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	±0.00000
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
57504	701.9531	3/2	701.9550	−0.00188
98304	1200.0000	2/1	1200.0000	±0.00000

See also

• 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)