Yahoo Tuning Groups Ultimate Backup tuning misc clean up (was Comments for Julia... & Is 19-et j.i.?)

Hello all,

To comment on & conclude for the most part my present public
expression on these matters.

1) Consonance/Dissonance: I found some very useful information
at <http://dactyl.som.ohio-
state.edu/Music829B/music829B.html>, which illustrates my
questions with regard to the these concepts.

2) Just Intonation and n-Limit, Odd v/s Prime :

While many people have stated that it involves using exclusively
small integer ratios, at least one definition that I found, John
Chalmers cited in Monzo's microtonal dictionary, does not
require 'small' integers. What the line between small and big
is, I don't know.

I've decided to sidestep 'Just Intonation', prime v/s odd limit,
and consonant/dissonant polemics. I am not suggesting there is
nothing of value there; quite the opposite. I feel I can easier
progress toward an understanding of the issues raised by placing
them within larger, more clearly defined contexts. I find it
easier to think in terms of musical acoustics and the harmonic
series, sans idealogical baggage, preconceptions, or prejudices.

I intend to continue my enquiry into these matters privately for
now. When I've developed my ideas further and have the music
(fancy that !) to back it up, I'll speak up again.

The University of New South Wales, Sydney, has a web site on
music acoustics at <http://www.phys.unsw.edu.au/music/>, if
anyone's interested.

And now for a few responses.

Paul Erlich :
> well, this kind of sidesteps the issue of anomalous saturated
> suspensions:
> http://www.cix.co.uk/~gbreed/ass.htm

Thanks for pointing this out. And it looks like I may have side
stepped the side stepping :)

Kraig Grady :
> I work with something for over 25 years,
As I said, I have a lot of respect for everyone here.

> you come along and tell me i should call it something
> else
I did not.

> to suit your own bias for ET
I have no bias toward any particular scale/tonal system or
scheme, least of all equal temperament.

> and imply that my reaction is religious.
I did not.

Gene Ward Smith :
To, '...rational numbers, i.e. any number of the form p/q where
p and q are integers (positive or negative) and q ≠ (is not
equal to) 0.' (Additional Mathematics, Patrick Murphy
> This isn't going to help much if we allow non-standard integers. :)

I've just begun looking at what 'non-standard' integers are -
thanks a lot, Gene :-(. But, in the context of our discussion,
does harmonic series involve intervals with 'non-standard
integer' ratios ?

To, '"Consonance" is a subjective impression, much like "Atonality".'
> It means something a little different in discussions of "odd limit"
> harmonies, which was Robert's point.

Could you elaborate what definition/theory of consonance that
would be ? Also, it was George Secor who said, "the
specification of a harmonic limit (e.g., 11-limit JI)
automatically defines the consonances.".

> As for atonality, why is that a subjective imp=
> ression? It seems to me you could define it statistically if
> you wanted to, =
> as a score which had no tonal center for lengths of time beyond
> some small a=
> mount. It certainly would be easy enough to produce triadic
> harmony with no =
> tonal center, and whatever subjective impression it gave, it
> would be atonal=
> .

For me such a piece of music would simply suggest something akin
to several tonal centres. Pantonal ? maybe. See
<http://www.xrefer.com/entry.jsp?xrefid=352585>.

> the series of partial tones does not go on to infinity and consists
> of integer multiples of a fundamental only within some margin.

Theoretically is not the harmonic series infinite ?

Julia Werntz :

I look forward to reading your work at the earliest opportunity.
I've been in agreement with everything you've said, in so far as I have the knowledge to do so.

> One has to pick one's battles, sometimes. Probably in the
> future I will search for
> the perfect alternative term.

There is undeniably something unique going on with 'atonal'
music, so it would be nice to have a more descriptive term.
Schoenberg's preference was apparently, 'pantonality'. At least
makes more sense than 'atonal'.

> If I write more essays, that is.

Please do ! I wonder if you've encountered misconstruction of
your work (or writing, at least) elsewhere as there's been here ?

To, 'My notion is that people who find a music "atonal" are like
people who don't *get* Jazz.'

> I'm just curious what you mean by this. Are you referring to
> those who use the
> term to describe, let's say "pantonal" music, in a derisive
> way, to mean something
> akin to "amusical," because they fail to see the beauty and
> lyricism of Webern's
> music, for example?

Yes !

George Secor:

To my suggestion that many are drawn to microtonality in a quest
for more pitches to play with, rather than a 'purer' whatever.

> Bravo! But the next question is always, "On what principle(s) shall
> I organize these new pitches?"
Indeed !

> Whoever needs to make decisions about the future would be wise to
> understand the past.
Yes.

> We arrived at 12-ET because it approximates the
> simplest rational intervals
Yes. And, we now have the technology and science to explore much
further than those simplest rational intervals.

> If you are interested in writing "tonal" (as opposed to "atonal"
> or "pantonal") music, then musical acoustics (and the mathematics of
> rational intervals) should be a significant factor in how you go
> about finding more pitches in the octave.

A basic understanding of musical acoustics would be good thing
no matter what kind of music one wishes to write. To suggest
otherwise is misleading. Dan Stearns' comments were also right
on the mark, especially when he says, 'Humans are a pretty
enterprising and curious lot and not at all entirely bound by
their physiology to blind obedience.'. But you add the bit about
rational intervals. Within the scope of musical acoustics, yes.
Within the concept(s) of JI ? Only if one makes an informed
decision to do so.

The rest of what you had to say about 'pantonal' (for lack of a
better term - 'atonal' is a non-starter) music reveals a
fundamental difference in the way you and I hear it. I hear it
as quite the opposite of, 'an architect designing a building,
but ignoring the laws of physics'. I see it as more akin to an
architect who understands the laws of physics in a manner that
elevates it to art.

