Replies...

I said:
>
>>> I don't know where the high third comes from. My point here is only that
>>> string players are not as likely to be influenced by keyboards as are >>>
>>> singers.
>>> That's _all. The question of the "high third" is irrelevant here (as far as
>>> I know).
>
> Needless to say, I disagree,

Needless to say???????? What does that mean? That you will disagree no
matter what I say? My point is that SINGERS ARE MORE LIKELY TO BE INFLUENCED
BY KEYBOARDS BECAUSE THEY LEARN THEIR "NOTES" BY BANGING THEM OUT ON A
KEYBOARD WHILE STRING PLAYERS DO NOT. What the h--l does the high third have
to do with that?

> and you
> can read the letters and comments of European musicians showing that in the
> 1720s, any sort of "high third" (especially one larger than 400�) was heard
> as quite abhorrent, while by the 1750s, due to the influence of the new
> temperaments coming on the scene, such thirds were becoming more and more
> acceptable.

Okay, Paul. Then explain why my uninitiated simple and unbiased students
sing a third that is higher than a 12-tET third when they have no reason to
do so. Are they are simply stupid? If so, they are _all stupid. Don't give
me the "because they have been listening to 12-tET all their lives" cr-p. It
just doesn't wash.

I suggest you ask yourself what it is in my observations that appears to
threaten an assumed "Truth" you have espoused. Paul, I have come to admire
your extensive knowledge of historical writings. Please don't blow it by
contributing illogical and irrelevant posts.
>
>>Paul, I think your reasoning here is a bit suspect. If my hundreds of
>>students were relying on a memory of 12-tET, why do they tune the third
>>below piano pitch before the fifth is sounded, and why do they consistently
>>move it above piano pitch while the fifth is sounding? Granted my "demo" had
>>problems, but it did show a narrower third (albeit nearly at the piano pitch
>>because of the basses sharp root) near the beginning of the example and a
>>larger third near the end. To my ear, neither of these thirds were 12-tET.
>
> As you know, I do believe the 4:5 "low third" is a powerful acoustical
> magnet that any sensitive singers would be drawn toward. I'm not sure that
> the third at the end was larger than a 12-tET third -- yes, the upper note
> was higher than the piano pitch, but I think the bass was higher than the
> corresponding piano pitch by an even larger amount, with all these
> deviations being unstable, uncertain, and particularly confused by the
> addition of the poorly intonated fifth and the distracting piano tones.
>
>>> I certainly don't
>>> hear an acoustical "locking" occuring at two distinct values for the major
>>> third in this example.
>
>>Do you mean you don't hear _any locking? Or do you mean the "two" thirds are
>>not different? As you would know, your answer to these questions is
>>important. If the two thirds sound the same to you, it means we are hearing
>>differently.
>
> What I really don't hear is a major third that locks initially, expands
> through an unstable range, and finally locks again at a different, yet
> stable, value.

I thought you said that the initial third was likely 2:5. Are you changing
that perception now?

> If this phenomenon does in fact occur with better singers, I
> gave you my possible explanation (involving 1/24:1/19:1/16) some time ago.
> Certainly there are no simpler numbers that would be compatible with the
> phenomenon, given your reaction to the chords with sharper major thirds in
> Joe Monzo's file. Numbers like 19 are so high, though, that I feel that even
> if this explanation is correct, it is an artifact of trying to achieve an
> approximation of 12-tET through acoustical means.

Huh?

> Here is a complete list of ratios using numbers up to 50 that represent
> intervals between 5:4 and 14:11 (which you though was too high to be the
> high third):
>
> 386.3137� 5:4
> 395.1692� 49:39
> 396.1783� 44:35
> 397.4471� 39:31
> 399.0904� 34:27
> 401.3028� 29:23
> 404.4420� 24:19
> 406.5623� 43:34
> 409.2443� 19:15
> 412.7453� 33:26
> 414.1626� 47:37
> 417.5080� 14:11

Am I supposed to chose one?????
>
> Jerry wrote,
>
>>Tonal music, in general, seems universal and probably predates God (at least
>>man's concept of him/her). At the change of the millennium, polyphony was
>>introduced in Western music, however it was still largely vocal,
>>particularly in the altus and superius voices, each tuning to the sustained
>>tenor.
>
> At that time, and for several centuries thereafter, there were no consonant
> triads,

What about consonant fifths and fourths? How were those determined? By
playing them on an instrument?

> no hint of major and minor modes, hence none of the elements that
> constitute "tonal music" in the sense it has in the title of Forte's book,
> and the sense that is relevant to our discussions here, all of which are
> framed in the context of this particular tonal system.

I agree. My point was that the century and a half that followed the middle
ages was still largely vocal. Did you understand that?
>
> As for universality, I suggest a bit of ethnomusicology for you. A recent
> PBS special would have been great. No hint of Western scales or tunings, let
> alone "tonal music", in most of these cultures.

Perhaps you are confusing "tonal music" with "functional harmony." The term
"tonal" simply means that the pitches used in a particular system are
defined in relation to a central pitch. Which ethnic musical cultures are
_not based on this concept?
>
>>I didn't mean that I think historical musicians were unaware of tuning
>>issues. I simply think that there would have been many, like many musicians
>>today, who understood the theory and then did what they "heard." I have
>>observed, in many arenas of life, that what people _think they do is not
>>always _what they do.
>
> What I was talking about was musicians who were using their ears, their
> knowledge of what the music that _they_ made sounded like, apart from any
> theory. Their own reactions to various tunings were as valid to them as your
> reactions are to you. Like you, they made music in the way that sounded most
> natural to them, and heard various proposed tunings relative to that. What
> is fascinating is the conviction with which one set of norms felt "natural"
> to a set of musicians in one period, a different set of norms being
> "natural" in another period, and occasionally the _same_ musician will
> express a _different_ opinion of what sounds best early vs. late in their
> life (if they lived in a transitional period).

No problem here.
>
> Before continuing to dismiss the importance of keyboards,

I have no lack of appreciation for keyboards. I just think they can't "hack
it" the way ears do.

> read Daniel Wolf's
> recent post and Margo Schulter's upcoming one. But there is one important
> point you may be missing. Whether keyboards were present or not, the _music_
> is what was changing. The very style of the music went hand in hand with the
> tuning used. What musicians were feeling in the eighteenth century (and at
> many other points in time) was not simply a brainwashing due to abstract
> mathematical theories of how keyboards should be tuned. It was a revolution
> in musical expression, an "out with the old and in with the new" kind of
> mentality in which a collective cultural shift was being sensed and
> participated in by a generation of musicians. As keyboards were the primary
> tool with which composers brought these changes about, yes, we did get stuck
> with some tuning ideas a bit biased toward a fixed-pitch paradigm. But
> without the keyboard, the aesthetic movement may never have found as full a
> means of being realized.

This seems unlikely to me, but I'll keep an open mind on it.

> The _mutually interacting_ and synergistic
> influences of the changes in keyboard tuning and the changes in musical
> style were strong enough to alter musicians' _aural_ conception of what was
> natural and what wasn't.

After my experience with the flexible tuning, as exhibited in my recent mp3
posts, I can never believe that any fixed keyboard tuning is anything but a
compromise. To be sure, styles changed throughout music history. But I have
a hard time supposing that the perceptual mechanics of ears changed much
from one period to another. As I said, I will believe what someone _does
more than what someone _says; and unfortunately we can't go back and give a
listen. (Opinion subject to change after reading your cited sources. :-)
>
> Now I'll go back to your reaction to the I-IV-V7-I files.
>
>>The mystery is why did six out of his eight
>>files open nicely in QuickTime, while the two others only opened a blank IE
>>window that would not go anywhere. The techie did not know about the IE
>>browser reaction, but I didn't think it was worth the time to wait another
>>hour and a half to find out what Microsoft had to say about it.
>
> I do hope you're able to listen to all eight files soon. Perhaps at someone
> else's PC?

