# 375edo

Jump to navigation Jump to search
 ← 374edo 375edo 376edo →
Prime factorization 3 × 53
Step size 3.2¢
Fifth 219\375 (700.8¢) (→73\125)
Semitones (A1:m2) 33:30 (105.6¢ : 96¢)
Dual sharp fifth 220\375 (704¢) (→44\75)
Dual flat fifth 219\375 (700.8¢) (→73\125)
Dual major 2nd 64\375 (204.8¢)
Consistency limit 3
Distinct consistency limit 3

375 equal divisions of the octave (abbreviated 375edo or 375ed2), also called 375-tone equal temperament (375tet) or 375 equal temperament (375et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 375 equal parts of exactly 3.2 ¢ each. Each step represents a frequency ratio of 21/375, or the 375th root of 2.

## Theory

375edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. It can be used as a temperament in the 2.9.5.7.13.17.19 subgroup, in which it tempers out 250047/250000, 589824/588245, and [8 7 -13 (parakleisma).

For the full 7-limit, the 375cd val is the best, where it tempers out 1029/1024 and 15625/15552, supporting tritikleismic. In the 11-limit it tempers out 385/384 and 441/440, supporting undecimal tritikleismic.

Using the patent val, it tempers out 6144/6125 and 177147/175616, supporting aufo. In the 11-limit it tempers out 540/539 and 5632/5625, supporting aufic and persephone.

### Odd harmonics

Approximation of odd harmonics in 375edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.16 +0.89 +0.77 +0.89 -0.92 +1.07 -0.27 +0.64 +0.09 -0.38 -1.07
Relative (%) -36.1 +27.7 +24.2 +27.8 -28.7 +33.5 -8.4 +20.1 +2.7 -11.9 -33.6
Steps
(reduced)
594
(219)
871
(121)
1053
(303)
1189
(64)
1297
(172)
1388
(263)
1465
(340)
1533
(33)
1593
(93)
1647
(147)
1696
(196)

### Subsets and supersets

Since 375 factors into 3 × 53, 375edo has subset edos 3, 5, 15, 25, 75, and 125. 1175edo, which triples it, gives a good correction to the harmonic 3 and is consistent to the 15-odd-limit.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [1189 -375 [375 1189]] -0.1404 0.1404 4.39
2.9.5 [8 7 -13, [97 -24 -9 [375 1189 871]] -0.2208 0.1615 5.05
2.9.5.7 250047/250000, 589824/588245, [8 7 -13 [375 1189 871 1053]] -0.2345 0.1418 4.43