Home > Musical tuning
This page is about musical 'systems' of tuning, for the musical 'process' of tuning see tuning.
Musical tuning is the system used to define which tones, or pitches, to use when playing music. In other words, it is the choice of level and spacing of frequency values which are used. The tuning systems are usually defined in such a way that a listener perceives it as "nice".
The history of tuning is much more complex than it at first seems; this index page can be used as a starting point.
1 Subjects in general
2 Ways of tuning the twelve-note chromatic scale
It is impossible to tune the twelve-note chromatic scale so that all intervals are perfect; many different methods with their own various compromises have thus been put forward. The main ones are:
- Pythagorean tuning, in which the ratios of the frequencies between all notes are all multiples of 3:2 - (.ogg format, 93.8KB)
- Just intonation, in which the ratios of the frequencies between all notes are based on relatively low whole numbers, such as 3:2, 5:4 or 7:4; or in which all pitches are based on the harmonic seriesSee Harmonic series (music) Harmonic series (mathematics) These two concepts are related., which are all whole number multiples of a single tone. Such a system may use two different ratios for what is the same interval in equal temperament depending on context; for instance, a major second may be either in the ratio 9:8 or 10:9. For this reason, just intonation may be less a suitable system for use on keyboard instrumentA keyboard instrument is a musical instrument played with a musical keyboard. Keyboard instruments can be wind instruments, string instruments, percussion instruments, or electronic instruments. The most popular keyboard instruments are probably the pianos or other instruments where the pitch of individual notes is not flexible. (On fretted instruments like guitars and lutes, multiple frets for one interval is practical.)
- Meantone temperamentMeantone temperament is a system of musical tuning. In it, the major third is tuned to a particular ratio ( 5:4), and then divided in half to make two whole tones of equal size. Since two fifths up and an octave down make up a whole tone, : four fifths up, a system of tuning which averages out pairs of ratios used for the same interval (such as 9:8 and 10:9), thus making it possible to tune keyboard instrumentA keyboard instrument is a musical instrument played with a musical keyboard. Keyboard instruments can be wind instruments, string instruments, percussion instruments, or electronic instruments. The most popular keyboard instruments are probably the pianos. Next to the twelve-equal temperament, which some would not regard as a form of meantone, the best known form of this temperament is quarter comma meantone, which tunes major thirds justly in the ratio of 5:4 and divides them into two whole tones of equal size. To do this, eleven perfect fifths in each octave are flattened by a quarter of a syntonic commaIntervals The syntonic comma also known as the comma of Didymus or Ptolemaic comma is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21. It is the difference between four justly tuned perfect fifths, and two octa, with the remaining fifth being left very sharp (such an unacceptably out-of-tune fifth is known as a wolf intervalWhen the twelve notes within the octave are tuned using meantone temperament, one of the fifths will be much sharper than the rest. The notes that meantone temperament was normally based around meant that the interval G# to Eb will be this anomalous inter). However, the fifth may be flattened to a greater or lesser degree than this and the tuning system will retain the essential qualities of meantone temperament; examples include the 31-equal fifth and Lucy tuningLucyTuning is a form of meantone temperament, in which the fifth is of size 600+300/π ( approximately 695. Its main advocate is Charles Lucy, who discovered it in the eighteenth century writings of John Harrison. The LucyTuned perfect fifth is 0. 0384.
- Both just intonation and meantone temperament can be regarded as forms of regular temperament.
- Well temperament, any one of a number of systems where the ratios between intervals are unequal, but approximate to ratios used in just intonation. Unlike meantone temperament, the amount of divergence from just ratios varies according to the exact notes being tuned, so that C-G will probably be tuned closer to a 3:2 ratio than, say, F#-C#. Because of this, well temperaments have no wolf intervals. A well temperament system is usually named after whoever first came up with it.
- Equal temperament, in which adjacent notes of the scale are all separated by logarithmically equal distances - (.ogg format, 96.9KB)
