Locking in

Robert Valentine posted:
>
> The discussion about "locking in" on various intervals
> brings up some left over issues from about a two year
> series of posts we had here about "complexity measures"
> of intervals, and concerns about significance of
> "prime limits", "odd limits" and the overtone series.
>
> Paul has a graph posted somewhere of an equation that
> shows troughs between 1 and 2 at the expected ratios
> in the expected manner, deep trough at 3/2, slightly
> less deep at 4/3, slightly less at 5/4 and 8/5 (these
> may not be exact, perhaps Paul will mention where and
> how it was produced).

Is that similar to the illustrations on p. 193 of Helmholz "Sensations"
(Ellis translation in paperback)?
>
> My question, to you sensitive singers over pedals, is...
>
> ...when you sing the most 'locked in' major second, is
> it 9/8, 8/7 or 10/9 or is it something else?

The difference between 9/8 and 8/7 is quite easy to hear. My impression is
that in an 8/7 second the upper pitch seems to be the "root" and in the 9/8
second the lower pitch seems to be the root. Regarding the 10/9 second, I
have often thought it would be interesting to construct a "blind hearing"
test in which experienced musicians were asked to identify 9/8 and 10/9
seconds as being scale steps 1-2 or 2-3 and see whether any consistency
occurs.

In regard to singing a major second over a pedal, it would seem a given that
the ear would like to hear 9/8--the drone being heard as "root."
>
> ...the most natural 'tritone' (for want of a less
> weighted term), is it 7/5, 11/8, 10/7 or something
> else?

The term "natural" may be a bit ambiguous here (see, Paul, I am listening),
but it is quite easy to hear the difference between the 7/5 diminished fifth
and the 10/7 augmented fourth. Today in my musicianship class I was tuning
(locking) these randomly and asking my third semester students to identify
them. They could readily do so by sensing whether the top pitch wanted to
resolve upward (leading tone to tonic) or downward (chord seventh to third).

The 11/8 "tritone" is not related to the other two, I feel. Its most
practical use, in my experience is to use it to color an "augmented 11th"
chord, along with the b7th and 9th. It works there not as a functional
tritone, but more as a timbral ingredient. I don't hear it wanting to "go"
anywhere specific. I heard one the other day on the radio that was tuned
exquisitely and appropriately "in the cracks" between 4 and #4. It was
performed by a female jazz vocalist, but they didn't slate the recording
afterward, so I don't know who it was.
>
> The idea here is that people who believe in greater
> importance for "prime limits", "odd limits" and
> "overtone series significance" would probably see some
> different sorting.

You left me here, Bob. I'd love to know what these phrases mean in layman's
English, particularly the first two. Also, how are you using the word
"sorting."

Jerry

Hi Gerald,

>The term "natural" may be a bit ambiguous here (see, Paul, I am listening),
>but it is quite easy to hear the difference between the 7/5 diminished
fifth
>and the 10/7 augmented fourth. Today in my musicianship class I was tuning
>(locking) these randomly and asking my third semester students to identify
>them. They could readily do so by sensing whether the top pitch wanted to
>resolve upward (leading tone to tonic) or downward (chord seventh to
third).

So, Gerald, to you the dominant seventh chord is 4:5:6:7, yet the major
triad is not 4:5:6?

Paul Erlich asked:

> So, Gerald, to you the dominant seventh chord is 4:5:6:7, yet the major
> triad is not 4:5:6?

I can "lock in" both the "low third" and the "high third" at will in both
the major triad and the dominant (major-minor) seventh chord. My "mystery"
has to do with an apparent singer preference for the high third in either or
both. I hope I didn't give the impression that I believe the 4:5:6 triad is
not the "real one." I simply would like to explore possible rationalizations
regarding the other one.

Lacking tools to verify the relative frequencies of "my" intervals (soon to
be remedied), I am simply assuming that my perception of the difference
between 5:7 and 7:10, for example, is actually that. All I know for sure is
that I clearly hear a "lock in" difference between the "tritones" when
inverted. Therefore, my use of the applicable low-number ratios is based on
an assumption that these are likely appropriate. If it looks like a cat,
acts like a cat, sounds like a cat, it must be a cat. The "problem" I am
researching is that the third in either of the chords cited above appears at
times to be two different cats.

