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A quarter tone is an interval
Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
 about half as wide (aurally, or logarithmically) as a semitone
Semitone

A semitone, also called a half step or a half tone,Aaron Copland, Leonard Bernstein, and others use "half tone".One source says that step is "chiefly US", and that half-tone is "chiefly N....
, which is half a whole tone.

Many composers are known for having written music including quarter tones or the quarter tone scale, first proposed by 19th-century music theorist Mikha'il Mishaqah (Touma 1996, p.16), including: Pierre Boulez
Pierre Boulez

Pierre Boulez is a French composer of contemporary classical music and Conducting....
, Julián Carrillo
Julián Carrillo

Juli?n Carrillo Trujillo was a Mexico composer, conductor, violinist and music theorist, who discovered the Thirteenth Sound....
, Mildred Couper
Mildred Couper

Mildred Couper , prominent American composer and pianist, was one of the first musicians to experiment with quarter-tone music. She was based in Santa Barbara, California, but her music and influence were felt around the world....
, Alberto Ginastera
Alberto Ginastera

Alberto Evaristo Ginastera was an Argentina composer of European classical music. He is considered one of the most important Latin American classical composers....
, Gérard Grisey
Gérard Grisey

G?rard Grisey was a France composer of contemporary music....
, Alois Hába
Alois Hába

File:H?ba.JPGAlois H?ba was a Czech composer, musical theorist and teacher. He is primarily known for his microtonal compositions, especially using the quarter tone scale, though he used others such as sixth-tones and twelfth-tones....
, Charles Ives
Charles Ives

Charles Edward Ives was an American musical modernism composer. He is widely regarded as one of the first American composers of international significance....
, Tristan Murail
Tristan Murail

Tristan Murail is a French composer associated with the "spectral music" technique of composition , which involves the use of the fundamental properties of sound as a basis for harmony, as well as the use of spectral analysis, FM, ring modulation, and amplitude modulation as a method of deriving polyphony....
, Krzysztof Penderecki
Krzysztof Penderecki

Krzysztof Penderecki is a Poland composer and conducting of European classical music....
, Giacinto Scelsi
Giacinto Scelsi

Giacinto Scelsi , Count of Ayala Valva was an Italy composer who also wrote surrealist poetry in French language.He is best known for writing music based around only one pitch , altered in all manners through microtonal oscillations, harmonics allusions, and changes in timbre and dynamics, as paradigmatically exemplified in his revolutiona...
, Tui St. George Tucker
Tui St. George Tucker

Tui St. George Tucker was an United States composer and recorder player.She was born in Fullerton, Orange County, California and attended Eagle Rock High School in northeast Los Angeles, California, graduating in 1941....
, Ivan Alexandrovich Wyschnegradsky, Iannis Xenakis
Iannis Xenakis

Iannis Xenakis was a Greeks modernist composer, musical theoretician, and architect. He is regarded as an important and influential composer of the twentieth century....
 (see List of quarter tone pieces
List of quarter tone pieces

A selection of compositions using quarter tones:*Jan Bach*Clarence Barlow*Hans Barth*Ernest Bloch*B?la Bart?k::String Quartet No. 6 ; the third movement Burletta contains quarter-tone tuning used for parodistic effect....
).

Types of quarter tones
The term quarter tone can refer to a number of different intervals, all very close in size.






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Encyclopedia


A quarter tone is an interval
Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
 about half as wide (aurally, or logarithmically) as a semitone
Semitone

A semitone, also called a half step or a half tone,Aaron Copland, Leonard Bernstein, and others use "half tone".One source says that step is "chiefly US", and that half-tone is "chiefly N....
, which is half a whole tone.

Many composers are known for having written music including quarter tones or the quarter tone scale, first proposed by 19th-century music theorist Mikha'il Mishaqah (Touma 1996, p.16), including: Pierre Boulez
Pierre Boulez

Pierre Boulez is a French composer of contemporary classical music and Conducting....
, Julián Carrillo
Julián Carrillo

Juli?n Carrillo Trujillo was a Mexico composer, conductor, violinist and music theorist, who discovered the Thirteenth Sound....
, Mildred Couper
Mildred Couper

Mildred Couper , prominent American composer and pianist, was one of the first musicians to experiment with quarter-tone music. She was based in Santa Barbara, California, but her music and influence were felt around the world....
, Alberto Ginastera
Alberto Ginastera

