3072edo: Difference between revisions
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'''3072EDO''' is the [[EDO|equal division of the octave]] into 3072 parts of exact 0.390625 cents each, which is to say 2<sup>(1/3072)</sup> as a frequency ratio. Its adjacent step is known as '''Octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu 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 5 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. | '''3072EDO''' is the [[EDO|equal division of the octave]] into 3072 parts of exact 0.390625 cents each, which is to say 2<sup>(1/3072)</sup> as a frequency ratio. Its adjacent step is known as '''Octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu 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 5 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== | ==Intervals== | ||
Revision as of 22:16, 4 October 2022
| ← 3071edo | 3072edo | 3073edo → |
3072EDO is the equal division of the octave into 3072 parts of exact 0.390625 cents each, which is to say 2(1/3072) as a frequency ratio. Its adjacent step is known as Octamu (eighth MIDI-resolution unit, 8mu, 28 = 256 equal divisions of the 12edo semitone). The internal data structure of the 8mu 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 5 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
3072EDO is consistent to the 11-limit, tempering out |37 25 -33> (whoosh) and |161 -84 -12> (atom) in the 5-limit; 250047/250000, |-2 -25 1 14>, and |-53 -1 9 12> in the 7-limit; 9801/9800, 151263/151250, 184549376/184528125, and 73525096183/73466403840 in the 11-limit.
See also
- Equal multiplications of MIDI-resolution units