288edo

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← 287edo288edo289edo →
Prime factorization 25 × 32
Step size 4.16667¢
Fifth 168\288 (700¢) (→7\12)
Semitones (A1:m2) 24:24 (100¢ : 100¢)
Dual sharp fifth 169\288 (704.167¢)
Dual flat fifth 168\288 (700¢) (→7\12)
Dual major 2nd 49\288 (204.167¢)
Consistency limit 3
Distinct consistency limit 3

288 equal divisions of the octave (abbreviated 288edo or 288ed2), also called 288-tone equal temperament (288tet) or 288 equal temperament (288et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 288 equal parts of about 4.167 ¢ each. Each step represents a frequency ratio of 21/288, or the 288th root of 2.

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 Hába and Ivan Wyschnegradsky, and has been used by jazz musician Joe Maneri. 96edo has been used by Julián Carrillo. This description as a corollary also fits every edo that is a multiple of 288, like 576 or 2016.

The 288beg val is a tuning for the tolerant and terrapyth temperaments in the 17-limit. The 288cdf val is a tuning for the rank-3 mirage temperament and period-72 omicronbeta temperament. The 288bcd val is a tuning for slendi temperament.

Odd harmonics

Approximation of odd harmonics in 288edo
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 (%) -47 +28 +48 +6 -32 +27 -18 -19 -40 +1 +21
Steps
(reduced)
456
(168)
669
(93)
809
(233)
913
(49)
996
(132)
1066
(202)
1125
(261)
1177
(25)
1223
(71)
1265
(113)
1303
(151)