193edo: Difference between revisions
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+data for the 23-limit |
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193edo is [[consistent]] to the [[11-odd-limit]], and almost consistent to the [[23-odd-limit]], the only failure being [[13/11]] and its [[octave complement]]. This makes it a strong 23-limit system. | 193edo is [[consistent]] to the [[11-odd-limit]], and almost consistent to the [[23-odd-limit]], the only failure being [[13/11]] and its [[octave complement]]. This makes it a strong 23-limit system. | ||
As an equal temperament, 193et [[tempering out|tempers out]] the [[15625/15552|kleisma]] in the 5-limit; [[5120/5103]] and [[16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], 4375/4356 in the 11-limit; [[325/324]], [[364/363]], [[625/624]], [[676/675]], [[1575/1573]], [[1716/1715]], [[4096/4095]] in the 13-limit; [[375/374]], [[442/441]], [[595/594]], [[715/714]], [[936/935]], [[1156/1155]], [[1225/1224]], [[2058/2057]], [[2431/2430]] in the 17-limit; [[400/399]], [[969/968]], [[1216/1215]], [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]] in the 19-limit; and [[529/528]] in the 23-limit. | As an equal temperament, 193et [[tempering out|tempers out]] the [[15625/15552|kleisma]] in the 5-limit; [[5120/5103]] and [[16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[3025/3024]], 4375/4356 in the 11-limit; [[325/324]], [[364/363]], [[625/624]], [[676/675]], [[1575/1573]], [[1716/1715]], [[4096/4095]] in the 13-limit; [[375/374]], [[442/441]], [[595/594]], [[715/714]], [[936/935]], [[1156/1155]], [[1225/1224]], [[2058/2057]], [[2431/2430]] in the 17-limit; [[400/399]], [[969/968]], [[1216/1215]], [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]] in the 19-limit; and [[460/459]], [[507/506]], [[529/528]] in the 23-limit. | ||
It provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-limit, and for the 13-limit [[minos]] and [[Mirkwai family #Indra|vish]] temperaments. | It provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-limit, and for the 13-limit [[minos]] and [[Mirkwai family #Indra|vish]] temperaments. | ||
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| 0.3191 | | 0.3191 | ||
| 5.13 | | 5.13 | ||
|- | |||
| 2.3.5.7.11.13.17.19.23 | |||
| 325/324, 364/363, 375/374, 400/399, 442/441, 460/459, 507/506, 529/528 | |||
| {{mapping| 193 306 448 542 668 714 789 820 873 }} | |||
| -0.1184 | |||
| 0.3078 | |||
| 4.95 | |||
|} | |} | ||
* 193et has a lower relative error in the 23-limit than any previous equal temperaments, past [[190edo|190g]] and followed by [[217edo|217]]. | * 193et has a lower relative error in the 23-limit than any previous equal temperaments, past [[190edo|190g]] and followed by [[217edo|217]]. | ||