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Encyclopedia of Microtonal Music Theory

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mu / MIDI-unit

[Joe Monzo]

In July 2003, Aaron Hunt suggested the general name 'Mu' for 'MIDI unit', and suggested that Greek prefixes be used to specify the number of bits resulting in the unit. Prefixes were offered and agreed upon by Aaron, Joe Monzo, Gene Ward Smith and John Chalmers.

The unit which called a 14mu (or "tetradekamu") is specified in the MIDI spec (1983) as the smallest increment available for the pitch-bend controller. Aaron Hunt prefers to call this unit simply "mu", whereas Monzo prefers to reserve "mu" for the general meaning of the term covering the whole family of different units.

Below is a table showing the number of bits resolution, the number of MIDI-units per semitone, the corresponding EDO, the approximate ratio of the MIDI-unit, and the cents-value of the interval. ("mu/ST" means "MIDI-units per semitone")

    name            bits  mu/ST   edo   -------- ~ratio --------  ------ exact cents ------

    -----            0      1      12  1.059463094      18:17    100
 1mu / enamu         1      2      24  1.029302237      35:34     50
 2mu / doamu         2      4      48  1.014545335      70:69     25
 3mu / triamu        3      8      96  1.007246412     139:138    12 1/2    12.5
 4mu / tetramu       4     16     192  1.003616666     555:553     6 1/4     6.25
 5mu / pentamu       5     32     384  1.001806701    1109:1107    3 1/8     3.125
 6mu / hexamu        6     64     768  1.000902943    2217:2215    1 9/16    1.5625
 7mu / heptamu       7    128    1536  1.00045137     4433:4431     25/32    0.78125
 8mu / oktamu        8    256    3072  1.000225659    8865:8863     25/64    0.390625
 9mu / enneamu       9    512    6144  1.000112823    8864:8863     25/128   0.1953125
10mu / dekamu       10   1024   12288  1.00005641    17728:17727    25/256   0.09765625
11mu / endekamu     11   2048   24576  1.000028205   35456:35455    25/512   0.048828125
12mu / dodekamu     12   4096   49152  1.000014102   70913:70912    25/1024  0.0244140625
13mu / tridekamu    13   8192   98304  1.000007051  141825:141824   25/2048  0.01220703125
14mu / tetradekamu  14  16384  196608  1.000003526  283608:283607   25/4096  0.006103515625
		

See the individual entries for each MIDI-unit for more information.

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