196608edo
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
There is a list for just intervals.
| 196608EDO steps |
cents value |
JI interval ratio |
JI interval cents |
error (steps) |
error (cents) |
|---|---|---|---|---|---|
| 0 | 0.000000000000 | 1/1 | 0.000000000000 | ±0.000000 | ±0.000000000000 |
| 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 |
| 43724 | 266.8701171875 | 7/6 | 266.870905603738 | −0.129174 | −0.000788416238 |
| 51715 | 315.643310546875 | 6/5 | 315.641287000553 | +0.331538 | +0.002023546322 |
| 56919 | 347.406005859375 | 11/9 | 347.407940633982 | −0.316993 | −0.001934774607 |
| 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 |
| 81600 | 498.046875 | 4/3 | 498.044999134613 | +0.307342 | +0.001875865387 |
| 90328 | 551.318359375 | 11/8 | 551.317942364757 | +0.068323 | +0.000417010243 |
| 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 |
| 196608 | 1200.000000000000 | 2/1 | 1200.000000000000 | ±0.000000 | ±0.000000000000 |