195edo: Difference between revisions

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'''195edo''' is the [[EDO|equal division of the octave]] into 195 parts of 6.1538 cents each. It is [[contorted]] in the 5-limit, 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.

[[~~Category:Equal divisions of~~ the ~~octave~~]]

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 ===

=== Subsets and supersets ===

Since 195 factors into {{factorization|195}}, 195edo has subset edos {{EDOs| 3, 5, 13, 15, 39, and 65 }}.

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-'''195edo''' is the [[EDO|equal division of the octave]] into 195 parts of 6.1538 cents each. It is [[contorted]] in the 5-limit, 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.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+edo 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 ===
+{{Harmonics in equal|195}}
+=== Subsets and supersets ===
+Since 195 factors into {{factorization|195}}, 195edo has subset edos {{EDOs| 3, 5, 13, 15, 39, and 65 }}.