
In
music
Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
, 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, and their theoretical bases.
Tuning practice

Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as
A = 440 Hz. The term "''out of tune''" refers to a pitch/tone that is either too high (
sharp) or too low (
flat) in relation to a given reference pitch. While an instrument might be in tune relative to its own range of notes, it may not be considered 'in tune' if it does not match the chosen reference pitch. Some instruments become 'out of tune' with temperature, humidity, damage, or simply time, and must be readjusted or repaired.
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
In music, ear training is the study and practice in which musicians learn various aural skills to detect and identify pitch (music), pitches, interval (music), intervals, melody (music), melody, chord (music), chords, rhythms, solfeges, and other ...
.
* Turning
pegs to increase or decrease the
tension on strings so as to control the pitch. Instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the
violin
The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino picc ...
can be tuned manually.
* Modifying the length or width of the tube of a
wind instrument
A wind instrument is a musical instrument that contains some type of resonator (usually a tube) in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at or near the end of the resonator. The pitch ...
,
brass instrument
A brass instrument is a musical instrument that produces sound by Sympathetic resonance, sympathetic vibration of air in a tubular resonator in sympathy with the vibration of the player's lips. The term ''labrosone'', from Latin elements meani ...
,
pipe,
bell
A bell /ˈbɛl/ () is a directly struck idiophone percussion instrument. Most bells have the shape of a hollow cup that when struck vibrates in a single strong strike tone, with its sides forming an efficient resonator. The strike may be m ...
, or similar instrument to adjust the pitch. In woodwind instruments, this is usually done by adjusting the instrument's
mouthpiece or neck to change the pitch. In brass instruments, this is usually done by moving a tuning slide.
The sounds of some instruments, notably
unpitched percussion instrument such as
cymbal
A cymbal is a common percussion instrument. Often used in pairs, cymbals consist of thin, normally round plates of various alloys. The majority of cymbals are of indefinite pitch, although small disc-shaped cymbals based on ancient designs sou ...
s, are of
indeterminate pitch
Pitch is a perceptual property that allows sounds to be ordered on a frequency-related scale,
or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. ...
, and have irregular overtones not conforming to the
harmonic series. See .
Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other. A
tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs ( ''tines'') formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it ag ...
or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a
piano
A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...
is used (as its pitch cannot be adjusted for each performance).
Symphony orchestra
An orchestra (; ) is a large instrumental ensemble typical of classical music, which combines instruments from different families. There are typically four main sections of instruments:
* String instruments, such as the violin, viola, cello, ...
s and
concert band
A concert band, also called a wind band, wind ensemble, wind symphony, wind orchestra, symphonic band, the symphonic winds, or symphonic wind ensemble, is a performing ensemble consisting of members of the woodwind instrument, woodwind, brass ...
s usually tune to an
A440 or a
B♭, respectively, provided by the principal
oboist or
clarinet
The clarinet is a Single-reed instrument, single-reed musical instrument in the woodwind family, with a nearly cylindrical bore (wind instruments), bore and a flared bell.
Clarinets comprise a Family (musical instruments), family of instrume ...
ist, who tune to the keyboard if part of the performance.
When only strings are used, then the principal string (violinist) typically has sounded the tuning pitch, but some orchestras have used an electronic tone machine for tuning.
[ Tuning can also be done through a prior recording; this method uses simultaneous audio.
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.
]Harmonic
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
s may be used to facilitate tuning of strings that are not themselves tuned to the unison. For example, lightly touching the highest string of a cello at the middle (at a node
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex).
Node may refer to:
In mathematics
* Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two or more curves, lines ...
) while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the perfect fifth between the fundamentals of the two strings.
Open strings
In music
Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
, the term open string refers to the fundamental note of the unstopped, full string.
The strings of a guitar
The guitar is a stringed musical instrument that is usually fretted (with Fretless guitar, some exceptions) and typically has six or Twelve-string guitar, twelve strings. It is usually held flat against the player's body and played by strumming ...
are normally tuned to fourths (excepting the G and B strings in standard tuning, which are tuned to a third), as are the strings of the bass guitar
The bass guitar (), also known as the electric bass guitar, electric bass, or simply the bass, is the lowest-pitched member of the guitar family. It is similar in appearance and construction to an Electric guitar, electric but with a longer nec ...
and double bass
The double bass (), also known as the upright bass, the acoustic bass, the bull fiddle, or simply the bass, is the largest and lowest-pitched string instrument, chordophone in the modern orchestra, symphony orchestra (excluding rare additions ...