> That said, I should quickly add that the element of "creative
> impulse" (in whatever form) in a musical composition outweighs all of
> our theorizing...

I agree wholeheartedly ! However, with regard to the mass appeal
bit preceding this, personally I am not concerned with (nor have
delusions of) writing music that will appeal to the majority of
society.

To, 'But, 419914/404871 *is* within the harmonic series.'.

> Theoretically, yes; for all practical purposes, no. You can't hear a
> harmonic that high in any musical tone because:
>
> 1) It wouldn't have sufficient amplitude;
>
> 2) Either it or its fundamental (or both) would be out of our range
> of hearing.

But this is unimportant for theoretical scale construction using
octave reduction. No ?

> The size of the number is very important when you are dealing with
> musical acoustics. What makes just intervals or chords "just"? It's
> the elimination of roughness, i.e., perceived beating between off-
> tuned harmonics or combination tones. Once the numbers reach a
> certain size, intervals begin to lose their identities, at which
> point they begin to sound like approximations of lower-numbered
> ratios. Then they can no longer be considered distinct consonances.
> So there is a practical limit to which one can take a harmonic limit.

I was simply pointing out the error in your definition of a
rational number. But, what is the cut-off point beyond which you
would consider an interval to not be 'Just' ?

> Regarding one's unsuspecting friends: one of the challenges of
> writing a microtonal composition is to use new intervals without
> making the result sound as if it is out of tune.

Perceiving music as 'out of tune' is a subjective thing, similar
and related to concepts of consonance and dissonance.
Consequently, what you suggest is not a goal of mine.

To, 'But, one may be thinking simply in terms of the harmonic
series with no sense or need for a "limit".'
> Then one has failed to recognize that the extent to which a harmonic
> limit may be successfully employed is not unlimited.
I disagree and stand by my original suggestion. Perhaps the
differences in understanding (and aesthetics) lie in the
distinctions of various conceptions of harmonic limit and
consonance/dissonance. Unless JI proponents think they've learnt
all there is to know. The end of science ? ;-)

> Where was it that we were talking about scales?
Everywhere !

From the OED:
Tuning: the process of putting a musical instrument in tune.
In tune: having the correct pitch or intonation.
It's provenance is the Greek 'teino', meaning 'stretch'.

Scale: Mus. an arrangement of all the notes in a system of music
in ascending or descending order.
It's provenance is the Latin 'scala' from 'scandere', meaning climb.

As I said, one tunes *to* a scale.

> In stating that temperaments are non-rational tunings, one would not
> logically conclude that all non-rational tunings are temperments.
Actually that is exactly the error you made, which I pointed out.

> The term "inharmonic" is generally applied to timbres having non-
> harmonic partials, not to scales or tunings.
My using it to refer to scales, chords, & intervals is a logical
extension. As consonance and dissonance are used to refer to all
these things.

> The term "just intonation" is widely accepted, and that is not likely
> to change for the foreseeable future.

It's easy to see that, given the intransigence of it's most
vigorous proponents. Well, having taken my train of thought to
it's logical course, I can more clearly state that I was merely
seeking a way to work beyond the confines of 'Just Intonation'.
I did not even suggest an new term. Merely said I'd like to just
call the harmonic series the harmonics series. Even that benign
unimpeachable notion turned out like ants in the pants for at
least one person here ! :-) Remarkable. Uninteresting.

> It's always good to know that someone out there is thinking!
Cogito ergo sum.

Existential tonality. That's how I can presently best describe
the essence of what I'm after :-)

BTW, any Turkish football fans here ? Kudos !!! Rustu rules !

Sincerely,
Joel

🔗jpehrson2 <jpehrson@rcn.com>

🔗genewardsmith <genewardsmith@juno.com>

🔗Joel Rodrigues <joelrodrigues@mac.com>

> --- In tuning@y..., Joel Rodrigues <joelrodrigues@m...> wrote:
>
> /tuning/topicId_38310.html#38310
>
>> Hello all,
>>
>> To comment on & conclude for the most part my present public
>> expression on these matters.
>>
>
> ***Thank you so much for your post, Joel but it seemed from your
> discussion that you are going to be continuing some comments at some
> point. Great!

Hi Joseph, thanks to what you pointed out re. RI & JI, it looks like I will indeed *have* to say something :) Seriously, although I am at times tempted to just not bother with this forum, I'm frequently humbled by the graciousness and thoughtful intelligence that is often displayed here. I'll miss Dan's presence, and wish him the very best in whatever he gets up to. I think Dan's characterisation of the situation on this list is accurate. I wish more people would join in.

> I would suggest, though, that you review the archives here on the
> Tuning List. We have been over and over and over and over and over
> (and out!) the distinctions between Just Intonation and Rational
> Intonation, and the numbers that should define them or the numbers
> that should *not* define them repeatedly, repeatedly, repeatedly. I
> can say *that* again!
I have the Tuning List archived on my hard drive. Having gone through them extensively, and done some brief research elsewhere, I've been able to further formulate my thoughts. I'll need another 24 hours or so to have a good think before posting.

> It's all on our *archives* here. Despite what many people have said
> about the Yahoo system, the *archiving* feature is quite good, and
> there's lots of information here.
It's my perpetual complaint,there's so much information accessible now and only one lifetime in which to digest it all !

> There's lots of *mis*-information,
No ! Really ?

> too, but it's usually straightened out.
More power to the dissenters, what ?

> In fact, probably when I finish going through the Xenharmonikons (if
> ever) I will take some time to review the archives here, especially
> that period close to three years ago now (whew, time fugues!) when I
> came on board!
Yeah, I thought I had it bad when I was a headbanging pointy-guitar player. Then I heard about microtonality & xenharmonics. Bleedin' all-consuming flame isn't it !?

