Pythagorean male voices (was: Re: Question on chords)

Johnny wrote,

>Paul, it is not what I "like" but what might be inherent in the the 81/64
>that allowed it to remain in practice for so long.

Let's explore what's inherent in it. As far as I can tell, the only thing
inherent in it, and the only reason it (or some approximation of it)
remained in practice through the Medieval era, is that it can be built up
from 4 fifths. When tuning 81/64 by itself, without reference to the
intervening fifths, I can't discern any characteristics that distinguish it
from its immediate neighbors. It was not considered a consonance in the
Medieval era, so its tuning would have been determined by melodic factors,
which would probably have kept it in the rough vicinity of 81/64, though
Marchettus and others suggested that it was larger in certain progressions .
. .

>Consider, wouldn't there only be an octave and a half of range in the
>Pythagorean men's voices?

I'll let Margo answer that, but assuming you're right, major thirds at the
top of the range would beat more than twice as fast as those in the bottom.

>I suggest this. So, if 16 beats per second make
>up thirds in a 3/2, then most other thirds (which will have smaller major
>thirds) will have less of a frequency than 16?

I'm confused about your meaning. But a Pythagorean major third only beats 16
times per second if the lower note is a modern middle C. That's near the top
of my range. An octave lower, a Pythagorean major third beats 8 times per
second. Wouldn't that fall into the category you described as "egregious"?
Meanwhile, a 12-tET major third with the lower note at modern middle C beats
10 times per second . . . and yet today everyone (people I've talked to
about it, Blackwood, me, etc.) seems to find the 12-tET major third more
consonant than the Pythagorean major third, in any register . . . or shall
we conduct more listening experiments?