any suggestions?

159 has far too flat a fifth to act anything like 55; this was why I
was suggesting 270--it has a meantone fifth close to where you seemed
you wanted it to be. However, 3 steps of 159 is one step of 53, and
that is a compromise between the Pythagorean and Didymus commas. The
major whole tone of 53 has nine steps, ie nine commas. So in that
sense some of this comma stuff is in there.

By the way, now that you are looking at meantone fifths this flat,
another possibility is 140.

140 won't do at all. The distribution of two consecutive fifths are haphazard. 270 is not the one I'm looking for either. I will, with your consent, stick with the 79-note MOS out of 159tET.

But I'm not sure calling it so is just, because I have aimed to optimize the two types of fifths by pushing them equally away from 3/2 in either direction. That 159 represents it with an error of 0.2 cents is only a very good approximation in my opinion.

Another optimization is done by taking 78 commas 15.1 cents wide plus 1 comma 22.2 cents wide. This simplification is the one I am planning to implement, seeing as the instrument-makers will show me the way to the door the instant I give them the ultra-precision calculations. So, 0.44 cents deviation from 159tET is acceptable for you then?

I'm pleased that 159 is triple 53. That is all the more convincing. Thanks!
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 12:56
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> But I want to implement a solution where the 55tET conceptualization
of 9 commas per whole tone take root within such huge systems. It
appears several pitches must be assigned single comma numbers to do
so. Any suggestions?

159 has far too flat a fifth to act anything like 55; this was why I
was suggesting 270--it has a meantone fifth close to where you seemed
you wanted it to be. However, 3 steps of 159 is one step of 53, and
that is a compromise between the Pythagorean and Didymus commas. The
major whole tone of 53 has nine steps, ie nine commas. So in that
sense some of this comma stuff is in there.

By the way, now that you are looking at meantone fifths this flat,
another possibility is 140.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> 140 won't do at all. The distribution of two consecutive fifths are
haphazard. 270 is not the one I'm looking for either. I will, with
your consent, stick with the 79-note MOS out of 159tET.

If it works, stick with it, I guess. It has a fifth quite different
than the one you started out discussing--betwen 43 and 55--but it can
make both a meantone and a Pythagorean diatonic scale.

> But I'm not sure calling it so is just, because I have aimed to
optimize the two types of fifths by pushing them equally away from 3/2
in either direction. That 159 represents it with an error of 0.2 cents
is only a very good approximation in my opinion.

But one of the fifths you were "pushing away" was chosen by you as a
certain number of cents, so I don't see that this is really an
approximation to that fifth. How can you approximate an approximation?
The other fifth is an approximation to a just fifth, and 159 does
excellently there.

> Another optimization is done by taking 78 commas 15.1 cents wide
plus 1 comma 22.2 cents wide. This simplification is the one I am
planning to implement, seeing as the instrument-makers will show me
the way to the door the instant I give them the ultra-precision
calculations. So, 0.44 cents deviation from 159tET is acceptable for
you then?

I don't see why instrument makers would find it any easier to tune to
this than to tune to steps of 159 calculated individually. It seems to
me it simply confuses the issue to do this; you have a nice system for
representing maqam tunings, so why not simply use it?

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 20:31
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> 140 won't do at all. The distribution of two consecutive fifths are
haphazard. 270 is not the one I'm looking for either. I will, with
your consent, stick with the 79-note MOS out of 159tET.

If it works, stick with it, I guess. It has a fifth quite different
than the one you started out discussing--betwen 43 and 55--but it can
make both a meantone and a Pythagorean diatonic scale.

Exactly! That's the deal. Besides, a correct optimization gives three fifths, two of which are Baroque and Super-Pythagorean (spaced equally away from the untempered fifth) and the third represents extremly well the pure fifth.

> But I'm not sure calling it so is just, because I have aimed to
optimize the two types of fifths by pushing them equally away from 3/2
in either direction. That 159 represents it with an error of 0.2 cents
is only a very good approximation in my opinion.

But one of the fifths you were "pushing away" was chosen by you as a
certain number of cents, so I don't see that this is really an
approximation to that fifth. How can you approximate an approximation?
The other fifth is an approximation to a just fifth, and 159 does
excellently there.

The three usable fifths in the system are: 694.407 cents 701.838 cents and 709.503 cents respectively. The middle fifth occurs more often here and there, providing a convenient stepping stone for the transition between Baroque and Pythagorean.

> Another optimization is done by taking 78 commas 15.1 cents wide
plus 1 comma 22.2 cents wide. This simplification is the one I am
planning to implement, seeing as the instrument-makers will show me
the way to the door the instant I give them the ultra-precision
calculations. So, 0.44 cents deviation from 159tET is acceptable for
you then?

I don't see why instrument makers would find it any easier to tune to
this than to tune to steps of 159 calculated individually. It seems to
me it simply confuses the issue to do this; you have a nice system for
representing maqam tunings, so why not simply use it?

Why? 159 is much more difficult to measure... what with all the digits required for the sake of correctness. My proposal is feasible, requiring only 78 commas 15.1 cents wide, and one 22.2 cents wide. Surely you don't object to it. That 159 tones are nearly identical to the system I came up with is very good, and I have no qualms about having found a temperament that is a MOS out of 159tET.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> I don't see why instrument makers would find it any easier to tune to
> this than to tune to steps of 159 calculated individually. It seems to
> me it simply confuses the issue to do this; you have a nice system for
> representing maqam tunings, so why not simply use it?

> Why? 159 is much more difficult to measure... what with all the
digits required for the sake of correctness.

I still don't get why it is any more difficult to measure. What are
you measuring with?

>My proposal is feasible, requiring only 78 commas 15.1 cents wide,
and >one 22.2 cents wide. Surely you don't object to it.

I think it is needlessly complicated, and can't see why in practice it
would be any easier.

>That 159 tones are nearly identical to the system I came up with is
very good, and I have no qualms about having found a temperament that
is a MOS out of 159tET.

It's kind of neat.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 13 Haziran 2005 Pazartesi 13:27
Subject: [tuning] Re: Meantone Maquams

> Why? 159 is much more difficult to measure... what with all the
digits required for the sake of correctness.

I still don't get why it is any more difficult to measure. What are
you measuring with?

It is not I, but instrument builders who are stuck with tuning units based on cent indicators that cannot be more accurate than the first decimal place at most. Besides, mathematical perfection does not equate to actual pitch-precision. Doubly so with the Qanun latches (mandals).

>That 159 tones are nearly identical to the system I came up with is
very good, and I have no qualms about having found a temperament that
is a MOS out of 159tET.

It's kind of neat.

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

Thanks! So, can it be nominated as a candidate for uniting the sound-scape of East and West?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
>
> ----- Original Message -----
> From: George D. Secor
>
> If you mean "sufficient resolution" of pitch for Maquam music,
then I
> would say that 43 is probably your best choice, since it's
comparable
> to 41. You would be a better judge about whether that amount of
> resolution is sufficient.
>
> But dear George, the issue is not a crude approximation when it
comes to affixing the mandals of a Qanun. I assure you, 43tET cannot
hope to suffice any more than 41. 55 or 67 don't cut it either. I had
to go all the way up to 79, and even then, I have to be content with
a wolf of 711 cents, which I am hoping to conceal with timbral
articulations.

