23-limit: Difference between revisions
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Revision as of 16:53, 9 May 2020
In 23-limit Just Intonation, all ratios contain no prime factors higher than 23.
Ratios of 23 in the 23-odd limit include:
24/23 .. 73.681¢ .. 23u1 .. twenty-thu 1sn
23/22 .. 76.956¢ .. 23o1u2 .. twenty-tholu 2nd
23/21 .. 157.493¢ .. 23or2 .. twenty-thoru 2nd
26/23 .. 212.253¢ .. 23u3o2 .. twenty-thutho 2nd
23/20 .. 241.961¢ .. 23og3 .. twenty-thogu 3rd
23/19 .. 330.761¢ .. 23o19u3 .. twenty-thonu 3rd
28/23 .. 340.552¢ .. 23uz3 .. twenty-thuzo 3rd
23/18 .. 424.364¢ .. 23o4 .. twenty-tho 4th
30/23 .. 459.994¢ .. 23uy3 .. twenty-thuyo 3rd
23/17 .. 523.319¢ .. 23o17u4 .. twenty-thosu 4th
32/23 .. 571.726¢ .. 23u4 .. twenty-thu 4th
23/16 .. 628.274¢ .. 23o5 .. twenty-tho 5th
34/23 .. 676.681¢ .. 23u17o5 .. twenty-thuso 5th
23/15 .. 740.006¢ .. 23og6 .. twenty-thogu 6th
36/23 .. 775.636¢ .. 23u5 .. twenty-thu 5th
23/14 .. 859.448¢ .. 23or6 .. twenty-thoru 6th
38/23 .. 869.239¢ .. 23u19o6 .. twenty-thuno 6th
40/23 .. 958.039¢ .. 23uy6 .. twenty-thuyo 6th
23/13 .. 987.747¢ .. 23o3u7 .. twenty-thothu 7th
42/23 ..1042.507¢ .. 23uz7 .. twenty-thuzo 7th
44/23 .. 1123.044¢ .. 23u1o7 .. twenty-thulo 7th
23/12 .. 1126.391¢ .. 23o8 .. twenty-tho 8ve
94edo is the first EDO to be consistent in the 23-limit. The smallest EDO where the 23-limit is distinctly consistent, meaning each element of the tonality diamond is distinguished, is 282edo.
See: Harmonic Limit, 19-limit, 17-limit
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