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A quarter tone is an interval about half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone.

In equal temperament the quarter tone is 50 cents, or a frequency ratio of 2^1/24 or 1.0293. In 24 tone equal temperament (24-TET), or the quarter tone scale, it is the smallest step. The 24 tone equal temperament does not offer any improvement to matching small ratios of the harmonic series relative to the 12-TET; 19-TET and 22-TET are better in this respect; 24 tones are mainly used out of convenience, as the widely used 12-TET is included as a subset of the 24-TET. Two equal temperament quarter tones equal a semitone, and three make a three-quarter tone. A three-quarter tone may also be considered half of a minor third.

In just intonation the quarter tone can be represented as 36:35 or 33:32, approximately half the semitone of 16:15 or 25:24.

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: Alberto Ginastera, Alois Hába, Charles Ives, Krzysztof Penderecki, Tui St. George Tucker, Ivan Alexandrovich Vïshnegradsky, Mildred Couper (see List of quarter tone pieces).

Contents 1 Playing quarter tones on musical instruments 2 Music of the Middle East 3 Greek tetrachords 4 Interval size in equal temperament 5 See also 6 Notes 7 References

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)
• Woodwind instruments, using special fingering or bending.
• Harmonica
• Flute
• Saxophone

Experimental instruments have been built to play in quarter tones, for example a quarter tone clarinet by Fritz Schüller (1883-1977) of Markneukirchen.

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

• See also: Arabic music and Arab tone system

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, Turkey, Iran, Assyria, Kurdistan and neighboring lands and areas for many centuries.

Many Arabic maqamat contain intervals of three-quarter tone size; a short list of these follows.^[1] (Note: Due to the lack of widespread support for Unicode 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 (بياتي): D E♭ F G A B♭ C D
• 2 - Hussayni
• 3 - Siga (سيكاه): E♭ F G A B♭ C D E♭
• 4 - Rast (راست): C D E♭ F G A B♭ C (with a B♭ replacing the B♭ in the descending scale)
• 6 - ‘Ajam
• Sabba (صبا): D E♭ F G♭ A B♭ C D

The medieval philosopher and scientist Al-Farabi 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

The enharmonic genus of the tetrachord described by the Greek Archytas consists of two quarter tones and a major third.

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

interval name	size (steps)	size (cents)	just ratio	just (cents)	difference
perfect fifth	14	700.00	3:2	701.95	1.95
tritone	12	600	7:5	582.51	-17.49
eleventh harmonic	11	550.00	11:8	551.32	1.32
perfect fourth	10	500	4:3	498.05	-1.95
tridecimal major third	9	450.00	13:10	454.21	4.21
septimal major third	9	450.00	9:7	435.08	-14.92
major third	8	400.00	5:4	386.31	-14.69
undecimal neutral third	7	350.00	5:4	347.41	-2.59
minor third	6	300.00	6:5	315.64	15.64
septimal minor third	5	250.00	7:6	266.88	16.88
tridecimal minor third	5	250.00	15:13	247.74	-2.26
septimal whole tone	5	250.00	8:7	231.17	-18.83
whole tone, major tone	4	200.00	9:8	203.91	3.91
neutral second, lesser undecimal	3	150.00	11:10	150.64	0.64
diatonic semitone, just	2	100.00	16:15	111.73	11.73

Moving from 12-TET 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 third, and (11:8) ratio, or the 11th harmonic. The septimal minor third and septimal major third 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.

• Temperament
• List of quarter tone pieces
• List of meantone intervals

• Habib Hassan Touma (1996). The Music of the Arabs, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.

Tunings	edit
Pythagorean · Just intonation · Harry Partch's 43-tone scale
Regular temperaments
Equal temperaments :   12-tone · 19-tone · 22-tone · 24-tone 31-tone · 34-tone · 41-tone · 53-tone · 72-tone · 88-tone Non-equal temperaments :   Meantone (Quarter-comma; Lucy tuning; Septimal) · Schismatic · Miracle
Irregular temperaments
Well temperament