As I thought I understood it, 41 won't work for you now, only because
you want a division compatible with meantone. With 41 (or 53, for
that matter) you previously would have been able to define each
combination of nominal-with-accidental as a specific JI ratio, and
approximations would occur only in instances where one of those
combinations represented more than one ratio. With 43 you could
still represent ratios with nominal-accidental combinations (with
fewer accidentals than required for 41), but there would be places
where the notational fifth would be false by a 5-comma, which would
not be very bad if you didn't have free modulation as a requirement.
It appears to me that you're attempting an approach that, when
applied to just intonation, is similar to what Ben Johnston did, and
the majority opinion in this group is that such an approach is too
confusing when you're modulating from one key to another, because the
false fifths maintain their absolute locations, which causes them to
occur in various locations relative to the tonic note. If, on the
other hand, you're advocating some sort of flexible notation in which
the false fifths move along with the tonic note so as to maintain
their positions relative to the tonic, then the notation may tend to
be confusing in that notated intervals are not constant in size, but
change according to the key.

For 79 you speak of a "wolf of 711 cents". The wide fifth of 79 is
almost 714 cents. I don't understand your requirements well enough
to see why 79 appeals to you. While it is a sort of meantone tuning,
its best 4:5 is not arrived at by a chain of 4 fifths.

> Do you think it feasible to sound a super-pythagorean C major
within this modified 79tET that I've been proposing?

By this are you referring to a triad with ratios 1/1, 9/7, 3/2? The
79 division is not 7-limit consistent (as to 5 vs. 7) or 1,3,7,9-
consistent, for that matter. Unless this inconsistency is something
you've found a way to exploit for your particular purposes, I expect
that you'll be encountering problems with it.

> > ...
> > If I do so, however, and choose any one of 41, 53 or 65 ETs
with a
> near-pure fifth, I must use your 5-comma flat for the 3rd and 7th
> degrees, and for the 6th degree when the occasion demands it.
> HOWEVER, I must avoid this at all costs. Rast scale for all
> instruments must be notated as I delineated above.

The cleanest way to notate JI in which the 5-comma occurs is to use a
5-comma symbol; however you say that must avoid this.

You expressed an interest in 31-ET, and also in flexible intonation
and ratios of 7 (as I infer from your "superpythagorean" comment.
Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
consistent, and is also one of the very best meantones available,
would you be interested in some sort of adaptive JI based on 217-ET,
a multiple of 31? You could use the Tartini accidentals for all of
the pitches of 31 and perhaps supplement them with small arrows
placed (optionally) to the left to serve as a guide (e.g., as
something like diacritical marks for Maqam musicians in training) to
indicate the direction and amount that the pitch should be adjusted
(in increments of ~5.5 cents). You might need them only rarely if
most of the adjustments are only a single increment. All of the
pitches of 217-ET may be reached by adjusting the closest pitch of 31-
ET by no more than ~17 cents (3 increments), which is still less than
a 5-comma.

BTW, should you need some small arrows, there are already some
Sagittal symbols for 1, 2, and 3 increments of 217-ET that could be
used in combination with the Tartini accidentals for this purpose.
Should you be interested, you can see them in our Sagittal paper:
http://dkeenan.com/sagittal/Sagittal.pdf
on page 16, Figure 9: the first 3 symbols in the row for 217 show
upward-pointing arrows; the down-arrows would simply be (vertical)
mirror-images of these.

> ...
> It would be reasonable to have the 11M and 11L symbols similar in
> physical size (as they are in Sagittal), because their rational
sizes
> are not very different (53 vs. 60 cents). Several months ago I
took
> the time to experiment with some symbols (both upward and
downward)
> for 11L that could have been used to expand the 41-tone Tartini-
plus
> symbols that we were working on for use in 53-ET. They're
similar in
> appearance to the 11L Sagittal symbols, but in a style closer to
the
> Tartini set. If you're interested in seeing them, I could make a
> figure showing a proposed 43-tone symbol sequence.
>
> Do please show them to me.

Only if you promise not to use them (now that I've suggested 31). ;-)

See file Tplus-53.gif located here:
/tuning-math/files/secor/notation/
The 53-ET symbol set is there, and below it a subset of those, re-
ordered to notate 43-ET.

All the best,

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> For 79 you speak of a "wolf of 711 cents". The wide fifth of 79 is
> almost 714 cents. I don't understand your requirements well enough
> to see why 79 appeals to you. While it is a sort of meantone tuning,
> its best 4:5 is not arrived at by a chain of 4 fifths.

It's not 79, it's 159. 79 is a MOS.

> You expressed an interest in 31-ET, and also in flexible intonation
> and ratios of 7 (as I infer from your "superpythagorean" comment.
> Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
> consistent, and is also one of the very best meantones available,
> would you be interested in some sort of adaptive JI based on 217-ET,
> a multiple of 31?

That would work, but it's got more notes in it that 159. If you are
going to take a multiple of a meantone system, the claims of 152 and
171 should be considered, but Ozan seems to find more interest in
multiples of 53.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > For 79 you speak of a "wolf of 711 cents". The wide fifth of 79
is
> > almost 714 cents. I don't understand your requirements well
enough
> > to see why 79 appeals to you. While it is a sort of meantone
tuning,
> > its best 4:5 is not arrived at by a chain of 4 fifths.
>
> It's not 79, it's 159. 79 is a MOS.

If the generator is 92deg159, then your best 4:5 is -15 generators
along the chain, not +4. However, if you wanted to consider the
tones separated by 19 generators as simply subtle variations of the
same notated pitch, then a 19-ET notation (with no new microtonal
symbols) would suffice. (But I think Ozan needs more than 19
pitches/octave.)

> > You expressed an interest in 31-ET, and also in flexible
intonation
> > and ratios of 7 (as I infer from your "superpythagorean"
comment.
> > Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
> > consistent, and is also one of the very best meantones available,
> > would you be interested in some sort of adaptive JI based on 217-
ET,
> > a multiple of 31?
>
> That would work, but it's got more notes in it that 159.

It depends on how you look at it. I was thinking that this is really
only 31 pitches/octave, with subtle variations in intonation that
could be indicated with little arrows that would guide students to
the desired pitch, but which Maqam masters would be free to
disregard, at their own discretion. You would never even come close
to using all 217 pitches, because you would only be modulating around
a circle of 31 (meantone) fifths.

> If you are
> going to take a multiple of a meantone system, the claims of 152 and
> 171 should be considered,

Yes, and as I pointed out, I don't expect that 19 pitches +
flexibility will be enough. Hmmm, now that I've said that, what
about two circles of 19? 38-ET would use the same Tartini
accidentals as 31-ET. All of the pitches of 152-ET can be arrived at
by increments up to +-2deg152, and there would be only 5 different
choices of pitch adjustment: down-large, down-small, none, up-small,
and up-large. Sagittal also has two small arrows for those, the
first two in the 152 row of Figure 9 of the Sagittal paper: the
smaller )|( is symmetrical, the larger )|~ assymetrical. The
Sagittal paper:
http://dkeenan.com/sagittal/Sagittal.pdf
also contains a footnote (#16 on page 20) suggesting that instruments
in 19, 31, or 38-ET could easily be used for JI, so this idea has
been around for at least a few years.

> but Ozan seems to find more interest in
> multiples of 53.

Okay, hold on a minute -- there's a connection to be made.

I believe you asked how Dave and I would notate 159. Scala will show
you if you enter "set nota sa159".

The first 7 symbols in the set:
159: |( ~|( /| |) (|( //| /|\ (|) )||( ~||( ||) ||\ (||
( /||) /||\
represent the best approximations of 5:7k (5103:5120), 17C
(4096:4131), 5C (80:81), 7C (63:64), 5:11S (44:45), 25C (6400:6561),
and 11M (32:33), respectively. The remaining symbols are their
apotome-complements.

But those are alterations to a chain of nominals generated by the
best fifth of 159. I think Ozan may want a notation that uses
nominals generated by a 159-meantone fifth (one degree smaller),
which would be something quite different. Gene, have you considered
looking at this as a chain of semi-159-meantone-fifths (46deg159)?
That's similar enough to 38-as-subset-of-152-ET that a chain of 38
tones could be notated with the Tartini symbols and fine-tuned as
increments +-2deg159.

