back to list

Nine Pythagorean nominals

🔗Gene Ward Smith <gwsmith@svpal.org>

4/24/2005 2:25:32 PM

Here is another way of naming nine nominals:

0: C
1: D
2: E
3: I
4: F
5: G
6: A
7: B
8: H
9: C

The idea of this is that it works as a chain of fifths, IHFCGDAEB, and
BACH spells out something with some sort of relationship to what BACH
is supposed to spell out in German note naming. An alternative way of
notating ennealimmal would be to use this, not for nine equally spaced
parts of an octave, but for 9 notes of a Pythagorean scale. Such a
Pythagorean scale, 1-9/8-32/27-81/64-4/3-3/2-27/16-16/9-243/128 is of
course much more irregular than 9EDO, but the range of size of
intervals from 256/243 to 9/8 is not extreme; we have limmas,
apotomes, and major whole tones, making for a reasonable scale. Rather
than continue to extend the chain of fifths, we would cut it off at
these nine nominals, using the ennealimmal band reduction to fill it
out to ennealimmal. The 19-tone comma, |-14 19 -19>, is equivalent in
ennealimmal to the schisma. 3/(6/5)^6 = 15625/15552 is equivalent to
225/224. Toss in the rest of your favorite commas for this purpose and
you'd have a notation with a more Pythagorean flavor.