291edo: Difference between revisions
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'''291edo''' is the [[EDO|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c) | '''291edo''' is the [[EDO|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c). | ||
Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[optimal patent val]] for the 13-limit [[Würschmidt family|hemiwürschmidt temperament]]. | |||
Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit. | |||
Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit. | |||
{{Harmonics in equal|291}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 03:17, 24 June 2023
| ← 290edo | 291edo | 292edo → |
291edo is the equal division of the octave into 291 parts of 4.1237 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c).
Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the optimal patent val for the 13-limit hemiwürschmidt temperament.
Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit.
Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.92 | +1.32 | +0.25 | +1.26 | +0.71 | -1.86 | -0.61 | -1.47 | +1.35 | +1.36 |
| Relative (%) | +0.0 | -22.4 | +31.9 | +6.0 | +30.5 | +17.2 | -45.2 | -14.7 | -35.7 | +32.8 | +32.9 | |
| Steps (reduced) |
291 (0) |
461 (170) |
676 (94) |
817 (235) |
1007 (134) |
1077 (204) |
1189 (25) |
1236 (72) |
1316 (152) |
1414 (250) |
1442 (278) | |