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Leapday

🔗Gene Ward Smith <gwsmith@svpal.org>

6/30/2004 11:36:38 AM

This is the 13-limit temperament with wedgie

<<1 21 15 11 8 31 21 14 9 -24 -47 -59 -21 -33 -13||

and mapping to primes

[<1 2 11 9 8 7|, <0 -1 -21 -15 -11 -8|]

The generator is a fourth or fifth, and if we want the completem
temperament, including fives, then in terms of equal temperaments
there is not a lot of point in tuning it to anything but 46; 27/46 is
a poptimal generator, and the next one I found was 254/615; hence
leapday is firmly wedded to 46.

The TM basis is {91/90, 121/120, 169/168, 352/351}, compatible as we
have seen with HTT. The no-fives version of leapday has a TM basis
{169/168, 352/351, 364/363}, which adds 169/168 to the commas of HTT.
It has a different TOP tuning, and we may want to use the 63-equal
tuning in place of 46 equal if we have no interest in 5, because this
gives better results for the other primes excepting 3, and is close to
the no-fives rms optimal value.

We have MOS of size 17 and 29, and a white-black analysis gives the 46
equal tuning as 29+17; the 63 equal tuning has a white-black of
46+17.

Here's a comparison of 46 and 63, using 21/63 = 400 cents in place of
20/63.

46 vs 63 sharpness of primes

3: 2.39 2.81
5: 4.99 13.67
7: -3.61 2.60
11: -3.49 1.06
13: -5.75 -2.43