157edo: Difference between revisions
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'''157edo''' is the [[EDO|equal division of the octave]] into 157 parts of 7.6433 | The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 157 parts of 7.6433 [[cent]]s each. | ||
157edo is the 37th [[prime EDO]]. | == Theory == | ||
157et tempers out 78732/78125 ([[sensipent comma]]) and 137438953472/134521003125 in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]]). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and 8019/8000 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 1573/1568, and 2197/2187 in the 13-limit. | |||
157edo is the 37th [[prime EDO]]. | |||
=== Prime harmonics === | |||
{{Primes in edo|157}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 18:22, 14 July 2021
The 157 equal divisions of the octave (157edo), or the 157(-tone) equal temperament (157tet, 157et) when viewed from a regular temperament perspective, is the equal division of the octave into 157 parts of 7.6433 cents each.
Theory
157et tempers out 78732/78125 (sensipent comma) and 137438953472/134521003125 in the 5-limit; 2401/2400, 5120/5103, and 110592/109375 in the 7-limit (supporting the hemififths and the catafourth). Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750 and 8019/8000 in the 11-limit; 351/350, 352/351, 847/845, 1573/1568, and 2197/2187 in the 13-limit.
157edo is the 37th prime EDO.
Prime harmonics
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