MIDI Tuning Standard

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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[edit]

If ƒ is a frequency, then the corresponding frequency data value d may be computed by

d = 69 + 12 \log_2 \left(\frac {f}{440\ \mathrm{Hz}}\right).\,

The quantity log2 (ƒ / 440 Hz) is the number of octaves above the 440-Hz concert A (it is negative if the frequency is below that pitch). Multiplying it by 12 gives the number of semitones above that frequency. Adding 69 gives the number of semitones above the C five octaves below middle C.

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, known as the midi note number.

Converting from midi note number (d) to frequency (f) is given by the following formula:

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

Frequency Data Format[edit]

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 = 12543.875 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[edit]

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++, alt-tuner, L'il Miss Scale Oven, Tune Smithy, Max Magic Microtuner, Gervill. Software plugin instruments which support MTS include Pianoteq, 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.

See also[edit]

References[edit]

  1. ^ Midi Manufacturers Association, Midi Tuning Specification ( http://www.midi.org/techspecs/midituning.php )

External links[edit]

MTS specification[edit]

Microtonal music software supporting MTS[edit]

Inactive links[edit]