1536edo

1536EDO is the equal division of the octave into 1536 parts of exact 0.78125 cents each, which is to say 2^(1/1536) 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
  • 24edo (1mu tuning)
  • 48edo (2mu tuning)
  • 96edo (3mu tuning)
  • 192edo (4mu tuning)
  • 384edo (5mu tuning)
  • 768edo (6mu tuning)
  • 3072edo (8mu tuning)
  • 6144edo (9mu tuning)
  • 12288edo (10mu tuning)
  • 24576edo (11mu tuning)
  • 49152edo (12mu tuning)
  • 98304edo (13mu tuning)
  • 196608edo (14mu tuning)