# 195edo

 ← 194edo 195edo 196edo →
Prime factorization 3 × 5 × 13
Step size 6.15385¢
Fifth 114\195 (701.538¢) (→38\65)
Semitones (A1:m2) 18:15 (110.8¢ : 92.31¢)
Consistency limit 5
Distinct consistency limit 5

195 equal divisions of the octave (abbreviated 195edo or 195ed2), also called 195-tone equal temperament (195tet) or 195 equal temperament (195et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 195 equal parts of about 6.15 ¢ each. Each step represents a frequency ratio of 21/195, or the 195th root of 2.

195edo is contorted in the 5-limit, with the same tuning as 65edo, tempering out 32805/32768 (schisma), 78732/78125 (sensipent comma), 393216/390625 (würschmidt comma), and 129140163/128000000 (graviton). Using the patent val, it tempers out 1029/1024, 10976/10935, and 395136/390625 in the 7-limit; 243/242, 3773/3750, 4000/3993, and 5632/5625 in the 11-limit; 196/195, 364/363, 729/728, 1001/1000, and 4096/4095 in the 13-limit. Using the 195d val, it tempers out 1728/1715, 177147/175616, and 250047/250000 in the 7-limit; 243/242, 1375/1372, 4000/3993, and 5632/5625 in the 11-limit; 351/350, 640/637, 1188/1183, 1575/1573, and 3584/3575 in the 13-limit. Using the 195ef val, it tempers out 385/384, 441/440, 19712/19683, and 47432/46875 in the 11-limit; 351/350, 847/845, 1287/1280, 1573/1568, and 2197/2187 in the 13-limit.

### Odd harmonics

Approximation of odd harmonics in 195edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.42 +1.38 -2.67 -0.83 +2.53 +2.55 +0.96 -0.34 -2.13 +3.07 -0.58
Relative (%) -6.8 +22.4 -43.4 -13.5 +41.1 +41.4 +15.6 -5.5 -34.6 +49.8 -9.5
Steps
(reduced)
309
(114)
453
(63)
547
(157)
618
(33)
675
(90)
722
(137)
762
(177)
797
(17)
828
(48)
857
(77)
882
(102)

### Subsets and supersets

Since 195 factors into 3 × 5 × 13, 195edo has subset edos 3, 5, 13, 15, 39, and 65.