98304edo: Difference between revisions

{{EDO intro|98304}} Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2¹³ = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu 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; all bits are 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.

== Theory ==

98304edo is [[consistent]] to the [[19-odd-limit]], tempering out {{monzo| 45 2 -28 6 }}, {{monzo| -54 15 -16 24 }}, and {{monzo| -29 135 -18 -51 }} in the 7-limit; {{monzo| -4 15 -14 7 -2 }}, {{monzo| -3 28 2 -9 -6 }}, {{monzo| -50 0 -2 17 2 }}, and {{monzo| 30 10 8 -2 -17}} in the 11-limit; 123201/123200, 32427005625/32426652544, 278924131584/278916015625, 37744795080531/37744172597248, and 156905298045000/156904157228819 in the 13-limit; 2000033/2000000, 154002541/154001250, 303464448/303460625, 338676338/338671875, 791249550/791243563, and 176846618624/176846076825 in the 17-limit; 89376/89375, 104976/104975, 709632/709631, 5836831/5836800, 494190983/494190000, 1206902781/1206878450, and 21867094832/21867015625 in the 19-limit.

! rowspan="2"| #

! rowspan="2"| Cents

! colspan="2"| JI Interval

! rowspan="2"| Error <br>(cents)

== See also ==

* [[Equal-step tuning|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)

** [[3072edo]] (8mu tuning)

** [[6144edo]] (9mu tuning)

** [[12288edo]] (10mu tuning)

** [[24576edo]] (11mu tuning)

** [[49152edo]] (12mu tuning)

** [[196608edo]] (14mu tuning)