# 288edo

← 287edo | 288edo | 289edo → |

^{5}× 3^{2}**288 equal divisions of the octave** (**288edo**), or **288-tone equal temperament** (**288tet**), **288 equal temperament** (**288et**) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 288 equal parts of about 4.17 ¢ each.

## 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 (%) | -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) |