--George

Hi again George,
----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 13 Haziran 2005 Pazartesi 22:33
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
>
> ----- Original Message -----
> From: George D. Secor
>
> If you mean "sufficient resolution" of pitch for Maquam music,
then I
> would say that 43 is probably your best choice, since it's
comparable
> to 41. You would be a better judge about whether that amount of
> resolution is sufficient.
>
> But dear George, the issue is not a crude approximation when it
comes to affixing the mandals of a Qanun. I assure you, 43tET cannot
hope to suffice any more than 41. 55 or 67 don't cut it either. I had
to go all the way up to 79, and even then, I have to be content with
a wolf of 711 cents, which I am hoping to conceal with timbral
articulations.

As I thought I understood it, 41 won't work for you now, only because
you want a division compatible with meantone.

Not only meantone, but also pythagorean. Gene reminded me that 79tET had nothing to with what I came up with in the end. See, it was 79 MOS out of 159tET all along, with one comma the size of 15.1 cents (78 of them one after the other) and another the size of 22.2 cents in the end. This gave me a narrow perfect fifth 695 cents wide, a pure fifth 702 cents wide, and a wide fifth 710 cents wide. I can thus switch between meantone and pythagorean notations at will.

With 41 (or 53, for
that matter) you previously would have been able to define each
combination of nominal-with-accidental as a specific JI ratio,

And do something I abhor! That is the primary reason I cannot consign to 41 or 53 or 65, since I cannot express Zarlino's diatonical scale without accidentals in those systems. Obviously, I need a meantone notation for that.

and
approximations would occur only in instances where one of those
combinations represented more than one ratio.

Such as?

With 43 you could
still represent ratios with nominal-accidental combinations (with
fewer accidentals than required for 41), but there would be places
where the notational fifth would be false by a 5-comma, which would
not be very bad if you didn't have free modulation as a requirement.

That is not possible. I need the three kinds of fifths I mentioned.

It appears to me that you're attempting an approach that, when
applied to just intonation, is similar to what Ben Johnston did, and
the majority opinion in this group is that such an approach is too
confusing when you're modulating from one key to another, because the
false fifths maintain their absolute locations, which causes them to
occur in various locations relative to the tonic note.

I don't know about Mr. Johnston's approach, but I believe you are confusing 79 MOS with 79tET. It is my incapacity to define concepts that misled you, I apologize about that!

If, on the
other hand, you're advocating some sort of flexible notation in which
the false fifths move along with the tonic note so as to maintain
their positions relative to the tonic, then the notation may tend to
be confusing in that notated intervals are not constant in size, but
change according to the key.
That is so indeed. the 79 MOS with three usable perfect fifths results in a Well-Temperament that is both Meantone and Pythagorean at the same time.

For 79 you speak of a "wolf of 711 cents". The wide fifth of 79 is
almost 714 cents. I don't understand your requirements well enough
to see why 79 appeals to you. While it is a sort of meantone tuning,
its best 4:5 is not arrived at by a chain of 4 fifths.

I was still formulating an infant, see? The new correct values rounded off I have provided above. By choosing 695 as basis, I can construct the Zarlino's diatonical scale where E is close enough to 5/4 to suit my purposes.

> Do you think it feasible to sound a super-pythagorean C major
within this modified 79tET that I've been proposing?

By this are you referring to a triad with ratios 1/1, 9/7, 3/2? The
79 division is not 7-limit consistent (as to 5 vs. 7) or 1,3,7,9-
consistent, for that matter. Unless this inconsistency is something
you've found a way to exploit for your particular purposes, I expect
that you'll be encountering problems with it.

I hope you can make an equally thorough analysis for my `79 MOS out of 159tET`. I don't think it is problematic in any way, do you?

> > ...
> > If I do so, however, and choose any one of 41, 53 or 65 ETs
with a
> near-pure fifth, I must use your 5-comma flat for the 3rd and 7th
> degrees, and for the 6th degree when the occasion demands it.
> HOWEVER, I must avoid this at all costs. Rast scale for all
> instruments must be notated as I delineated above.

The cleanest way to notate JI in which the 5-comma occurs is to use a
5-comma symbol; however you say that must avoid this.

Unavoidably so.

You expressed an interest in 31-ET, and also in flexible intonation
and ratios of 7 (as I infer from your "superpythagorean" comment.
Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
consistent, and is also one of the very best meantones available,
would you be interested in some sort of adaptive JI based on 217-ET,
a multiple of 31?

Uh, I am not sure, but I can always tell a good marketing strategy when I see one!

You could use the Tartini accidentals for all of
the pitches of 31 and perhaps supplement them with small arrows
placed (optionally) to the left to serve as a guide (e.g., as
something like diacritical marks for Maqam musicians in training) to
indicate the direction and amount that the pitch should be adjusted
(in increments of ~5.5 cents). You might need them only rarely if
most of the adjustments are only a single increment. All of the
pitches of 217-ET may be reached by adjusting the closest pitch of 31-
ET by no more than ~17 cents (3 increments), which is still less than
a 5-comma.

It certainly deserves attention, but is not 79 MOS out of 159tET a better, simpler alternative that encompasses both meantone and pythagorean notations so as to express both Rast and Suz-i Dilara as C natural gamme on the staff?

BTW, should you need some small arrows, there are already some
Sagittal symbols for 1, 2, and 3 increments of 217-ET that could be
used in combination with the Tartini accidentals for this purpose.
Should you be interested, you can see them in our Sagittal paper:
http://dkeenan.com/sagittal/Sagittal.pdf
on page 16, Figure 9: the first 3 symbols in the row for 217 show
upward-pointing arrows; the down-arrows would simply be (vertical)
mirror-images of these.

I was more inclined to expressing each pack of tones within a certain region by a single accidental alone, whose meaning would depend on the flow of the maqam that I would painstakingly explain in minute detail.

> ...
> It would be reasonable to have the 11M and 11L symbols similar in
> physical size (as they are in Sagittal), because their rational
sizes
> are not very different (53 vs. 60 cents). Several months ago I
took
> the time to experiment with some symbols (both upward and
downward)
> for 11L that could have been used to expand the 41-tone Tartini-
plus
> symbols that we were working on for use in 53-ET. They're
similar in
> appearance to the 11L Sagittal symbols, but in a style closer to
the
> Tartini set. If you're interested in seeing them, I could make a
> figure showing a proposed 43-tone symbol sequence.
>
> Do please show them to me.

Only if you promise not to use them (now that I've suggested 31). ;-)

Uh, are they poisonous? Will they cause indigestion once consumed? Haha, that was a good one.

See file Tplus-53.gif located here:
/tuning-math/files/secor/notation/
The 53-ET symbol set is there, and below it a subset of those, re-
ordered to notate 43-ET.

All the best,

--George

Ah, they are indeed very lovely. But you won't let me use them I suppose. 9-) So, will you help me notate this 79 MOS using only your wonderous quarter-tone accidentals?

Cordially,
Ozan

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> If the generator is 92deg159, then your best 4:5 is -15 generators
> along the chain, not +4. However, if you wanted to consider the
> tones separated by 19 generators as simply subtle variations of the
> same notated pitch, then a 19-ET notation (with no new microtonal
> symbols) would suffice. (But I think Ozan needs more than 19
> pitches/octave.)

The whole generator question is murky. The MOS in question has a
generator of 2deg159, but he wants to use it for both 92deg159 and
93deg159 as nearly as I can tell. How that works is unclear.

> > If you are
> > going to take a multiple of a meantone system, the claims of 152 and
> > 171 should be considered,
>
> Yes, and as I pointed out, I don't expect that 19 pitches +
> flexibility will be enough. Hmmm, now that I've said that, what
> about two circles of 19? 38-ET would use the same Tartini
> accidentals as 31-ET. All of the pitches of 152-ET can be arrived at
> by increments up to +-2deg152, and there would be only 5 different
> choices of pitch adjustment: down-large, down-small, none, up-small,
> and up-large.