Alberto Evaristo Ginastera was an Argentina composer of European classical music. He is considered one of the most important Latin American classical composers....
, Gérard Grisey
Gérard Grisey

G?rard Grisey was a France composer of contemporary music....
, Alois Hába
Alois Hába

File:H?ba.JPGAlois H?ba was a Czech composer, musical theorist and teacher. He is primarily known for his microtonal compositions, especially using the quarter tone scale, though he used others such as sixth-tones and twelfth-tones....
, Charles Ives
Charles Ives

Charles Edward Ives was an American musical modernism composer. He is widely regarded as one of the first American composers of international significance....
, Tristan Murail
Tristan Murail

Tristan Murail is a French composer associated with the "spectral music" technique of composition , which involves the use of the fundamental properties of sound as a basis for harmony, as well as the use of spectral analysis, FM, ring modulation, and amplitude modulation as a method of deriving polyphony....
, Krzysztof Penderecki
Krzysztof Penderecki

Krzysztof Penderecki is a Poland composer and conducting of European classical music....
, Giacinto Scelsi
Giacinto Scelsi

Giacinto Scelsi , Count of Ayala Valva was an Italy composer who also wrote surrealist poetry in French language.He is best known for writing music based around only one pitch , altered in all manners through microtonal oscillations, harmonics allusions, and changes in timbre and dynamics, as paradigmatically exemplified in his revolutiona...
, Tui St. George Tucker
Tui St. George Tucker

Tui St. George Tucker was an United States composer and recorder player.She was born in Fullerton, Orange County, California and attended Eagle Rock High School in northeast Los Angeles, California, graduating in 1941....
, Ivan Alexandrovich Wyschnegradsky, Iannis Xenakis
Iannis Xenakis

Iannis Xenakis was a Greeks modernist composer, musical theoretician, and architect. He is regarded as an important and influential composer of the twentieth century....
 (see List of quarter tone pieces
List of quarter tone pieces

A selection of compositions using quarter tones:*Jan Bach*Clarence Barlow*Hans Barth*Ernest Bloch*B?la Bart?k::String Quartet No. 6 ; the third movement Burletta contains quarter-tone tuning used for parodistic effect....
).

Types of quarter tones


The term quarter tone can refer to a number of different intervals, all very close in size. In the quarter tone scale, also called 24 tone equal temperament
Equal temperament

Equal temperament is a musical temperament, or a system of Musical tuning in which every pair of adjacent notes has an identical frequency ratios....
 (24-TET), the quarter tone is 50 cents
Cent (music)

The cent is a logarithmic scale unit of measure used for musical interval . Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes....
, or a frequency ratio of 21/24 or 1.0293. In this scale the quarter tone is the smallest step. A semitone is thus made of two steps, and three steps make a three-quarter tone or neutral second
Neutral second

A neutral second or medium second is a musical interval between a minor second and a major second. Three distinct intervals may be termed neutral seconds....
, half of a minor third
Minor third

A minor third is a Interval of three semitones. It is the smaller of two commonly occurring musical intervals compounded of two steps of the diatonic scale....
.

In just intonation
Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series ....
 the quarter tone can be represented as 36:35 or 33:32, approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone. This just ratio is also the difference between a minor third
Minor third

A minor third is a Interval of three semitones. It is the smaller of two commonly occurring musical intervals compounded of two steps of the diatonic scale....
 (6:5) and septimal minor third
Septimal minor third

In music, the septimal minor third , also called the subminor third is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies....
 (7:6).

Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. 22-TET
22 equal temperament

In music, 22 equal temperament, called 22-tet, equal division of the octave, or 22-et, is the Temperament scale derived by dividing the octave into 22 equally large steps....
 contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET
53 equal temperament

In music, 53 equal temperament, called 53-TET, 53-equal division of the octave, or 53-ET, is the Temperament scale derived by dividing the octave into fifty-three equally large steps....
 has an interval of 45.28 cents, slightly smaller. 72-TET
72 equal temperament

In music, 72 equal temperament, called twelfth-tone, 72-tet, equal division of the octave, or 72-et, is the Temperament scale derived by dividing the octave into twelfth-tones, or in other words 72 equally large steps....
 also has equally-tempered quarter-tones, and indeed contains 3 quarter tone scales, since 72 is divisible by 24.

Playing quarter tones on musical instruments

Because many musical instruments manufactured today are designed for the 12-tone scale, not all are usable for playing quarter tones. Sometimes special playing techniques must be used.

