192edo: Difference between revisions

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'''192edo''' is the [[EDO|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. 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.

'''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.

==See also==

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

**[[24edo]] (1mu tuning)

**[[48edo]] (2mu tuning)

**[[96edo]] (3mu tuning)

**[[384edo]] (5mu tuning)

**[[768edo]] (6mu tuning)

**[[1536edo]] (7mu tuning)

**[[3072edo]] (8mu tuning)

**[[6144edo]] (9mu tuning)

**[[12288edo]] (10mu tuning)

**[[24576edo]] (11mu tuning)

**[[49152edo]] (12mu tuning)

**[[98304edo]] (13mu tuning)

**[[196608edo]] (14mu tuning)

[[Category:Edo]]

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-'''192edo''' is the [[EDO|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. 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.
+'''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.
+==See also==
+*[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units
+**[[24edo]] (1mu tuning)
+**[[48edo]] (2mu tuning)
+**[[96edo]] (3mu tuning)
+**[[384edo]] (5mu tuning)
+**[[768edo]] (6mu tuning)
+**[[1536edo]] (7mu tuning)
+**[[3072edo]] (8mu tuning)
+**[[6144edo]] (9mu tuning)
+**[[12288edo]] (10mu tuning)
+**[[24576edo]] (11mu tuning)
+**[[49152edo]] (12mu tuning)
+**[[98304edo]] (13mu tuning)
+**[[196608edo]] (14mu tuning)
 [[Category:Edo]]