That makes sense, but this whole question is hard to work on without a
better idea of what the target actually is. What would a list of
ideally tuned maqams be? If we had that, we could began to optimize.

> But those are alterations to a chain of nominals generated by the
> best fifth of 159. I think Ozan may want a notation that uses
> nominals generated by a 159-meantone fifth (one degree smaller),
> which would be something quite different. Gene, have you considered
> looking at this as a chain of semi-159-meantone-fifths (46deg159)?

Hey, we induct injera, godzilla/semaphore or semififhts into the maqam
business! No, I didn't consider it; I'm not clear on what the target
really is.

Here are some hints then. This is Rast:

F-(702)-C-(695)-G-(702)-D-(695)-A-(702)-E-(695)-B

An altered Rast would be:

Bb-(702)-F-(702)-C-(695)-G-(702)-D-(710)-A-(702)-E

This is Suz-i Dilara:

F-(702)-C-(710)-G-(702)-D-(710)-A-(702)-E-(710)-B

An altered Suz-i Dilara would be:

F-(702)-C-(710)-G-(702)-D-(695)-A-(702)-E-(710)-B

Ok, enough hints for now!

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 14 Haziran 2005 Salı 7:49
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> If the generator is 92deg159, then your best 4:5 is -15 generators
> along the chain, not +4. However, if you wanted to consider the
> tones separated by 19 generators as simply subtle variations of the
> same notated pitch, then a 19-ET notation (with no new microtonal
> symbols) would suffice. (But I think Ozan needs more than 19
> pitches/octave.)

The whole generator question is murky. The MOS in question has a
generator of 2deg159, but he wants to use it for both 92deg159 and
93deg159 as nearly as I can tell. How that works is unclear.

> > If you are
> > going to take a multiple of a meantone system, the claims of 152 and
> > 171 should be considered,
>
> Yes, and as I pointed out, I don't expect that 19 pitches +
> flexibility will be enough. Hmmm, now that I've said that, what
> about two circles of 19? 38-ET would use the same Tartini
> accidentals as 31-ET. All of the pitches of 152-ET can be arrived at
> by increments up to +-2deg152, and there would be only 5 different
> choices of pitch adjustment: down-large, down-small, none, up-small,
> and up-large.

That makes sense, but this whole question is hard to work on without a
better idea of what the target actually is. What would a list of
ideally tuned maqams be? If we had that, we could began to optimize.

> But those are alterations to a chain of nominals generated by the
> best fifth of 159. I think Ozan may want a notation that uses
> nominals generated by a 159-meantone fifth (one degree smaller),
> which would be something quite different. Gene, have you considered
> looking at this as a chain of semi-159-meantone-fifths (46deg159)?

Hey, we induct injera, godzilla/semaphore or semififhts into the maqam
business! No, I didn't consider it; I'm not clear on what the target
really is.

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--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Hi again George,
> ----- Original Message -----
> From: George D. Secor
> To: tuning@yahoogroups.com
> Sent: 13 Haziran 2005 Pazartesi 22:33
> Subject: [tuning] Re: Meantone Maquams
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
> >
> > ----- Original Message -----
> > From: George D. Secor
>
> As I thought I understood it, 41 won't work for you now, only
because
> you want a division compatible with meantone.
>
> Not only meantone, but also pythagorean. Gene reminded me that
79tET had nothing to with what I came up with in the end. See, it was
79 MOS out of 159tET all along, with one comma the size of 15.1 cents
(78 of them one after the other) and another the size of 22.2 cents
in the end. This gave me a narrow perfect fifth 695 cents wide, a
pure fifth 702 cents wide, and a wide fifth 710 cents wide. I can
thus switch between meantone and pythagorean notations at will.

So you're actually going to be switching back and forth between
different notations for a single tuning that approximates all of the
ratios you require. Fascinating! (I hope it will work the way you
expect.)

> ...
> [GS:]
> With 41 (or 53, for
> that matter) you previously would have been able to define each
> combination of nominal-with-accidental as a specific JI ratio,
>
> [OY:]
> And do something I abhor! That is the primary reason I cannot
consign to 41 or 53 or 65, since I cannot express Zarlino's
diatonical scale without accidentals in those systems. Obviously, I
need a meantone notation for that.
>
> [GS:]
> and
> approximations would occur only in instances where one of those
> combinations represented more than one ratio.
>
> [OY:]
> Such as?

11/10 and 10/9 are both 6 degrees of 41, or 12/11 and 11/10 are both
7 degrees of 53.

> [OY:]
> ... the 79 MOS with three usable perfect fifths results in a Well-
Temperament that is both Meantone and Pythagorean at the same time.

I don't understand exactly how you would use it that way, but, yes,
you could have a circle of (varied-)fifths.

> [OY:]
> > Do you think it feasible to sound a super-pythagorean C major
> within this modified 79tET that I've been proposing?
>
> By this are you referring to a triad with ratios 1/1, 9/7, 3/2?
The
> 79 division is not 7-limit consistent (as to 5 vs. 7) or 1,3,7,9-
> consistent, for that matter. Unless this inconsistency is
something
> you've found a way to exploit for your particular purposes, I
expect
> that you'll be encountering problems with it.
>
> I hope you can make an equally thorough analysis for my `79 MOS
out of 159tET`. I don't think it is problematic in any way, do you?

159-ET is 17-limit consistent, so you can disregard what I said about
the 79 division. I don't know enough about the maqamat and how
you're relating them to your MOS scale to be able to say any more
than that.

> ...
> [GS:]
> You expressed an interest in 31-ET, and also in flexible
intonation
> and ratios of 7 (as I infer from your "superpythagorean"
comment.
> Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
> consistent, and is also one of the very best meantones available,
> would you be interested in some sort of adaptive JI based on 217-
ET,
> a multiple of 31?
>
> [OY:]
> Uh, I am not sure, but I can always tell a good marketing
strategy when I see one!

I was just looking at the bits and pieces of phrases about which you
expressed interest -- meantone, superpythagorean (good 7th harmonic),
flexible intonation, Tartini accidentals -- and came up something
that manages to tie all of these together, with varying success.
This was just to bring up another idea that you might consider. My
thoughts about this came together before I had read and digested your
latest (about the 79-MOS), so I'm having to volley them back at a
moving target. :-)

> [GS:]
> You could use the Tartini accidentals for all of
> the pitches of 31 and perhaps supplement them with small arrows
> placed (optionally) to the left to serve as a guide (e.g., as
> something like diacritical marks for Maqam musicians in training)
to
> indicate the direction and amount that the pitch should be
adjusted
> (in increments of ~5.5 cents). You might need them only rarely
if
> most of the adjustments are only a single increment. All of the
> pitches of 217-ET may be reached by adjusting the closest pitch
of 31-
> ET by no more than ~17 cents (3 increments), which is still less
than
> a 5-comma.
>
> [OY:]
> It certainly deserves attention, but is not 79 MOS out of 159tET
a better, simpler alternative that encompasses both meantone and
pythagorean notations so as to express both Rast and Suz-i Dilara as
C natural gamme on the staff?

I don't know, because I haven't taken a close look at that MOS and
don't know enough about the maqamat to make any judgment about its
suitability. (At the moment there are too many demands on my time to
get too involved in something like this, because I know from past
experience that it will take much more of my time than I intended. I
expected the Sagittal notation project to take several months, but
after more than 3 years it's still going ahead "full steam.")

