125edo
The 125 equal temperament divides the octave into 125 equal parts of exactly 9.6 cents each.
Theory
125edo defines the optimal patent val for 7- and 11-limit slender temperament. It tempers out 15625/15552 in the 5-limit; 225/224 and 4375/4374 in the 7-limit; 385/384 in the 11-limit; and 275/273 in the 13-limit. Being the cube closest to division of the octave by the Germanic long hundred, it has a unit step which is the cubic (fine) relative cent of 1edo.
Prime harmonics
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Regular temperament properties
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 4\125 | 38.4 | 49/48 | Slender |
| 1 | 19\125 | 182.4 | 10/9 | Mitonic |
| 1 | 24\125 | 230.4 | 8/7 | Gamera |
| 1 | 33\125 | 316.8 | 6/5 | Hanson / catakleismic |
| 1 | 52\125 | 499.2 | 4/3 | Gracecordial |
| 1 | 61\125 | 585.6 | 7/5 | Merman |