192edo: Difference between revisions

Line 1:

~~'''192edo''' is the [[~~EDO|~~equal division of the octave]] into~~ 192 ~~parts of 6.25 [[cent]]s each exactly. Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup>~~ = ~~16 equal divisions of the [[12edo]] semitone). It~~ is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.

==Theory==

192edo is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.

=== Significance in digital audio ===

Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone).

=== Odd harmonics ===

==See also==

*[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''192edo''' is the [[EDO|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone). It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.
+{{EDO intro|192}}
+==Theory==
+edo is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.
+=== Significance in digital audio ===
+Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone).
+=== Odd harmonics ===
+{{harmonics in equal|192}}
 ==See also==
 *[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units