Your suggestion was just in time. I pulled the "rejects" out of the trash
and will take them to school tomorrow.
>
> Anyway, I'll now give you the lowdown on the files you listened to.

Good. I'm curious.
>
>>1. keenan. mid - harmless and familiar, a nice even control of dissonance
>>but not "in tune." The thirds are all a bit low
>
> The thirds are all exactly 5:4 above the roots.

I guess that's why I thought they were a bit low. I've been "culturized."
>
>>and the roots in IV (I
>>think) and V are flat.
>
> The root of the IV chord is 488.9� above the tonic, but the root of the V
> chord is 711.1� above the tonic, hence the root of the V would probably be
> considered sharp, not flat.

Apparently I should have put the "I think" after the V.
>
>>2. 71-64-81.mid - I and IV generally agreeable, V7 like a french accordian.
>>(That means: @^*#_*^%$)
>
> The V7 chord here has a low seventh (969�=7:4) and a high third
> (408�=Pythagorean). Evidently this does not satisfy you as the dominant
> chord with high third and low seventh.

Fer sure (to quote my Encino charges).
>
>>3. 7I.mid - fantastic, lovely, wonderful, A+, ideal, real nice. :-)
>
> The ":-)" indicates that you might be joking,

You like Joe Pehrson was regarding my "demo"? No, I wasn't joking. I really
liked it--"low" thirds and all.

> but assuming you're not, this
> is the version that has pure 4:5:6 triads, 4:5:6:7 dominant seventh, and the
> roots related by perfect 2:3 or 3:4 ratios. Evidently the large shift in the
> tuning of the fourth scale degree does not bother you the way it _really_
> bothers me and some of the other people who have commented on this file. So
> unless you're joking, it appears that your theory is to some extent
> consistent with what you really like to hear.

This was the smoothest of the lot. Perhaps you and the "other people" have
been "culturized" toward 12-tET to the extent that a raw 4:7 seventh sounds
"out of tune." To me it sounds exactly "right." Yes, the "large" shift in
the tuning of scale step four when it appears in the IV and V chords results
"naturally" when singers seek optimum tuning. I wish there were a chance of
adding this "alternate" scale step to our "system," but alas I know that is
not going to happen. Nevertheless, it doesn't prevent me from making my
students aware of it. At very least, it explains why scale step 4 sounds so
different when heard in these two harmonic contexts.
>
>>4. 51-5-9.mid - a decent I and IV, the root (I think, or is it the seventh)
>>obnoxiously sharp in the V7.
>
> It's the seventh, which is 5:9 = 1018� above the root.
>
>>5. pythag.mid - a flat third in both the I and IV, and a ridiculous V7
>>chord.
>
> The I and IV are pure 4:5:6 triads, and the V7 (and only the V7) is in
> Pythagorean tuning, with a 408� major third and a 996� minor seventh.

At least I'm somewhat consistent regarding my thirds. The Pythagorean tuning
here tends to verify my contention that it is quite "unhooked" from the real
world.
>
>>6. 1-4c-mt.mid - reasonable I and IV, a very flat leading tone in V7
>
> 1/4-comma meantone. Here the thirds are exactly 5:4 over the roots, but the
> fifths are about 697�. The roots are related by these flat fifths (sharp
> fourths), which (combined with the 5:4 thirds) is why the leading tone
> sounds so flat (major seventh = 386 + 697 = 1083�) relative to what you're
> used to. The dominant seventh here has a seventh that is 1007� above the
> root -- surprisingly, no one seems to have been bothered by this.

Yes, quite surprising. I didn't notice the seventh being a problem (perhaps
because I was distracted by the flat leading tone?).
>
> Now I'm _really_ curious as to how you would react to the other two files.
> So far, it's interesting how the 5:4 major thirds please you in some
> contexts but not in others.

Since you're curious, I will do my best to accommodate you. Yes, it is
interesting about the various reactions to the thirds. Maybe we're on to
something here.

Paul, I really appreciate your tranlating my reactions into tuning-ese. What
you did rather quickly (I presume) would have taken me considerable time.
I'm very grateful.

Jerry

In-Reply-To: <200002230702.XAA09785@snipe.prod.itd.earthlink.net>
> Okay, Paul. Then explain why my uninitiated simple and unbiased students
> sing a third that is higher than a 12-tET third when they have no
> reason to
> do so. Are they are simply stupid? If so, they are _all stupid. Don't
> give
> me the "because they have been listening to 12-tET all their lives"
> cr-p. It
> just doesn't wash.

Well, forgive me for intruding on a private argument, but there are a
number of reasons why either could be the case.

Say they're happily singing a pure major third, and then a fifth comes in.
They think "hey, this isn't what a major chord usually sounds like". So,
they raise the third, and it sounds more the thing. Because this high
third seems to work, they over-compensate a bit so that it gets even
higher than Equal Temperament. As the human ear is more sensitive to
flatness than sharpness, this will not be such a critical error.

Or maybe they start out with pure thirds, and after practicing a few times
discover that they have to sing sharp to produce a "real" major chord.
After a while longer, they come to know where the Equal Tempered third
should be, but still remember that they should be singing sharp, and so
again over-compensate.

As for them all being stupid, well, stupid or not, it only takes one
person to confidently sing a high third, and the rest will find they can
lock in with that.

Now have a look at the list Paul gave you:

> 386.3137� 5:4
> 395.1692� 49:39
> 396.1783� 44:35
> 397.4471� 39:31
> 399.0904� 34:27
> 401.3028� 29:23
> 404.4420� 24:19
> 406.5623� 43:34
> 409.2443� 19:15
> 412.7453� 33:26
> 414.1626� 47:37
> 417.5080� 14:11

If the chord "locks" it probably means an interval from this list is being
chosen. The small-integer theory is quite good for explaining harmonic
phenomena, especially locking. If you're singing a major third, and you
expect it to be around 400 cents, and decide a 5:4 is too low, the most
likely intervals to lock into would be 24:19 or 19:15. The only number
put on the high third so far is 404 cents, which would suggest 24:19.
That's interesting, as it would make a major triad the inversion of a
16:19:24 minor triad. Although 19:15 is simpler than 24:19, it is more
complex relative to the 3:2, so is less likely. Once they get used to
high thirds, they may even reach 33:26 or 14:11.

So it's quite reasonable that singers enculturated with Equal Temperament
will end up locking in to a high third at 404 cents. As for why they
alter pitch when the fifth comes in, well, bare major thirds are ugly in
Equal Temperament. You don't hear many of them, and the tendency will be
to make them just.

To move this discussion onwards, try recording more examples, and measure
the position and range of tolerance of this high third. Also, it may be
useful to know how it changes as the singers become more experienced.

You may try taking a fresh group of students, and soaking them in meantone
of JI examples before they start singing. See if it makes a difference.

Jerry wrote,

>>> I don't know where the high third comes from. My point here is only that
>>> string players are not as likely to be influenced by keyboards as are
>>>
>>> singers.
>>> That's _all. The question of the "high third" is irrelevant here (as far
as
>>> I know).

I wrote,

>> Needless to say, I disagree,

Jerry wrote,

>Needless to say???????? What does that mean? That you will disagree no
>matter what I say?

Of course not, Jerry. Calm down. I wrote "needless to say" because I think
I've made my point of view on this rather clear already.

>My point is that SINGERS ARE MORE LIKELY TO BE INFLUENCED
>BY KEYBOARDS BECAUSE THEY LEARN THEIR "NOTES" BY BANGING THEM OUT ON A
>KEYBOARD WHILE STRING PLAYERS DO NOT. What the h--l does the high third
have
>to do with that?

