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In music, there are two common meanings for tuning:

Tuning practice: The act of tuning an instrument or voice.
Tuning systems: The various systems of pitches used to tune an instrument.

Tuning practice

Tuning is the process of producing or preparing to produce a certain pitch in relation to another, usually matched at the unison but often at some other interval relationship. Out of tune refers to a pitch that is too high or too low, corresponding to sharp or flat, respectively.

Different methods of sound production require different methods of adjustment:

Tuning to a pitch with one's voice is called matching pitch and is the most basic skill learned in ear training.
Turning the pegs on a guitar (on the machine head) or violin to increase or decrease the tension on the strings so as to make them higher or lower in pitch.
Modifying the length or width of the tube of a wind instrument, brass instrument, pipe, bell, or similar instrument to adjust the pitch.

Some instruments do not have a regular harmonic series, and are known as inharmonic. This makes their tuning complicated, and usually compromised. The tuning of bells, for instance, is extremely involved.

Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other. A tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used (as its pitch cannot be adjusted for each rehearsal). Symphony orchestras tend to tune to an A provided by the principal oboist.

Interference beats are used to objectively measure the accuracy of tuning. As the two pitches approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected. For other intervals, this is dependent on the tuning system being used.

Harmonics may be used to check the tuning of strings which are not tuned to the unison. For example, lightly touching the highest string of a cello at halfway down its length (at a node) while bowing produces the same pitch as doing the same one third of the way down its second highest string.

Basic tuning (open strings)

In music, the term open string refers to string of a string instrument when it is played at full length on the instrument —ie. played without shortening its length (ie. fretting on a guitar) on the fingerboard.

The strings of a guitar are normally tuned to fourths (excepting the G and B strings in standard tuning), as are the strings of the bass guitar and double bass. Violin, viola, and cello strings are tuned to fifths. However, nonstandard tunings (callse scordatura may be used, which require alternative methods.

To tune an instrument, usually only one reference pitch is given. This reference is used to tune one string, which is then used to tune all of the others. On a guitar, often the lowest string is tuned to an E. From this, each successive string can be tuned by fingering the fifth fret of an already tuned string and comparing it with the next higher string played open. (This works with the exception of the G string, which must be stopped at the fourth fret to sound B against the open B string above.)

This table lists open strings on some common string instruments and their standard tunings.

Violin	G, D, A, E
Viola, Cello	C, G, D, A
Double bass	E, A, D, G
Guitar	E, A, D, G, B, E

Altered tunings

Unconventional tunings, or scordatura (It., from scordare, to mistune); were first used in the 16th century by Italian lutenists. It was primarily used to facilitate difficult passages, but was also used to alter timbral characteristics, reinforce tonalities through the use of open strings, and to extend the range of the instrument.

Violin scordatura was employed in the 17th and 18th centuries by Italian and German composers, namely, Biagio Marini, Antonio Vivaldi, Johann Pachelbel and J.S. Bach; whose Fifth Suite For Unaccompanied Cello calls for the lowering of the A string to G. In Mozart's Sinfonia Concertante K. 364, all the strings of the violin are raised one half-step, most likely to make more open strings available.

Scordatura for the violin was also used in the 19th and 20th centuries in works by Paginini, Schumann, Saint-Saens and Bartok. In Saint-Saens "Danse Macabre", the high string of the violin is lower half a tone to Eb the so as to have the most accented note of the main theme sound on an open string. In Bartok's Contrasts, the violin is tuned G#-D-A-Eb to facilitate the playing of tritones on open strings.

American folk violinists of the Appalachians and Ozarks often employ alternate tunings for dance songs and ballads. The most commonly used tuning is A-E-A-E.

Tuning systems

A tuning system is the system used to define which tones, or pitches, to use when playing music. In other words, it is the choice of number and spacing of frequency values which are used.

Due to the psychoacoustic properties of tones, various pitch combinations will sound more or less "natural" when used in combination. For example, a tone caused by a vibration twice the speed of another (the ratio of 1:2) forms the natural sounding octave. Another natural resonance found in musical scales the world over is the ratio of 1:3 (2:3 when octave reduced) which is often called a perfect fifth. More complex musical effects can be created through other relationships.^[1]

The creation of a tuning system is complicated because musicians want to make music with more than just a few differing tones. As the number of tones is increased, conflicts arise in how each tone combines with every other. Finding a successful combination of tunings has been the cause of debate, and has lead to the creation of many different tuning systems across the world. Each tuning system has its own characteristics, strengths and weaknesses.

