User:Eliora/Commatose
|
This user page is editable by any wiki editor.
As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages. However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits). |
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
- 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