Re: [tuning] Pythagorean male voices (was: Re: Question on chords)

In a message dated 8/17/00 8:57:45 PM Eastern Daylight Time,
PERLICH@ACADIAN-ASSET.COM writes:

> 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?

First off, the middle ages were a melodic period and there were few 81/64
interval heard as a relationship with any particular prominence. It is a
melodic construct in its divination, from two 9/8 whole tones. Now the large
204 cent whole tone is probably etched in everyone's mind after some hundreds
of years. It is this stretch upwards (distinguishing it from either an 8/9
or a meantone whole tone is especially easy to reproduce. It is after all
the full step. Reproducing it a second time is simple enough, no?

Also, I bet most of the usage of 81/64 is in the upper ranges, based on
Paul's input. The higher range always moved the fastest, and through the
most melisma. But really now this historic info may not alter at all what a
modern will make of it. I was passing on what I had learned, that the 81/64
beat enough times as to mask its egregiousness.

Johnny Reinhard

Dear Paul H. Erlich;
I find it interesting that the preferred rate of beating between "unisons" is between 6-16
in Java and Bali. This beating third, like vibrato, could be preferred by some?
Banaphshu

"Paul H. Erlich" wrote:

> 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?

-- Banaphshu
North American Embassy of Anaphoria island
www.anaphoria.com