3072edo

← 3071edo

3072edo

3073edo →

Prime factorization	210 × 3
Step size	0.390625 ¢
Fifth	1797\3072 (701.953 ¢) (→ 599\1024)
Semitones (A1:m2)	291:231 (113.7 ¢ : 90.23 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

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.

Significance in digital audio software

3072edo's 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.

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)