Jerry

Bob Valentine wonders:

> Is feeling of locking stronger on 8/7 than 10/9? In 8/7, part of the
> dyad will be an 'octave' of the difference tone, whereas neither the
> 10/9 has that strong of a relation...

It has been a bit of light-hearted sport through the years to walk into an
advanced ear training class, walk past the piano striking a minor third on
the way to the desk and ask "What interval is that?" More often than not,
the quick answer of the class is "major third." In order to understand my
point, please note that intervals really do not convey a "major" or "minor
flavor (a minor third is a major sixth in inversion). Also, realize that
these students understand the difference between major and minor thirds. I
think they are subjectively supplying a "phantom root" of 4:5:6 in
imagination and in fact "hearing" a major triad.

Very likely, the same principle might apply to the 9:10 "major second." It
would be very interesting to know (as I mentioned earlier) to know if
experienced ears can consistently hear 8:9 as scale steps 1-2 and 9:10 as
scale steps 2-3. After I get my golf score consistently under 80, I may
conduct a research experiment to find out (if no one else has done so by
that time).

Jerry

Bob Valentine reports:

> In both cases, I THOUGHT I was 'locking' on the 11/8 (not the term I used
> but thats the feeling). Now I realize that I was probably NOT that far
> South! I'll have to go back and see just what that tritone I was singing...
>
> Others mentioned the 45/32, and I think that is probably a strong
> candidate.
>
> Ooops, snipped your comments about 11/8. I do believe that this is used
> melodically. Before you joined the list we had some discussions with John
> Link regarding altered dominant chords or thier logical inverse,
> the "lydian dominant" sound 7 9 #11 13. In my experiments I was not
> convinced that this was properly tuned in the "lower overtone"
> manner, (7:9:11:13) but felt that the "upper structure triad" needed to
> be expressed, which would make it more
>
> 7/4 9/8 45/32 27/16.
>
> I was somewhat convinced in these discussions that some of the big
> jazz chords I like are really coming more from the tempered world than
> some other.

Perhaps. But after experiencing hundreds of hours hearing singers "adjust"
such sonorities, I doubt that the "tempered world" has much to do with
locking in these "big jazz chords" instinctively. I don't think sensitive
singers are influenced much by having been exposed to tempered tuning. Once
they sense and experience "acoustic" tuning, tempered tuning can no longer
compete for their attention.

Regarding high harmonic ratios such as 45/32 and 27/16, do you really think
human perception operates in that vicinity??? I can't imagine "locking in"
on such high ratios. I'm perfectly willing to relinquish that domain to the
instrumental number crunchers.

BTW, I am really enjoying your contributions to this thread. But please
watch out for those inadvertent snips. I worked hard on that post. ;-)

Jerry

From: DWolf:

> I've been pondering the apparent raised third by choral groups. It seems to
> very difficult to find positive grounds for identify the interval with a 9:7,
> especially within a triadic context.

Thanks for your interest and your post. I'm all ears at this point.

> Perhaps we're framing the question wrong. If, as a warm up, we were to sing
> the triad c-e-g, I might very well sing the "e" raised, in anticipation of
> moving to an f in a subdominant harmony. The exact interval of that raising
> need not be as important as the sensation of "leading-toneness". If,
> however, I sang that "e" following a dominant harmony, I would probably relax
> the intonation, seeking a restful conclusion on a 4:5:6 triad.

Keep in mind that the "experiments" that raised the question of the "high
third" do not involve musical context. The observation is simply that when
the fifth is introduced to a sounding root and third, singers consistently
"float" the established 4:5 third well above the 12-tET tempered tuning. I
have observed this consistently many times with many choral groups--most of
them not trained by me.

I understand what you are saying about the tendency to raise leading tones
and release tension of chord sevenths. It is entirely possible that these
are often exaggerated by performers sensitive to these dynamic ingredients
in expressive performance.

BTW, Did you see my post regarding the tunings of the third by Sheila
Chandra? On the first track, she consistently uses the "high third" when
preceded by scale step 4 (granted not in a V7 chord but over a double
drone). This seems contrary to your experience, but I'm anxious to gather
all available opinion and experience on the subject.

> It would be interesting if Gerald could record a choral group singing the
> same triad three times: (1) alone, (2) before a subdominant chord, and (3)
> after a dominant chord.

