More replies to Gerald Eskelin

I wrote,

>> Ironically, Jerry, a strict application of "piled-up fifths"
>> leads to Pythagorean tuning, which is the only system (out of Pyth.,
>> meantone, and various classic JI systems) that _agrees_ with of what you
>> "have 'known' all [your] early and professional life" -- G# being higher
>> than Ab, etc.

Jerry wrote,

>Ironic, perhaps. But I know you well enough (I think) that you wouldn't
>logically conclude from this that it must therefore explain the high third.

Of course. If the high third is at all based on an acoustical interaction
between simultaneously sounding notes, as you suggest, there's no way it
could be the Pythagorean third, since the numbers in the ratio (64:81) are
way to high to "do" anything. However, a believer in a Pythagorean
interpretation might claim that a series of piled-up fifths could easily
influence a progression like I-III-VI-II-V-I; if the fifths in this
progression are strong enough to influence the tuning of successive roots, a
skilled musical ensemble would have to imagine them beforehand and tune the
III according to a Pythagorean third relative to the I. It is a short step
from there to believing that, conditioned by such progressions, the tuning
of scale degree 3 is generally "attracted" to the Pythagorean third above
the tonic. Certainly this would be a logical point of view for someone who,
like yourself, believes that the major thirds of skilled performers often
end up rather sharp of 4:5, and that this is not due to any influence on the
part of 12-tET tunings of fixed-pitch instruments.

>> Anyway, Handel probably composed his
>> choral works at the organ (or other keyboard) -- are you suggesting that
the
>> enharmonic relations in these works would naturally assume a reversed
>> direction relative to how Handel heard them if performed by an
unaccompanied
>> choir?

>No.

So G# is not higher than Ab for all kinds of music, is it?

>I'm just suggesting that keyboard tuning was and is irrelevant to the
>way ears tend to tune music if left to their own devices.

I think you have to look beyond your concept of a universal "music" to
specific styles and compositions and the type of tuning issues involved in
each of them, both in their creation and their subsequent realization. Also
you should be more cognizant of the degree to which music is a cultural
"game", and the how meaning of music for us is so strongly dependent on our
previous experiences with it and the associations it carries.

>Very likely,
>"mistuned" keyboards in Handel's day were a bane to vocal tuning, just as
>they are today.

As far as we know, the pure thirds and low leading tones of meantone tuning
were most comfortable for the singers of the time.

More on nature vs. nurture:

In Arabic music, the minor third is divided melodically into two nearly
equal neutral seconds (go listen to some Arabic music and you'll hear this).
This is a most natural thing for Arabic musicians to sing and they sing it
without thought. Now you try it. Unless you've listened to a lot of Arabic
music, you'll probably find this impossible to do. Why? Are our brains,
ears, or throats structured differently from those of Arabic musicians? Of
course not. It's just that we've never _experienced_ this, having listened
to lullabies, symphonies, and other musical events _with cultural meaning_
in diatonic scales all our lives. What is this new experience? It's got to
be a mistake, an unskilled amateur trying to sing, right? At first, that's
what it sounds like. But once we've heard this phenomenon enough times, our
brain begins to characterize it as something distinct, something meaningful,
with its own quality, until it finally sounds like a real musical phrase.
Once one hears it this way, it immediately becomes _far_ easier to sing
(this happened to me). In the context of Arabic music, which has no triadic
or functional harmony, this is undoubtedly the _right_ thing to sing,
whether there is instrumental backing or not. The musical motifs of the
maqamat have their own structural logic that _coevolved_ with the tuning
they use. Tuning and style are intimately intertwined and one cannot make
judgments of "right" and "wrong" in one independently of the other.