Avicennmic temperaments

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This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 temperaments tempering out the avicennma, 525/512, also known as Avicenna's enharmonic diesis.

Tempereaments discussed elsewhere are:

Considered below is submerged.

Submerged

Named by Fitzgerald Lee in 2025, submerged tempers out 3125/3087, the gariboh comma. It may be described as the 16 & 29 temperament, generated by a sharply tuned ~8/5, eleven of which minus seven octaves make a perfect fifth; its ploidacot is therefore zeta-hendecacot. 45edo makes for an excellent tuning.

Subgroup: 2.3.5.7

Comma list: 525/512, 3125/3087

Mapping[1 -6 3 9], 0 11 -1 -9]]

mapping generators: ~2, ~8/5

Optimal tunings:

  • WE: ~2 = 1203.3342 ¢, ~8/5 = 829.2070 ¢
error map: +3.334 -0.683 -5.518 -1.681]
  • CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9483 ¢
error map: 0.000 -5.523 -13.262 -11.361]

Optimal ET sequence16, 29, 45, 74cd, 119bccdd

Badness (Sintel): 3.98

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 525/512

Mapping: [1 -6 3 9 0], 0 11 -1 -9 5]]

Optimal tunings:

  • WE: ~2 = 1203.6231 ¢, ~8/5 = 829.4195 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9730 ¢

Optimal ET sequence: 16, 29, 45e, 74cde, 119bccddeee

Badness (Sintel): 1.93

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/64, 105/104, 121/120, 441/440

Mapping: [1 -6 3 9 0 3], 0 11 -1 -9 5 1]]

Optimal tunings:

  • WE: ~2 = 1203.6316 ¢, ~8/5 = 829.4249 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9677 ¢

Optimal ET sequence: 16, 29, 45ef, 74cdef, 119bccddeeeff

Badness (Sintel): 1.35