158edo: Difference between revisions
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158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and {{monzo| -1 0 0 4 -19 15 }}. | 158edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with five mappings possible for the 13-limit: {{val| 158 250 367 444 547 585 }} ([[patent val]]), {{val| 158 '''251''' 367 444 547 585 }} (158b), {{val| 158 250 '''366''' '''443''' '''546''' '''584''' }} (158cdef), {{val| 158 250 367 '''443''' '''546''' 585 }} (158de), and {{val| 158 250 367 '''443''' '''546''' '''584''' }} (158def). | ||
Using the patent val, it [[tempering out|tempers out]] the [[Würschmidt comma]], 393216/390625 and 3486784401/3355443200 in the 5-limit; [[225/224]], 8748/8575, and 40960000/40353607 in the 7-limit; [[441/440]], 1375/1372, [[4000/3993]], and 19683/19208 in the 11-limit, providing the [[optimal patent val]] for the 11-limit [[marvolo]] temperament; [[144/143]], [[640/637]], 2025/2002, [[2200/2197]] and 3159/3125 in the 13-limit. | |||
Using the 158de val, it tempers out [[126/125]], 33075/32768, and 118098/117649 in the 7-limit; [[243/242]], [[385/384]], 1617/1600, and 117649/117128 in the 11-limit; [[196/195]], [[351/350]], [[1287/1280]], [[1575/1573]], and 4455/4394 in the 13-limit. Using the 158def val, it tempers out [[676/675]], [[847/845]], [[1573/1568]], 1701/1690, and 3159/3136 in the 13-limit. | |||
Using the 158cdef val, it tempers out the [[magic comma]], 3125/3072 and the [[python comma]], 43046721/41943040 in the 5-limit; [[2401/2400]], [[19683/19600]], and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; [[325/324]], 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit [[harry]] temperament. | |||
Using the 158b val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo| -1 -33 23 }} in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, [[625/624]], 640/637, and 1625/1617 in the 13-limit. | |||
158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out [[9801/9800]], 35750/35721, and {{monzo| -1 0 0 4 -19 15 }}. | |||
Revision as of 08:44, 11 May 2024
| ← 157edo | 158edo | 159edo → |
158edo is inconsistent to the 5-odd-limit and higher limits, with five mappings possible for the 13-limit: ⟨158 250 367 444 547 585] (patent val), ⟨158 251 367 444 547 585] (158b), ⟨158 250 366 443 546 584] (158cdef), ⟨158 250 367 443 546 585] (158de), and ⟨158 250 367 443 546 584] (158def).
Using the patent val, it tempers out the Würschmidt comma, 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit marvolo temperament; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit.
Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.
Using the 158cdef val, it tempers out the magic comma, 3125/3072 and the python comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit harry temperament.
Using the 158b val, it tempers out the diaschisma, 2048/2025 and [-1 -33 23⟩ in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit.
158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and [-1 0 0 4 -19 15⟩.