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12-et commas

🔗Gene Ward Smith <gwsmith@svpal.org>

1/15/2004 7:10:36 PM

We can find an infinity of ever more precise 5-limit 12 equal commas
by taking the ratios of the logs of two of them, such as the
diaschisma and the schisma, and using the numerators and denomenators
of the convergents as exponents. In this way we can get Fokker blocks
as close as we like to 12-equal inside the 5-limit. If I knew what
this was good for, I'd be happy. Here are the first commas from the
ratio of the logs of the diaschisma and schisma:

[161, -84, -12]
[-20462, 10676, 1525]
[102471, -53464, -7637]
[-327875, 171068, 24436]
[7315721, -3816960, -545229]
[-7643596, 3988028, 569665]
[825180493, -430535956, -61499384]
[-832824089, 434523984, 62069049]
[2490828671, -1299583924, -185637482]
[-28231939470, 14729947148, 2104081351]