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Notating EJI with nine nominals

🔗Gene W Smith <genewardsmith@juno.com>

2/10/2003 7:16:38 PM

"wallyesterpaulrus <wallyesterpaulrus@yahoo.com>" writes:

{{in fact, gene ward smith has proposed using 9-equal as a basis for <BR>
the notation of 7-limit music.}}

Extendable to 18-equal as a basis for 11-limit music.

{{why? partly because a chain of nine 7:6s comes awfully close to
closing on itself (two octaves higher, if you don't octave-reduce).}}

That gives a 7-limit comma, (7/6)^9 / 4 = 1.83 cents. We also have a
strictly 5-limit
comma, 2 (25/27)^9 = .86 cents, and an 11-limit comma, smallest of all,
8 (49/55)^18 = .36 cents. Nine nominals suffice for 7-limit music, which
means they can be noted nicely on a usual staff; a half-step symbol
extends this to 18 nominals, which works for 11-limit "EJI"--where by EJI
I mean effectively just, but not strictly rational intonation. If anyone
objects to that description, note that this system is more accurate than
putting cents values in as Johnny does.

Limitations of this system are that people would need to learn it, and
that it stops at the 11-limit and does not work as it stands for
temperaments. On the plus side, it is very simple, very accurate and
needs no special plugins or software to notate.