MIDI Tuning Standard

MIDI Tuning Standard (MTS) is a specification of precise musical pitch agreed to by the MIDI Manufacturers Association in the MIDI protocol. MTS allows for both a bulk tuning dump message, giving a tuning for each of 128 notes, and a tuning message for individual notes as they are played.

Frequency values

If ƒ is a frequency, then the corresponding scale number may be computed by

$d = 69 + 12 \cdot \log_2(\frac {f}{440\ \mbox{Hz}}).\,$

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, converting back to frequency is computed by

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

so that the two notations are equivalent.

Format

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 digit represents the MIDI note, or integer notation, value. The next two digits represent the fraction of a semitone (fraction of 100 cents) by which the standard equal-tempered pitch is raised (i.e., made sharp). The second and third 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.

Applications

The precision pitch values may be used in microtonal music, just intonation, meantone temperament, or other alternative tunings. Software which supports MTS includes Scala, TiMidity, L'il Miss Scale Oven, Tune Smithy, Max Magic Microtuner, Gervill and the Native Instruments FM7 softsynth.

See also

• Microtonal music
• Microtuner
• Musical tuning

External links

MTS specification

• MTS specification
• Detailed MTS specification
• MTS extensions

Microtonal music software supporting MTS

• L'il Miss' Scale Oven (Mac)
• Scala (Windows, Linux, Mac)
• TiMidity++ (Windows, Linux, Mac)
• Tune Smithy (Windows)
• Gervill (Windows, Linux, Mac)