. Violin
The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino picc ...
, viola
The viola ( , () ) is a string instrument of the violin family, and is usually bowed when played. Violas are slightly larger than violins, and have a lower and deeper sound. Since the 18th century, it has been the middle or alto voice of the ...
, and cello
The violoncello ( , ), commonly abbreviated as cello ( ), is a middle pitched bowed (sometimes pizzicato, plucked and occasionally col legno, hit) string instrument of the violin family. Its four strings are usually intonation (music), tuned i ...
strings are tuned to fifths. However, non-standard tunings (called scordatura
Scordatura (; literally, Italian for "discord", or "mistuning") is a Musical tuning, tuning of a string instrument that is different from the normal, standard tuning. It typically attempts to allow special effects or unusual Chord (music), chords ...
) exist to change the sound of the instrument or create other playing options.
To tune an instrument, often only one reference pitch is given. This reference is used to tune one string, to which the other strings are tuned in the desired intervals. 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. Alternatively, each string can be tuned to its own reference tone.
Note that while the guitar and other modern stringed instruments with fixed frets are tuned in equal temperament
An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...
, string instruments without frets, such as those of the violin family, are not. The violin, viola, and cello are tuned to beatless
''Beatless'' is a Japanese science fiction serial novel written by Satoshi Hase and illustrated by Redjuice. The series has inspired three spin-off manga series and a 24-episode anime television series by Diomedéa, which aired from Janu ...
just perfect fifths and ensembles such as string quartets and orchestras tend to play in fifths based Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifthsBruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh editi ...
or to compensate and play in equal temperament, such as when playing with other instruments such as the piano. For example, the cello, which is tuned down from A220, has three more strings (four total) and the just perfect fifth is about two cents off from the equal tempered perfect fifth, making its lowest string, C−, about six cents more flat than the equal tempered C.
This table lists open strings on some common string instruments and their standard tunings from low to high unless otherwise noted.
Altered tunings
Violin scordatura was employed in the 17th and 18th centuries by Italian and German composers, namely, Biagio Marini, Antonio Vivaldi
Antonio Lucio Vivaldi (4 March 1678 – 28 July 1741) was an Italian composer, virtuoso violinist, impresario of Baroque music and Roman Catholic priest. Regarded as one of the greatest Baroque composers, Vivaldi's influence during his lif ...
, Heinrich Ignaz Franz Biber
Heinrich Ignaz Franz von Biber correctly ''Biber von Bibern'' ( bapt. 12 August 1644, Stráž pod Ralskem – 3 May 1704, Salzburg) was a Bohemian-Austrian composer and violinist. Biber worked in Graz and Kroměříž before he illegally left ...
(who in the ''Rosary Sonatas'' prescribes a great variety of scordaturas, including crossing the middle strings), Johann Pachelbel
Johann Pachelbel (also Bachelbel; baptised – buried 9 March 1706) was a German composer, organist, and teacher who brought the south German organ schools to their peak. He composed a large body of sacred and secularity, secular music, and ...
and Johann Sebastian Bach
Johann Sebastian Bach (German: Help:IPA/Standard German, �joːhan zeˈbasti̯an baχ ( – 28 July 1750) was a German composer and musician of the late Baroque music, Baroque period. He is known for his prolific output across a variety ...
, whose '' Fifth Suite For Unaccompanied Cello'' calls for the lowering of the A string to G. In Mozart
Wolfgang Amadeus Mozart (27 January 1756 – 5 December 1791) was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his rapid pace of composition and proficiency from an early age ...
's '' Sinfonia Concertante'' in E-flat major (K. 364), all the strings of the solo viola are raised one half-step, ostensibly to give the instrument a brighter tone so the solo violin does not overshadow it.
Scordatura for the violin was also used in the 19th and 20th centuries in works by Niccolò Paganini
Niccolò (or Nicolò) Paganini (; ; 27 October 178227 May 1840) was an Italian violinist and composer. He was the most celebrated violin virtuoso of his time, and left his mark as one of the pillars of modern violin technique. His 24 Caprices ...
, Robert Schumann
Robert Schumann (; ; 8 June 181029 July 1856) was a German composer, pianist, and music critic of the early Romantic music, Romantic era. He composed in all the main musical genres of the time, writing for solo piano, voice and piano, chamber ...
