98304edo
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| ← 98303edo | 98304edo | 98305edo → |
Template:EDO intro 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 [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.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00188 | +0.00220 | -0.00266 | +0.00042 | -0.00032 | +0.00065 | -0.00325 | -0.00286 | +0.00044 | -0.00383 |
| Relative (%) | +0.0 | -15.4 | +18.1 | -21.8 | +3.4 | -2.6 | +5.3 | -26.6 | -23.5 | +3.6 | -31.4 | |
| Steps (reduced) |
98304 (0) |
155808 (57504) |
228255 (31647) |
275974 (79366) |
340076 (45164) |
363768 (68856) |
401814 (8598) |
417588 (24372) |
444684 (51468) |
477559 (84343) |
487017 (93801) | |
Selected intervals
| # | Cents | 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
- Equal multiplications of MIDI-resolution units