> Joseph Pehrson

Cheers,
Joel

🔗emotionaljourney22 <paul@stretch-music.com>

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., Joel Rodrigues <joelrodrigues@m...> wrote:
> Hello all,
>
> ... And now for a few responses.
>
> George Secor:
>
> > ... I should quickly add that the element of "creative
> > impulse" (in whatever form) in a musical composition outweighs
all of
> > our theorizing...
>
> I agree wholeheartedly ! However, with regard to the mass appeal
> bit preceding this, personally I am not concerned with (nor have
> delusions of) writing music that will appeal to the majority of
> society.

Nor should any of us, which is why I said:
<< when it comes to taste, "mass" often correlates with "crass." >>

> To, 'But, 419914/404871 *is* within the harmonic series.'.
>
> > Theoretically, yes; for all practical purposes, no. You can't
hear a
> > harmonic that high in any musical tone because:
> >
> > 1) It wouldn't have sufficient amplitude;
> >
> > 2) Either it or its fundamental (or both) would be out of our
range
> > of hearing.
>
> But this is unimportant for theoretical scale construction using
> octave reduction. No ?

The traditional concept of just intonation involves intervals in
which the roughness due to beating harmonics is eliminated when the
harmonics are made to coincide (i.e., just tuning = elimination of
beats). This is meaningless if either the fundamentals or harmonics
in question cannot be heard. I was attempting to make this point in
what I said next:

> > The size of the number is very important when you are dealing with
> > musical acoustics. What makes just intervals or chords "just"?
It's
> > the elimination of roughness, i.e., perceived beating between off-
> > tuned harmonics or combination tones. Once the numbers reach a
> > certain size, intervals begin to lose their identities, at which
> > point they begin to sound like approximations of lower-numbered
> > ratios. Then they can no longer be considered distinct
consonances.
> > So there is a practical limit to which one can take a harmonic
limit.
>
> I was simply pointing out the error in your definition of a
> rational number.

Where did I give an erroneous definition of "rational number" or use
the term incorrectly? (I'll have more to say about definitions
below.)

> But, what is the cut-off point beyond which you
> would consider an interval to not be 'Just' ?

I haven't decided exactly where that would be, but it would be above
the 19 limit, and possibly below the 43 limit (I do know of a couple
of uses for ratios of 41). While I doubt that ratios of 17 and 19
can be tuned by ear successfully by eliminating beats between
harmonics, I have found that consonant chords can be created using
these intervals if the difference tones can be made to coincide,
e.g., 13:16:19:22 or 13:17:21:25. By "consonant" I mean that you can
hear something go out of tune if you mistune one of the tones. This
is the sort of phenomenon that defines the whole concept of "just
intonation" and makes it so attractive to its advocates.

I suspect that the cut-off point you asked about would be arrived at
when the harmonic entropy (or disorder) becomes large enough that the
collective dissonance produced by beating harmonics (and whatever) in
a chord significantly outweighed the consonance connected with
coincident difference (and other combinational) tones. I'll have to
experiment with this sometime to see if I can reach any definite
conclusion.

> > Regarding one's unsuspecting friends: one of the challenges of
> > writing a microtonal composition is to use new intervals without
> > making the result sound as if it is out of tune.
>
> Perceiving music as 'out of tune' is a subjective thing, similar
> and related to concepts of consonance and dissonance.
> Consequently, what you suggest is not a goal of mine.

One could intentionally use a microtonal scale to parody a
conventional diatonic scale (to give the impression that it is out of
tune) to portray a drunken or disoriented character in a piece of
music. I believe that success of this effect would depend mostly on
the skill of the composer and very little on the listener (assuming
that the listener has previously heard diatonic music played in tune).

Likewise I believe that it is possible for a composer to control the
various factors (whatever they may be) that will determine whether or
not a piece of music will sound strange and different or whether it
will merely sound out of tune. I remember the first time I ever
heard a recording of a Javanese gamelan -- it sounded quite unlike
anything I had ever heard before, but it definitely didn't sound out
of tune.

> To, 'But, one may be thinking simply in terms of the harmonic
> series with no sense or need for a "limit".'

> > Then one has failed to recognize that the extent to which a
harmonic
> > limit may be successfully employed is not unlimited.

> I disagree and stand by my original suggestion. Perhaps the
> differences in understanding (and aesthetics) lie in the
> distinctions of various conceptions of harmonic limit and
> consonance/dissonance. Unless JI proponents think they've learnt
> all there is to know. The end of science ? ;-)

Then we will agree to disagree.

Just for the record, I'm neither a JI nor an ET partisan -- my
preference is actually for what has lately been called "middle path"
tunings, which for me include well-temperaments and near-just
temperaments. But I have tried to formulate definitions or
descriptions of "just intonation" and "consonance" that are both
useful and meaningful, whatever one's tuning preference may be.

> > Where was it that we were talking about scales?
> Everywhere !

Most of what I had to say about just intonation and rational numbers
had to do with intervals and chords, and I don't think I mentioned
scales until you brought them up. (See below.)

> From the OED:
> Tuning: the process of putting a musical instrument in tune.
> In tune: having the correct pitch or intonation.
> It's provenance is the Greek 'teino', meaning 'stretch'.
>
> Scale: Mus. an arrangement of all the notes in a system of music
> in ascending or descending order.
> It's provenance is the Latin 'scala' from 'scandere', meaning climb.
>
> As I said, one tunes *to* a scale.

I don't ordinary think of a scale as all of the tones in a system or
tuning (although that's one of its definitions), but rather as a
subset of that system or tuning. You seemed to be using the word
that way when you were making a distinction between the two:

<< This is partly correct. First it is scales we're concerned in this
instance, not tunings. >>

It's counter-productive to quote a definition for a word out of a
dictionary (and not even a music dictionary) when a somewhat
different definition is being used in the discussion.

