23-limit: Difference between revisions
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Ratios of 23 in the 23-odd limit include: | Ratios of 23 in the 23-odd limit include: | ||
24/23 .. 73.681¢ .. 23u1 .. | 24/23 .. 73.681¢ .. 23u1 .. twethu 1sn | ||
23/22 .. 76.956¢ .. 23o1u2 .. | 23/22 .. 76.956¢ .. 23o1u2 .. twetholu 2nd | ||
23/21 .. 157.493¢ .. 23or2 .. | 23/21 .. 157.493¢ .. 23or2 .. twethoru 2nd | ||
26/23 .. 212.253¢ .. 23u3o2 .. | 26/23 .. 212.253¢ .. 23u3o2 .. twethutho 2nd | ||
23/20 .. 241.961¢ .. 23og3 .. | 23/20 .. 241.961¢ .. 23og3 .. twethogu 3rd | ||
23/19 .. 330.761¢ .. 23o19u3 .. | 23/19 .. 330.761¢ .. 23o19u3 .. twethonu 3rd | ||
28/23 .. 340.552¢ .. 23uz3 .. | 28/23 .. 340.552¢ .. 23uz3 .. twethuzo 3rd | ||
23/18 .. 424.364¢ .. 23o4 .. | 23/18 .. 424.364¢ .. 23o4 .. twetho 4th | ||
30/23 .. 459.994¢ .. 23uy3 .. | 30/23 .. 459.994¢ .. 23uy3 .. twethuyo 3rd | ||
23/17 .. 523.319¢ .. 23o17u4 .. | 23/17 .. 523.319¢ .. 23o17u4 .. twethosu 4th | ||
32/23 .. 571.726¢ .. 23u4 .. | 32/23 .. 571.726¢ .. 23u4 .. twethu 4th | ||
23/16 .. 628.274¢ .. 23o5 .. | 23/16 .. 628.274¢ .. 23o5 .. twetho 5th | ||
34/23 .. 676.681¢ .. 23u17o5 .. | 34/23 .. 676.681¢ .. 23u17o5 .. twethuso 5th | ||
23/15 .. 740.006¢ .. 23og6 .. | 23/15 .. 740.006¢ .. 23og6 .. twethogu 6th | ||
36/23 .. 775.636¢ .. 23u5 .. | 36/23 .. 775.636¢ .. 23u5 .. twethu 5th | ||
23/14 .. 859.448¢ .. 23or6 .. | 23/14 .. 859.448¢ .. 23or6 .. twethoru 6th | ||
38/23 .. 869.239¢ .. 23u19o6 .. | 38/23 .. 869.239¢ .. 23u19o6 .. twethuno 6th | ||
40/23 .. 958.039¢ .. 23uy6 .. | 40/23 .. 958.039¢ .. 23uy6 .. twethuyo 6th | ||
23/13 .. 987.747¢ .. 23o3u7 .. | 23/13 .. 987.747¢ .. 23o3u7 .. twethothu 7th | ||
42/23 ..1042.507¢ .. 23uz7 .. | 42/23 ..1042.507¢ .. 23uz7 .. twethuzo 7th | ||
44/23 .. 1123.044¢ .. 23u1o7 .. | 44/23 .. 1123.044¢ .. 23u1o7 .. twethulo 7th | ||
23/12 .. 1126.391¢ .. 23o8 .. | 23/12 .. 1126.391¢ .. 23o8 .. twetho 8ve | ||
[[94edo|94edo]] is the first [[EDO|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|282edo]]. | [[94edo|94edo]] is the first [[EDO|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|282edo]]. | ||
Revision as of 22:16, 13 December 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 .. twethu 1sn
23/22 .. 76.956¢ .. 23o1u2 .. twetholu 2nd
23/21 .. 157.493¢ .. 23or2 .. twethoru 2nd
26/23 .. 212.253¢ .. 23u3o2 .. twethutho 2nd
23/20 .. 241.961¢ .. 23og3 .. twethogu 3rd
23/19 .. 330.761¢ .. 23o19u3 .. twethonu 3rd
28/23 .. 340.552¢ .. 23uz3 .. twethuzo 3rd
23/18 .. 424.364¢ .. 23o4 .. twetho 4th
30/23 .. 459.994¢ .. 23uy3 .. twethuyo 3rd
23/17 .. 523.319¢ .. 23o17u4 .. twethosu 4th
32/23 .. 571.726¢ .. 23u4 .. twethu 4th
23/16 .. 628.274¢ .. 23o5 .. twetho 5th
34/23 .. 676.681¢ .. 23u17o5 .. twethuso 5th
23/15 .. 740.006¢ .. 23og6 .. twethogu 6th
36/23 .. 775.636¢ .. 23u5 .. twethu 5th
23/14 .. 859.448¢ .. 23or6 .. twethoru 6th
38/23 .. 869.239¢ .. 23u19o6 .. twethuno 6th
40/23 .. 958.039¢ .. 23uy6 .. twethuyo 6th
23/13 .. 987.747¢ .. 23o3u7 .. twethothu 7th
42/23 ..1042.507¢ .. 23uz7 .. twethuzo 7th
44/23 .. 1123.044¢ .. 23u1o7 .. twethulo 7th
23/12 .. 1126.391¢ .. 23o8 .. twetho 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