Because the high third does not seem to be explicable in terms of a simple
acoustical agreement between the notes, and because musicians (string
players included) were quite aware of their intonation in the 16th through
early 18th centuries and shunned any kind of high third, and because their
opinion on this issue changed dramatically later in the 18th century, I'm
forced to conclude that the high third is more a cultural (let's say
"musical") than acoustical phenomenon.

>Okay, Paul. Then explain why my uninitiated simple and unbiased students
>sing a third that is higher than a 12-tET third when they have no reason to
>do so. Are they are simply stupid? If so, they are _all stupid. Don't give
>me the "because they have been listening to 12-tET all their lives" cr-p.
It
>just doesn't wash.

So far, the example you posted did not demonstrate a third _wider_ that
12-tET: the upper note was higher, but so was the lower note. However, I
believe you know what you're talking about. I've given you my suggestion
several times -- see below.

>I suggest you ask yourself what it is in my observations that appears to
>threaten an assumed "Truth" you have espoused. Paul, I have come to admire
>your extensive knowledge of historical writings. Please don't blow it by
>contributing illogical and irrelevant posts.

You need to slow down and read them again. I assure you they're all logical
and relevant. Perhaps I have not communicated my thoughts to you
successfully yet. That shouldn't lead you to conclude I'm full of hot air.

>> What I really don't hear is a major third that locks initially, expands
>> through an unstable range, and finally locks again at a different, yet
>> stable, value.

>I thought you said that the initial third was likely 2:5. Are you changing
>that perception now?

Not really. The initial third is a very fuzzy version of a 2:5 -- I wouldn't
call it locking, but clearly it's highly influenced by the acoustical
simplicity of the 2:5 ratio. The main point, though, is the rest of my
sentence: "What I really don't hear is a major third that . . . expands
through an unstable range, and finally locks again at a different, yet
stable, value."

>> If this phenomenon does in fact occur with better singers, I
>> gave you my possible explanation (involving 1/24:1/19:1/16) some time
ago.
>> Certainly there are no simpler numbers that would be compatible with the
>> phenomenon, given your reaction to the chords with sharper major thirds
in
>> Joe Monzo's file. Numbers like 19 are so high, though, that I feel that
even
>> if this explanation is correct, it is an artifact of trying to achieve an
>> approximation of 12-tET through acoustical means.

>Huh?

Which part is confusing?

>> Here is a complete list of ratios using numbers up to 50 that represent
>> intervals between 5:4 and 14:11 (which you though was too high to be the
>> high third):
>
>> 386.3137� 5:4
>> 395.1692� 49:39
>> 396.1783� 44:35
>> 397.4471� 39:31
>> 399.0904� 34:27
>> 401.3028� 29:23
>> 404.4420� 24:19
>> 406.5623� 43:34
>> 409.2443� 19:15
>> 412.7453� 33:26
>> 414.1626� 47:37
>> 417.5080� 14:11

>Am I supposed to chose one?????

I just thought this might be interesting and relevant.

>> At that time, and for several centuries thereafter, there were no
consonant
>> triads,

>What about consonant fifths and fourths? How were those determined? By
>playing them on an instrument?

As I said, I believe these intervals arose vocally. Most world scales
feature some repetition at the fifth or fourth.

>> no hint of major and minor modes, hence none of the elements that
>> constitute "tonal music" in the sense it has in the title of Forte's
book,
>> and the sense that is relevant to our discussions here, all of which are
>> framed in the context of this particular tonal system.

>I agree. My point was that the century and a half that followed the middle
>ages was still largely vocal. Did you understand that?

Yes, although the very notation used by composers had a very important
shaping influence on what types of progressions could or could not be
entertained. Ones that could included any that involved the 80:81 comma
(such as what would later be called a I-vi-ii-V-I progression), ones that
could not included, for example, ones that involved the 250:243 comma (such
as Herman Miller's recent beautiful example).

>> As for universality, I suggest a bit of ethnomusicology for you. A recent
>> PBS special would have been great. No hint of Western scales or tunings,
let
>> alone "tonal music", in most of these cultures.

>Perhaps you are confusing "tonal music" with "functional harmony." The term
>"tonal" simply means that the pitches used in a particular system are
>defined in relation to a central pitch.

Look up five paragraphs in this message: I'm talking about "'tonal music' in
the sense it has in the title of Forte's book, and the sense that is
relevant to our discussions here, all of which are framed in the context of
this particular tonal system." By "our discussions here" I mean I-IV-V7-I,
etc.

>After my experience with the flexible tuning, as exhibited in my recent mp3
>posts, I can never believe that any fixed keyboard tuning is anything but a
>compromise.

It's more than a compromise. At the very least, it makes certain singable
progressions available to the composer, and others unavailable.

[your favorite was]
>> the version that has pure 4:5:6 triads, 4:5:6:7 dominant seventh, and the
>> roots related by perfect 2:3 or 3:4 ratios.

>I wish there were a chance of
>adding this "alternate" scale step to our "system," but alas I know that is
>not going to happen.

Why never? In 31-equal, for example, we can play this progression almost
exactly as C-E-G F-A-C G-B-D-E# C-E-G. Perhaps when Monz gets back he can
code this up and you can tell us how you like it. 31-equal has proved quite
workable on keyboards (Fokker's organ) and guitars (Catler, etc.); it is
only a matter of overcoming cultural inertia to make it more widespread.
(OK, I'm a dreamer, but all change is instigated by dreamers).

>At least I'm somewhat consistent regarding my thirds. The Pythagorean
tuning
>here tends to verify my contention that it is quite "unhooked" from the
real
>world.

Does the Pythagorean third (408�) sound too high to be the "high third"? In
Monz' examples you placed it at the upper limit of the acceptable "high
third" candidates. Perhaps with a seventh on top the "high third" is
different that without it?

>Paul, I really appreciate your tranlating my reactions into tuning-ese.
What
>you did rather quickly (I presume) would have taken me considerable time.
>I'm very grateful.

Jerry, I know you have a great ear and are a highly skilled musician within
at least one style. It is therefore of great interest to me to understand
tuning as it works for you, and to help put a quantitative underpinning to
the things you hear.

Graham wrote,

>The only number
>put on the high third so far is 404 cents,

Actually, Jerry thought the 400�, 404�, and 408� thirds in Monz's example
were all reasonable candidates for the high third, but wasn't sure due to
the vibrato. The vibrato is now gone, by the way.

>which would suggest 24:19.
>That's interesting, as it would make a major triad the inversion of a
>16:19:24 minor triad. Although 19:15 is simpler than 24:19, it is more
>complex relative to the 3:2, so is less likely.

Exactly.

>Once they get used to
>high thirds, they may even reach 33:26 or 14:11.

Why? Even Jerry thought the 14:11 third made the triad start to sound like a
sus chord.

>So it's quite reasonable that singers enculturated with Equal Temperament
>will end up locking in to a high third at 404 cents.

That's exactly what I've been trying to say.

>As for why they
>alter pitch when the fifth comes in, well, bare major thirds are ugly in
>Equal Temperament. You don't hear many of them, and the tendency will be
>to make them just.

Right, since the fifth isn't there to make for a clear "root" perception.
Also, the fifth provides a common overtone (its 16th) with the 24:19
interval, allowing the latter to lock in more easily.

>You may try taking a fresh group of students, and soaking them in meantone
>of JI examples before they start singing. See if it makes a difference.

This would have to be a pretty intensive soaking; you'd have to forbid them
to listen to 12-tET music for a while. A tall order.

A new and welcome voice is heard...that of...? of...? of someone whose email
address says "graham."