Conventional musical instruments which can play quarter tones include

  • Synthesizers (if design permits)
  • Fretless string instruments (on fretted string instruments it is possible with bending or special tuning)
  • Slide brass instruments (trombone
    Trombone

    The trombone is a musical instrument in the brass instrument family. Like all brass instruments, it is a lip-reed aerophone: sound is produced when the player?s vibrating lips cause the air column inside the instrument to vibrate....
    )
  • Woodwind instruments, using special fingering or bending.
  • Harmonica
    Harmonica

    The harmonica is a free reed aerophone wind instrument which is played by blowing air into it or drawing air out by placing lips over individual holes or multiple holes....
  • Flute
    Flute

    The flute is a musical instrument of the woodwind family. Unlike other woodwind instruments, a flute is a reedless wind instrument that produces its sound from the flow of air against an edge....
  • Clarinet
    Clarinet

    The clarinet is a musical instrument in the woodwind family. The name derives from adding the suffix -et meaning little to the Italian word clarino meaning a particular type of trumpet, as the first clarinets had a strident tone similar to that of a trumpet....
  • Saxophone
    Saxophone

    The saxophone is a conical-Bore transposing instrument musical instrument considered a member of the woodwind family. Saxophones are usually made of brass and are played with a Single-reed instrument mouthpiece similar to the clarinet....
  • Harp
    Harp

    The 'harp' is a stringed instrument which has the plane of its strings positioned perpendicular to the Sounding board. It is also considered to be a percussion instrument....


Experimental instruments have been built to play in quarter tones, for example a quarter tone clarinet
Quarter tone clarinet

A quarter tone clarinet is an experimental clarinet designed to play music using quarter tone intervals. Using special fingerings, quarter tones may be produced by a skilled player on a conventional clarinet....
 by Fritz Schüller (1883-1977) of Markneukirchen
Markneukirchen

Markneukirchen is a town in the Vogtlandkreis district, in the Free State of Saxony, Germany. It lies in between the Erzgebirge and the Fichtelgebirge in the Elstergebirge, 24 km southeast of Plauen, and 14 km northeast of A?....
.

Other instruments can be used to play quarter tones when using audio signal processing
Audio signal processing

Audio signal processing, sometimes referred to as audio processing, is the intentional alteration of sound Signal , or sound. As audio signals may be electronically represented in either digital or analog signal format, signal processing may occur in either domain....
 effects such as pitch shifting.

Pairs of conventional instruments tuned a quarter tone apart can be used to play some quarter tone music. Indeed, "quarter tone pianos" have been built which consist essentially of two pianos stacked one above the other in a single case, one tuned a quarter tone higher than the other.

Music of the Middle East


While the use of quarter tones in Western music is a more recent and experimental phenomenon, these and other microtonal intervals have been an important part of the music of the Arab world
Arab world

The Arab World refers to Arabic-speaking countries stretching from the Atlantic Ocean in the west to the Arabian Sea in the east, and from the Mediterranean Sea in the north to the Horn of Africa and the Indian Ocean in the southeast....
, Turkey
Turkey

Turkey , known officially as the Republic of Turkey , is a Eurasian country that stretches across the Anatolian peninsula in southwest Asia and Thrace in the Balkans region of Southern Europe....
, Iran
Iran

Iran , officially the Islamic Republic of Iran and formerly known internationally as Persian Empire until 1935, is a country in Central Eurasia, located on the northeastern shore of the Persian Gulf and the southern shore of the Caspian Sea....
, Assyria
Assyria

Assyria was a political state centered on the Upper Tigris river, in Mesopotamia , that came to rule regional empires a number of times in history....
, Kurdistan
Kurdistan

Kurdistan is an extensive plateau and mountainous area in the Middle East, inhabited mainly by Kurdish people. It covers parts of eastern Turkish Kurdistan, northern Iraqi Kurdistan, northwestern Iranian Kurdistan and smaller parts of northern Syria and Armenia....
 and neighboring lands and areas for many centuries.

Many Arabic maqamat
Arabic maqam

Arabic maqam is the system of mode used in traditional Arabic music, which is mainly melodic music. The word maqam in Arabic means place, location or rank....
 contain intervals of three-quarter tone size; a short list of these follows. (Note: Due to the lack of widespread support for Unicode
Unicode

Unicode is a computing industry standard allowing computers to consistently represent and manipulate Character expressed in most of the world's writing systems....
 quarter tone characters, a regular flat symbol is used with a strikethrough. The proper form has a short diagonal stroke through the stem, not a straight stroke through the bowl. ?)

