Ennealimmal notation

I've worked out 441, which never needs more than three accidentals,
and 612, which never needs more than four. The only problem I see is
that sometimes there are as many as six different ways to write the
same note. It seems to me it might make sense to eliminate all but the
possibilities where the minimum size of accidental is maximized.

Notating 72, 99, 171, 270, 441 and 612 in ennealimmal, and 72, 270,
342 and 612 in hemiennealimmal seems like the thing to do. For
hemiennealimmal, nine nominals A to I (or J) and then nine more AX to
IX makes sense to me.

Gene, how would you notate 34tET? I have a hunch that this recent preference of mine might be a very good system for expressing both pythagorean, meantone and maqam practice.

Cordially,
Ozan
----- Original Message -----
From: Gene Ward Smith
To: tuning-math@yahoogroups.com
Sent: 11 Nisan 2005 Pazartesi 22:14
Subject: [tuning-math] Ennealimmal notation

I've worked out 441, which never needs more than three accidentals,
and 612, which never needs more than four. The only problem I see is
that sometimes there are as many as six different ways to write the
same note. It seems to me it might make sense to eliminate all but the
possibilities where the minimum size of accidental is maximized.

Notating 72, 99, 171, 270, 441 and 612 in ennealimmal, and 72, 270,
342 and 612 in hemiennealimmal seems like the thing to do. For
hemiennealimmal, nine nominals A to I (or J) and then nine more AX to
IX makes sense to me.

--- In tuning-math@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Gene, how would you notate 34tET? I have a hunch that this recent
preference of mine might be a very good system for expressing both
pythagorean, meantone and maqam practice.

I think the most obvious approaches are kleismic--chains of minor
thirds--or diaschismic. The latter seems to make the most sense if you
are thinking Pythagorean, since it is two chains of 17-et fifths, a
half-octave apart.