> > ...
> [GS:]
> > It would be reasonable to have the 11M and 11L symbols
similar in
> > physical size (as they are in Sagittal), because their
rational sizes
> > are not very different (53 vs. 60 cents). Several months ago
I took
> > the time to experiment with some symbols (both upward and
downward)
> > for 11L that could have been used to expand the 41-tone
Tartini-plus
> > symbols that we were working on for use in 53-ET. They're
similar in
> > appearance to the 11L Sagittal symbols, but in a style closer
to the
> > Tartini set. If you're interested in seeing them, I could
make a
> > figure showing a proposed 43-tone symbol sequence.
> >
> > [OY:]
> > Do please show them to me.
>
> [GS:]
> Only if you promise not to use them (now that I've suggested
31). ;-)
>
> [OY:]
> Uh, are they poisonous? Will they cause indigestion once
consumed? Haha, that was a good one.

Caveat "emptor." (Let the "buyer" beware. ;-)

> [GS:]
> See file Tplus-53.gif located here:
> /tuning-math/files/secor/notation/
> The 53-ET symbol set is there, and below it a subset of those, re-
> ordered to notate 43-ET.
>
> [OY:]
> Ah, they are indeed very lovely. But you won't let me use them I
suppose. 9-)

They're not needed for 79, and I imagine your MOS wouldn't require
them either. (But I see that they would be useful for 159-ET.)

> [OY:]
> So, will you help me notate this 79 MOS using only your wonderous
quarter-tone accidentals?

Please, they're Tartini's (and Mildred Couper's) accidentals, and I
don't see exactly how they would be used in this MOS. With the
meantone fifth of 159, the apotome is 8deg, but you find the interval
of 4deg (semi-apotome) only after making a chain of 76 meantone
fourths (assuming that's an appropriate way to use the symbol). My
reason for suggesting a hemi-(meantone-)fifth generator to Gene is
that it's an easy way to get the semi-apotome into the chain of
intervals, but then I haven't checked to see how many tones would be
in the MOS's of that generator. (Not having Paul Erlich's paper
handy, I would have to guess that 76 would be among them.)

Before even beginning to address the question of notation, I think
you will need to clarify with Gene how (and whether) this MOS is
really going to live up to your expectations.

Best,

--George

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Here are some hints then. This is Rast:
>
> F-(702)-C-(695)-G-(702)-D-(695)-A-(702)-E-(695)-B
>
> An altered Rast would be:
>
> Bb-(702)-F-(702)-C-(695)-G-(702)-D-(710)-A-(702)-E
>
> This is Suz-i Dilara:
>
> F-(702)-C-(710)-G-(702)-D-(710)-A-(702)-E-(710)-B
>
> An altered Suz-i Dilara would be:
>
> F-(702)-C-(710)-G-(702)-D-(695)-A-(702)-E-(710)-B
>
> Ok, enough hints for now!

What is this? I was expecting to see ratios! Are not maqams JI?

--George

George,
----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 14 Haziran 2005 Salı 21:12
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Hi again George,
> ----- Original Message -----
> From: George D. Secor
> To: tuning@yahoogroups.com
> Sent: 13 Haziran 2005 Pazartesi 22:33
> Subject: [tuning] Re: Meantone Maquams
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
> >
> > ----- Original Message -----
> > From: George D. Secor
>
> As I thought I understood it, 41 won't work for you now, only
because
> you want a division compatible with meantone.
>
> Not only meantone, but also pythagorean. Gene reminded me that
79tET had nothing to with what I came up with in the end. See, it was
79 MOS out of 159tET all along, with one comma the size of 15.1 cents
(78 of them one after the other) and another the size of 22.2 cents
in the end. This gave me a narrow perfect fifth 695 cents wide, a
pure fifth 702 cents wide, and a wide fifth 710 cents wide. I can
thus switch between meantone and pythagorean notations at will.

So you're actually going to be switching back and forth between
different notations for a single tuning that approximates all of the
ratios you require. Fascinating! (I hope it will work the way you
expect.)

Precisely! And by the way, I've made some further studies, and saw that 67 MOS out of 135tET with three fifths 693.069 cents, 702.412 cents and 710.841 cents respectively is much simpler, and much better as a system to be implemented for fixed-tuning instruments. The first 66 commas are 17.771 cents and the last is 27.113 cents wide, which can be

Likewise beautiful and concrete is 55 MOS out of 111tET, with three fifths 691.156 cents, 703.232 cents and 712.754 cents respectively. This I will consign to theory on paper, since it contains 54 commas 21.599 cents wide, and the last comma is 33.675 cents wide. I believe it is also compatible with the 9-comma per whole-tone approach.

> ...
> [GS:]
> With 41 (or 53, for
> that matter) you previously would have been able to define each
> combination of nominal-with-accidental as a specific JI ratio,
>
> [OY:]
> And do something I abhor! That is the primary reason I cannot
consign to 41 or 53 or 65, since I cannot express Zarlino's
diatonical scale without accidentals in those systems. Obviously, I
need a meantone notation for that.
>
> [GS:]
> and
> approximations would occur only in instances where one of those
> combinations represented more than one ratio.
>
> [OY:]
> Such as?

11/10 and 10/9 are both 6 degrees of 41, or 12/11 and 11/10 are both
7 degrees of 53.

Ah, just as I assumed. Now, I would like you to focus on 67 MOS instead, which can simply be taken as 66 times 15.8 cents plus 25.2 cents. Are 13/12 and 12/11 represented by the same number of steps?

> [OY:]
> ... the 79 MOS with three usable perfect fifths results in a Well-
Temperament that is both Meantone and Pythagorean at the same time.

I don't understand exactly how you would use it that way, but, yes,
you could have a circle of (varied-)fifths.

You will see.

> [OY:]
> > Do you think it feasible to sound a super-pythagorean C major
> within this modified 79tET that I've been proposing?
>
> By this are you referring to a triad with ratios 1/1, 9/7, 3/2?
The
> 79 division is not 7-limit consistent (as to 5 vs. 7) or 1,3,7,9-
> consistent, for that matter. Unless this inconsistency is
something
> you've found a way to exploit for your particular purposes, I
expect
> that you'll be encountering problems with it.
>
> I hope you can make an equally thorough analysis for my `79 MOS
out of 159tET`. I don't think it is problematic in any way, do you?

159-ET is 17-limit consistent, so you can disregard what I said about
the 79 division. I don't know enough about the maqamat and how
you're relating them to your MOS scale to be able to say any more
than that.

You will see again.

> ...
> [GS:]
> You expressed an interest in 31-ET, and also in flexible
intonation
> and ratios of 7 (as I infer from your "superpythagorean"
comment.
> Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
> consistent, and is also one of the very best meantones available,
> would you be interested in some sort of adaptive JI based on 217-
ET,
> a multiple of 31?
>
> [OY:]
> Uh, I am not sure, but I can always tell a good marketing
strategy when I see one!

I was just looking at the bits and pieces of phrases about which you
expressed interest -- meantone, superpythagorean (good 7th harmonic),
flexible intonation, Tartini accidentals -- and came up something
that manages to tie all of these together, with varying success.
This was just to bring up another idea that you might consider. My
thoughts about this came together before I had read and digested your
latest (about the 79-MOS), so I'm having to volley them back at a
moving target. :-)

I'm sure my evasive manoeuvres are confusing. But I assure you, I'm not running to and fro without purpose!

> [GS:]
> You could use the Tartini accidentals for all of
> the pitches of 31 and perhaps supplement them with small arrows
> placed (optionally) to the left to serve as a guide (e.g., as
> something like diacritical marks for Maqam musicians in training)
to
> indicate the direction and amount that the pitch should be
adjusted
> (in increments of ~5.5 cents). You might need them only rarely
if
> most of the adjustments are only a single increment. All of the
> pitches of 217-ET may be reached by adjusting the closest pitch
of 31-
> ET by no more than ~17 cents (3 increments), which is still less
than
> a 5-comma.
>
> [OY:]
> It certainly deserves attention, but is not 79 MOS out of 159tET
a better, simpler alternative that encompasses both meantone and
pythagorean notations so as to express both Rast and Suz-i Dilara as
C natural gamme on the staff?