I had posted:

>> Okay, Paul. Then explain why my uninitiated simple and unbiased students
>> sing a third that is higher than a 12-tET third when they have no
>> reason to
>> do so. Are they are simply stupid? If so, they are _all stupid. Don't
>> give
>> me the "because they have been listening to 12-tET all their lives"
>> cr-p. It
>> just doesn't wash.
>
> Well, forgive me for intruding on a private argument, but there are a
> number of reasons why either could be the case.

No intrusion. Where have you been? This whole exchange would probably take a
much more productive direction if more members would get involved.
>
> Say they're happily singing a pure major third, and then a fifth comes in.
> They think "hey, this isn't what a major chord usually sounds like". So,
> they raise the third, and it sounds more the thing. Because this high
> third seems to work, they over-compensate a bit so that it gets even
> higher than Equal Temperament. As the human ear is more sensitive to
> flatness than sharpness,

Really? Tell me more. I don't know about this.

> this will not be such a critical error.
>
> Or maybe they start out with pure thirds, and after practicing a few times
> discover that they have to sing sharp to produce a "real" major chord.
> After a while longer, they come to know where the Equal Tempered third
> should be, but still remember that they should be singing sharp, and so
> again over-compensate.
>
> As for them all being stupid, well, stupid or not, it only takes one
> person to confidently sing a high third, and the rest will find they can
> lock in with that.

Consider that the "demo" I described has been tested many dozens of times
with groups of singers who never met the others. Are you suggesting that
_every group had an overexuberant singer? I doubt that.
>
> Now have a look at the list Paul gave you:
>
>> 386.3137� 5:4
>> 395.1692� 49:39
>> 396.1783� 44:35
>> 397.4471� 39:31
>> 399.0904� 34:27
>> 401.3028� 29:23
>> 404.4420� 24:19
>> 406.5623� 43:34
>> 409.2443� 19:15
>> 412.7453� 33:26
>> 414.1626� 47:37
>> 417.5080� 14:11
>
> If the chord "locks" it probably means an interval from this list is being
> chosen.

That was my initial hope--to find such a simple explanation. However, look
at the size of those numbers. I don't _think_ so.

> The small-integer theory is quite good for explaining harmonic
> phenomena, especially locking. If you're singing a major third, and you
> expect it to be around 400 cents, and decide a 5:4 is too low, the most
> likely intervals to lock into would be 24:19 or 19:15. The only number
> put on the high third so far is 404 cents, which would suggest 24:19.
> That's interesting, as it would make a major triad the inversion of a
> 16:19:24 minor triad. Although 19:15 is simpler than 24:19, it is more
> complex relative to the 3:2, so is less likely. Once they get used to
> high thirds, they may even reach 33:26 or 14:11.

Interesting.
>
> So it's quite reasonable that singers enculturated with Equal Temperament
> will end up locking in to a high third at 404 cents. As for why they
> alter pitch when the fifth comes in, well, bare major thirds are ugly in
> Equal Temperament.

Ugly? Well, maybe....depending on one's standard. However, remember that
many if not most singers continually imitate ET thirds.

> You don't hear many of them,

Huh?

> and the tendency will be
> to make them just.

I wish!!!
>
> To move this discussion onwards, try recording more examples, and measure
> the position and range of tolerance of this high third.

An excellent proposal. I need to acquire some means of measuring.

> Also, it may be
> useful to know how it changes as the singers become more experienced.

In my observation, both beginners and amateurs tend to arrive at the same
"lock" on the high third, but then I could be mistaken. It would be good to
know for sure.
>
> You may try taking a fresh group of students, and soaking them in meantone
> of JI examples before they start singing. See if it makes a difference.

A pretty wild idea. I think it would take considerable time to "reculturize"
modern young people who are constantly drenched in MTV.

Thanks for your ideas, .......Graham(?)

Jerry
>
>

In-Reply-To: <200002240306.TAA28898@avocet.prod.itd.earthlink.net>
Gerald Eskelin wrote:

> A new and welcome voice is heard...that of...? of...? of someone whose
> email
> address says "graham."

Oh, that was me again. I use different addresses depending on where I
write from, and it looks like my name wasn't getting through this time.

Actually, it appears that the address I sent from was over-written with my
default OneList address, and my name removed in the process. This hasn't
happened before. I wonder if the list processor has changed.

> No intrusion. Where have you been? This whole exchange would probably
> take a
> much more productive direction if more members would get involved.

Well, I don't have a good enough ear to know a high third when I hear it,
and don't have experience of choral singing. So there's not really much I
can say, but it would be interesting if you could put numbers on this.

> > As the human ear is more sensitive to
> > flatness than sharpness,
>
> Really? Tell me more. I don't know about this.

I can't give a reference off hand, but physics of music books tend to
cover this sort of thing. It also agrees with anecdotal evidence: I've
heard more singers criticised for being flat than sharp.

> Consider that the "demo" I described has been tested many dozens of
> times
> with groups of singers who never met the others. Are you suggesting that
> _every group had an overexuberant singer? I doubt that.

No, but it's a possibility that the most confident singer will always be
the one with the best memory of what the "real" chord should sound like.
This could be tested: take randomly selected newbies, and get them to sing
individually against a tape playing the root and fifth.

> > If the chord "locks" it probably means an interval from this list is
> > being
> > chosen.
>
> That was my initial hope--to find such a simple explanation. However,
> look
> at the size of those numbers. I don't _think_ so.

You mean the size of the cent-intervals or the size of the ratios? I'm
open to the possibility that 24:19 could be perceived as such. If you can
show people consistently hitting this, it would be good proof.

> > So it's quite reasonable that singers enculturated with Equal
> > Temperament
> > will end up locking in to a high third at 404 cents. As for why they
> > alter pitch when the fifth comes in, well, bare major thirds are ugly
> > in
> > Equal Temperament.
>
> Ugly? Well, maybe....depending on one's standard. However, remember that
> many if not most singers continually imitate ET thirds.

I saw a post on Usenet recently where somebody said that parallel major
thirds increase the tension. I presume he meant bare thirds (parallel
fifths mean something else in voice leading, but again I'm no expert).
That went against my experience, so I tried it, and it is the case --
provided they're tuned to 12-equal. So it's the out-of-tuneness that
gives the tension, not the third-ness. However, the remark went by
without comment, so I took it to be generally agreed that bare thirds
(which most know only in their Equal Tempered form) are essentially
dissonances. Maybe he did mean voices moving in parallel thirds, I dunno.

Anyway, my experience is that a bad third in a triad is less of a problem
than a bad third on its own.

> > You don't hear many of them,
>
> Huh?

Well, provide an example if you like. Bare fifths are used a lot. I went
through a Slayer music book, and nearly every chord is an open fifth
(that's the term, isn't it?). The exception was one bare third in the
whole album. In normal music, thirds are hidden away inside chords. The
theory books may not say so, but musicians know which intervals are in
tune.

> > and the tendency will be
> > to make them just.
>
> I wish!!!

For a naive singer I'm sure this would be the case. Although I've now
heard enough meantone to be an atypical listener, I don't really recognise
the sound of an isolated tempered major third. I don't think anyone who
hasn't been through ear training would hear such an interval as correct.
Whereas the just third will stand out as a consonance maximum to anybody.
Guitarists discover this through tuning by ear, and have to be told why
they're wrong.

Now, if I were singing a major third, I don't know if I'd get it
accurately to say if it were a 5:4, 7:9 or even 9:11. I should really try
these things.

> > To move this discussion onwards, try recording more examples, and
> > measure
> > the position and range of tolerance of this high third.
>
> An excellent proposal. I need to acquire some means of measuring.

If you can record the MP3s, people will be able to analyse them. Can
anybody recommend spectral analysis software for Windows (even Linux)?

