135edo: Difference between revisions

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'''135edo''' is the [[EDO|equal division of the octave]] into 135 parts of 8.8888 cents each. It tempers out 32805/32768 (schisma) and 30517578125/29386561536 (quintriyo comma) in the 5-limit; [[225/224]], 3125/3087, and 28824005/28697814 in ~~the 7-limit. It is consistent to~~ the 7-limit, ~~but there is a large relative delta for 5th harmonic. Using the patent val, it tempers out~~ [[385/384]], 540/539, 2200/2187, 12005/11979 and [[~~Quartisma|117440512/117406179~~]] in the 11-limit; 275/273, [[325/324]], 352/351, and 729/728 in the 13-limit. Using the 135c val, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; 126/125, 10976/10935, and 589824/588245 in the 7-limit; [[176/175]], 441/440, 14641/14580 and 16384/16335 in the 11-limit; 196/195, [[351/350]], [[352/351]], 676/675, and 6656/6655 in the 13-limit.

'''135edo''' is the [[EDO|equal division of the octave]] into 135 parts of 8.8888 cents each.

== Theory ==

135edo is consistent to the 7-odd-limit, but there is a large relative delta for 5th harmonic. Using the [[patent val]], 135et tempers out 32805/32768 ([[schisma]]) and 30517578125/29386561536 (quintriyo comma) in the 5-limit; [[225/224]], [[3125/3087]], and 28824005/28697814 in the 7-limit, [[385/384]], [[540/539]], 2200/2187, 12005/11979 and the [[quartisma]] in the 11-limit; [[275/273]], [[325/324]], [[352/351]], and [[729/728]] in the 13-limit. Using the 135c val, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; [[126/125]], [[10976/10935]], and 589824/588245 in the 7-limit; [[176/175]], [[441/440]], [[14641/14580]] and 16384/16335 in the 11-limit; [[196/195]], [[351/350]], 352/351, [[676/675]], and 6656/6655 in the 13-limit.

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

[[Category:Quartismic]]

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-'''135edo''' is the [[EDO|equal division of the octave]] into 135 parts of 8.8888 cents each. It tempers out 32805/32768 (schisma) and 30517578125/29386561536 (quintriyo comma) in the 5-limit; [[225/224]], 3125/3087, and 28824005/28697814 in the 7-limit. It is consistent to the 7-limit, but there is a large relative delta for 5th harmonic. Using the patent val, it tempers out [[385/384]], 540/539, 2200/2187, 12005/11979 and [[Quartisma|117440512/117406179]] in the 11-limit; 275/273, [[325/324]], 352/351, and 729/728 in the 13-limit. Using the 135c val, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; 126/125, 10976/10935, and 589824/588245 in the 7-limit; [[176/175]], 441/440, 14641/14580 and 16384/16335 in the 11-limit; 196/195, [[351/350]], [[352/351]], 676/675, and 6656/6655 in the 13-limit.
+'''135edo''' is the [[EDO|equal division of the octave]] into 135 parts of 8.8888 cents each.
+== Theory ==
+edo is consistent to the 7-odd-limit, but there is a large relative delta for 5th harmonic. Using the [[patent val]], 135et tempers out 32805/32768 ([[schisma]]) and 30517578125/29386561536 (quintriyo comma) in the 5-limit; [[225/224]], [[3125/3087]], and 28824005/28697814 in the 7-limit, [[385/384]], [[540/539]], 2200/2187, 12005/11979 and the [[quartisma]] in the 11-limit; [[275/273]], [[325/324]], [[352/351]], and [[729/728]] in the 13-limit. Using the 135c val, it tempers out 1594323/1562500 and 50331648/48828125 in the 5-limit; [[126/125]], [[10976/10935]], and 589824/588245 in the 7-limit; [[176/175]], [[441/440]], [[14641/14580]] and 16384/16335 in the 11-limit; [[196/195]], [[351/350]], 352/351, [[676/675]], and 6656/6655 in the 13-limit.
+=== Prime harmonics ===
+{{Primes in edo|135}}
 [[Category:Equal divisions of the octave]]
 [[Category:Quartismic]]