I don't know, because I haven't taken a close look at that MOS and
don't know enough about the maqamat to make any judgment about its
suitability. (At the moment there are too many demands on my time to
get too involved in something like this, because I know from past
experience that it will take much more of my time than I intended. I
expected the Sagittal notation project to take several months, but
after more than 3 years it's still going ahead "full steam.")

It's pleasing to see that all good things don't come to an end.

> > ...
> [GS:]
> > It would be reasonable to have the 11M and 11L symbols
similar in
> > physical size (as they are in Sagittal), because their
rational sizes
> > are not very different (53 vs. 60 cents). Several months ago
I took
> > the time to experiment with some symbols (both upward and
downward)
> > for 11L that could have been used to expand the 41-tone
Tartini-plus
> > symbols that we were working on for use in 53-ET. They're
similar in
> > appearance to the 11L Sagittal symbols, but in a style closer
to the
> > Tartini set. If you're interested in seeing them, I could
make a
> > figure showing a proposed 43-tone symbol sequence.
> >
> > [OY:]
> > Do please show them to me.
>
> [GS:]
> Only if you promise not to use them (now that I've suggested
31). ;-)
>
> [OY:]
> Uh, are they poisonous? Will they cause indigestion once
consumed? Haha, that was a good one.

Caveat "emptor." (Let the "buyer" beware. ;-)

> [GS:]
> See file Tplus-53.gif located here:
> /tuning-math/files/secor/notation/
> The 53-ET symbol set is there, and below it a subset of those, re-
> ordered to notate 43-ET.
>
> [OY:]
> Ah, they are indeed very lovely. But you won't let me use them I
suppose. 9-)

They're not needed for 79, and I imagine your MOS wouldn't require
them either. (But I see that they would be useful for 159-ET.)

And what would 67 MOS require? Could we represent 55, 67 and 79 with a single notation?

> [OY:]
> So, will you help me notate this 79 MOS using only your wonderous
quarter-tone accidentals?

Please, they're Tartini's (and Mildred Couper's) accidentals, and I
don't see exactly how they would be used in this MOS. With the
meantone fifth of 159, the apotome is 8deg, but you find the interval
of 4deg (semi-apotome) only after making a chain of 76 meantone
fourths (assuming that's an appropriate way to use the symbol).

Something tells me that some symbols should be less attached to the cycle of fifths, and be taken with a grain of salt.

My reason for suggesting a hemi-(meantone-)fifth generator to Gene is
that it's an easy way to get the semi-apotome into the chain of
intervals, but then I haven't checked to see how many tones would be
in the MOS's of that generator. (Not having Paul Erlich's paper
handy, I would have to guess that 76 would be among them.)

And how would that help us?

Before even beginning to address the question of notation, I think
you will need to clarify with Gene how (and whether) this MOS is
really going to live up to your expectations.

I believe we are making good progress already. Maybe I will call this family of MOS temperaments "bi-linear MOS", because of the possibility of switching from meantone to pythagorean.

Best,

--George

Cordially,
Ozan

Indeed they are! But this was according to 79 MOS.
----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 14 Haziran 2005 Salı 21:22
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Here are some hints then. This is Rast:
>
> F-(702)-C-(695)-G-(702)-D-(695)-A-(702)-E-(695)-B
>
> An altered Rast would be:
>
> Bb-(702)-F-(702)-C-(695)-G-(702)-D-(710)-A-(702)-E
>
> This is Suz-i Dilara:
>
> F-(702)-C-(710)-G-(702)-D-(710)-A-(702)-E-(710)-B
>
> An altered Suz-i Dilara would be:
>
> F-(702)-C-(710)-G-(702)-D-(695)-A-(702)-E-(710)-B
>
> Ok, enough hints for now!

What is this? I was expecting to see ratios! Are not maqams JI?

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> What is this? I was expecting to see ratios! Are not maqams JI?
>
> --George

Hello George,

How are you? It's been a while. I remember meeting you and playing
your Scalatron in Erv's home in the late 1970's.

Anyway, I would answer your question in the affirmative.

Cris Forster

> Hello George,
>
> How are you? It's been a while. I remember meeting you and playing
> your Scalatron in Erv's home in the late 1970's.
>
> Cris Forster

Hi, Chris! That was during the summer of 1979, so it's been a very
long time. I spent 15+ years away from microtonality, got back into it
gradually around 1997, and am busier than ever now.

Nice to "see" you again!

--George

Hi George,

In those days, we all had a wonderful time with Erv
and his great generosity toward all.

Thank you for all your mathematically unbiased contributions
to tuning theory.

Sincerely,

Cris

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > Hello George,
> >
> > How are you? It's been a while. I remember meeting you and
playing
> > your Scalatron in Erv's home in the late 1970's.
> >
> > Cris Forster
>
> Hi, Chris! That was during the summer of 1979, so it's been a
very
> long time. I spent 15+ years away from microtonality, got back
into it
> gradually around 1997, and am busier than ever now.
>
> Nice to "see" you again!
>
> --George

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> George,
> ----- Original Message -----
> From: George D. Secor
> To: tuning@yahoogroups.com
> Sent: 14 Haziran 2005 Salý 21:12
> Subject: [tuning] Re: Meantone Maquams
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
> > Hi again George,
> > ----- Original Message -----
> > From: George D. Secor
> > To: tuning@yahoogroups.com
> > Sent: 13 Haziran 2005 Pazartesi 22:33
> > Subject: [tuning] Re: Meantone Maquams
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman"
<ozanyarman@s...>
> wrote:
> > >
> > > ----- Original Message -----
> > > From: George D. Secor
> > [GS:]
> > As I thought I understood it, 41 won't work for you now, only
because
> > you want a division compatible with meantone.
> > [OY:]
> > Not only meantone, but also pythagorean. Gene reminded me
that
> 79tET had nothing to with what I came up with in the end. See, it
was
> 79 MOS out of 159tET all along, with one comma the size of 15.1
cents
> (78 of them one after the other) and another the size of 22.2
cents
> in the end. This gave me a narrow perfect fifth 695 cents wide, a
> pure fifth 702 cents wide, and a wide fifth 710 cents wide. I can
> thus switch between meantone and pythagorean notations at will.
> ...
> [GS:]
> So you're actually going to be switching back and forth between
> different notations for a single tuning that approximates all of
the
> ratios you require. Fascinating! (I hope it will work the way
you
> expect.)
> [OY:]
> Precisely! And by the way, I've made some further studies, and
saw that 67 MOS out of 135tET with three fifths 693.069 cents,
702.412 cents and 710.841 cents respectively is much simpler, and
much better as a system to be implemented for fixed-tuning
instruments. The first 66 commas are 17.771 cents and the last is
27.113 cents wide, which can be
>
> Likewise beautiful and concrete is 55 MOS out of 111tET, with
three fifths 691.156 cents, 703.232 cents and 712.754 cents
respectively. This I will consign to theory on paper, since it
contains 54 commas 21.599 cents wide, and the last comma is 33.675
cents wide. I believe it is also compatible with the 9-comma per
whole-tone approach.

Your thoughts continue to be a moving target, and there is no chance
of my shooting them down if they won't stay put! ;-) Anyway, moving
right along ...

