1536edo: Difference between revisions

{{EDO intro|1536}} 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.  

1536edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for 5-limit: {{val| 1536 2435 3566 }} ([[patent val]]), {{val| 1536 '''2434''' 3566 }} (1536b val, [[enfactoring|enfactored]] through the 17-limit, see [[768edo]]), and {{val| 1536 2435 '''3567''' }} (1536c val). Using the patent val, it tempers out {{monzo| 71 -36 -6 }} and {{monzo| -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 {{monzo| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.