180edo: Difference between revisions
Adopt intro, cleanup |
Cleanup. +subsets. Its 2.5.13 subgroup is enfactored 90et. |
||
| Line 2: | Line 2: | ||
{{EDO intro|180}} | {{EDO intro|180}} | ||
The equal temperament [[tempering out|tempers out]] 531441/524288 ([[pythagorean comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); [[1029/1024]], [[3136/3125]], and 118098/117649 in the 7-limit. | |||
Using the [[patent val]], it tempers out [[540/539]], 2835/2816, [[4000/3993]], and 6912/6875 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], and 1701/1690 in the 13-limit. Using the 180e val, it tempers out [[385/384]], [[441/440]], [[3388/3375]], and 216513/214375 in the 11-limit; 351/350, [[1188/1183]], [[1287/1280]], [[1573/1568]], and 3146/3125 in the 13-limit. | |||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|180}} | {{harmonics in equal|180}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
180edo is the 11th [[highly composite edo]]; its nontrivial subsets are: {{EDOs| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90 }}. | |||
180edo is the 11th [[highly composite | |||
Revision as of 09:21, 25 April 2024
| ← 179edo | 180edo | 181edo → |
The equal temperament tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit.
Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | +0.35 | -2.16 | +2.76 | +2.02 | -0.53 | -1.60 | +1.71 | +2.49 | +2.55 | -1.61 |
| Relative (%) | -29.3 | +5.3 | -32.4 | +41.3 | +30.2 | -7.9 | -24.0 | +25.7 | +37.3 | +38.3 | -24.1 | |
| Steps (reduced) |
285 (105) |
418 (58) |
505 (145) |
571 (31) |
623 (83) |
666 (126) |
703 (163) |
736 (16) |
765 (45) |
791 (71) |
814 (94) | |
Subsets and supersets
180edo is the 11th highly composite edo; its nontrivial subsets are: 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90.