3072edo

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
  • 24edo (1mu tuning)
  • 48edo (2mu tuning)
  • 96edo (3mu tuning)
  • 192edo (4mu tuning)
  • 384edo (5mu tuning)
  • 768edo (6mu tuning)
  • 1536edo (7mu tuning)
  • 6144edo (9mu tuning)
  • 12288edo (10mu tuning)
  • 24576edo (11mu tuning)
  • 49152edo (12mu tuning)
  • 98304edo (13mu tuning)
  • 196608edo (14mu tuning)