, Camille Saint-Saëns
Charles-Camille Saint-Saëns (, , 9October 183516 December 1921) was a French composer, organist, conductor and pianist of the Romantic music, Romantic era. His best-known works include Introduction and Rondo Capriccioso (1863), the Piano ...
, Gustav Mahler
Gustav Mahler (; 7 July 1860 – 18 May 1911) was an Austro-Bohemian Romantic music, Romantic composer, and one of the leading conductors of his generation. As a composer he acted as a bridge between the 19th-century Austro-German tradition and ...
, and Béla Bartók
Béla Viktor János Bartók (; ; 25 March 1881 – 26 September 1945) was a Hungarian composer, pianist and ethnomusicologist. He is considered one of the most important composers of the 20th century; he and Franz Liszt are regarded as Hunga ...
. In Saint-Saëns' "Danse Macabre
The ''Danse Macabre'' (; ), also called the Dance of Death, is an artistic genre of allegory from the Late Middle Ages on the universality of death.
The ''Danse Macabre'' consists of the dead, or a personification of death, summoning represen ...
", the high string of the violin is lower half a tone to the E so as to have the most accented note of the main theme sound on an open string. In Mahler's Symphony No. 4, the solo violin is tuned one whole step high to produce a harsh sound evoking Death as the Fiddler. In Bartók's ''Contrasts'', the violin is tuned G-D-A-E to facilitate the playing of tritones on open strings.
American folk violinists of the Appalachians and Ozarks
The Ozarks, also known as the Ozark Mountains, Ozark Highlands or Ozark Plateau, is a physiographic region in the U.S. states of Missouri, Arkansas, and Oklahoma, as well as a small area in the southeastern corner of Kansas. The Ozarks cover ...
often employ alternate tunings for dance songs and ballads. The most commonly used tuning is A-E-A-E. Likewise banjo players in this tradition use many tunings to play melody in different keys. A common alternative banjo tuning for playing in D is A-D-A-D-E. Many Folk guitar players also used different tunings from standard, such as D-A-D-G-A-D, which is very popular for Irish music.
A musical instrument that has had its pitch deliberately lowered during tuning is said to be ''down-tuned'' or ''tuned down''. Common examples include the electric guitar and electric bass in contemporary heavy metal music
Heavy metal (or simply metal) is a Music genre, genre of rock music that developed in the late 1960s and early 1970s, largely in the United Kingdom and United States. With roots in blues rock, psychedelic rock and acid rock, heavy metal band ...
, whereby one or more strings are often tuned lower than concert pitch. This is not to be confused with electronically changing the fundamental frequency
The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a n ...
, which is referred to as pitch shifting.
Tuning of unpitched percussion instruments
Many percussion instruments are ''tuned'' by the player, including pitched percussion instruments such as timpani
Timpani (; ) or kettledrums (also informally called timps) are musical instruments in the percussion instrument, percussion family. A type of drum categorised as a hemispherical drum, they consist of a Membranophone, membrane called a drumhead, ...
and tabla
A ''tabla'' is a pair of hand drums from the Indian subcontinent. Since the 18th century, it has been the principal percussion instrument in Hindustani classical music, where it may be played solo, as an accompaniment with other instruments a ...
, and unpitched percussion instruments such as the snare drum
The snare drum (or side drum) is a percussion instrument that produces a sharp staccato sound when the head is struck with a drum stick, due to the use of a series of stiff wires held under tension against the lower skin. Snare drums are often u ...
.
Tuning pitched percussion follows the same patterns as tuning any other instrument, but tuning unpitched percussion does not produce a specific pitch. For this reason and others, the traditional terms '' tuned percussion'' and '' untuned percussion'' are avoided in recent organology
Organology (; ) is the science of musical instruments and their classifications. It embraces study of instruments' history, instruments used in different cultures, technical aspects of how instruments produce sound, and musical instrument classi ...
.
Tuning systems
A ''tuning system'' is the system used to define which tones, or pitches, to use when playing music
Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
. In other words, it is the choice of number and spacing of frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
values used.
Due to the psychoacoustic interaction of tones and timbre
In music, timbre (), also known as tone color or tone quality (from psychoacoustics), is the perceived sound of a musical note, sound or tone. Timbre distinguishes sounds according to their source, such as choir voices and musical instrument ...
s, various tone combinations sound more or less "natural" in combination with various timbres. For example, using harmonic timbres:
* A tone caused by a vibration twice the frequency of another (the ratio of 1:2) forms the natural sounding octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
.
