1536edo

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Template:EDO intro 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.

← 1535edo 1536edo 1537edo →
Prime factorization 29 × 3
Step size 0.78125 ¢ 
Fifth 899\1536 (702.344 ¢)
Semitones (A1:m2) 149:113 (116.4 ¢ : 88.28 ¢)
Dual sharp fifth 899\1536 (702.344 ¢)
Dual flat fifth 898\1536 (701.563 ¢) (→ 449\768)
Dual major 2nd 261\1536 (203.906 ¢) (→ 87\512)
Consistency limit 3
Distinct consistency limit 3

1536edo is inconsistent to the 5-odd-limit and higher limits, with three mappings possible for 5-limit: 1536 2435 3566] (patent val), 1536 2434 3566] (1536b val, enfactored through the 17-limit, see 768edo), 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