I'll make a note of this idea and work it in during the next week or so.
(Semester began Monday and the new group is just getting organized.) The
fact that the root of IV is a higher "step 4" pitch than the seventh of V7
should favor your thesis. I'll let you know what happens. I need to get my
MP3 act together soon. I guess I'll have to forgo a couple rounds of golf.

Jerry

Gerald Eskelin wrote,

>I doubt that the "tempered world" has much to do with
>locking in these "big jazz chords" instinctively. I don't think sensitive
>singers are influenced much by having been exposed to tempered tuning. Once
>they sense and experience "acoustic" tuning, tempered tuning can no longer
>compete for their attention.

I totally disagree, Gerald. Although the singers may indeed find "acoustic"
or locked versions of these chords, many of them exist in the first place
due to temperament, and the tempered versions that they've heard over and
over again without deviation all their lives are the ones providing a
reference for what is "right".

John Link wrote,

>felt that the "upper structure triad" needed to
>> be expressed, which would make it more
>>
>Regarding high harmonic ratios such as 45/32 and 27/16, do you really think
human perception operates in that vicinity??? I can't imagine "locking in"
on such high ratios. I'm perfectly willing to relinquish that domain to the
instrumental number crunchers.> 7/4 9/8 45/32 27/16.

Sorry that got garbled.

John Link
>>Before you joined the list we had some discussions with John
>> Link regarding altered dominant chords or thier logical inverse,
>> the "lydian dominant" sound 7 9 #11 13. In my experiments I was not
>> convinced that this was properly tuned in the "lower overtone"
>> manner, (7:9:11:13) but
>>felt that the "upper structure triad" needed to
>> be expressed, which would make it more
>>
>> 7/4 9/8 45/32 27/16.

Gerald Eskelin wrote,

>Regarding high harmonic ratios such as 45/32 and 27/16, do you really think
>human perception operates in that vicinity??? I can't imagine "locking in"
>on such high ratios. I'm perfectly willing to relinquish that domain to the
>instrumental number crunchers.

Gerald, you're being misled by these ratios. 45/32 and 27/16 form a 4:5:6
triad with 9/8, so with 9/8 there, they would be very easy to "lock into".
To be fair, I agree that these ratios alone would be too difficult to lock
into on their own, but that was not the context here -- it was a full chord.

>From: "Gerald Eskelin" <stg3music@earthlink.net>

>It would be very interesting to know (as I mentioned earlier) to know if
>experienced ears can consistently hear 8:9 as scale steps 1-2 and 9:10 as
>scale steps 2-3.

I don't see any reason why that would be the case, since the tuning of the
tones of the scale steps depends upon the harmonization. You seem to have
fallen prey to what you identified in your book "Lies My Music Teacher Told
Me" as lie #6: A scale is a series of eight fixed pitches.

Consider the following progression in the key of C major:

Cmaj7 Dmin7 Emin7 Fmaj7

S: B C D E

A: G A B C

T: E F G A

B: C D E F

Note that both the soparano(S) and the baritone(B) sing the sequence C, D,
E. I expect that they would tune the steps differently. I would expect the
soprano to sing C, D, E as a 9/8 followed by a 10/9, and the baritione to
sing a 10/9 followed by a 9/8.

John Link

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Gerald Eskelin wrote,

>>It would be very interesting to know (as I mentioned earlier) to know if
>>experienced ears can consistently hear 8:9 as scale steps 1-2 and 9:10 as
>>scale steps 2-3.

John Link wrote,

>I don't see any reason why that would be the case, since the tuning of the
>tones of the scale steps depends upon the harmonization.

I agree with John here. However, over a _low_ tonic drone, there would be a
tendency to lock scale step 1 at 4:1, scale step 2 at 9:2, and scale step 3
at 5:1, giving the proportions Gerald indicates.

Gerald Eskelin wrote,

>It would be very interesting to know (as I mentioned earlier) to know if
>experienced ears can consistently hear 8:9 as scale steps 1-2 and 9:10 as
>scale steps 2-3.