> > ...
> > [GS:]
> > approximations would occur only in instances where one of
those
> > combinations represented more than one ratio.
> >
> > [OY:]
> > Such as?
> [GS:]
> 11/10 and 10/9 are both 6 degrees of 41, or 12/11 and 11/10 are
both
> 7 degrees of 53.
>
> Ah, just as I assumed. Now, I would like you to focus on 67 MOS
instead, which can simply be taken as 66 times 15.8 cents plus 25.2
cents. Are 13/12 and 12/11 represented by the same number of steps?

Yes, at least as long as the disjunct step does not come between the
tones separated by those intervals.

> ...
> > [OY:]
> > > Do you think it feasible to sound a super-pythagorean C
major
> > within this modified 79tET that I've been proposing?
> >
> > By this are you referring to a triad with ratios 1/1, 9/7,
3/2? The
> > 79 division is not 7-limit consistent (as to 5 vs. 7) or
1,3,7,9-
> > consistent, for that matter. Unless this inconsistency is
something
> > you've found a way to exploit for your particular purposes, I
expect
> > that you'll be encountering problems with it.
> >
> > I hope you can make an equally thorough analysis for my `79
MOS
> out of 159tET`. I don't think it is problematic in any way, do
you?
>
> 159-ET is 17-limit consistent, so you can disregard what I said
about
> the 79 division. I don't know enough about the maqamat and how
> you're relating them to your MOS scale to be able to say any more
> than that.
>
> You will see again.

There is something that you need to see that pertains to any MOS
scale, including the 79-tone MOS: There will be very few maqams that
can be transposed exactly from one starting tone to another, and
certain none that can be transposed exactly by a fifth. When you
spoke of your desire for "free modulation", did you mean exact
transposition, or were you allowing that some of the intervals in a
maqam would change slightly when the starting note is different?
Only in an equal temperament can you have exact transposition to any
given tone, and only if you have the capability of using any given
tone of the entire ET, which would not seem to be the case with a MOS
scale.

I personally cannot see why you would need to be able to transpose a
maqam to 159 different tones in the octave -- you would not even be
able to hear a transposition by 1deg159! You need to answer this
question: how many different tones in the octave should be able to
serve as a possible starting note for maqams?

Which leads right into the next point:

> > ...
> > [GS:]
> > You expressed an interest in 31-ET, and also in flexible
intonation
> > and ratios of 7 (as I infer from your "superpythagorean"
comment.
> > Since 31 represents both 4:5 and 4:7 extremely well, is 11-
limit
> > consistent, and is also one of the very best meantones
available,
> > would you be interested in some sort of adaptive JI based on
217-ET,
> > a multiple of 31?

To rephrase my question: is 31 enough starting tones/octave? What
about two parallel chains of 19 fifths (38-ET, which could also be
thought of as a single chain of hemififths)? Each of those pitches
could be supplemented by tones slightly above and below that would
comprise 31 or 38 pitch clusters notated using only the
Tartini/Couper symbols. Optional diacritical marks might be used to
indicate the degree and/or direction of deviation from the strict
ET. (I'll have suggestions about these, should you decide this could
be useful.)

Another possibility is a circle of 53 fifths, supplemented by two
other circles 1deg159 above and below that -- 53 pitch-clusters, with
3 tones per cluster. You notate 53-ET (probably *not* with the
symbols in file Tplus-53.gif, since I have a variation on that idea)
and optionally indicate the above- and below-tones in the cluster
with a 7:5-kleisma scroll that could be affixed to the existing
accidental. (If the maqam world now recognizes the 53 division in
its theory, then this will be right up their alley.) Hang on --
there's more.

For the meantone version of this, you use a chain of hemi-meantone-
fifths (46deg159) at least 38 tones in length using a 38-ET notation
(Tartini/Couper symbol set). The tones 39 generators distant in the
chain are 1deg159 apart, so they're pairs of a cluster, capable of
being notated with the same symbol (with optional 7:5k-scroll and 17C-
symbol marks ranging from +-2deg159).

This is my last "latest and greatest" brainstorm, but you're probably
runing for shelter -- I can predict that you won't like this, because
it won't notate Rast as C natural gamme on the staff. I can
appreciate that this might be important to you, but there's something
else to consider. 'Most everyone here believes that the most logical
tuning for a scale consisting completely of the natural notes in a
chain of fifths from F thru B is one in which the fifths are all the
same size, and the reason for that is none other than -- ease of
transposition (see below)!

> > [OY:]
> > Uh, I am not sure, but I can always tell a good marketing
> strategy when I see one!
>
> I was just looking at the bits and pieces of phrases about which
you
> expressed interest -- meantone, superpythagorean (good 7th
harmonic),
> flexible intonation, Tartini accidentals -- and came up something
> that manages to tie all of these together, with varying success.
> This was just to bring up another idea that you might consider.
My
> thoughts about this came together before I had read and digested
your
> latest (about the 79-MOS), so I'm having to volley them back at a
> moving target. :-)
>
> I'm sure my evasive manoeuvres are confusing. But I assure you,
I'm not running to and fro without purpose!

Hmmm, perhaps it's because I've been shooting too many thoughts your
way. ;-)

> > [GS:]
> > You could use the Tartini accidentals for all of
> > the pitches of 31 and perhaps supplement them with small
arrows
> > placed (optionally) to the left to serve as a guide (e.g., as
> > something like diacritical marks for Maqam musicians in
training) to
> > indicate the direction and amount that the pitch should be
adjusted
> > (in increments of ~5.5 cents). You might need them only
rarely if
> > most of the adjustments are only a single increment. All of
the
> > pitches of 217-ET may be reached by adjusting the closest
pitch of 31-
> > ET by no more than ~17 cents (3 increments), which is still
less than
> > a 5-comma.
> >
> > [OY:]
> > It certainly deserves attention, but is not 79 MOS out of
159tET
> a better, simpler alternative that encompasses both meantone and
> pythagorean notations so as to express both Rast and Suz-i Dilara
as
> C natural gamme on the staff?

I mentioned that some of us had a difficulty with Ben Johnston's
approach to notating JI. The thing we specifically don't like about
it is that not all fifths in a chain of natural notes from F to B
were of the same size, so that when you transpose something from one
key to another, you must introduce one or more comma-accidentals in
order to keep the transposition exact, and 'most every time you
transpose, the comma-accidentals will occur in different places, so
it's not always easy to keep track of where they should go. Your 79
MOS scale also has this characteristic.

> ... (At the moment there are too many demands on my time to
> get too involved in something like this, because I know from past
> experience that it will take much more of my time than I
intended. I
> expected the Sagittal notation project to take several months,
but
> after more than 3 years it's still going ahead "full steam.")
>
> It's pleasing to see that all good things don't come to an end.

On the other hand, it's frustrating to find that some good things
take so long to accomplish that it seems they will never end.

I was trying to break it to you gently that it has become evident
that my participation in this discussion will be requiring more of my
time than I'm able to spare at present. It has come to the point
where I would have to familiarize myself with some of the maqam
scales in order to be able to offer an informed opinion about the
suitability of a given MOS scale and suggestions regarding notation.
I'm currently working with Dave Keenan in a (hopefully) final effort
to complete a systematic derivation, definition, and classification
of at least 233 different Sagittal accidentals ranging up to an
apotome in size, and that has had to be done a little at a time, when
I can find a few minutes to work on it. And after that I have some
things that I have been writing and composing that await my return.
My life has had more than its share of good intentions and unfinished
business, and I hope to complete at least a few of those things while
I still have the ability to do so.

In a perfect world we would all have unlimited time to do the things
that matter most to us (and likewise to help others with theirs), but
there is so much already left unfinished that I must, regretfully,
take leave of this discussion -- once I've made a few final comments.

> ...
> And what would 67 MOS require? Could we represent 55, 67 and 79
with a single notation?

I couldn't say offhand, without delving into the details of those
first two (which I'm not prepared to do, for reasons I just
explained).