Ideally, each voice would be multitracked and analyzed individually. That
should have been done a long time ago by somebody with a research grant,
but to my knowledge hasn't been. Experimental data on how instruments are
tuned in real performances are surprisingly hard to come by.

> > Also, it may be
> > useful to know how it changes as the singers become more experienced.
>
> In my observation, both beginners and amateurs tend to arrive at the
> same
> "lock" on the high third, but then I could be mistaken. It would be
> good to
> know for sure.

And either way, it'd be nice to see such things documented. Music
theory's in a bad way when it claims to be based on the major triad, but
can't even say how average singers will render it!

> > You may try taking a fresh group of students, and soaking them in
> > meantone
> > of JI examples before they start singing. See if it makes a
> > difference.
>
> A pretty wild idea. I think it would take considerable time to
> "reculturize"
> modern young people who are constantly drenched in MTV.

Well, try for half an hour and see if it makes a difference. Or even tune
a keyboard to JI, hit a major chord and say "sing this". Or -- now here's
an idea -- play a JI chord on a string patch, and get them to sing along.
Then remove notes one by one, and see if the third changes as the keyboard
loses it. Try the same thing with the meantone fifth.

> Thanks for your ideas, .......Graham(?)

That's okay. One other thing I was thinking about. You were saying
before about how Sheila Chandra sang a high E with a low F. It's also an
article of faith (with some experimental backing) that minor seconds in
melody tend to be narrowed, whereas larger intervals tend to be widened.
The whole subject of melodic intonation tends to be ignored relative to
vertical harmony. I think the reason is that harmony can be easily
explained with reference to the harmonic series, but nobody really
understands pure melody in terms of anything more fundamental. So, if you
think you have something to say about melody, the field's wide open.

But more specifically, the idea (which I agree with) that E# should be
lower than F is entirely based on tuning to low-integer-ratio intervals.
It has nothing to do with how scales will most likely be tuned
melodically. So you may find a melodic F appearing where a harmonic E#
should be. This is why I think it may be better to assume E# and F are
the same pitch class, outside of an explicit meantone context. If the
harmonic and melodic rules lead to a different order of pitches, neither
can be relied upon as a standard.

Another thread: the measured values for C, E and G in "Can't Buy Me Love"
(see earlier in the month) are 262, 337 and 405 Hz. That's consistent
with the melodic intervals being stretched. 405/337, the measured minor
third, is close to just, and so wider than ET. A just major third would
be narrower than ET, and so has to be stretched. I wonder if the
approximations to 9/7 and 6/5 are a coincidence.

To remove ambiguity, it's:

Graham Breed
http://x31eq.com/

Hi, I'm new to the list...hopefully I won't ask anything too moronic.

I'm wondering if this issue of 'sharpness' has any significance in two
isolated situations. There was a small New York jazz scene (early 80's)
where players were intentionally trying to play as sharp as possible, maybe
to increase tension or a sense of 'outsideness'. As well, it seemed to me
that a couple years back, alot of pop albums were coming out where the
singers were singing sharp. It seemed like a conscious decision (I think
maybe Alanis Morrisette might have accidentally started the trend). Any
insight on the aesthetics of sharpness?

Also, is there some bit of info I'm missing? I don't think I've had trouble
singing a 5/4 (since I've become aware of tuning issues) - are we talking
about a specific situation in which these low ratios are difficult to tune?

Oh yeah, where can I find the article by 'Margo'

Thanks, Paul Ruston

-----Original Message-----
From: graham@microtonal.co.uk <graham@microtonal.co.uk>
To: tuning@onelist.com <tuning@onelist.com>
Cc: gbreed@cix.compulink.co.uk <gbreed@cix.compulink.co.uk>
Date: Thursday, February 24, 2000 10:18 AM
Subject: Re: [tuning] Replies...

>From: graham@microtonal.co.uk
>
>In-Reply-To: <200002240306.TAA28898@avocet.prod.itd.earthlink.net>
>Gerald Eskelin wrote:
>
>> A new and welcome voice is heard...that of...? of...? of someone whose
>> email
>> address says "graham."
>
>Oh, that was me again. I use different addresses depending on where I
>write from, and it looks like my name wasn't getting through this time.
>
>Actually, it appears that the address I sent from was over-written with my
>default OneList address, and my name removed in the process. This hasn't
>happened before. I wonder if the list processor has changed.
>
>> No intrusion. Where have you been? This whole exchange would probably
>> take a
>> much more productive direction if more members would get involved.
>
>Well, I don't have a good enough ear to know a high third when I hear it,
>and don't have experience of choral singing. So there's not really much I
>can say, but it would be interesting if you could put numbers on this.
>
>> > As the human ear is more sensitive to
>> > flatness than sharpness,
>>
>> Really? Tell me more. I don't know about this.
>
>I can't give a reference off hand, but physics of music books tend to
>cover this sort of thing. It also agrees with anecdotal evidence: I've
>heard more singers criticised for being flat than sharp.
>
>> Consider that the "demo" I described has been tested many dozens of
>> times
>> with groups of singers who never met the others. Are you suggesting that
>> _every group had an overexuberant singer? I doubt that.
>
>No, but it's a possibility that the most confident singer will always be
>the one with the best memory of what the "real" chord should sound like.
>This could be tested: take randomly selected newbies, and get them to sing
>individually against a tape playing the root and fifth.
>
>> > If the chord "locks" it probably means an interval from this list is
>> > being
>> > chosen.
>>
>> That was my initial hope--to find such a simple explanation. However,
>> look
>> at the size of those numbers. I don't _think_ so.
>
>You mean the size of the cent-intervals or the size of the ratios? I'm
>open to the possibility that 24:19 could be perceived as such. If you can
>show people consistently hitting this, it would be good proof.
>
>> > So it's quite reasonable that singers enculturated with Equal
>> > Temperament
>> > will end up locking in to a high third at 404 cents. As for why they
>> > alter pitch when the fifth comes in, well, bare major thirds are ugly
>> > in
>> > Equal Temperament.
>>
>> Ugly? Well, maybe....depending on one's standard. However, remember that
>> many if not most singers continually imitate ET thirds.
>
>I saw a post on Usenet recently where somebody said that parallel major
>thirds increase the tension. I presume he meant bare thirds (parallel
>fifths mean something else in voice leading, but again I'm no expert).
>That went against my experience, so I tried it, and it is the case --
>provided they're tuned to 12-equal. So it's the out-of-tuneness that
>gives the tension, not the third-ness. However, the remark went by
>without comment, so I took it to be generally agreed that bare thirds
>(which most know only in their Equal Tempered form) are essentially
>dissonances. Maybe he did mean voices moving in parallel thirds, I dunno.
>
>Anyway, my experience is that a bad third in a triad is less of a problem
>than a bad third on its own.
>
>> > You don't hear many of them,
>>
>> Huh?
>
>Well, provide an example if you like. Bare fifths are used a lot. I went
>through a Slayer music book, and nearly every chord is an open fifth
>(that's the term, isn't it?). The exception was one bare third in the
>whole album. In normal music, thirds are hidden away inside chords. The
>theory books may not say so, but musicians know which intervals are in
>tune.
>
>> > and the tendency will be
>> > to make them just.
>>
>> I wish!!!
>
>For a naive singer I'm sure this would be the case. Although I've now
>heard enough meantone to be an atypical listener, I don't really recognise
>the sound of an isolated tempered major third. I don't think anyone who
>hasn't been through ear training would hear such an interval as correct.
>Whereas the just third will stand out as a consonance maximum to anybody.
>Guitarists discover this through tuning by ear, and have to be told why
>they're wrong.
>
>Now, if I were singing a major third, I don't know if I'd get it
>accurately to say if it were a 5:4, 7:9 or even 9:11. I should really try
>these things.
>
>> > To move this discussion onwards, try recording more examples, and
>> > measure
>> > the position and range of tolerance of this high third.
>>
>> An excellent proposal. I need to acquire some means of measuring.
>
>If you can record the MP3s, people will be able to analyse them. Can
>anybody recommend spectral analysis software for Windows (even Linux)?
>
>Ideally, each voice would be multitracked and analyzed individually. That
>should have been done a long time ago by somebody with a research grant,
>but to my knowledge hasn't been. Experimental data on how instruments are
>tuned in real performances are surprisingly hard to come by.
>
>> > Also, it may be
>> > useful to know how it changes as the singers become more experienced.
>>
>> In my observation, both beginners and amateurs tend to arrive at the
>> same
>> "lock" on the high third, but then I could be mistaken. It would be
>> good to
>> know for sure.
>
>And either way, it'd be nice to see such things documented. Music
>theory's in a bad way when it claims to be based on the major triad, but
>can't even say how average singers will render it!
>
>> > You may try taking a fresh group of students, and soaking them in
>> > meantone
>> > of JI examples before they start singing. See if it makes a
>> > difference.
>>
>> A pretty wild idea. I think it would take considerable time to
>> "reculturize"
>> modern young people who are constantly drenched in MTV.
>
>Well, try for half an hour and see if it makes a difference. Or even tune
>a keyboard to JI, hit a major chord and say "sing this". Or -- now here's
>an idea -- play a JI chord on a string patch, and get them to sing along.
>Then remove notes one by one, and see if the third changes as the keyboard
>loses it. Try the same thing with the meantone fifth.
>
>> Thanks for your ideas, .......Graham(?)
>
>That's okay. One other thing I was thinking about. You were saying
>before about how Sheila Chandra sang a high E with a low F. It's also an
>article of faith (with some experimental backing) that minor seconds in
>melody tend to be narrowed, whereas larger intervals tend to be widened.
>The whole subject of melodic intonation tends to be ignored relative to
>vertical harmony. I think the reason is that harmony can be easily
>explained with reference to the harmonic series, but nobody really
>understands pure melody in terms of anything more fundamental. So, if you
>think you have something to say about melody, the field's wide open.
>
>But more specifically, the idea (which I agree with) that E# should be
>lower than F is entirely based on tuning to low-integer-ratio intervals.
>It has nothing to do with how scales will most likely be tuned
>melodically. So you may find a melodic F appearing where a harmonic E#
>should be. This is why I think it may be better to assume E# and F are
>the same pitch class, outside of an explicit meantone context. If the
>harmonic and melodic rules lead to a different order of pitches, neither
>can be relied upon as a standard.
>
>
>Another thread: the measured values for C, E and G in "Can't Buy Me Love"
>(see earlier in the month) are 262, 337 and 405 Hz. That's consistent
>with the melodic intervals being stretched. 405/337, the measured minor
>third, is close to just, and so wider than ET. A just major third would
>be narrower than ET, and so has to be stretched. I wonder if the
>approximations to 9/7 and 6/5 are a coincidence.
>
>
>To remove ambiguity, it's:
>
> Graham Breed
> http://x31eq.com/
>
>
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Jerry wrote,

