MIDI-unit, mu

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, myself, Gene Ward Smith and John Chalmers.

The unit which i call a tetradekamu is specified in the MIDI spec (1983) as the smallest increment available for the pitch-bend controller. Aaron prefers to call this unit simply "mu", whereas i prefer 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
enamu         1      2      24  1.029302237      35:34     50
doamu         2      4      48  1.014545335      70:69     25
triamu        3      8      96  1.007246412     139:138    12 1/2    12.5 
tetramu       4     16     192  1.003616666     555:553     6 1/4     6.25
pentamu       5     32     384  1.001806701    1109:1107    3 1/8     3.125  
hexamu        6     64     768  1.000902943    2217:2215    1 9/16    1.5625   
heptamu       7    128    1536  1.00045137     4433:4431     25/32    0.78125 
oktamu        8    256    3072  1.000225659    8865:8863     25/64    0.390625
enneamu       9    512    6144  1.000112823    8864:8863     25/128   0.1953125
dekamu       10   1024   12288  1.00005641    17728:17727    25/256   0.09765625
endekamu     11   2048   24576  1.000028205   35456:35455    25/512   0.048828125
dodekamu     12   4096   49152  1.000014102   70913:70912    25/1024  0.0244140625
tridekamu    13   8192   98304  1.000007051  141825:141824   25/2048  0.01220703125
tetradekamu  14  16384  196608  1.000003526  283608:283607   25/4096  0.006103515625 

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

See also:


enamu
doamu
triamu
tetramu
pentamu
hexamu
heptamu
oktamu
enneamu
dekamu
endekamu
dodekamu
tridekamu
tetradekamu
cawapu
midipu
my Gentle Introduction to the MIDI Tuning Specification
the Official MIDI Tuning Specification.

[from Joe Monzo, JustMusic: A New Harmony]

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For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

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