User:Eliora/Commatose

Commatose uses the Pythagorean comma as a generator. It was developed by Eliora to highlight the near-perfect expression of 9/8 by 1789edo, while at the same time the fact that it completely misses 3/2. It is described as the 460 & 1329 temperament. In the 13-limit extension 24 generators are equal to ~13/9.

Temperament data

Subgroup: 2.9.5.7

Comma list: [28 -2 -19 8⟩, [9 -25 23 6⟩

Subgroup-val mapping: [⟨1 -289 -182 -508], ⟨0 298 188 521]]

mapping generators: ~2, ~1048576/531441

Optimal tunings:

• WE: ~2 = 1199.9727 ¢, ~1048576/531441 = 1176.4969 ¢
• CWE: ~2 = 1200.0000 ¢, ~1048576/531441 = 1176.5236 ¢

Optimal ET sequence: 460, 869, 1329

Badness (Sintel): 30.9

2.9.5.7.11

Subgroup: 2.9.5.7.11

Comma list: [-7 7 -3 2 -4⟩, [17 0 -13 1 3⟩, [11 -2 -6 7 -3⟩

Subgroup-val mapping: [⟨1 -289 -182 -508 -625], ⟨0 298 188 521 641]]

Optimal tunings:

• WE: ~2 = 1199.9833 ¢, ~531441/524288 = 1176.5070 ¢
• CWE: ~2 = 1200.0000 ¢, ~531441/524288 = 1176.5234 ¢

Optimal ET sequence: 460, 869e, 1329, 1789, 3118

Badness (Sintel): 8.67

2.9.5.7.11.13

Subgroup: 2.9.5.7.11.13

Comma list: 123201/123200, 1016064/1015625, 2250423/2249390, 2599051/2598156

Subgroup-val mapping: [⟨0 -289 -182 -508 -625 -312], ⟨0 298 188 521 641 322]]

Optimal tunings:

• WE: ~2 = 1200.0000 ¢, ~7056/3575 = 23.4767 ¢
• CWE: ~2 = 1200.0000 ¢, ~7056/3575 = 23.4767 ¢

Optimal ET sequence: 460, 869e, 1329, 1789, 3118

Badness (Sintel): 3.30