* A tone caused by a vibration three times the frequency of another (the ratio of 1:3) forms the natural sounding perfect twelfth, or perfect fifth
In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval f ...
(ratio of 2:3) when octave-reduced.
More complex musical effects can be created through other relationships.[W. A. Mathieu (1997) ''Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression''. Inner Traditions.]
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 led 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
The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...
so that all intervals are pure. For instance, three pure major thirds stack up to , which at is nearly a quarter tone away from the octave (1200 cents). So there is no way to have both the octave and the major third in just intonation for all the intervals in the same twelve-tone system. Similar issues arise with the fifth , and the minor third , or any other choice of harmonic-series based pure intervals.
Many different compromise methods are used to deal with this, each with its own characteristics, and advantages and disadvantages.
The main ones are:
; Just intonation
In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...
:
: In just intonation, the frequencies of the scale notes are related to one another by simple numeric ratios, a common example of this being to define the ratios for the seven notes in a C major scale, plus the return to the tonic an octave up on the 8th ( "perfect 8th" or octave). In this example, though many intervals are pure, the interval from D to A ( to ) is instead of the expected . The same issue occurs with most just intonation tunings. This can be dealt with to some extent using alternative pitches for the notes. Even that, however, is only a partial solution, as an example makes clear: If one plays the sequence C G D A E C in just intonation, using the intervals , , and , then the second C in the sequence is higher than the first by a syntonic comma
In music theory
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first i ...
of . This is the infamous " comma pump". Each time around the comma pump, the pitch continues to spiral upwards. This shows that it is impossible to keep to any small fixed system of pitches if one wants to stack musical intervals this way. So, even with ''adaptive tuning'', the musical context may sometimes require playing musical intervals that are not pure. Instrumentalists with the ability to vary the pitch of their instrument may micro-adjust some of the intervals naturally; there are also systems for adaptive tuning in software ( microtuners). Harmonic fragment scales form a rare exception to this issue. In tunings such as , all the pitches are chosen from the harmonic series (divided by powers of 2 to reduce them to the same octave), so all the intervals are related to each other by simple numeric ratios.
; Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifthsBruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh editi ...
:
: A Pythagorean tuning is technically both a type of just intonation and a zero-comma
The comma is a punctuation mark that appears in several variants in different languages. Some typefaces render it as a small line, slightly curved or straight, but inclined from the vertical; others give it the appearance of a miniature fille ...
meantone tuning, in which the frequency ratios of the notes are all derived from the number ratio 3:2. Using this approach for example, the 12 notes of the Western chromatic scale would be tuned to the following ratios: Also called "3-limit" because it uses no prime factors other than 2 and 3, this Pythagorean system was of primary importance in Western musical development in the Medieval and Renaissance periods. As with nearly all just intonation systems, it has a wolf interval. In the example given, it is the interval between the and the (F to D, if one tunes the to C). The major and minor thirds are also impure, but at the time when this system was at its zenith, the third was considered a dissonance, so this was of no concern. See also: Shí-èr-lǜ.
; Meantone temperament
Meantone temperaments are musical temperaments; that is, a variety of Musical tuning#Tuning systems, tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within th ...
:
: A system of tuning that averages out pairs of ratios used for the same interval (such as 9:8 and 10:9). The best known form of this temperament is quarter-comma meantone
Quarter-comma meantone, or -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma with ...
, which tunes major thirds justly in the ratio of 5:4 and divides them into two whole tones of equal size – this is achieved by flattening the fifths of the Pythagorean system slightly (by a quarter of a syntonic comma
In music theory
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first i ...
). However, the fifth may be flattened to a greater or lesser degree than this and the tuning system retains the essential qualities of meantone temperament
Meantone temperaments are musical temperaments; that is, a variety of Musical tuning#Tuning systems, tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within th ...
. Historical examples include and meantone.
; Well temperament
Well temperament (also good temperament, circular or circulating temperament) is a type of musical temperament, tempered musical tuning, tuning used for keyboard instruments of the seventeenth and eighteenth centuries. The term is modeled on the G ...
:
: 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 is probably tuned closer to a 5:4 ratio than, say, D–F. Because of this, well temperaments have no wolf intervals.
; Equal temperament
An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...
