192edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|192}} | |||
==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 === | |||
{{harmonics in equal|192}} | |||
==See also== | ==See also== | ||
*[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units | *[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units | ||
Revision as of 23:10, 21 December 2022
| ← 191edo | 192edo | 193edo → |
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 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, 24 = 16 equal divisions of the 12edo semitone).
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | +1.19 | -0.08 | +2.34 | -1.32 | -3.03 | -0.77 | +1.29 | +2.49 | -2.03 | +2.98 |
| Relative (%) | -31.3 | +19.0 | -1.2 | +37.4 | -21.1 | -48.4 | -12.3 | +20.7 | +39.8 | -32.5 | +47.6 | |
| Steps (reduced) |
304 (112) |
446 (62) |
539 (155) |
609 (33) |
664 (88) |
710 (134) |
750 (174) |
785 (17) |
816 (48) |
843 (75) |
869 (101) | |
See also
- Equal multiplications of MIDI-resolution units