  1. Bayati
    ?????
  2. D E? F G A B? C D
  3. Hussayni
  4. Siga
    ?????
  5. E? F G A B? C D E?
  6. Rast
    ????
  7. C D E? F G A B? C
  8. with a B? replacing the B? in the descending scale
  9. ‘Ajam
  • Sabba
    ???
  • D E? F G? A B? C D


The medieval philosopher and scientist Al-Farabi
Al-Farabi

Abu Nasr al-Farabi , known in the Western world as Alpharabius , was a Muslim polymath and one of the greatest Islamic sciences and Early Islamic philosophys of History of Iran and the Islamic Golden Age in his time....
 described a number of intervals in his work in music, including a number of quarter tones.

Assyrian/Syriac Church scale:
  • 1 - Qadmoyo (Bayati)
  • 2 - Trayono (Hussayni)
  • 3 - Tlithoyo (Segah)
  • 4 - Rbi‘oyo (Rast)
  • 5 - Hmishoyo
  • 6 - Shtithoyo (‘Ajam)
  • 7 - Shbi‘oyo
  • 8 - Tminoyo


Quarter tone scale

The quarter tone scale was developed in the Middle East in the eighteenth century and many of the first detailed writings in the nineteenth century Syria describe the scale as being of 24 equal tones The invention of the scale is attributed to Mikhail Mishaqa
Mikhail Mishaqa

Mikhail Mishaqa born in Rashaya District, Lebanon is "the first historian of modern Syria" as well as the "virtual founder of the twenty-four equal quarter tone scale"....
 whose work Essay on the Art of Music for the Emir Shihab (al-Risala al-shihabiyya fi 'l-?ina‘a al-musiqiyya) is devoted to the topic but also makes clear his teacher Sheikh Muhammad al-‘Attar (1764-1828) was one of many already familiar with the concept.

The quarter tone scale may be primarily considered a theoretical
Music theory

Music theory is the field of study that deals with how music works. It examines the language and notation of music. It identifies patterns that govern composer techniques....
 construct in Arabic music. The quarter tone gives musicians a "conceptual map" which with to discuss and compare intervals by number of quarter tones and this may be one of the reasons it accompanies a renewed interest in theory, with instruction in music theory being a mainstream requirement since that period.

Previously pitches of a mode where chosen from a scale consisting of seventeen tones, developed by Safi 'I-Din al-Urmawi in the thirteenth century.

In Popular Music

Several songs by the American alternative rock group Ween
Ween

Ween is an alternative rock group formed in 1984 in New Hope, Pennsylvania when Aaron Freeman and Mickey Melchiondo met in an eighth grade typing class....
 are detuned by exactly one quarter tone. "So Many People In The Neighbourhood" is in F-half-flat Mixolydian, "Baby Bitch" is in F-half-sharp minor, "Back to Basom" is in A-half-flat major, and "Buckingham Green" is in A-half-flat minor. In concert, Ween perform the last two songs in Concert A.

Greek tetrachords

The enharmonic genus
Enharmonic genus

The enharmonic genus has historically been the most mysterious and controversial of the three Greek genus . Its characteristic interval is a major third, leaving the remainder of the tetrachord to be divided by two intervals smaller than a semitone ....
 of the tetrachord
Tetrachord

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row....
 described by the Greek
Ancient Greece

The term Ancient Greece refers to the period of History of Greece lasting from the Greek Dark Ages ca. 1100 BC and the Dorian invasion, to 146 BC and the Roman Republic conquest of Greece after the Battle of Corinth ....
 Archytas
Archytas

Archytas was an Ancient Greece philosopher, mathematician, astronomer, statesman, and military strategy. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato....
 consists of two quarter tones and a major third
Major third

A major third is one of two commonly occurring musical intervals that span three diatonic scale degrees, the other being the minor third. It is denoted 'major' because it is the larger of the two: the major third is a leap of four semitones, the minor third three....
.

