23-limit

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