> > [OY:]
> > So, will you help me notate this 79 MOS using only your
wonderous
> quarter-tone accidentals?
>
> Please, they're Tartini's (and Mildred Couper's) accidentals, and
I
> don't see exactly how they would be used in this MOS. With the
> meantone fifth of 159, the apotome is 8deg, but you find the
interval
> of 4deg (semi-apotome) only after making a chain of 76 meantone
> fourths (assuming that's an appropriate way to use the symbol).
>
> Something tells me that some symbols should be less attached to
the cycle of fifths, and be taken with a grain of salt.

Huh? Maverick symbols with an independent agenda -- to be taken less
seriously? That sounds subversive to me ;-) -- but rather like
what I suggested when I mentioned pitch-clusters.

> My reason for suggesting a hemi-(meantone-)fifth generator to
Gene is
> that it's an easy way to get the semi-apotome into the chain of
> intervals, but then I haven't checked to see how many tones would
be
> in the MOS's of that generator. (Not having Paul Erlich's paper
> handy, I would have to guess that 76 would be among them.)
>
> And how would that help us?

I thought that It would help if you *require* that the Tartini
semisharp and Couper semiflat symbols be used (but that was before I
understood the exact nature of the MOS scale). Anyway, I suspect
that requirement is not at the top of your list.

> Before even beginning to address the question of notation, I
think
> you will need to clarify with Gene how (and whether) this MOS is
> really going to live up to your expectations.
>
> I believe we are making good progress already. Maybe I will call
this family of MOS temperaments "bi-linear MOS", because of the
possibility of switching from meantone to pythagorean.

I should caution you that a few of us have been using the terms "bi-
linear" and "multi-linear" for a class of tunings (having equidistant
parallel lines of generators) quite different from your MOS scale (in
which the two types of lines intersect), and Paul Erlich has had
reservations about even that prior usage being potentially misleading.

Ozan, I hope my thoughts and ideas have been helpful. (If you have
something that needs clarification, I'll be peeking at the lists from
time to time.)

Wishing you the best,

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> > And what would 67 MOS require? Could we represent 55, 67 and 79
> with a single notation?
>
> I couldn't say offhand, without delving into the details of those
> first two (which I'm not prepared to do, for reasons I just
> explained).

Which MOS is this? The obvious point about 55, 67, and 79 as edos is
that we have a common notation from notating them in the standard way
with sharps and flats. The meantone third of 79edo is not its best 5,
and the meantone 7 not its best 7, but that doesn't mean we can't use
the notation.

Hi Kraig,

I love you!

Thanks for the public apology. It means a lot to me, since I admire you
as an embodiment of the true artistic spirit. I wouldn't want to be
involved in an endeavor where my motives were mistrusted by artists in
the relevant field -- I'd rather shut up and restrict myself to
performing/composing, in such a scenario. Seemingly, it hasn't come to
that :)

I recognize there are many shortcomings in the way I interact with
people on these lists, and will consider it my responsibility to
correct my manner so as to avoid future misunderstanings . . . and I
sincerely apologize to all those whom I've rubbed the wrong way so far.
I'm sorry!

Honestly, ASCII + strong opinions = danger, no matter which list you're
talking about. The Firefly (a local Burning Man type event) list, which
consists of the kinds of people you'd think would be the last to start
a flame war, eventually ended up seeing a very heated debate on whether
the potentially unsafe activity of fire-breathing ought to be allowed
at such an event. Soon enough, the list was overrun with requests for
removal by dozens of (then-) members.

Back to tuning, I don't care to rehash any of this, but in case anyone
is wondering, here are some of the original posts behind the now-
defused debacle:

/tuning/topicId_57318.html#57318
/tuning/topicId_57318.html#57340
/tuning/topicId_57318.html#57351
/tuning/topicId_57325.html#57346
/tuning/topicId_57325.html#57414

I certainly don't think these matters are off-topic, though. Where
better to discuss them but here? You may have noticed (in the _Middle
Path_ paper that I snail-mailed to dozens of people here) that I tried
to give credit to the original discoverer of each system (including
George Secor, by referencing his most recent paper on what even he
calls "Miracle" now), at least by naming the system after them (Hanson,
Compton, Helmholtz, Negri . . .) The 'fanciful' names are for systems
that have come to light on these lists and not previously, to our
knowledge. One of the reasons I sent the paper to so many people is to
try to learn of earlier mentions of any of these systems so that I may
give proper credit.

Another reason was to make it a better, clearer paper. Some people
found it a lot more comprehensible than the earlier version which was
in the files folder of the tuning-math list for a little while (the
last version Jon Szanto took a look at). I've been mailing out copies
of the more recent version since late August (mainly to those who
responded to my posts asking for willing or interested readers), and
gotten some excellent replies. Especially from Yahya, who seemed
willing to go much farther than anyone else in actually *reading* the
whole paper, and in getting into lengthy discussions with me as to how
to improve it, even before having a full understanding of it. Thanks
Yahya! That will be most helpful. I want to thank everyone else who
sent comments too!!

John Chalmers has given me a little more time, for now, to revise the
paper again. Unfortunately he's one of the gurus who *hasn't* given me
any comments. Others whose comments I'm eagerly awaiting -- please
please please!! -- include

Bill Sethares

Daniel Wolf

Graham Breed

and . . . you know who you are! Without your help, I fear this paper
will fail to be all that it could be, and will probably make less of an
impact, be less correct, and give insufficient credit to those who
deserve it as a result.

Love,
Paul

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> I publicly apologize for having some grave misunderstandings about
> Paul's actions
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Hi Paul,

It's good to have you back.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> John Chalmers has given me a little more time, for now, to revise the
> paper again. Unfortunately he's one of the gurus who *hasn't* given me
> any comments. Others whose comments I'm eagerly awaiting -- please
> please please!! -- include
>
> Bill Sethares
>
> Daniel Wolf
>
> Graham Breed
>
> and . . . you know who you are! Without your help, I fear this paper
> will fail to be all that it could be, and will probably make less of an
> impact, be less correct, and give insufficient credit to those who
> deserve it as a result.

I think the paper is just fine. If these folk haven't commented by
now, it is probably because they can find no fault in it worth
mentioning. It doesn't have to be perfect, and you can't please
everybody anyway. Let's not Give John Chalmers any reason to further
delay Xenharmonikon 18.

-- Dave Keenan

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> and . . . you know who you are! Without your help, I fear this paper
> will fail to be all that it could be, and will probably make less of an
> impact, be less correct, and give insufficient credit to those who
> deserve it as a result.

Why don't you stick a web version up and invite comments from one and all?

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> and . . . you know who you are! Without your help, I fear this paper
> will fail to be all that it could be, and will probably make less of an
> impact, be less correct, and give insufficient credit to those who
> deserve it as a result.

I mostly have picky math comments. I didn't think you were interested
in any more paper critiquing until I read this, but I can certainly
send picky comments along if you want them.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > and . . . you know who you are! Without your help, I fear this
paper
> > will fail to be all that it could be, and will probably make less
of an
> > impact, be less correct, and give insufficient credit to those
who
> > deserve it as a result.
>
> I mostly have picky math comments. I didn't think you were
interested
> in any more paper critiquing until I read this, but I can certainly
> send picky comments along if you want them.

Sure. I already took a few of your picky comments into account in the
current version, in case you didn't notice. I'm planning to show the
lattices both with 90-degree angles between the axes, and with a far
smaller angle, because different things can be gleaned from each
representation, and in the math I'm using you can say that angles
aren't defined at all or -- easier to visualize -- that the measures
I use (taxicab distance and similar metrics for area, etc.) are
invariant as to the angle chosen. One could think of the angle
varying continuously and unpredictably, and the relevant measures are
those that remain constant.

You should probably reply to the tuning-math list.

Best,
Paul