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==Intervals==
==Intervals==
98304EDO is [[consistent]] to the [[19-odd-limit|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.
98304EDO is [[consistent]] to the [[19-odd-limit|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.
 
{| class="wikitable"
|-
! rowspan="2"| 98304EDO <br>steps
! rowspan="2"| cents <br>value
! colspan="2"| JI interval
! rowspan="2"| error <br>(cents)
|-
! | ratio
! | cents
|-
| | 0
| | 0.0000
| | [[1/1]]
| | 0.0000
| | &plusmn;0.0000
|-
| | 3995
| | 48.7671
| | [[36/35]]
| | 48.7704
| | &minus;0.00329
|-
| | 4111
| | 50.1831
| | 35/34
| | 50.1842
| | &minus;0.00111
|-
| | 4234
| | 51.6846
| | 34/33
| | 51.6825
| | +0.00210
|-
| | 4364
| | 53.2715
| | [[33/32]]
| | 53.2729
| | &minus;0.00146
|-
| | 5158
| | 62.9639
| | [[28/27]]
| | 62.9609
| | +0.00296
|-
| | 5352
| | 65.3320
| | [[27/26]]
| | 65.3373
| | &minus;0.00531
|-
| | 5562
| | 67.8955
| | [[26/25]]
| | 67.9002
| | &minus;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
| | &minus;0.00440
|-
| | 8598
| | 104.9561
| | [[17/16]]
| | 104.9554
| | +0.00065
|-
| | 9153
| | 111.7310
| | [[16/15]]
| | 111.7313
| | &minus;0.00033
|-
| | 9785
| | 119.4458
| | [[15/14]]
| | 119.4428
| | +0.00299
|-
| | 10510
| | 128.2959
| | [[14/13]]
| | 128.2982
| | &minus;0.00235
|-
| | 11352
| | 138.5742
| | [[13/12]]
| | 138.5727
| | +0.00156
|-
| | 12340
| | 150.6348
| | [[12/11]]
| | 150.6371
| | &minus;0.00229
|-
| | 13517
| | 165.0024
| | [[11/10]]
| | 165.0042
| | &minus;0.00179
|-
| | 14943
| | 182.4097
| | [[10/9]]
| | 182.4037
| | +0.00596
|-
| | 15774
| | 192.5537
| | [[19/17]]
| | 192.5576
| | &minus;0.00390
|-
| | 16704
| | 203.9063
| | [[9/8]]
| | 203.9100
| | &minus;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
| | &minus;0.00079
|-
| | 23049
| | 281.3599
| | [[20/17]]
| | 281.3583
| | +0.00156
|-
| | 23692
| | 289.2090
| | [[13/11]]
| | 289.2097
| | &minus;0.00074
|-
| | 24372
| | 297.5098
| | [[19/16]]
| | 297.5130
| | &minus;0.00325
|-
| | 25857
| | 315.6372
| | [[6/5]]
| | 315.6413
| | &minus;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
| | [[Octave|2/1]]
| | 1200.0000
| | &plusmn;0.0000
|}


==See also==
==See also==

Revision as of 12:54, 21 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, 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

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