288edo: Difference between revisions
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== Theory == | == Theory == | ||
288edo is the least common multiple of [[72edo]] and [[96edo]], which are historically notable. 72edo has been used in [[Wikipedia:Byzantine music|Byzantine chanting]], has been theoreticized by [[wikipedia:Alois Hába|Alois Haba]] and [[Ivan Wyschnegradsky]], and has been used by jazz musician [[Joe Maneri]]. 96edo has been used by [[Julian Carrillo]]. This description as a corollary also fits every edo that is a multiple of 288, like [[576edo|576]] or [[2016edo|2016]]. | 288edo is the least common multiple of [[72edo]] and [[96edo]], which are historically notable. 72edo has been used in [[Wikipedia:Byzantine music|Byzantine chanting]], has been theoreticized by [[wikipedia:Alois Hába|Alois Haba]] and [[Ivan Wyschnegradsky]], and has been used by jazz musician [[Joe Maneri]]. 96edo has been used by [[Julian Carrillo]]. This description as a corollary also fits every edo that is a multiple of 288, like [[576edo|576]] or [[2016edo|2016]]. | ||
288beg val is a tuning for the [[tolerant]] and [[terrapyth]] temperaments in the 17-limit. | 288beg val is a tuning for the [[tolerant]] and [[terrapyth]] temperaments in the 17-limit. 288cdf val is a tuning for the rank-3 [[mirage]] temperament and period-72 [[omicronbeta]] temperament. 288bcd val is a tuning for [[slendi]] temperament. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|288}} | {{Harmonics in equal|288}} | ||
[[Category:Equal divisions of the octave|###]] | [[Category:Equal divisions of the octave|###]] | ||
Revision as of 20:20, 1 October 2022
Theory
288edo is the least common multiple of 72edo and 96edo, which are historically notable. 72edo has been used in Byzantine chanting, has been theoreticized by Alois Haba and Ivan Wyschnegradsky, and has been used by jazz musician Joe Maneri. 96edo has been used by Julian Carrillo. This description as a corollary also fits every edo that is a multiple of 288, like 576 or 2016.
288beg val is a tuning for the tolerant and terrapyth temperaments in the 17-limit. 288cdf val is a tuning for the rank-3 mirage temperament and period-72 omicronbeta temperament. 288bcd val is a tuning for slendi temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | +1.19 | +2.01 | +0.26 | -1.32 | +1.14 | -0.77 | -0.79 | -1.68 | +0.05 | +0.89 |
| Relative (%) | -46.9 | +28.5 | +48.2 | +6.2 | -31.6 | +27.3 | -18.4 | -18.9 | -40.3 | +1.3 | +21.4 | |
| Steps (reduced) |
456 (168) |
669 (93) |
809 (233) |
913 (49) |
996 (132) |
1066 (202) |
1125 (261) |
1177 (25) |
1223 (71) |
1265 (113) |
1303 (151) | |