This would imply scale step 3 is consistently 5:4 above scale step 1. What
happened to your "high third"? Furthermore, if steps can really be heard as
ratios in this way, wouldn't it be kind of natural to interpret the "high
third" as the product of two 8:9 steps, i.e., a Pythagorean major third?
That is the usual take on Indian music, where the just (5/4) and Pythagorean
(81/64) major thirds are sruti #s 7 and 8 out of a 22-sruti octave. Now it
is true that the Pythagorean major third wouldn't lock harmonically as part
of a triad, so for the third time I suggest the possibility of
1/24:1/19:1/16 for your locked major triad with high third.

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
>Gerald Eskelin wrote,
>
>>>It would be very interesting to know (as I mentioned earlier) to know if
>>>experienced ears can consistently hear 8:9 as scale steps 1-2 and 9:10 as
>>>scale steps 2-3.
>
>I wrote,
>
>>I don't see any reason why that would be the case, since the tuning of the
>>tones of the scale steps depends upon the harmonization.
>
>I agree with John here. However, over a _low_ tonic drone, there would be a
>tendency to lock scale step 1 at 4:1, scale step 2 at 9:2, and scale step 3
>at 5:1, giving the proportions Gerald indicates.

Agreed.

John Link

****************************************************************************

Watch for the CD "Live at Saint Peter's" by the JOHN LINK VOCAL QUINTET,
featuring original compositions as well as arrangements of instrumental
music by Brahe and Taylor, Chick Corea, Miles Davis, Claude Debussy, Bill
Evans, Ennio and Andrea Morricone, Modeste Mussorgsky, Erik Satie, and Earl
Zindars.

****************************************************************************

Check out WWW.DUESBERG.COM for information that could make the difference
between life and death for you or someone you know.

****************************************************************************

To my post:
>
> << BTW, Did you see my post regarding the tunings of the third by Sheila
> Chandra? On the first track, she consistently uses the "high third" when
> preceded by scale step 4 (granted not in a V7 chord but over a double
> drone). This seems contrary to your experience, but I'm anxious to gather
> all available opinion and experience on the subject. >>

DWolf offered:

> I wasn't thinking about Hindustani music in my post. There, harmonic
> considerations would be altogether out-of-place, an one has an extended
> vocabulary of melodic intervals in general, as well as for individual
> artists. Do you know where she comes from, or from what tradition? Do the
> recording give names for the compositions or rags? With a bit more
> information, we might be able to contextualize her performances a bit.

The "Moonsung" CD insert leaves little doubt that her background is Indian
but she appears to have done some pop recordings as well. It also clearly
indicates that her performance is grounded in harmonics. She says: "In any
performance, the voice and the acoustic environment become one." Her
performances (here) are firmly based on pitches that agree with my sense of
acoustic consonance. (So does much of the Indian folk music I have heard.)

I realize that in many exotic styles, vocalist are able to imitate pitch
relations likely learned from instruments tuned to "arbitrary" intervals
that are not particularly consonant. But then so do many Western singers
who's intonation is influenced (sadly) by the tempered keyboard. That has no
bearing, I believe, on the mystery of the "high third" produced "naturally"
and performed consistently by pitch sensitive singers and string players.
The singers I hear have grown up with tempered keyboards so their sense of
"acoustic" tuning is learned and expressed IN SPITE OF instrumental tuning
environments.

I hate to be a trouble-making pain in the ass, but at least I'm a sincere,
honest and sometimes lovable pain in the ass.

Thanks for your input, D. If you like, find her recording and let me know
what you think. In the meantime I'll be working on my "objectification
program."

Jerry

> Gerald Eskelin wrote,
>
>>I doubt that the "tempered world" has much to do with
>>locking in these "big jazz chords" instinctively. I don't think sensitive
>>singers are influenced much by having been exposed to tempered tuning. Once
>>they sense and experience "acoustic" tuning, tempered tuning can no longer
>>compete for their attention.

To which Paul Erlich "totally" disagreed:
>
> I totally disagree, Gerald. Although the singers may indeed find "acoustic"
> or locked versions of these chords, many of them exist in the first place
> due to temperament, and the tempered versions that they've heard over and
> over again without deviation all their lives are the ones providing a
> reference for what is "right".

Paul, why do you continually "totally" disagree. Why not simply question the
statement on some basis or other and give your reason for doing so. You
can't logically say that doodlaboppins don't exist until you have
experienced doodlaboppins not existing. My LA Jazz Choir, bless its little
retired heart, sang hot jazz chords (even hot triads, for that matter) that
a piano could only dream about. Now, if you are referring to vocal jazz
groups that model after keyboard-tuned chords, you are likely correct; but I
don't think these will be very exciting to experienced vocal jazz listeners.

