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re: Dan Stearns' Notation idea

🔗Christopher Bailey <cb202@columbia.edu>

4/25/2001 7:19:47 AM

I don't quite get where you're figuring out what name to give each scale
degree. I mean, I see the chains of 3rds as far as alphabet-letter goes,
but I don't quite get where the b's are coming from. . .

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http://music.columbia.edu/~chris/

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🔗D.Stearns <STEARNS@CAPECOD.NET>

4/25/2001 2:42:48 PM

Hi Chris,

Sharps and flats are always moving by 1N relative to the unaltered C D
E F G A B that falls between the -1 and 5 in a generator chain where
the 6th interval in the chain is one greater than -1st interval in the
chain.

So in 22-EDO for instance the generator that agrees with this
criterion is 19. And the C D E F G A B that falls between -1 and 5 in
the generator chain is 0 3 7 10 13 16 19. So here's that idea with the
chain carried out to N.

C
D 3 19 B
Eb 6 16 A
Fb 9 13 G
Gb 12 10 F
Ab 15 7 E
Bb 18 4 D#
Cb 21 1 C#
Db 2 20 B#
Ebb 5 17 A#
Fbb 8 14 G#
Gbb 11 11 F#
Abb 14 8 E#
Bbb 17 5 D##
Cbb 20 2 C##
Dbb 1 21 B##
Ebbb 4 18 A##
Fbbb 7 15 G##
Gbbb 10 12 F##
Abbb 13 9 E##
Bbbb 16 6 D###
Cbbb 19 3 C###
Dbbb 0 22 B###

Another notation that I remember using quite a while back with 22 was
a variation of the ME method I posted this morning that used the 22
fifth to move accidentals by 2N.

I think the staff notation for that was something on the order of:

------------------------------------------

------------------------------------------

------------------------------------------

-------------------------------------Gb---
F- F F+ F#
--------------------Eb-(E-)-E--E+---------
Db D- D D+
-C- -C+-

-----------------------------------------

-----------------------------------------
C- C
-------------------------Bb-(B-)-B--B+---
Ab A- A A+
-Gb-(G-)-G-G+----------------------------
F#
-----------------------------------------

--Dan Stearns