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 $f$ is a

Hertz (Hz)

, then the corresponding MIDI note number

N

_MIDI is given by the formula

N_{\mathsf {MIDI}}=69+12\cdot \log _{2}\left({\frac {f}{\ 440\ \mathrm {Hz} \ }}\right)=69+{\frac {12}{\ \log 2\ }}\log \left({\frac {f}{\ 440\ \mathrm {Hz} \ }}\right)\ ,

where " $log$ " in the second expression is any logarithm (e.g. either the common logarithm $log 10$ , the natural logarithm $ln \equiv log e$ , or any other).

The quantity $log2( .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px} f / 440 Hz  )$ is the number of

middle C

.

Not only is 440

integer notation

, known as the MIDI note number,

N

_MIDI .

Converting from MIDI note number ( $N$ _MIDI) to frequency ( $f$ ) is given by the following formula:

\ f=440\ {\mathsf {Hz}}\cdot 2^{\left[\ \left(\ N_{\mathsf {MIDI}}\ -\ 69\ \right)/12\ \right]}\ =440\ {\mathsf {Hz}}\cdot \exp \left[\ {\frac {\ \ln 2\ }{12}}\left(\ N_{\mathsf {MIDI}}\ -\ 69\ \right)\ \right]~.

Frequency Data Format

The frequency data format allows for the precise notation of frequencies that differ from equal temperament.

"Frequency data shall be defined in [units] which are fractions of a semitone. The frequency range starts at MIDI note 0, C = 8.1758 Hz, and extends above MIDI note 127, G = 12543.854 Hz. The first byte of the frequency data word specifies the highest equal-tempered semitone not exceeding the frequency. The next two bytes (14 bits) specify the fraction of 100 cents above the semitone at which the frequency lies. Effective resolution = 100 cents / 2¹⁴ = .0061 cents."^[1]

This higher resolution allows a logarithmic representation of pitch in which the semitone is divided into 128² = 2¹⁴ = 16384 parts, which means the octave is divided into 196608 (logarithmically) equal parts. These parts are exactly 100/16384 cents (approximately 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++, ZynAddSubFX and FluidSynth

.

Software plugin instruments which support MTS include Native Instruments FM8, Synthogy Ivory, and Xen-Arts' various xenharmonic VSTi plugins, including the FMTS FM synthesizer, Ivor virtual analog synthesizer, and XenFont SoundFont sample player.

Hardware instruments in current production which support MTS include: Dave Smith Instruments (DSI) Rev-2, Prophet-12, Prophet-6, Oberheim OB-6, Moog Sub37, Minitaur, Novation Bass Station II, Peak, Sonoclast Plastic Pitch Plus, and the Waldorf Kyra.