You read my account in my "Lies" book of the development of the LA Jazz
Choir, Paul. You know what I'm talking about here. Singing tunings other
than those learned from the keyboard was the whole reason for being of the
Pierce College Jazz Choir and later the LA Jazz Choir.

The key phrase in my post was "sensitive singers." So please don't
generalize my reports of specific experiences in order to "totally
disagree," please. I suggest you slow down, read carefully, ponder a bit,
and perhaps you will further expand your already considerable knowledge of
"Truth."

Respectfully submitted,

Jerry (AKA Gerald)

Jerry wrote,

>You read my account in my "Lies" book of the development of the LA Jazz
>Choir, Paul.

No, I haven't read your book.

>Now, if you are referring to vocal jazz
>groups that model after keyboard-tuned chords, you are likely correct; but
I
>don't think these will be very exciting to experienced vocal jazz
listeners.

Let me put my point another way -- a good singing group will certainly find
tunings for certain chords, one might say "acoustic" tunings, that are
smoother than 12-tone equal tempered tuning. However, the music itself will
have been composed on a 12-tET instrument, or at least within a set of rules
and conventions that spring mainly from the harmonic and melodic balances,
resources, and limitations of 12-tET (and partially those of tunings used
earlier). Hence in performing the music the musicians will choose those
acoustically resonant tunings which preserve these relations, and not ones
which don't. The tuning of a good group singing Gesualdo would be informed
by a different set of compositional desiderata than that of a group singing
jazz.

My point was mainly than many jazz chords and progressions arose precisely
from the way closed 12-tone tunings manage to tie together intervals that
would be incompatible in pure just intonation. Mostly these are horizontal
issues, but often they are vertical as well. Singing these progressions one
can only go so far in retuning them before their essential structure is
lost.

The main reason I like to bring this up is that there are myriad
acoustically "locked" chords that would _not_ be used in any rendition of
jazz or popular music, precisely because these styles arose from (or at
least along with) rather rigid tuning models. What many of us on the list
would like to do is investigate ways of creating new styles of music that
explore these sonorities, or at least would allow them to be explored by a
sensitive choir. Even chords like 14:18:21 might take their place in a new
melodic/harmonic vocabulary that is divorced from the familiar styles that
have arisen over the last few hundred years (for example, Margo Schulter has
suggested using this chord in a Xeno-Gothic context where the major third
(in this case tuned 7:9) typically resolves outward into a perfect fifth).

[Paul Erlich:]
> However, the music itself will have been composed on a 12-tET
instrument, or at least within a set of rules and conventions that
spring mainly from the harmonic and melodic balances, resources, and
limitations of 12-tET (and partially those of tunings used earlier).
Hence in performing the music the musicians will choose those
acoustically resonant tunings which preserve these relations, and not
ones which don't.

Though there are many things in this point of view that I agree with
(and find very helpful in understanding certain tuning issues), this
seems to me to be casting their net (so to speak) way way too far!
(But then again Morimoto is my favorite Iron Chef...)

>The tuning of a good group singing Gesualdo would be informed by a
different set of compositional desiderata than that of a group singing
jazz.

Well yeah, but the second part of this point seems to me to be way too
broad... some particular someone's "jazz" would seem maybe... but
"jazz" is a pretty broad beast, no?

>Singing these progressions one can only go so far in retuning them
before their essential structure is lost.

How far? Who's to say... I think these are a lot more aesthetically
oriented issues than I think your giving them credit for being.

> The main reason I like to bring this up is that there are myriad
acoustically "locked" chords that would _not_ be used in any rendition
of jazz or popular music, precisely because these styles arose from
(or at least along with) rather rigid tuning models.

Yikes! This just seems so restrictive a point of view to *generally*
espouse, that I'm actually getting claustrophobic just reading it!

Dan

I wrote,

>>Singing these progressions one can only go so far in retuning them
>>before their essential structure is lost.

Dan Stearns wrote,

>How far? Who's to say... I think these are a lot more aesthetically
>oriented issues than I think your giving them credit for being.