Systems for 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:

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 series (music), 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 instruments or other instruments where the pitch of individual notes is not flexible. (On fretted instruments like guitars and lutes, multiple frets for one interval can be practical.)
Pythagorean tuning, in which the ratios of the frequencies between all notes are all multiples of 3:2. The Pythagorean system was further developed by Safi ad-Din al-Urmawi, who divided the octave into seventeen parts (limmas and commas) and used in the Turkish and Persian tone systems.
Meantone temperament, 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 instruments. 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 comma, with the remaining fifth being left very sharp (such an unacceptably out-of-tune fifth is known as a wolf interval). 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 tuning.
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-E will probably be tuned closer to a 5:4 ratio than, say, Db-F. 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 (a special case of well-temperament), in which adjacent notes of the scale are all separated by logarithmically equal distances (100 cents) - A harmonized C major scale in equal temperament (.ogg format, 96.9KB). This is the most common tuning system used in Western music, and is the standard system for tuning a piano. Since this scale divides an octave into twelve equal-ratio steps, the frequency ratio between adjacent notes is then the twelfth root of two, 2^1/12, or ~1.05946309...

Other scale systems

Slendro, a scale used in Indonesian gamelan music with five notes to the octave
Pelog, the other main gamelan scale, with seven notes to the octave
43-tone scale, created by Harry Partch, an American composer who wrote musical and dramatic works in just intonation
Bohlen-Pierce scale
LucyTuning, a microtuning system created by Charles Lucy, devised from Pi and the writings of John 'Longitude' Harrison. Designed to emulate Eastern tuning systems as well as Western.
Alpha and beta scales of Wendy Carlos
Quarter tone scale, first presented by Mikha'il Mishaqah, used in the theory of Arab music tone systems. From this the heptatonic scales consisting of minor, neutral, and major seconds of maqamat are chosen, this system was first promoted by al-Farabi using a 25 tone scale.
Stretched tuning makes an octave represent slightly more than a doubling in frequency. It is usually applied to keyboard instruments with tines or thick strings, where the ratio of harmonic to fundamental can be slightly greater than a true integer ratio (typically piano and electric piano). Stretched tuning is sometimes claimed to give a "warmer" sound to chords.

Comparisons and controversies among tunings

All musical tunings have advantages and disadvantages. Twelve tone equal temperament (12-TET) is the standard and most usual tuning system used in Western music today because it gives the advantage of modulation to any key without dramatically going out of tune, as all keys are equally and slightly out of tune. However, just intonation provides the advantage of being entirely in tune, with at least some, and possible a great deal, loss of ease in modulation. The composer Terry Riley, said "Western music is fast because it's not in tune", meaning that its inherent beating forces motion. Twelve tone equal temperament also, currently, has an advantage over just intonation in that most musicians are trained in, and have instruments designed to play in equal temperament. Other tuning systems have other advantages and disadvantages and are chosen for various qualities. It must be realized, however, that just as many people who play music today in equal temperament without having heard of it as musicians throughout the world that use just intonation without "knowing" it.

The octave (or even other intervals, such as the so-called tritave, or twelfth) can advantageously be divided into a number of equal steps different from twelve. Popular choices for such an equal temperament include 19, 22, 31, 53 and 72 parts to an octave, each of these and the many other choices possible have their own distinct characteristics.

Non-equal and non-just tunings also provide advantages. For instance, William Sethares shows that the tunings of Balinese gamelans are related to the inharmonic spectra or timbre of their metallophones and the harmonic spectra of stringed instruments such as the rebab, just as just intonation and twelve tone equal temperament are related to the spectra or timbre of harmonic instruments alone.

Some instruments, such as the violin, don't limit the musician to particular pitches, allowing to choose the tuning system "on the fly". Many performers on such instruments adjust the notes to be more in tune than the equal temperament system allows, perhaps even without realizing it.

References

^ W. A. Mathieu (1997) Harmonic Experience : Tonal Harmony from Its Natural Origins to Its Modern Expression. Inner Traditions

J. Murray Barbour Tuning and Temperament: A Historical Survey ISBN 0-486-43406-0

External links

Alternate Tunings For Bass
Schmidt-Jones, C. (2005, November 22). Tuning Systems. Connexions
Tonalsoft Encyclopedia of Microtonal Music theory
History of tuning by Kyle Gann
Article on the history of absolute pitch to today's A=440 standard
Tuning for beginners
The 7-Note Solution -- Why are so many 5 & 7-note scales found among ancient writings and archaeological artifacts?
Understanding Temperaments - a concise, but comprehensive explanation of temperaments.
Temperament resources on the Web - lots more links
Albert Gräf: Musical scale rationalization - a graph-theoretic approach (the paper is number 45 on the list, and is in .pdf format)
HyperPhysics: Temperament and Musical Scales
The Keyboard Tuning of Domenico Scarlatti
The Ring of Truth - mathematical derivation of the western musical intervals, by Peter Wakefield Sault
LucyTuning
Bach Tuning
Bells worth listening to: A composer and a sculptor from Melbourne have developed the world's first harmonic bells
Report from archaeological conference on ancient Chinese flutes & temperament
Musical Tuning: Frequency ratio to cents conversion

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