MIDI Tuning Standard
Encyclopedia
MIDI Tuning Standard 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.
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 cent
s. 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
so that the two notations are equivalent.
-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 cent
s) 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.
, 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.
MIDI Manufacturers Association
The MIDI Manufacturers Association is an organization where companies work together to create the standards that assure compatibility among MIDI products. The MMA is a U.S. organization established in 1985 by the original developers of the MIDI 1.0 Specification in 1983. Since 1985 the MMA has...
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 bySince 440 Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
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 cent
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
s. 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
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 byteByte
The byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...
-sized digits, represented in hexadecimal
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
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 cent
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
s) by which the standard equal-tempered pitch is raised (i.e., made sharp
Sharp (music)
In music, sharp, dièse , or diesis means higher in pitch and the sharp symbol raises a note by a half tone. Intonation may be flat, sharp, or both, successively or simultaneously...
). 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 musicMicrotonal music
Microtonal music is music using microtones—intervals of less than an equally spaced semitone. Microtonal music can also refer to music which uses intervals not found in the Western system of 12 equal intervals to the octave.-Terminology:...
, just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
, meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
, or other alternative tunings. Software which supports MTS includes Scala
Scala (program)
Scala is a freeware software application with versions supporting Windows, Mac OS X, and Linux. It allows users to create and archive musical scales, analyze and transform them with built-in theoretical tools, play them with an on-screen keyboard or from an external MIDI keyboard, and export them...
, TiMidity
TiMidity
TiMidity++, originally and still frequently informally called TiMidity, is a software synthesizer that can play MIDI files without a hardware synthesizer...
, L'il Miss Scale Oven, Tune Smithy
Tune Smithy
Tune Smithy is a Windows-based shareware application, with freeware features.It is an algorithmic composition tool to make fractal music. It is now also used frequently as a retuning tool for microtonal composition, and for music therapy in conjunction with Barbara Hero’s Lambdoma keyboard...
, Max Magic Microtuner, Gervill and the Native Instruments
Native Instruments
Native Instruments is a technology company that develops software and hardware for music production and DJing. The company has originally been identified mostly with software instruments, but has also expanded to various other music equipment segments in recent years.Current products of Native...
FM7 softsynth.