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

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

• Interval size measure
• 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)
  • 98304edo (13mu tuning)