source file: m1559.txt
Date: Wed, 21 Oct 1998 13:02:22 -0500 (CDT)

Subject: Re: Septimal schisma as xenharmonic bridge?

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Wed, 21 Oct 1998, M. Schulter wrote:
> Possibly less well known, the septimal schisma of 33554432:33480783 or
> about 3.80 cents is a bridge to a quasi-7-based world of
> "superefficient" cadences and third-tone steps. It is the difference
> between the Pythagorean comma and the septimal comma (64:63, about
> 27.26 cents) which separates basic Pythagorean intervals from their
> 7-based counterparts.

Oddly enough, I was just poking around in some old tuning list messages
today, and guess what I found:

| Date: Mon, 13 Mar 95 08:52:11 -0800
| From: Manuel Op de Coul <COUL@ezh.nl>
| Reply-To: tuning@eartha.mills.edu
| To: manynote@library.wustl.edu
| Subject: Other harmonic 7th comma
| 
| Bosanquet has written that 14 fifths downwards (the Pythagorean double
| diminished octave) is very close to the harmonic seventh. Is the
| comma belonging to it, 33554432/33480783 = 2^25 * 3^-14 * 7^-1 =
| 3.8041 cents ever called Bosanquet's comma, does anyone know?
| 
| Manuel Op de Coul    coul@ezh.nl

Another interval that might be a candidate for the name "septimal
schisma" is the 2401/2400, about .72 cents.  It is the difference
between the 50/49 and the 49/48, both intervals which result fairly
directly from septimal voice-leading.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Foul?  What the hell for?"
  -\-\-- o   "Because you are chalking your cue with the 3-ball."

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