Anyway, not to belabor the point, I think that it's *tones sounded
simultaneously* (i.e., intervals and chords rather than scales or
tunings) that are more relevant to our discussion of what is just
intonation and what is consonant.

> > In stating that temperaments are non-rational tunings, one would
not
> > logically conclude that all non-rational tunings are temperments.
> Actually that is exactly the error you made, which I pointed out.

I was trying to say that I didn't make that (or some such) error, but
that it appeared that you inferred that I had.

> > The term "inharmonic" is generally applied to timbres having non-
> > harmonic partials, not to scales or tunings.
> My using it to refer to scales, chords, & intervals is a logical
> extension. As consonance and dissonance are used to refer to all
> these things.

All I can say is, watch your definitions and usages of terms. If you
aren't careful with them, you're going to misunderstand others and
also be misunderstood. Dictionaries are limited in their helpfulness
when words have multiple meanings; get the particular meanings that
others are using by taking everything in context.

> > The term "just intonation" is widely accepted, and that is not
likely
> > to change for the foreseeable future.
>
> It's easy to see that, given the intransigence of it's most
> vigorous proponents.

The term is found in virtually all music dictionaries and
encylopedias, which, if they could be called partisan in any way, are
almost always pro-equal temperament. So your feud is not only with
the JI partisans. Rather than try to change the term, it's best to
try to promote a proper understanding of the concept.

--George

🔗emotionaljourney22 <paul@stretch-music.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗emotionaljourney22 <paul@stretch-music.com>

🔗Joel Rodrigues <joelrodrigues@mac.com>

Hello George,

> "gdsecor" <gdsecor@yahoo.com>
> --- In tuning@y..., Joel Rodrigues <joelrodrigues@m...> wrote:

>> To, 'But, 419914/404871 *is* within the harmonic series.'.
>>
>>> Theoretically, yes; for all practical purposes, no. You can't hear a
>>> harmonic that high in any musical tone because:
>>>
>>> 1) It wouldn't have sufficient amplitude;
>>>
>>> 2) Either it or its fundamental (or both) would be out of our range
>>> of hearing.
>>
>> But this is unimportant for theoretical scale construction using
>> octave reduction. No ?
>
> The traditional concept of just intonation involves intervals in
> which the roughness due to beating harmonics is eliminated when the
> harmonics are made to coincide (i.e., just tuning = elimination of
> beats). This is meaningless if either the fundamentals or harmonics
> in question cannot be heard. I was attempting to make this point in
> what I said next:

You say 'for all practical purposes, no', which I deduce from your further comment that this is with ref. to JI. Which was never my question. The harmonic series *is* theoretically infinite. 2:1 reduction allows us to go as far up the harmonic series as we choose. Whether someone thinks that the harmonic series is musically valid only up to a certain limit, is besides the point, and arguably (I'm almost afraid to use that word in this forum:-)) a matter of personal taste.

>> I was simply pointing out the error in your definition of a
>> rational number.
>
> Where did I give an erroneous definition of "rational number" or use
> the term incorrectly?

OK, it seems as though I was confused by this:
"JI includes only systems or sets of tones related by intervals that are defined as small-number (i.e., rational) ratios."
Where you seem to be equating 'small-number' to 'rational', practically implying that 419914/404871 is not rational. So, to get back to Robert Walker's original question, 419914/404871 may not be a 'Just' interval (as in 'Just Intonation'), I don't care to take a stand as I seem to have found a way to think and work beyond that, but it is a rational interval (as in Rational Intonation), as well as a harmonic interval (as in Harmonic Intonation, and before anyone pounces, I've done my homework on this turn of phrase).

>> But, what is the cut-off point beyond which you
>> would consider an interval to not be 'Just' ?
>
> I haven't decided exactly where that would be, but it would be above
> the 19 limit, and possibly below the 43 limit (I do know of a couple
> of uses for ratios of 41). While I doubt that ratios of 17 and 19
> can be tuned by ear successfully by eliminating beats between
> harmonics, I have found that consonant chords can be created using
> these intervals if the difference tones can be made to coincide,
> e.g., 13:16:19:22 or 13:17:21:25. By "consonant" I mean that you can
> hear something go out of tune if you mistune one of the tones. This
> is the sort of phenomenon that defines the whole concept of "just
> intonation" and makes it so attractive to its advocates.
>
> I suspect that the cut-off point you asked about would be arrived at
> when the harmonic entropy (or disorder) becomes large enough that the
> collective dissonance produced by beating harmonics (and whatever) in
> a chord significantly outweighed the consonance connected with
> coincident difference (and other combinational) tones. I'll have to
> experiment with this sometime to see if I can reach any definite
> conclusion.

Thank you for this, George. It helps with *my* (_evolving_) understanding of JI as a conception of a 'beatless aesthetic', as Margo once put it.

>>> Regarding one's unsuspecting friends: one of the challenges of
>>> writing a microtonal composition is to use new intervals without
>>> making the result sound as if it is out of tune.
>>
>> Perceiving music as 'out of tune' is a subjective thing, similar
>> and related to concepts of consonance and dissonance.
>> Consequently, what you suggest is not a goal of mine.
>
> One could intentionally use a microtonal scale to parody a
> conventional diatonic scale (to give the impression that it is out of
> tune) to portray a drunken or disoriented character in a piece of
> music. I believe that success of this effect would depend mostly on
> the skill of the composer and very little on the listener (assuming
> that the listener has previously heard diatonic music played in tune).
>
> Likewise I believe that it is possible for a composer to control the
> various factors (whatever they may be) that will determine whether or
> not a piece of music will sound strange and different or whether it
> will merely sound out of tune. I remember the first time I ever
> heard a recording of a Javanese gamelan -- it sounded quite unlike
> anything I had ever heard before, but it definitely didn't sound out
> of tune.

