Yahoo Tuning Groups Ultimate Backup tuning Replies to Gerald Eskelin

>As a newcomer here, I am still learning the jargon. Can I assume that
>"adoptive tuning" is similar to what I experience as scale steps moving to
>accommodate changing roots?

Adaptive tuning, yes.

>Is the "pump" an expression referring to that
>process?

Not exactly. The pump is what happens when you play progressions like
I-vi-ii-V-I in just intonation and observe all common tones: you end on a I
a comma lower than the starting I.

>a tribute to the fact that with all of the "pumping"
>we had done we came out in the same key we started with.

In other words, you managed to use adaptive tuning to avoid any net pumping.
That's something John deLaubenfels did program into his adaptive tuning
software.

>> or three major seconds,

>Yes.

>> or an
>> augmented fourth.

>No.

OK, what do _you_ want to call the interval formed by three major seconds?
And why do you want to change the terminology which has been standard for
hundreds of years?

>The term "tritone" could only be spawned by a 12-tET keyboard concept of
>music.

Absolutely false. It is many times older than 12-tET keyboards, older even
than keyboards in general.

>In keyboard terms, both "augmented fourth"
>and "diminished fifth" are (uuuuuughhhhhhgggggg!!!!!!!) "tritones."

That was _not_ true in keyboard terms, until the establishment of a 12-tET
standard around 1850. Strictly speaking, an augmented fourth is three major
seconds, and a diminished fifth is two major seconds and two minor seconds.
Two minor seconds make a diminished third. Only in 12-tET (or
well-temperament) is a diminished third the same thing as a major second.

>Keyboard
>tritones are invertible. Acoustic "tritones" are not.

Only 12-tET keyboard tritones are "invertible". Older keyboard tritones were
not.

>Unfortunately, Capitol Records did not have a branch office in any of the
>ancient centers of musical art. And casting ancient tunes into a "best
>guess" notation that was developed for later musical styles is not a
>particularly solid foundation on which to assume any particular tunings.

I'm not getting your drift here. What is it you're saying with regard to
notation, and what are you saying about tuning?

>Apparently, [Dave Keenan's] conclusion that singers would sing a dominant
seventh chord
>with a 5:6 third from fifth to seventh is a result of your need to minimize
>"drift." Believe me, drift does not occur when singers tune the dominant
>seventh chord as 4:5:6:7. The "adjustment" occurs melodically in the
>"less-than-half-step" resolution of the chord seventh.

I think, if the high third is synthesis&analysis experiment number 1, the
I-IV-V7-I progression should be synthesis&analysis experiment number 2.

Jerry wrote,

>In my post I said:

>> I don't 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 relevant here (as far as
I
>> know).

>I meant "is irrelevant here (as far as I know)."

>Sorry I missed it. I hope it wasn't a problem.

I figured that that's what you meant. Needless to say, I disagree, 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.

>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. 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.

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

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, 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.

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.

>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).

Before continuing to dismiss the importance of keyboards, 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. 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.

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?

Anyway, I'll now give you the lowdown on the files you listened to.

>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.

>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.

>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.

>3. 7I.mid - fantastic, lovely, wonderful, A+, ideal, real nice. :-)

The ":-)" indicates that you might be joking, 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.

>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.

>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.

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.

Replies to Gerald Eskelin

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗Gerald Eskelin <stg3music@earthlink.net>

🔗Carl Lumma <clumma@nni.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>