196608edo

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196608EDO is the equal division of the octave into 196608 parts of exact 0.006103515625 cents each, which is to say 2(1/196608) as a frequency ratio. Its adjacent step is known as the MIDI Tuning Standard unit (MTSU) or Tetradecamu (fourteenth MIDI-resolution unit, 14mu, 214 = 16384 equal divisions of the 12edo semitone). The 14mu is specified in the MIDI spec (1983) as the smallest increment available for the pitch-bend controller, and as the frequency data format for MTS (1999). The 14mu is the smallest unit of tuning resolution which has ever been put into common musical use, and provides extremely accurate tuning in microtonal electronic music.

Intervals

Below is a list for just intervals.

196608EDO
steps
cents
value
JI interval error
(steps)
error
(cents)
ratio cents
0 0.000000000000 1/1 0.000000000000 ±0.000000 ±0.000000000000
18306 111.73095703125 16/15 111.731285269778 −0.053779 −0.000328238528
19570 119.44580078125 15/14 119.442808261097 +0.490295 +0.002992520153
21020 128.2958984375 14/13 128.298244699814 −0.384412 −0.002346262314
22704 138.57421875 13/12 138.572660903923 +0.255238 +0.001557846077
24680 150.634765625 12/11 150.637058500631 −0.375665 −0.002292875631
27034 165.00244140625 11/10 165.004228499922 −0.292797 −0.001787093672
29885 182.403564453125 10/9 182.403712134060 −0.024196 −0.000147680935
33409 203.912353515625 9/8 203.910001730775 +0.385316 +0.002351784850
37876 231.1767578125 8/7 231.174093530875 +0.436516 +0.002664281625
40590 247.74169921875 15/13 247.741052960912 +0.105883 +0.000646257838
43724 266.8701171875 7/6 266.870905603738 −0.129174 −0.000788416238
47384 289.208984375 13/11 289.209719404554 −0.120427 −0.000735029554
51715 315.643310546875 6/5 315.641287000553 +0.331538 +0.002023546322
56919 347.406005859375 11/9 347.407940633982 −0.316993 −0.001934774607
58896 359.47265625 16/13 359.472338230689 +0.052104 +0.000318019311
63294 386.31591796875 5/4 386.313713864835 +0.361120 +0.002204103915
68405 417.510986328125 14/11 417.507964104368 +0.495161 +0.003022223757
71284 435.0830078125 9/7 435.084095261650 −0.178168 −0.001087449150
74418 454.21142578125 13/10 454.213947904476 −0.413225 −0.002522123226
81600 498.046875 4/3 498.044999134613 +0.307342 +0.001875865387
87974 536.95068359375 15/11 536.950772365466 −0.014544 −0.000088771716
90328 551.318359375 11/8 551.317942364757 +0.068323 +0.000417010243
92305 563.385009765625 18/13 563.382339961464 +0.437421 +0.002669804161
95439 582.513427734375 7/5 582.512192604290 +0.202364 +0.001235130085
101169 617.486572265625 10/7 617.487807395710 −0.202364 −0.001235130085
106280 648.681640625 16/11 648.682057635243 −0.068323 −0.000417010243
115008 701.953125 3/2 701.955000865387 −0.307342 −0.001875865387
125324 764.9169921875 14/9 764.915904738350 +0.178168 +0.001087449150
128203 782.489013671875 11/7 782.492035895632 −0.495161 −0.003022223757
133314 813.68408203125 8/5 813.686286135165 −0.361120 −0.002204103915
139689 852.593994140625 18/11 852.592059366018 +0.316993 +0.001934774607
144893 884.356689453125 5/3 884.358712999447 −0.331538 −0.002023546322
152884 933.1298828125 12/7 933.129094396262 +0.129174 +0.000788416238
158732 968.8232421875 7/4 968.825906469125 −0.436516 −0.002664281625
163199 996.087646484375 16/9 996.089998269225 −0.385316 −0.002351784850
166723 1017.596435546875 9/5 1017.596287865940 +0.024196 +0.000147680935
169574 1034.99755859375 20/11 1034.995771500078 +0.292797 +0.001787093672
171928 1049.365234375 11/6 1049.362941499369 +0.375665 +0.002292875631
196608 1200.000000000000 2/1 1200.000000000000 ±0.000000 ±0.000000000000

See also