>> To, 'But, one may be thinking simply in terms of the harmonic
>> series with no sense or need for a "limit".'
>
>>> Then one has failed to recognize that the extent to which a
> harmonic
>>> limit may be successfully employed is not unlimited.
>
>> I disagree and stand by my original suggestion. Perhaps the
>> differences in understanding (and aesthetics) lie in the
>> distinctions of various conceptions of harmonic limit and
>> consonance/dissonance. Unless JI proponents think they've learnt
>> all there is to know. The end of science ? ;-)
>
> Then we will agree to disagree.

I don't think it's as much a matter of disagreement as it is about the width one's vision.

>>> Where was it that we were talking about scales?
>> Everywhere !
>
> Most of what I had to say about just intonation and rational numbers
> had to do with intervals and chords, and I don't think I mentioned
> scales until you brought them up. (See below.)
>> From the OED:
>> Tuning: the process of putting a musical instrument in tune.
>> In tune: having the correct pitch or intonation.
>> It's provenance is the Greek 'teino', meaning 'stretch'.
>>
>> Scale: Mus. an arrangement of all the notes in a system of music
>> in ascending or descending order.
>> It's provenance is the Latin 'scala' from 'scandere', meaning climb.
>>
>> As I said, one tunes *to* a scale.
>
> I don't ordinary think of a scale as all of the tones in a system or
> tuning (although that's one of its definitions), but rather as a
> subset of that system or tuning. You seemed to be using the word
> that way when you were making a distinction between the two:
>

You, along with many others continue to call scales 'tunings'. This is wrong. A tuning is more about the physical state of a musical instrument, i.e. tuning a piano to the Bohlen-Pierce scale.

> << This is partly correct. First it is scales we're concerned in this
> instance, not tunings. >>
>
> It's counter-productive to quote a definition for a word out of a
> dictionary (and not even a music dictionary) when a somewhat
> different definition is being used in the discussion.

The reason for my elaborating on a word's provenance, is not to be pedantic. I find that knowing the roots of a word helps to understand what it may or may not mean. The roots of 'scale' and 'tuning' show that they are not synonymous, nor is a scale a subset of a tuning. Your understanding of what a scale is appears to be tainted by mainstream incorrect use of terminology.

>>> In stating that temperaments are non-rational tunings, one would not
>>> logically conclude that all non-rational tunings are temperments.
>> Actually that is exactly the error you made, which I pointed out.
>
> I was trying to say that I didn't make that (or some such) error, but
> that it appeared that you inferred that I had.

"Any tuning in which a rational interval (no matter how small) vanishes is by definition a temperament, not a rational tuning." What you said.

>>> The term "inharmonic" is generally applied to timbres having non-
>>> harmonic partials, not to scales or tunings.
>> My using it to refer to scales, chords, & intervals is a logical
>> extension. As consonance and dissonance are used to refer to all
>> these things.
>
> All I can say is, watch your definitions and usages of terms. If you
> aren't careful with them, you're going to misunderstand others and
> also be misunderstood. Dictionaries are limited in their helpfulness
> when words have multiple meanings; get the particular meanings that
> others are using by taking everything in context.

I am extremely careful (but not infallible) with the words I use. The new thread about the misuse, inconsistency, and overall weirdness in commonly used mainstream musical terminology raises a long overdue issue. I know what I'm talking about in the above particular case, and I've done enough research into it (before discussing it in public) to know my logic is correct.

Just because I enter a room where a bunch of people insist on calling a dog a cat, is not going to intimidate me into joining in the absurdity.

Dictionaries are invaluable. And I always look into a word's etymology to be reasonably certain I know what I'm talking about.

>>> The term "just intonation" is widely accepted, and that is not likely
>>> to change for the foreseeable future.
>>
>> It's easy to see that, given the intransigence of it's most
>> vigorous proponents.
>
> The term is found in virtually all music dictionaries and
> encylopedias, which, if they could be called partisan in any way, are
> almost always pro-equal temperament. So your feud is not only with
> the JI partisans. Rather than try to change the term, it's best to
> try to promote a proper understanding of the concept.

As I've tried to explain, I am not interested in changing the term. I have no need to. I've always thought plainly in terms of the harmonic series. I was simply looking for a way discuss this without encountering Just Intonation rhetoric. I found it. When I ask about the harmonic series, I have zero interest in nonobjective JI coloured reaction.

> --George

Sincerely,
Joel

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., Joel Rodrigues <joelrodrigues@m...> wrote:
> Hello George,
>
> > "gdsecor" <gdsecor@y...>
> > --- In tuning@y..., Joel Rodrigues <joelrodrigues@m...> wrote:
>
> >> But, what is the cut-off point beyond which you
> >> would consider an interval to not be 'Just' ?
> >
> > I haven't decided exactly where that would be, but it would be
above
> > the 19 limit, and possibly below the 43 limit (I do know of a
couple
> > of uses for ratios of 41). While I doubt that ratios of 17 and 19
> > can be tuned by ear successfully by eliminating beats between
> > harmonics, I have found that consonant chords can be created using
> > these intervals if the difference tones can be made to coincide,
> > e.g., 13:16:19:22 or 13:17:21:25. By "consonant" I mean that you
can
> > hear something go out of tune if you mistune one of the tones.
This
> > is the sort of phenomenon that defines the whole concept of "just
> > intonation" and makes it so attractive to its advocates.
> >
> > I suspect that the cut-off point you asked about would be arrived
at
> > when the harmonic entropy (or disorder) becomes large enough that
the
> > collective dissonance produced by beating harmonics (and
whatever) in
> > a chord significantly outweighed the consonance connected with
> > coincident difference (and other combinational) tones. I'll have
to
> > experiment with this sometime to see if I can reach any definite
> > conclusion.
>
> Thank you for this, George. It helps with *my* (_evolving_)
> understanding of JI as a conception of a 'beatless aesthetic',
> as Margo once put it.