Interval size in equal temperament


Here are the sizes of some common intervals in a 24-note equally tempered scale:

interval name size (steps) size (cents) midi just ratio just (cents) midi difference
perfect fifth
Perfect fifth

The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F, and so on....
 14 700.00 3:2 701.95 1.95
tritone
Tritone

The tritone is a musical interval that spans three major second. The tritone is the same as an augmented fourth, which in equal temperament is enharmonic to a diminished fifth....
 12 600 7:5 582.51 -17.49
eleventh harmonic 11 550.00 11:8 551.32 1.32
perfect fourth
Perfect fourth

The perfect fourth is a musical interval which spans four diatonic scale scale degree. It consists of the note and the note five semitones above it on the musical scale....
 10 500 4:3 498.05 -1.95
tridecimal major third
Major third

A major third is one of two commonly occurring musical intervals that span three diatonic scale degrees, the other being the minor third. It is denoted 'major' because it is the larger of the two: the major third is a leap of four semitones, the minor third three....
 9 450.00  13:10 454.21 4.21
septimal major third
Septimal major third

In music, the septimal major third , also called the supermajor third and sometimes Bohlen-Pierce third is the musical interval exactly or approximately equal to a 9:7 ratio of frequencies....
 9 450.00 9:7 435.08 -14.92
major third
Major third

A major third is one of two commonly occurring musical intervals that span three diatonic scale degrees, the other being the minor third. It is denoted 'major' because it is the larger of the two: the major third is a leap of four semitones, the minor third three....
 8 400.00 5:4 386.31 -13.69
undecimal neutral third
Neutral third

A neutral third is a musical interval between a minor third and a major third . Three distinct intervals may be termed neutral thirds:* The undecimal neutral third has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents ....
 7 350.00 11:9 347.41 -2.59
minor third
Minor third

A minor third is a Interval of three semitones. It is the smaller of two commonly occurring musical intervals compounded of two steps of the diatonic scale....
 6 300.00 6:5 315.64 15.64
septimal minor third
Septimal minor third

In music, the septimal minor third , also called the subminor third is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies....
 5 250.00  7:6 266.88 16.88
tridecimal minor third 5 250.00  15:13 247.74 -2.26
septimal whole tone
Septimal whole tone

In music, the septimal whole tone is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 cent wide....
 5 250.00 8:7 231.17 -18.83
whole tone, major tone 4 200.00 9:8 203.91 3.91
neutral second
Neutral second

A neutral second or medium second is a musical interval between a minor second and a major second. Three distinct intervals may be termed neutral seconds....
, lesser undecimal		 3 150.00 12:11 150.64 0.64
diatonic semitone, just
Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series ....
 2 100.00 16:15 111.73 11.73
septimal quarter tone
Septimal quarter tone

A septimal quarter-tone is an Interval with the ratio of 36:35 , which is the difference between Septimal minor third and Limit minor thirds ....
, just
Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series ....
 1 50.00 36:35 48.77 -1.23


Moving from 12-TET
Equal temperament

Equal temperament is a musical temperament, or a system of Musical tuning in which every pair of adjacent notes has an identical frequency ratios....
 to 24-TET does not improve the matches to any intervals in the harmonic series, but it adds a number of new intervals not available in 12-TET. New intervals matched particularly closely include the neutral second
Neutral second

A neutral second or medium second is a musical interval between a minor second and a major second. Three distinct intervals may be termed neutral seconds....
, neutral third
Neutral third

A neutral third is a musical interval between a minor third and a major third . Three distinct intervals may be termed neutral thirds:* The undecimal neutral third has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents ....
, and (11:8) ratio, or the 11th harmonic. The septimal minor third
Septimal minor third

In music, the septimal minor third , also called the subminor third is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies....
 and septimal major third
Septimal major third

In music, the septimal major third , also called the supermajor third and sometimes Bohlen-Pierce third is the musical interval exactly or approximately equal to a 9:7 ratio of frequencies....
 are approximated rather poorly; the (13:10) and (15:13) ratios, involving the 13th harmonic, are matched very closely. Overall, 24-TET can be viewed as matching the 11th harmonic more closely than the 7th.

See also

  • Temperament
  • Microtonal music
    Microtonal music

    Microtonal music is music using microtones ? musical interval of less than an Equal Temperament semitone.Microtonal music can also refer to music which uses intervals not found in the Western system of 12 equal intervals to the octave....
  • List of quarter tone pieces
    List of quarter tone pieces

    A selection of compositions using quarter tones:*Jan Bach*Clarence Barlow*Hans Barth*Ernest Bloch*B?la Bart?k::String Quartet No. 6 ; the third movement Burletta contains quarter-tone tuning used for parodistic effect....
  • List of meantone intervals
    List of meantone intervals

    The following is a list of intervals of meantone temperament. These intervals constitute the standard vocabulary of intervals for the Western common practice era....


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