??? I think they are totally aesthetically oriented issues.

>> The main reason I like to bring this up is that there are myriad
>>acoustically "locked" chords that would _not_ be used in any rendition
>>of jazz or popular music, precisely because these styles arose from
>>(or at least along with) rather rigid tuning models.

>Yikes! This just seems so restrictive a point of view to *generally*
>espouse, that I'm actually getting claustrophobic just reading it!

I don't know what you mean. What about my next sentence, where I say we
should create music where these sounds _are_ aesthetically appropriate? Does
that make you claustrophobic?

I said to Paul Erlich:

>>You read my account in my "Lies" book of the development of the LA Jazz
>>Choir, Paul.

And he responded:
>
> No, I haven't read your book.

I'll be damned! I could swear you mentioned it when you, John, Mark and I
shared some thoughts during my pre-List days. As I remember, you (I thought)
raised a number of interesting questions regarding some of my concepts (so
what's new?). Are you sure you're not just suppressing the memory of an
unpleasant experience? LOL

Me:

>>Now, if you are referring to vocal jazz
>>groups that model after keyboard-tuned chords, you are likely correct; but I
>>don't think these will be very exciting to experienced vocal jazz listeners.

Paul:

> Let me put my point another way -- a good singing group will certainly find
> tunings for certain chords, one might say "acoustic" tunings, that are
> smoother than 12-tone equal tempered tuning. However, the music itself will
> have been composed on a 12-tET instrument, or at least within a set of rules
> and conventions that spring mainly from the harmonic and melodic balances,
> resources, and limitations of 12-tET (and partially those of tunings used
> earlier). Hence in performing the music the musicians will choose those
> acoustically resonant tunings which preserve these relations, and not ones
> which don't. The tuning of a good group singing Gesualdo would be informed
> by a different set of compositional desiderata than that of a group singing
> jazz.

The key thought here, I think, is your suggestion that "musicians will
choose those acoustically resonant tunings which preserve these relations,
and not ones which don't." I acknowledge that many jazz chords are hard to
spell, giving testimony that 12-tET has likely spawned them. I think,
however, that when such chords are given the benefit of flexible tuning, the
result is usually an improvement of the essence of the sonority rather than
a compromise of it. Also, consider that sensitive singers are not likely to
insist on JI tunings if these do not help the chord "pop." Whether their
choices are 12-tET or JI is, of course, a matter to research. (As we are
attempting to do here.)

Actually, Gesualdo may be a good analogy of the principle. His bizarre
harmonic progressions are very much like the "off the wall" chord changes in
jazz. I have to think that late Renaissance ears were essentially the same
as our "new" ones, at least insofar as acoustical synthesis of
simultaneously sounding pitches is concerned. And since keyboards (fixed
pitch) were not a strong influence on what was essentially an "a cappella"
(or viol/recorder) music culture, it would seem that Mother Nature was
readily available to direct sensitive ears to optimum tunings.

I realize that "authorities" have proclaimed the "mode o' day" of
Renaissance musical styles, but I wonder whether they are any more accurate
than today's music educators. Lacking recordings, I'll go with logic every
time.

> My point was mainly than many jazz chords and progressions arose precisely
> from the way closed 12-tone tunings manage to tie together intervals that
> would be incompatible in pure just intonation. Mostly these are horizontal
> issues, but often they are vertical as well. Singing these progressions one
> can only go so far in retuning them before their essential structure is
> lost.

Huh? We never found such a chord in the life of LA Jazz Choir, and we sang
some pretty bizarre ones. Do you have an example, Paul?

> The main reason I like to bring this up is that there are myriad
> acoustically "locked" chords that would _not_ be used in any rendition of
> jazz or popular music, precisely because these styles arose from (or at
> least along with) rather rigid tuning models.

For example? No "better mouse traps" in this case?

> What many of us on the list
> would like to do is investigate ways of creating new styles of music that
> explore these sonorities, or at least would allow them to be explored by a
> sensitive choir.

I'm in there (I think). I suspect that a "sensitive choir" that is also
aware of period styles would tune these sonorities instinctively--probably
the same way fourteenth century singers did. But did I misunderstand? Do you
mean to teach (condition) instrumentally produced (mathematically conceived)
tunings to singers, and to induce them to forego their natural penchant for
optimum acoustic tuning? Or just to train them to recognize the difference
between say a 4:5 third and a 7:9 third. I would like that.