And thank you for directing my attention to the need for testing for
a possible cutoff point for JI intervals.

> >> To, 'But, one may be thinking simply in terms of the harmonic
> >> series with no sense or need for a "limit".'
> >
> >>> Then one has failed to recognize that the extent to which a
> > harmonic
> >>> limit may be successfully employed is not unlimited.
> >
> >> I disagree and stand by my original suggestion. Perhaps the
> >> differences in understanding (and aesthetics) lie in the
> >> distinctions of various conceptions of harmonic limit and
> >> consonance/dissonance. Unless JI proponents think they've learnt
> >> all there is to know. The end of science ? ;-)
> >
> > Then we will agree to disagree.
>
> I don't think it's as much a matter of disagreement as it is
> about the width one's vision.

To summarize, then, it's the width of your vision vs. the limitations
of my hearing.

> >>> Where was it that we were talking about scales?
> >> Everywhere !
> >
> > Most of what I had to say about just intonation and rational
numbers
> > had to do with intervals and chords, and I don't think I mentioned
> > scales until you brought them up. (See below.)
> >> From the OED:
> >> Tuning: the process of putting a musical instrument in tune.
> >> In tune: having the correct pitch or intonation.
> >> It's provenance is the Greek 'teino', meaning 'stretch'.
> >>
> >> Scale: Mus. an arrangement of all the notes in a system of music
> >> in ascending or descending order.
> >> It's provenance is the Latin 'scala' from 'scandere', meaning
climb.
> >>
> >> As I said, one tunes *to* a scale.
> >
> > I don't ordinary think of a scale as all of the tones in a system
or
> > tuning (although that's one of its definitions), but rather as a
> > subset of that system or tuning. You seemed to be using the word
> > that way when you were making a distinction between the two:
>
> You, along with many others continue to call scales 'tunings'.
> This is wrong. A tuning is more about the physical state of a
> musical instrument, i.e. tuning a piano to the Bohlen-Pierce
> scale.
>
> > << This is partly correct. First it is scales we're concerned in
this
> > instance, not tunings. >>
> >
> > It's counter-productive to quote a definition for a word out of a
> > dictionary (and not even a music dictionary) when a somewhat
> > different definition is being used in the discussion.
>
> The reason for my elaborating on a word's provenance, is not to
> be pedantic. I find that knowing the roots of a word helps to
> understand what it may or may not mean. The roots of 'scale' and
> 'tuning' show that they are not synonymous, nor is a scale a
> subset of a tuning. Your understanding of what a scale is
> appears to be tainted by mainstream incorrect use of terminology.

Our problem is that words have multiple meanings, and "scale" is no
exception. I generally think of a scale as a subset of a tuning or
tonal system, e.g., a major or minor scale as a subset of any number
of different tunings (by which word I am including temperaments).
And if I am going to choose an organization of tones (say 5 to 10 in
number) out of a system such as 31-ET or 72-ET to write a melody,
what would I call call that set of tones, if not a scale?

Now if you consider this incorrect use of terminology, I guess you're
entitled to your own opinion; but don't expect everyone else to
assume that immediately.

> >>> In stating that temperaments are non-rational tunings, one
would not
> >>> logically conclude that all non-rational tunings are
temperments.
> >> Actually that is exactly the error you made, which I pointed out.
> >
> > I was trying to say that I didn't make that (or some such) error,
but
> > that it appeared that you inferred that I had.
>
> "Any tuning in which a rational interval (no matter how small)
> vanishes is by definition a temperament, not a rational tuning."
> What you said.

We've gone around in a circle without resolving anything and are
still talking past one another. I give up!

> >
> > All I can say is, watch your definitions and usages of terms. If
you
> > aren't careful with them, you're going to misunderstand others and
> > also be misunderstood. Dictionaries are limited in their
helpfulness
> > when words have multiple meanings; get the particular meanings
that
> > others are using by taking everything in context.
>
> I am extremely careful (but not infallible) with the words I
> use. The new thread about the misuse, inconsistency, and overall
> weirdness in commonly used mainstream musical terminology raises
> a long overdue issue. I know what I'm talking about in the above
> particular case, and I've done enough research into it (before
> discussing it in public) to know my logic is correct.
>
> Just because I enter a room where a bunch of people insist on
> calling a dog a cat, is not going to intimidate me into joining
> in the absurdity.
>
> Dictionaries are invaluable. And I always look into a word's
> etymology to be reasonably certain I know what I'm talking about.

Then I know you'll enjoy Joe Monzo's dictionary, if you haven't
already see it:

http://www.ixpres.com/interval/dict

There's a lot of good stuff in there, and it's being updated all the
time. (Just taking an opportunity to express some appreciation for
your efforts, Monz -- keep up the good work!)

--George

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > My examples of isoharmonic chords don't require rich timbres (or
even
> > *any* harmonic partials at all) in the tones to make apparent
> > whatever consonance those chords may have, so I would consider
the
> > coinciding combinational tones to be a much better justification
for
> > consonance at higher harmonic limits than coinciding harmonics.
>
> right -- this would also imply that the effective, audibly
> meaningful "limit" for otonalities is much higher than for
> utonalities (or even ASSes). the former may benefit from coinciding
> combinational tones, and even a clear overall virtual pitch or root
> or periodicity to the whole sonic pattern, while the latter have
only
> coinciding harmonics with which to "justify" them, and even those
> occur in the midst of considerable sonic chaos.

That's very much the way I see and hear it. I never had much
interest in utonality for harmony, even in the 9 limit -- when I
first heard it, I thought that 1/7:1/6:1/5:1/4 sounded like a parody
of 5:6:7:9. To get the variety I wanted using only otonalities, I
simply raised my harmonic limit, which is presently at 19.