>A new and welcome voice is heard...that of...? of...? of someone whose
email
>address says "graham."

Graham Breed has been on this list for years, and his web page is the best
in the (tuning) business.

>However, remember that
>many if not most singers continually imitate ET thirds.

Jerry, it is but a small step from there to what I have been trying to say
-- the major triad with high third may simply be an imitation of an ET
triad, and the 1/24:1/19:1/16 tuning that seems to be in the range of what
you consider a "major triad with high third" would be the only way for
highly skilled, overtone-sensitive singers to "lock in" to an imitation of
an ET triad -- only with a major third 4�� larger and minor third 2��
smaller.

>>bare major thirds are ugly in
>> Equal Temperament.
>> You don't hear many of them,

>Huh?

It's true, major thirds in ET usually occur as part of larger chords.

Graham wrote,

>I saw a post on Usenet recently where somebody said that parallel major
>thirds increase the tension.

Parallel _major_ thirds would be a very non-diatonic phenomenon (q.v. _Close
to the Edge_ by Yes) and increase tension due to its borrowing from distant
keys.

>In normal music, thirds are hidden away inside chords.

For virtually all music written since the demise of meantone, this is true.

>Whereas the just third will stand out as a consonance maximum to anybody.
>Guitarists discover this through tuning by ear, and have to be told why
>they're wrong.

I've carefully watched guitarists who tune by ear for years and most
intermediate ones tune the G-B major third nice and sharp, close to the
12-tET value. One pro (with incredible piano skills and voice) I played with
always tried to tune it just, and would end up complaining about his tuning,
especially if the tune was not in the key of G (or a capoed-up G form). I
tried explaining the tuning situation to him once, but he was to much of an
egomaniac to listen to what a sideman might say (see, it was all our fault,
since he claimed he never had problems when playing solo). We ended up all
buying tuners.

>Another thread: the measured values for C, E and G in "Can't Buy Me Love"
>(see earlier in the month) are 262, 337 and 405 Hz. That's consistent
>with the melodic intervals being stretched. 405/337, the measured minor
>third, is close to just, and so wider than ET. A just major third would
>be narrower than ET, and so has to be stretched. I wonder if the
>approximations to 9/7 and 6/5 are a coincidence.

As it turned out, the first note was about a quarter-tone flat relative to
the eventual instrumentally-defined tonic. I think is was mainly a case of
un-warmed-up vocal cords on that first note, which sounds almost "spoken".

Welcome Paul Ruston!

>Also, is there some bit of info I'm missing? I don't think I've had
trouble
>singing a 5/4 (since I've become aware of tuning issues) - are we talking
>about a specific situation in which these low ratios are difficult to tune?

Nope -- Gerald Eskelin is claiming that although professional a cappella
groups tend to use 5/4 for a bare major third, they tend to use a major
third _higher_ than the 12-tone-equal-tempermant value in a full major
triad, although they can quite easily use the 5/4 third if they so desire.

>Oh yeah, where can I find the article by 'Margo'

It was posted Tuesday night -- check the www.onelist.com archives. She
posted another article last night that we're sure to be discussing as well.

Graham wrote:
> If you can record the MP3s, people will be able to analyse them. Can
> anybody recommend spectral analysis software for Windows (even Linux)?
>

Spectrogram is the way to go. Windows Freeware and accurate to +/- 1.3
hertz

I have it anyone wants it. It is small and easily emailable.

darren

>From: "Paul Swoger-Ruston" <pruston@yorku.ca>
>
>I'm wondering if this issue of 'sharpness' has any significance in two
>isolated situations. There was a small New York jazz scene (early 80's)
>where players were intentionally trying to play as sharp as possible, maybe
>to increase tension or a sense of 'outsideness'. As well, it seemed to me
>that a couple years back, alot of pop albums were coming out where the
>singers were singing sharp. It seemed like a conscious decision (I think
>maybe Alanis Morrisette might have accidentally started the trend). Any
>insight on the aesthetics of sharpness?

You've reminded me of something I heard a long time ago. Somebody said that
each of the sections in an orchestra, unless constrained by the conductor,
will tend to tune sharper and sharper in order to make their parts stand
out more.

John Link

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

The CD "Live at Saint Peter's" by the JOHN LINK VOCAL QUINTET is now available!
To purchase the CD visit www.johnlinkmusic.com, or write to johnlink@con2.com.

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

Paul,

Again, thank you for your continued interest in this topic. However, it
seems to me that it would be helpful to all--including you and me--to narrow
this discussion and refocus it to the essentials. With this in mind I'll try
to combine our three separate exchanges into one, and drop the issues that
are, in my mind, somewhat irrelevant. Needless to say, if I appear to ignore
something that you feel is critical, please revive it.

