384edo: Difference between revisions
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Royalmilktea (talk | contribs) 384edo/5mu page, infobox et, harmonics, and other mu temps. added |
cleanup and a new fact |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|384}} | |||
{{ | |||
== Theory == | |||
384edo is consistent in the 7-limit, tempering out the misty comma [[Misty comma|[26 -12 -3⟩]], and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma|250047/250000]], and the mistisma [[Mistismic temperaments|458752/455625]] in the 7-limit. | 384edo is consistent in the 7-limit, tempering out the misty comma [[Misty comma|[26 -12 -3⟩]], and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma|250047/250000]], and the mistisma [[Mistismic temperaments|458752/455625]] in the 7-limit. | ||
=== Relation to powers of two === | |||
Its adjacent step is known as '''Pentamu''' (fifth MIDI-resolution unit, 5mu, 2<sup>5</sup> = 32 equal divisions of the [[12edo]] semitone). In addition, in light of 384 being a multiple of 32, 384bc val supports [[windrose]] temperament in the 7-limit. | |||
=== Prime harmonics === | |||
{{harmonics in equal|384|prec=3|start=2|intervals=prime}} | |||
== See also == | == See also == | ||
Revision as of 21:24, 22 December 2022
| ← 383edo | 384edo | 385edo → |
Theory
384edo is consistent in the 7-limit, tempering 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.
Relation to powers of two
Its adjacent step is known as Pentamu (fifth MIDI-resolution unit, 5mu, 25 = 32 equal divisions of the 12edo semitone). In addition, in light of 384 being a multiple of 32, 384bc val supports windrose temperament in the 7-limit.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.170 | +1.186 | -0.076 | -1.318 | +0.097 | +1.295 | -0.638 | -0.149 | -1.452 | -1.286 | -1.344 |
| Relative (%) | +37.4 | +38.0 | -2.4 | -42.2 | +3.1 | +41.4 | -20.4 | -4.8 | -46.5 | -41.1 | -43.0 | |
| Steps (reduced) |
609 (225) |
892 (124) |
1078 (310) |
1328 (176) |
1421 (269) |
1570 (34) |
1631 (95) |
1737 (201) |
1865 (329) |
1902 (366) |
2000 (80) | |
See also
- Equal multiplications of MIDI-resolution units