> on the other hand, i can't say i've had much experience finding
those
> higher-limit otonal chords "consonant" per se. in the midst of
> discussions on tetrads on the harmonic_entropy list, joe monzo
(iirc)
> created a 9:11:13:15 chord (at my request), and i don't think
anyone
> found it "consonant" -- at least not nearly as consonant as many
> tetrads with a higher "otonal limit" but containing more consonant
> dyads . . . so, though i'm sure it's relatively easy to tune
> 9:11:13:15 by ear with natural timbres, i'm not yet convinced that
> one would want to :)

What???!!! That's been one of my favorite isoharmonic chords for
many years now, one that I liked the first time I tried it. I enjoy
its resolution to 18:21:24:30, then to 4:5:6:8. (Ivor Darreg also
wrote me many years ago about another chord progression in which he
used it and liked the effect.)

> of course, these kinds of discussions are always imperiled by
> unstated considerations of timbre, register, amplitude, audio
> reproduction equipment, stereo separation, musical context, musical
> training, and acquired taste, which may be different among the
> participants . . .

I guess I would have to emphasize *musical context*. Now that I've
thought about it, I can see why you might not appreciate 9:11:13:15
if you only heard it by itself. Once I had an instrument on which I
could improvise with many different kinds of chords in a lot of
different tunings, my whole perspective changed.

--George

🔗M. Schulter <MSCHULTER@VALUE.NET>

Hello, there, everyone, and reflecting a bit on this thread, I might
propose three aspects of Just Intonation or JI:

Harmonic Intonation (HI)
The inclusion in a JI system of some small integer ratios
with audibly pure or "coupling" partials, e.g. 2:3:4.

Combinatorial Intonation (CI)
The inclusion in a JI system of some "intermediate"
integer ratios where the blending of combinatorial
tones can give certain sonorities a "pure" rather
than "tempered" effect, as discussed by George Secor.

Rational Intonation (RI)
More generally, the use of _any_ integer ratios,
whether or not they also produce HI or CI effects.

For example, a Pythagorean intonation system of 13th-14th century
Europe meets the HI concept inasmuch as it includes some pure
sonorities of 2:3:4, and also for example 4:6:9 or 6:8:9, with small
integer ratios having an audible "purity" based on matching of
partials. Additionally, it includes some complex RI ratios such as
64:81:96 treated in practice and theory as _relatively_ "concordant,"
but not involving any obvious HI or CI relationship, since the numbers
are so large.

More generally, the term "JI" in its classic usage seems to imply an
RI system (all intervals defined by integer ratios) where at least
some of these ratios also fit an HI or CI category.

(However, the kind of "perceptual JI" discussed by Dave Keenan, and
also "adaptive JI" as discussed by Paul Erlich and others, often
involve the elements of audible HI or CI without the element of a
tuning system based on integer ratios only -- see the discussion near
the end of this article.)

Many of the "What is JI?" debates tend to focus on what I would
consider rather exceptional systems where complex RI generators or
sets of intervals are used without any HI or CI intervals.
Kirnberger's 12-EDO approximation of 1766 using a generator of
10935:8192 (almost identical to a 500-cent fourth) could provide one
example, and an instrument fretted in 25:24 steps as an approximation
of 17-EDO could provide another.

In these instances, we have a rational approximation of an irrational
temperament, where the very large integer ratios seem to have little
connection to the HI or CI themes typical of the JI outlook.

Turning to more typical JI systems, I would like to affirm that the
set of RI intervals is indeed unbounded, and that very large ratios
indeed may be generated by systems such as Pythagorean or 2-3-prime
intonation.

However, with George Secor I would agree that from an HI or even CI
viewpoint, the range of independently significant ratios does have
some limit, even if it is difficult to define with any precision.
The music of LaMonte Young is famous for making impressively large
ratios perceptibly "harmonic" or "combinatorial."

Of course, very large ratios may also have great HI or CI
significance, but because they closely "converge" with simpler
ratios in what Joe Monzo and I have sometimes called a "xenharmonic
bridge." Thus I speak of "_independent_ significance" from an HI/CI
viewpoint as a quality mainly of small to "intermediate" ratios.

In describing the HI or CI side of JI, I might propose the term
"correspondence" to describe the matching or blending of harmonic
partials or combinatorial tones.

Thus for JI systems premised on an "n-odd-limit," one might say that
this limit defines the scope of deliberate correspondence.

I find "correspondence" possibly a preferable term to "consonance,"
since the latter can often be a graduated spectrum in a given
practical or theoretical tradition. Thus in a Gothic Pythagorean
setting, a regular third at 81:64 or 32:27 is typically accorded a
considerable degree of "partial concord," but does not necessarily
imply what we might call HI or CI "correspondence."

One trait of classic JI systems is that simpler ratios with HI or CI
qualities tend to "ramify" into more complex RI intervals. This is a
different kind of structure, at least in intention, than where large
RI ratios are chosen to approximate some irrational temperament.

Thus one might call a system of rational ratios without any HI or CI
intervals as "formally JI," but not "typically JI."

Historically, I might consider a point made by scholars such as Bill
Alves and Jacky Ligon: the _melodic_ aspects of a JI system, for
example the use of superparticular steps, may in some traditions play
at least as important a role as the express or inferred HI or CI
aspects. For example, the rational tunings of ancient Greek and the
medieval Near East could be using steps such as 12:11 as much for
their melodic qualities as for any vertical "correspondence" of these
intervals.

In my view, the mixture of simpler (HI and CI) with more complex (RI)
intervals is one of the main attractions of JI, permitting variety and
contrast.