Upon rereading some of my heated statements, I think these are partly
symptomatic of my frustration in not finding much insight regarding my
initial purpose for being here (although I have enjoyed the experience and
have learned an enormous amount of valuable information). As I mentioned to
some members off-List, I guess I had initially assumed that many here would
have already experienced the "high third" phenomenon. It soon was clear that
most of the members approach tuning from a historical/keyboard point of view
and that this was not the case.

It was mentioned by some that much of this discussion has been conducted
without the benefit of sound examples. That, too, was partly because I hoped
that others would have already been familiar with the "high third," simply
because it appeared to me to be a "natural" phenomenon. I understand now why
that would not likely be the case (except for singers like John Link, of
course, and perhaps some others who have been silent). I apologize again for
it taking me so long to learn to upload sound files. It wasn't that it was
hard to do; it was simply a matter of finding the time.

I hope that my posting of excerpts last weekend was helpful in clarifying
where I'm coming from. Since I had to removed them from my site (do to being
over my meg limit), I will be happy to email them directly to any folks who
missed them but would like to hear them.

There is at least one more "demo" that we discussed earlier that might be
helpful--that is, my own singing of preferred tunings against fixed pitches.
I'll see what I can do about that next week.

So, here are my replies to what I consider to be the more important points
that seem unresolved:

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

I rudely screamed:
>
>>My point is that SINGERS ARE MORE LIKELY TO BE INFLUENCED
>>BY KEYBOARDS BECAUSE THEY LEARN THEIR "NOTES" BY BANGING THEM OUT ON A
>>KEYBOARD WHILE STRING PLAYERS DO NOT. What the h--l does the high third have
>>to do with that?

And you, Paul, calmly and politely, ignored the point again:
>
> Because the high third does not seem to be explicable in terms of a simple
> acoustical agreement between the notes, and because musicians (string
> players included) were quite aware of their intonation in the 16th through
> early 18th centuries and shunned any kind of high third, and because their
> opinion on this issue changed dramatically later in the 18th century, I'm
> forced to conclude that the high third is more a cultural (let's say
> "musical") than acoustical phenomenon.

Does this avoidance of my simple statement mean that you _don't think that
singers are more likely than string players to be influenced by keyboards?
My concern here is not that I disagree with your paragraph, but that my
statement is not concerned with anything other than the difference in the
way singers and string player learn tuning. That's all.

While this point is not critical to our discussion of the "high third," it
may be helpful, I feel, to demonstrate to you that you have a tendency to
read things into statements that are not intended by the writer.
Apparently, your continued enthusiasm for driving home the point that
historical practices have something to do with how flexible-pitch musicians
tune, you didn't get the essential import of my statement. The context in
which it was originally offered is no longer in my memory, so I'll be happy
just to drop this one.

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

Regarding the high third, Paul said:

>>> If this phenomenon does in fact occur with better singers, I
>>> gave you my possible explanation (involving 1/24:1/19:1/16) some time ago.
>>> Certainly there are no simpler numbers that would be compatible with the
>>> phenomenon, given your reaction to the chords with sharper major thirds in
>>> Joe Monzo's file. Numbers like 19 are so high, though, that I feel that even
>>> if this explanation is correct, it is an artifact of trying to achieve an
>>> approximation of 12-tET through acoustical means.
>
>>Huh?
>
> Which part is confusing?

Reading it at 1 in the afternoon is much better than reading it at 1 in the
morning. :-) I not only understand it now, but I agree that the high numbers
are not likely to represent the phenomenon. It was the last phrase that
raised my eyebrow. If tuning-aware singers are in fact "trying to achieve an
approximation of 12-tET" why do they seem to agree on a third _higher than
the keyboard third? In any case, I think we can put to rest the notion that
the "high third" phenomenon can be explained by any small-number ratio. For
that progress, your efforts (and those of many others here) are appreciated.
>
-------------

It had occurred to me to suggest:
>
>>Perhaps you are confusing "tonal music" with "functional harmony." The term
>>"tonal" simply means that the pitches used in a particular system are
>>defined in relation to a central pitch.

Which you sidestepped by saying:
>
> Look up five paragraphs in this message: I'm talking about "'tonal music' in
> the sense it has in the title of Forte's book, and the sense that is
> relevant to our discussions here, all of which are framed in the context of
> this particular tonal system." By "our discussions here" I mean I-IV-V7-I,
> etc.

Clearly you were not using the term as I had intended it. (Note Margo's
mention of the various uses of "tonal.") Instead of insisting we use _your
definition, it might have been more profitable to simply accept my
clarification. You have a very strong tendency to assume that your terms are
the "right" ones. Perhaps, this needless "train wreck" will convince you to
try more to understand the writers point, rather than to make his/her words
fit your own usage.

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

I said:

>>After my experience with the flexible tuning, as exhibited in my recent mp3
>>posts, I can never believe that any fixed keyboard tuning is anything but a
>>compromise.
>
> It's more than a compromise. At the very least, it makes certain singable
> progressions available to the composer, and others unavailable.

Begging your pardon, I think this response is another diversion. You must
know by now that my singers are seeking "best" tuning for each important
chord. No keyboard can do that. Your statement seems to be offered from the
viewpoint of the keyboard. To be sure, meantone and 12t-tET have provided
the means for keyboards to play in the main arena. But singers could _always
seek the "best" tuning as I have described it. Whether they actually did, or
were influenced by keyboards is another interesting matter for discussion.
My point, to be clear, has to do with the quest for "nature's" intervals.
Singers do it "naturally" (in my experience) while keyboards haven't a
prayer as chords change in musical context.

Your phrase "makes certain singable progressions available" is significant.
Adapting keyboard tuning makes those progressions available to the
_keyboard, not to tuning-sensitive singers (who can tune just about anything
to a reasonable "lock."
>
>>> [your favorite was]
>>> the version that has pure 4:5:6 triads, 4:5:6:7 dominant seventh, and the
>>> roots related by perfect 2:3 or 3:4 ratios.

I rest my case. (Skip the "high third" in this discussion. JI is basic.)

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

I said:

>>At least I'm somewhat consistent regarding my thirds. The Pythagorean tuning
>>here tends to verify my contention that it is quite "unhooked" from the real
>>world.
>
> Does the Pythagorean third (408�) sound too high to be the "high third"? In
> Monz' examples you placed it at the upper limit of the acceptable "high
> third" candidates. Perhaps with a seventh on top the "high third" is
> different that without it?

I haven't experimented with the "action" of the third with the well-tuned
seventh sounding. Perhaps I'll give it a go next week.
>
>>Paul, I really appreciate your tranlating my reactions into tuning-ese. What
>>you did rather quickly (I presume) would have taken me considerable time.
>>I'm very grateful.
>
> Jerry, I know you have a great ear and are a highly skilled musician within
> at least one style. It is therefore of great interest to me to understand
> tuning as it works for you, and to help put a quantitative underpinning to
> the things you hear.

I appreciate your continued interest in this research.

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

Paul said:
>
> The only basic pitch relations that I'm willing to believe can be perceived
> regardless of period or geographical style are the very simplest ratios --

That has been my basic assumption, and continues to be.

> musical style then leads to combinations (of these ratios) of
> ever-increasing complexity and intonational mutability. Why would I believe
> anything else? There's no evidence, and Occam's razor (combined with my
> knowledge of psychoacoustics) speaks against introducing other intervals
> (like the high third) into the palette of universally perceived pitch
> relations.

Yeah! I know! I would drop the subject in an LA minute except that I have
witnessed overwhelming evidence that something is going on here. Believe me,
it would simplify my life to find out it is an illusion.

