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Heptadecal temperament

🔗Gene Ward Smith <genewardsmith@juno.com> <genewardsmith@juno.com>

1/9/2003 5:10:31 PM

I mentioned that I've looked at 5 and 11 limit poptimal generators. One thing I discovered is that generators can be "universal" (stuck on one value of p; dF/dp = 0 in the objective function F) so there is no use trying to prove it can't happen.

The example is the temperament deriving from the heptadecal comma,
(25/24)^17 ~ 2, which is not to be confused with the minortone comma,
(10/9)^17 ~ 6, though if you use the 901-et you can have both and marry the 17 Revolution to 53-et besides. It gives a microtemperament which can be described as 17-equal divisions, separated by intervals of exactly sqrt(3) for the optimum tuning. Since 485/612 is only
0.00289 cents sharper than sqrt(3), there is no practical reason not to use it to notate Heptadecal, but it belligerently persists in wanting sqrt(3) for all values of p.