195edo
| ← 194edo | 195edo | 196edo → |
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 6.154 ¢ 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
| 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 (%) | -7 | +22 | -43 | -14 | +41 | +41 | +16 | -6 | -35 | +50 | -9 | |
| 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.