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

I said:
>
>>My hope is that you understand what I have
>>described. I'm not sure you do.
>
> I think I do (please correct me if I'm wrong), and I've been trying to help
> understand how this "high third" phenomenon might arise. It clearly isn't a
> matter of "all music is made up of the simplest acoustical phenomena =
> simplest ratios" since there are myriad ratios simpler than any of the "high
> third" candidates but which are clearly not used in Western music.

Right. So where do we go from here?

Jerry

[Paul Erlich:]
> I've carefully watched guitarists who tune by ear for years and most
intermediate ones tune the G-B major third nice and sharp, close to
the 12-tET value.

Hmm, my observations (from teaching and working at the music store)
are similar, in that most will eventually settle the issue "nice and
sharp." But I also think that most beginners (etc.) who tune by ear,
which usually means a combination of fretted note to open strings and
ear, tend to do pretty much OK with the fourths, but do seem to me
(and pretty much uniformly I think), to unduly fiddle and fidget with
the major third... Also the I think there is a decided tendency to
readjust open-tunings (with a major third) nearer to JI (i.e., nearer
a 5/4 than a 4/12) after first tuning them by fretted and open string
unisons.

>We ended up all buying tuners.

I also find that a lot of guitarist are -- since the (relatively
recent) widespread proliferation of cheap guitar tuners -- very much
addicted to tuners.

My fretless Les Paul has no fret markers or neck dots, and though I
still can't play a lot of things on it that I can with markers,
getting used to playing it without them changed my playing and
composing for good... not being apprehensive of playing "out of tune"
force-fed my ears something they would have been damnably hard pressed
to find on their own... playing out of tune changed my life.

Dan

Jerry wrote,

>Does this avoidance of my simple statement mean that you _don't think that
>singers are more likely than string players to be influenced by keyboards?
>My concern here is not that I disagree with your paragraph, but that my
>statement is not concerned with anything other than the difference in the
>way singers and string player learn tuning. That's all.

I think that the way both string players and singers learn tuning is a far
more complex issue than simply the degree to which they are directly
influenced by keyboards. They may primarily be influenced by string players
and singers they heard while growing up, by the structural characteristics
of the style of music they play/sing, and perhaps less strongly by their
experience hearing other instruments. The point I was trying to make with
the Arabic bit was that each culture establishes its own norms for
intonation and it is through cultural experience that a feeling of
certainty, or "naturalness" if you will, is attained by musicians. The fact
is that today, the third of a pure 4:5:6 sounds "flat" to most musicians (it
even did to you in some of the examples). To me, that (combined with the
best historical documentation we have) is evidence that tastes have changed
and tuning is not simply a matter of acoustical or physiological
"universals".

>Apparently, your continued enthusiasm for driving home the point that
>historical practices have something to do with how flexible-pitch musicians
>tune

Fixed-pitch musicians?

>The context in
>which it was originally offered is no longer in my memory, so I'll be happy
>just to drop this one.

OK.

>Clearly you were not using the term as I had intended it. (Note Margo's
>mention of the various uses of "tonal.") Instead of insisting we use _your
>definition, it might have been more profitable to simply accept my
>clarification. You have a very strong tendency to assume that your terms
are
>the "right" ones. Perhaps, this needless "train wreck" will convince you to
>try more to understand the writers point, rather than to make his/her words
>fit your own usage.

As I recall, the reason we started using the term "tonal music" was because
I suggested that the V7-I progression, etc., were rather recent and
geographically localized phenomena, and I used the term "tonal music" to
cover these phenomena. I'd be happy to use a different term (I was just
using the term as in the title of Forte's book), and I never insisted that
anyone use my definition. Why don't we say "common practice" instead and
move on.

>> It's more than a compromise. At the very least, it makes certain singable
>> progressions available to the composer, and others unavailable.

>Begging your pardon, I think this response is another diversion. You must
>know by now that my singers are seeking "best" tuning for each important
>chord. No keyboard can do that. Your statement seems to be offered from the
>viewpoint of the keyboard. To be sure, meantone and 12t-tET have provided
>the means for keyboards to play in the main arena. But singers could
_always
>seek the "best" tuning as I have described it. Whether they actually did,
or
>were influenced by keyboards is another interesting matter for discussion.
>My point, to be clear, has to do with the quest for "nature's" intervals.
>Singers do it "naturally" (in my experience) while keyboards haven't a
>prayer as chords change in musical context.

You completely misunderstood my statement above, and I agree with what you
say in your "response" (although the high third is a clear exception) as
evidenced by my continual endorsement of adaptive JI tuning (such as
Vicentino's). It is not chords I was speaking of, it is _progressions_.

Regarding "Blue in Green": Would you mind giving the notes for the last few
chords?

By the way, Jerry, the post of Margo's that I was anticipating was not the
one you liked so much (which I liked too), but the following one
("Keyboards, polyphony, and intonation (850-1640)"). Give that one a good
read if you find the time.

>From: "D.Stearns" <STEARNS@CAPECOD.NET>
>
>I also find that a lot of guitarist are -- since the (relatively
>recent) widespread proliferation of cheap guitar tuners -- very much
>addicted to tuners.

When tuning in the vicinity of a drummer, horn player, piano player, or
bartender, an electronic tuner is a NECESSITY for a guitarist.

John Link

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

The CD "Live at Saint Peter's" by the JOHN LINK VOCAL QUINTET is now available!
To purchase the CD visit www.johnlinkmusic.com, or write to johnlink@con2.com.

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

[John Link:]
> When tuning in the vicinity of a drummer, horn player, piano player,
or bartender, an electronic tuner is a NECESSITY for a guitarist.

Well I don't know about a "NECESSITY," I (and countless others no
doubt) seemed to have managed OK without one! Seriously though, I do
understand your point, but it is different from the one that I was
trying to make (which pertained to guitar tuners as a habitual crutch
because many beginners start right off with them, and then seem to
have a hard time being weaned of them, a habitual dependency which
seems to me to just be more of an interesting phenomena of their
widespread usage at the get-go than anything else).

Dan

[Paul H. Erlich:]
>I think that the way both string players and singers learn tuning is
a far more complex issue than simply the degree to which they are
directly influenced by keyboards. They may primarily be influenced by
string players and singers they heard while growing up, by the
structural characteristics of the style of music they play/sing, and
perhaps less strongly by their experience hearing other instruments.

I think these are all really good points... Some of my very favorite
(rock/popular musics) singers, Robert Wyatt for instance (or I suppose
I could even say Elvis Costello, as more people would perhaps be
familiar with him anyway), have extremely funky intonation - check out
Wyatt's singing on "Who Will Accuse?" (NEWS FROM BABEL, _Letters
Home_)! Accuracy of intonation -- whether it's doing ones best to
accurately mimic a temperament, or whether it's an attempt to
'optimally adhere to mother nature' -- is not the only, or necessarily
the best solution for a given music, a given instrument, etc.

Dan

i prefer Wyatt and Soft Machine over costello anyday....
Pat

Well sure, I prefer Wyatt myself as well... and FWIW, it was just an
off the cuff, parenthetical reference that was trying to use a perhaps
more well known example of a vocalist whose intonation was
deliberately neither here nor there so to speak... I remember hearing
two things of Costello's that in this context stood out in my
mind/memory; one was the Brodsky Quartet collaboration, _The Juliet
Letters_ (which I quite liked), and the other was the Bacharach
collaboration _Painted From Memory_ (which I didn't much like). Keep
in mind though that I only heard these CDs maybe once through, so I'm
going by the memory of what someone else played for me awhile back, on
the other hand, I have some Wyatt, and *can* cite (and be sure of)
particular intonational examples of what it is that I'm talking about.

Dan

----- Original Message -----
From: Patrick Pagano

> i prefer Wyatt and Soft Machine over costello anyday....
> Pat