> Even chords like 14:18:21 might take their place in a new
> melodic/harmonic vocabulary that is divorced from the familiar styles that
> have arisen over the last few hundred years (for example, Margo Schulter has
> suggested using this chord in a Xeno-Gothic context where the major third
> (in this case tuned 7:9) typically resolves outward into a perfect fifth).

As in the chromatically adjusted Landini cadence, I presume? A historically
unique form of "dominant"/tonic progression, to be sure. I can imagine the
7:9 third in this context with its "raised four" tugging anxiously toward
the final chord fifth.

Paul, thanks for your thought-provoking ideas (as usual). Your posts never
fail to waken me from a drowsy email session (for one reason or another ;-).

Jerry

I wrote,

>> No, I haven't read your book.

Jerry wrote,

>I'll be damned! I could swear you mentioned it when you, John, Mark and I
>shared some thoughts during my pre-List days.

Nope -- John was the one who read your book.

>The key thought here, I think, is your suggestion that "musicians will
>choose those acoustically resonant tunings which preserve these relations,
>and not ones which don't." I acknowledge that many jazz chords are hard to
>spell, giving testimony that 12-tET has likely spawned them. I think,
>however, that when such chords are given the benefit of flexible tuning,
the
>result is usually an improvement of the essence of the sonority rather than
>a compromise of it.

Agreed!

>Also, consider that sensitive singers are not likely to
>insist on JI tunings if these do not help the chord "pop."

That's right -- JI doesn't necessarily represent the most sonorous tuning of
complex jazz chords.

>Whether their
>choices are 12-tET or JI is, of course, a matter to research. (As we are
>attempting to do here.)

I would say their choices are often neither, as I thought you were just
implying above (maybe I misunderstood you).

>> My point was mainly than many jazz chords and progressions arose
precisely
>> from the way closed 12-tone tunings manage to tie together intervals that
>> would be incompatible in pure just intonation. Mostly these are
horizontal
>> issues, but often they are vertical as well. Singing these progressions
one
>> can only go so far in retuning them before their essential structure is
>> lost.

>Huh? We never found such a chord in the life of LA Jazz Choir, and we sang
>some pretty bizarre ones. Do you have an example, Paul?

The three examples that keep coming up on this list lately: the major 6/9
chord (C E G A D); the augmented triad; and the diminished seventh chord.

>> The main reason I like to bring this up is that there are myriad
>> acoustically "locked" chords that would _not_ be used in any rendition of
>> jazz or popular music, precisely because these styles arose from (or at
>> least along with) rather rigid tuning models.

>For example?

8:10:11:12; just about anything with 13 in it (such as 10:13:16, 11:13:15);
utonal versions of all of these, etc.

>No "better mouse traps" in this case?

Huh?

>Do you
>mean to teach (condition) instrumentally produced (mathematically
conceived)
>tunings to singers, and to induce them to forego their natural penchant for
>optimum acoustic tuning?

I don't think so!

>Or just to train them to recognize the difference
>between say a 4:5 third and a 7:9 third. I would like that.

I'd be all for that.

>> Even chords like 14:18:21 might take their place in a new
>> melodic/harmonic vocabulary that is divorced from the familiar styles
that
>> have arisen over the last few hundred years (for example, Margo Schulter
has
>> suggested using this chord in a Xeno-Gothic context where the major third
>> (in this case tuned 7:9) typically resolves outward into a perfect
fifth).

>As in the chromatically adjusted Landini cadence, I presume? A historically
>unique form of "dominant"/tonic progression, to be sure.

Margo is talking about Gothic music, which predates "dominant/tonic",
"major/minor", or many other concepts which seem to come from Mother Nature,
but are in fact unique to our little (imperialistic) corner of space-time.
In Gothic times, the major third was an unstable sonority, and would
typically resolve outward (i.e., in contrary motion) to a perfect fifth.
Following the mathematically ambiguous suggestions of Marchetto and other
authors, this third may have often been tuned even wider than its nominal
Pythagorean value, 64:81 = 407.8�. An _extremely_ wide value (even wider
than the ones which evoked a perfect fourth in your ears when part of a
triad) would be 7:9 = 435.4�.