98304edo: Difference between revisions
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'''98304EDO''' is the [[EDO|equal division of the octave]] into 98304 parts of exact 0.01220703125 cents each, which is to say 2<sup>(1/98304)</sup> as a frequency ratio. Its adjacent step is known as | '''98304EDO''' is the [[EDO|equal division of the octave]] into 98304 parts of exact 0.01220703125 cents each, which is to say 2<sup>(1/98304)</sup> as a frequency ratio. Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 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. | ||
==Intervals== | ==Intervals== | ||
Revision as of 00:29, 20 March 2019
98304EDO is the equal division of the octave into 98304 parts of exact 0.01220703125 cents each, which is to say 2(1/98304) as a frequency ratio. 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.
Intervals
98304EDO is consistent to the 19-limit, tempering out |45 2 -28 6>, |-54 15 -16 24>, and |-29 135 -18 -51> in the 7-limit; |-4 15 -14 7 -2>, |-3 28 2 -9 -6>, |-50 0 -2 17 2>, and |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, 791249550/791243563, and 1206902781/1206878450 in the 19-limit.
See also
- Equal multiplications of MIDI-resolution units