195edo

Revision as of 14:02, 16 April 2024 by FloraC (talk | contribs) (Cleanup; +error table; +subsets and supersets)

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← 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

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.