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Tuning the diminished temperament

🔗Gene Ward Smith <gwsmith@svpal.org>

7/11/2004 12:16:31 AM

The diminished temperament seems to have a pretty good degree of
consistency in TOP tuning between the 5-limit and 7/9; but if we use
pure octaves things are different. The top tunings are less than a cent
apart, [299.16, 101.67] for 5-limit, and [298.53, 101.46] for 7/9 limit.
Poptimal generators are a different story; for the 5-limit we get
2^(-15/8) sqrt(15), at 94.13 cents; for the 7-limit, 76/1068 is
poptimal, and that is 85.39 cents; the poptimal range extends from
here up to 85.7 cents. Quite a difference! In the 9-limit, things
change once again; the poptimal generator is sqrt(9/8), at 101.96
cents. Speaking as someone with no experience using this temperament,
these numbers suggest to me that tuning it in TOP might be the best
practical solution.

Has anyone (Herman?) taken the diminished plunge? What do you think,
if so?