384edo: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
Rework (-windrose (16 gensteps isn't available in this edo)); +subsets and supersets |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
384edo is consistent in the 7-limit | 384edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[misty comma]] {{monzo| 26 -12 -3 }}, and the 5-limit tritriple comma {{monzo| 31 20 -27 }} in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma|250047/250000]], and the [[mistisma]] 458752/455625 in the 7-limit. | ||
=== | === As a tuning standard === | ||
A step of 384edo is known as a '''pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone). The internal data structure of the 5mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and one other bit which is not used. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|384|intervals=prime}} | |||
=== Subsets and supersets === | |||
Since 384 factors into {{factorization|384}}, 384edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, and 192 }}. | |||
== See also == | == See also == | ||
* [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units | * [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units | ||
** [[24edo]] (1mu tuning) | ** [[24edo]] (1mu tuning) | ||
| Line 28: | Line 29: | ||
** [[98304edo]] (13mu tuning) | ** [[98304edo]] (13mu tuning) | ||
** [[196608edo]] (14mu tuning) | ** [[196608edo]] (14mu tuning) | ||
== External links == | |||
* [http://tonalsoft.com/enc/number/5mu.aspx Tonalsoft Encyclopedia | ''5mu / pentamu''] | |||
Revision as of 08:32, 7 November 2023
| ← 383edo | 384edo | 385edo → |
Theory
384edo is consistent in the 7-odd-limit. The equal temperament tempers out the misty comma [26 -12 -3⟩, and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and 3136/3125, 5120/5103, 250047/250000, and the mistisma 458752/455625 in the 7-limit.
As a tuning standard
A step of 384edo is known as a pentamu (fifth MIDI-resolution unit, 5mu, 25 = 32 equal divisions of the 12edo semitone). The internal data structure of the 5mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and one other bit which is not used.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.17 | +1.19 | -0.08 | -1.32 | +0.10 | +1.29 | -0.64 | -0.15 | -1.45 | -1.29 |
| Relative (%) | +0.0 | +37.4 | +38.0 | -2.4 | -42.2 | +3.1 | +41.4 | -20.4 | -4.8 | -46.5 | -41.1 | |
| Steps (reduced) |
384 (0) |
609 (225) |
892 (124) |
1078 (310) |
1328 (176) |
1421 (269) |
1570 (34) |
1631 (95) |
1737 (201) |
1865 (329) |
1902 (366) | |
Subsets and supersets
Since 384 factors into 27 × 3, 384edo has subset edos 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, and 192.
See also
- Equal multiplications of MIDI-resolution units