1536edo: Difference between revisions
format and link related interval size units |
m Cleanup |
||
| Line 1: | Line 1: | ||
'''1536EDO''' is the [[EDO|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup> | '''1536EDO''' is the [[EDO|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 6 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning. | ||
==Intervals== | |||
1536EDO is inconsistent to the [[5-limit]] and higher limit, with three mappings possible for 5-limit: | == Intervals == | ||
==See also== | 1536EDO is inconsistent to the [[5-limit]] and higher limit, with three mappings possible for 5-limit: {{val| 1536 2435 3566 }} (patent val), {{val| 1536 '''2434''' 3566 }} (1536b val, contorted through the 17-limit), and {{val| 1536 2435 '''3567''' }} (1536c val). Using the patent val, it tempers out {{monzo| 71 -36 -6 }} and {{monzo| -32 -34 37 }} in the 5-limit; [[703125/702464]], [[4802000/4782969]], and 54975581388800/54936068900769 in the 7-limit. Using the 1536c val, it tempers out 6115295232/6103515625 ([[vishnuzma]]) and {{monzo| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit. | ||
*[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units | |||
**[[24edo]] (1mu tuning) | == See also == | ||
**[[48edo]] (2mu tuning) | * [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units | ||
**[[96edo]] (3mu tuning) | ** [[24edo]] (1mu tuning) | ||
**[[192edo]] (4mu tuning) | ** [[48edo]] (2mu tuning) | ||
**[[384edo]] (5mu tuning) | ** [[96edo]] (3mu tuning) | ||
**[[768edo]] (6mu tuning) | ** [[192edo]] (4mu tuning) | ||
**[[3072edo]] (8mu tuning) | ** [[384edo]] (5mu tuning) | ||
**[[6144edo]] (9mu tuning) | ** [[768edo]] (6mu tuning) | ||
**[[12288edo]] (10mu tuning) | ** [[3072edo]] (8mu tuning) | ||
**[[24576edo]] (11mu tuning) | ** [[6144edo]] (9mu tuning) | ||
**[[49152edo]] (12mu tuning) | ** [[12288edo]] (10mu tuning) | ||
**[[98304edo]] (13mu tuning) | ** [[24576edo]] (11mu tuning) | ||
**[[196608edo]] (14mu tuning) | ** [[49152edo]] (12mu tuning) | ||
** [[98304edo]] (13mu tuning) | |||
** [[196608edo]] (14mu tuning) | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 10:21, 2 June 2021
1536EDO is the equal division of the octave into 1536 parts of exact 0.78125 cents each, which is to say 21/1536 as a frequency ratio. Its adjacent step is known as Heptamu (seventh MIDI-resolution unit, 7mu, 27 = 128 equal divisions of the 12edo semitone). The internal data structure of the 7mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 6 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.
Intervals
1536EDO is inconsistent to the 5-limit and higher limit, with three mappings possible for 5-limit: ⟨1536 2435 3566] (patent val), ⟨1536 2434 3566] (1536b val, contorted through the 17-limit), and ⟨1536 2435 3567] (1536c val). Using the patent val, it tempers out [71 -36 -6⟩ and [-32 -34 37⟩ in the 5-limit; 703125/702464, 4802000/4782969, and 54975581388800/54936068900769 in the 7-limit. Using the 1536c val, it tempers out 6115295232/6103515625 (vishnuzma) and [169 -111 3⟩ in the 5-limit; 250047/250000, 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.
See also
- Equal multiplications of MIDI-resolution units