Thus I would say that _any_ integer-based interval is a legitimate
element which could be included in some JI systems, while recognizing
at the same time that in a typical JI system, HI and/or CI intervals
play an important role.

To put this in terms like those of Paul Erlich's harmonic entropy,
subject always to his friendly and helpful correction or
clarification:

(1) A JI system typically includes some small integer
or "lower entropy" ratios which combine to
generate larger integer ratios with a "higher
entropy effect."

(2) Sometimes simple HI or CI ratios may combine to
generate larger integer ratios closely "converging"
with smaller ratios, and thus having a similar
"lower entropy" effect, like a slightly tempered
version of the simpler ratio.

Thus "JI" itself is an open concept, having a scope including the set
of all rational ratios (RI), but HI or CI implies a kind of vertical
correspondence generally implying "not-too-large" ratios.

The usual convention that "typical JI" systems include _some_ HI or CI
intervals recognizes both the openness and the generally implied
structure of a system of "just" or "pure" intonation.

Having suggested this approach to "classic JI" (all RI ratios, some HI
or CI ratios), I might add that contributors here such as Dave Keenan
have proposed a "perceptual" definition of "JI" as "audibly HI,"
whatever mathematical concepts the performers might or might not
entertain about what they are doing.

Also, in "adaptive JI," HI or CI sonorities result from intonational
systems involving some irrational intervals -- whether in a fixed
tuning such as Nicola Vicentino's evident scheme of 1555 and 1561
based on two 19-note gamuts in 1/4-comma meantone at 1/4 comma apart,
or in the flexible adaptive tuning algorithms of a Bill Sethares or
John deLaubenfels.

Again, as Dave Keenan might emphasize, performers on flexible pitch
instruments such as the human voice might achieve this result with or
without the influence of a mathematical model of tuning. Barbershop
singing, and the kind of Renaissance intonation achieved by Bob
Wendell and his choral group, are possible examples -- with the
theoretical or mathematical outlook of the performers likely varying

Most appreciatively,

Margo Schulter
mschulter@value.net

🔗Kraig Grady <kraiggrady@anaphoria.com>

Hello George!
You can also find thus type of chord formation with common difference tones also in Augusto Novaro. At one point i examined the inversions of different harmonic tetrads up to the 11th harmonic (sets of 4 out of 6) and every once in a while such an animal as above would show its head which caused me to believe that "coincidence" in difference tones has an effect on the perception of consonance.
I constructed quite a few pieces using nothing more than different inversions of tetrads. The same notes can go from one extreme to another.

>
> From: "gdsecor" <gdsecor@yahoo.com>
> Subject: Isoharmonic chords (was: misc clean up ... )
>
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> >
> > > My examples of isoharmonic chords don't require rich timbres (or
> even
> > > *any* harmonic partials at all) in the tones to make apparent
> > > whatever consonance those chords may have, so I would consider
> the
> > > coinciding combinational tones to be a much better justification
> for
> > > consonance at higher harmonic limits than coinciding harmonics.
> >
> > right -- this would also imply that the effective, audibly
> > meaningful "limit" for otonalities is much higher than for
> > utonalities (or even ASSes). the former may benefit from coinciding
> > combinational tones, and even a clear overall virtual pitch or root
> > or periodicity to the whole sonic pattern, while the latter have
> only
> > coinciding harmonics with which to "justify" them, and even those
> > occur in the midst of considerable sonic chaos.
>
> That's very much the way I see and hear it. I never had much
> interest in utonality for harmony, even in the 9 limit -- when I
> first heard it, I thought that 1/7:1/6:1/5:1/4 sounded like a parody
> of 5:6:7:9. To get the variety I wanted using only otonalities, I
> simply raised my harmonic limit, which is presently at 19.
>
> > on the other hand, i can't say i've had much experience finding
> those
> > higher-limit otonal chords "consonant" per se. in the midst of
> > discussions on tetrads on the harmonic_entropy list, joe monzo
> (iirc)
> > created a 9:11:13:15 chord (at my request), and i don't think
> anyone
> > found it "consonant" -- at least not nearly as consonant as many
> > tetrads with a higher "otonal limit" but containing more consonant
> > dyads . . . so, though i'm sure it's relatively easy to tune
> > 9:11:13:15 by ear with natural timbres, i'm not yet convinced that
> > one would want to :)
>
> What???!!! That's been one of my favorite isoharmonic chords for
> many years now, one that I liked the first time I tried it. I enjoy
> its resolution to 18:21:24:30, then to 4:5:6:8. (Ivor Darreg also
> wrote me many years ago about another chord progression in which he
> used it and liked the effect.)
>
> > of course, these kinds of discussions are always imperiled by
> > unstated considerations of timbre, register, amplitude, audio
> > reproduction equipment, stereo separation, musical context, musical
> > training, and acquired taste, which may be different among the
> > participants . . .
>
> I guess I would have to emphasize *musical context*. Now that I've
> thought about it, I can see why you might not appreciate 9:11:13:15
> if you only heard it by itself. Once I had an instrument on which I
> could improvise with many different kinds of chords in a lot of
> different tunings, my whole perspective changed.
>
> --George
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

misc clean up (was Comments for Julia... & Is 19-et j.i.?)

🔗Joel Rodrigues <joelrodrigues@mac.com>

🔗jpehrson2 <jpehrson@rcn.com>

🔗genewardsmith <genewardsmith@juno.com>

🔗Joel Rodrigues <joelrodrigues@mac.com>

🔗emotionaljourney22 <paul@stretch-music.com>

🔗emotionaljourney22 <paul@stretch-music.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗emotionaljourney22 <paul@stretch-music.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗emotionaljourney22 <paul@stretch-music.com>

🔗Joel Rodrigues <joelrodrigues@mac.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗M. Schulter <MSCHULTER@VALUE.NET>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗graham@microtonal.co.uk