98304edo
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, 1206902781/1206878450, and 21867094832/21867015625 in the 19-limit.
| 98304EDO steps |
cents value |
JI interval | error (cents) | |
|---|---|---|---|---|
| ratio | cents | |||
| 0 | 0.0000 | 1/1 | 0.0000 | ±0.0000 |
| 3995 | 48.7671 | 36/35 | 48.7704 | −0.00329 |
| 4111 | 50.1831 | 35/34 | 50.1842 | −0.00111 |
| 4234 | 51.6846 | 34/33 | 51.6825 | +0.00210 |
| 4364 | 53.2715 | 33/32 | 53.2729 | −0.00146 |
| 5158 | 62.9639 | 28/27 | 62.9609 | +0.00296 |
| 5352 | 65.3320 | 27/26 | 65.3373 | −0.00531 |
| 5562 | 67.8955 | 26/25 | 67.9002 | −0.00473 |
| 6598 | 80.5420 | 22/21 | 80.5370 | +0.00496 |
| 7275 | 88.8062 | 20/19 | 88.8007 | +0.00545 |
| 7668 | 93.6035 | 19/18 | 93.6030 | +0.00050 |
| 8106 | 98.9502 | 18/17 | 98.9546 | −0.00440 |
| 8598 | 104.9561 | 17/16 | 104.9554 | +0.00065 |
| 9153 | 111.7310 | 16/15 | 111.7313 | −0.00033 |
| 9785 | 119.4458 | 15/14 | 119.4428 | +0.00299 |
| 10510 | 128.2959 | 14/13 | 128.2982 | −0.00235 |
| 11352 | 138.5742 | 13/12 | 138.5727 | +0.00156 |
| 12340 | 150.6348 | 12/11 | 150.6371 | −0.00229 |
| 13517 | 165.0024 | 11/10 | 165.0042 | −0.00179 |
| 14943 | 182.4097 | 10/9 | 182.4037 | +0.00596 |
| 15774 | 192.5537 | 19/17 | 192.5576 | −0.00390 |
| 16704 | 203.9063 | 9/8 | 203.9100 | −0.00375 |
| 17751 | 216.6870 | 17/15 | 216.6867 | +0.00032 |
| 18938 | 231.1768 | 8/7 | 231.1741 | +0.00266 |
| 20295 | 247.7417 | 15/13 | 247.7411 | +0.00065 |
| 20792 | 253.8086 | 22/19 | 253.8049 | +0.00367 |
| 21862 | 266.8701 | 7/6 | 266.8709 | −0.00079 |
| 23049 | 281.3599 | 20/17 | 281.3583 | +0.00156 |
| 23692 | 289.2090 | 13/11 | 289.2097 | −0.00074 |
| 24372 | 297.5098 | 19/16 | 297.5130 | −0.00325 |
| 25857 | 315.6372 | 6/5 | 315.6413 | −0.00408 |
| 27536 | 336.1328 | 17/14 | 336.1295 | +0.00331 |
| 28460 | 347.4121 | 11/9 | 347.4079 | +0.00417 |
| 29448 | 359.4727 | 16/13 | 359.4723 | +0.00032 |
| 31647 | 386.3159 | 5/4 | 386.3137 | +0.00220 |
| 40800 | 498.0469 | 4/3 | 498.0450 | +0.00188 |
| 98304 | 1200.0000 | 2/1 | 1200.0000 | ±0.0000 |
See also
- Equal multiplications of MIDI-resolution units