:
: The standard twelve-tone equal temperament is a special case of meantone temperament (extended eleventh-comma), in which the twelve notes are separated by logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
ically equal distances (100 cents): /upload.wikimedia.org/wikipedia/commons/b/b3/Et_scale.ogg A harmonized C major scale in equal temperament(.ogg format, 96.9 KB). This is the most common tuning system used in Western music, and is the standard system used as a basis for tuning a piano. Since this scale divides an octave into twelve equal-ratio steps and an octave has a frequency ratio of two, the frequency ratio between adjacent notes is then the twelfth root of two, However, the octave can be divided into other than 12 equal divisions, some of which may be more harmonically pleasing, as far as thirds, sixths, and harmonic seventh
The harmonic seventh interval, also known as the septimal minor seventh,
or subminor seventh,
is one with an exact 7:4 ratio
(about 969 cent (music), cents).
This is about 32 cents narrower, with a more stable and consonant sound, than a ...
s (via augmented sixths) are concerned, such as 19 equal temperament
In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 Equal temperament, ET, is the musical temperament, tempered scale derived by dividing the octave into 19 equal steps ...
(extended meantone), 31 equal temperament
In music, 31 equal temperament, which can also be abbreviated (31 tone ) or (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equally-proportioned steps (e ...
(extended quarter-comma meantone) and 53 equal temperament
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios) (). Each step represents a frequency ratio of or 22.64 ...
(extended Pythagorean tuning).
Tuning systems that are not produced with exclusively just intervals are usually referred to as '' temperaments''.
Other scale systems
* Natural overtone scale, a scale derived from the harmonic series
* Slendro, a pentatonic scale
A pentatonic scale is a musical scale with five notes per octave, in contrast to heptatonic scales, which have seven notes per octave (such as the major scale and minor scale).
Pentatonic scales were developed independently by many ancient ci ...
used in Indonesian gamelan music
* Pelog, the other main gamelan scale
* Harry Partch's 43-tone scale
* Bohlen–Pierce scale
The Bohlen–Pierce scale (BP scale) is a musical musical tuning, tuning and scale (music), scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Classical music, Western and other musics, spec ...
* Alpha
Alpha (uppercase , lowercase ) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter ''aleph'' , whose name comes from the West Semitic word for ' ...
, beta
Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...
, delta
Delta commonly refers to:
* Delta (letter) (Δ or δ), the fourth letter of the Greek alphabet
* D (NATO phonetic alphabet: "Delta"), the fourth letter in the Latin alphabet
* River delta, at a river mouth
* Delta Air Lines, a major US carrier ...
, and gamma scales of Wendy Carlos
Wendy Carlos (born Walter Carlos; November 14, 1939) is an American musician and composer known for electronic music and film scores.
Born and raised in Rhode Island, Carlos studied physics and music at Brown University before moving to New Y ...
* Quarter tone scale
* Thirteenth Sound
* 19 equal temperament
In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 Equal temperament, ET, is the musical temperament, tempered scale derived by dividing the octave into 19 equal steps ...
* 22 equal temperament
* 31 equal temperament
In music, 31 equal temperament, which can also be abbreviated (31 tone ) or (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equally-proportioned steps (e ...
* 53 equal temperament
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios) (). Each step represents a frequency ratio of or 22.64 ...
* Schismatic temperament
* Miracle temperament
* Hexany
See also
* 3rd bridge
* ''Beauty in the Beast
''Beauty in the Beast'' is a studio album from the American keyboardist and composer Wendy Carlos, released in 1986, on Audion Records, her first for a label other than Columbia Records since 1968. The album uses alternate musical tunings and mus ...
''
* Chinese musicology
* Dynamic tonality
* Electronic tuner
* Ethnomusicology
Ethnomusicology is the multidisciplinary study of music in its cultural context. The discipline investigates social, cognitive, biological, comparative, and other dimensions. Ethnomusicologists study music as a reflection of culture and investiga ...
* Mathematics of musical scales
* Mersenne's laws
* Microtonal music
* Microtuner
* MIDI
Musical Instrument Digital Interface (; MIDI) is an American-Japanese technical standard that describes a communication protocol, digital interface, and electrical connectors that connect a wide variety of electronic musical instruments, ...
* MIDI tuning standard
* Musical theory
* Open chord
* Physics of music
* Pseudo-octave
* Psychoacoustics
Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, ...
* Standard tuning
* Stretched tuning
* Vibrating string
* Xenharmonic
References
Further reading
*Barbour, J. Murray (1951). ''Tuning and Temperament: A Historical Survey''. East Lansing: Michigan State College Press. .
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