98304edo

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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 ±0.00000
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
33132 404.4434 24/19 404.4420 +0.00137
33525 409.2407 19/15 409.2443 −0.00358
34202 417.5049 14/11 417.5080 −0.00308
35642 435.0830 9/7 435.0841 −0.00109
36566 446.3623 22/17 446.3625 −0.00023
37209 454.2114 13/10 454.2139 −0.00252
38046 464.4287 17/13 464.4277 +0.00096
38566 470.7764 21/16 470.7809 −0.00454
40800 498.0469 4/3 498.0450 +0.00188
43310 528.6865 19/14 528.6871 −0.00059
43987 536.9507 15/11 536.9508 −0.00009
44484 543.0176 26/19 543.0146 +0.00293
45164 551.3184 11/8 551.3179 +0.00042
46152 563.3789 18/13 563.3823 −0.00343
47719 582.5073 7/5 582.5122 −0.00487
48906 596.9971 24/17 596.9996 −0.00252
49398 603.0029 17/12 603.0004 +0.00252
50585 617.4927 10/7 617.4878 +0.00487
57504 701.9531 3/2 701.9550 −0.00188
62662 764.9170 14/9 764.9159 +0.00109
66657 813.6841 8/5 813.6863 −0.00220
72447 884.3628 5/3 884.3587 +0.00408
76442 933.1299 12/7 933.1291 +0.00079
79366 968.8232 7/4 968.8259 −0.00266
98304 1200.0000 2/1 1200.0000 ±0.00000

See also