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# MIDI Tuning Standard

In music, the MIDI Tuning Standard (MTS) is a specification of musical pitch agreed to by the MIDI Manufacturers Association. It allows for both a bulk tuning dump message, giving a tuning for each of 128 notes, and an individual tuning message.

If ƒ is a frequency in hertz, then we may compute a corresponding logarithmic frequency value by

$d = 69 + 12 cdot log_2\left(f/440\right).,$

Since 440 Hz is a widely-used standard concert A (e.g. USA, UK), and since that is represented in MIDI terms by the integer 69 (nine semitones above middle C, which is 60), this gives a real number which expresses pitch in a manner consistent with MIDI and integer notation. These numerical units do not seem to have a recognized name, though it has been called the dollar in analogy to cents. While "dollars" and cents do not represent the same thing, since the former is a logarithmic measure of frequency and the latter a logarithmic measure of frequency ratios, a difference of one dollar equals one hundred cents. Given this "dollar" value, we can convert back to frequency by

$f = 440 cdot 2^\left\{\left(d-69\right)/12\right\}$

so that the two notations are equivalent.

The pitch values of MTS can be briefly described as dollar values, converted into three digits of base 128. These are byte-sized digits, represented in hexadecimal notation by 00 through 7F, which is to say, from 0 to 127 in base 10. The first byte digit represents the MIDI note, or integer notation, value. The next two digits allow the semitone to be divided into 1282 = 214 = 16384 parts, which means the octave is divided into 196608 equal parts. These parts are 100/16384 = 0.0061 cents in size, which is far below the threshold of human pitch perception and which therefore allows a very accurate representation of pitch.

## Programs supporting MTS

Most software making use of MIDI does not support, or at least fully support, MTS. In particular there is a notable lack of MIDI players which play files using it. Software which does support the MIDI tuning standard includes Scala, TiMidity, L'il Miss Scale Oven, Tune Smithy, Max Magic Microtuner, and the Native Instruments FM7 softsynth.