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Kleismic fifth notation

🔗Gene Ward Smith <gwsmith@svpal.org>

4/28/2005 3:55:26 PM

If we take a fifth and lower it by a kleisma to (3/2)(15552/15625) =
23328/15625, we get a flat meantone fifth of about 3/8 comma flat,
which is the size of the kleisma. If we used this for ennealimmal
nominals as well as sharps and flats, we have changed ennealimmal from
being an "octave is not a period, and the fifth is not a multiple of a
generator" temperament to an "octave is not a period, and the fifth is
a multiple of a generator" temperament. Those are easier to notate in
something like conventional terms. Symbols for 36/35 (one generator)
49/48 (two generators) and 126/125 (three generators) would already
fill out the chain. Then 225/224 ([19 -8] in terms of period and 6/5
generators) gets you one period mod octaves, 36/35 or 126/125 two
periods, 81/80 three periods, and 49/48 or 64/63 four periods. Hence
36/35, 49/48, 81/80, 125/125, and 225/224 plus the kleismic fifth
might make sense.