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A quarter tone (play^ⓘ) is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.

Quarter tone has its roots in the music of the Middle East and more specifically in Persian traditional music.^[1] However, the first evidenced proposal of quarter tones, or the quarter-tone scale (24 equal temperament), was made by 19th-century music theorists Heinrich Richter in 1823^[2] and Mikha'il Mishaqah about 1840.^[3] Composers who have written music using this scale include: Pierre Boulez, Julián Carrillo, Mildred Couper, George Enescu, Alberto Ginastera, Gérard Grisey, Alois Hába, Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Ammar El Sherei, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Alexandrovich Wyschnegradsky, and Iannis Xenakis. (See List of quarter tone pieces.)

Types

Equal-tempered tuning systems

The term quarter tone can refer to a number of different intervals, all very close in size. For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g., D♯–E♭).^[2] In the quarter-tone scale, also called 24-tone equal temperament (24-TET), the quarter tone is 50 cents, or a frequency ratio of ²⁴√2 or approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). 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 play^ⓘ or neutral second, half of a minor third. The 8-TET scale is composed of three-quarter tones (Play^ⓘ). Four steps make a whole tone play^ⓘ.

Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, slightly smaller. 72-TET also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. The smallest interval in 31 equal temperament (the "diesis" of 38.71 cents) is half a chromatic semitone, one-third of a diatonic semitone and one-fifth of a whole tone, so it may function as a quarter tone, a fifth-tone or a sixth-tone.

Just intonation tuning systems

In just intonation the quarter tone can be represented by the septimal quarter tone, 36:35 (48.77 cents), or by the undecimal quarter tone (i.e. the thirty-third harmonic), 33:32 (53.27 cents), 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 (6:5) and septimal minor third (7:6).

Composer Ben Johnston, to accommodate the just septimal quarter tone, uses a small "7" () as an accidental to indicate a note is lowered 49 cents, or an upside down "7" () to indicate a note is raised 49 cents,^[5] or a ratio of 36:35.^[6] Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33:32, or 53 cents.^[6] The Maneri-Sims notation system designed for 72-et uses the accidentals and for a quarter tone (36:35 or 48.77 cents) up and down.

Playing quarter tones

Any tunable musical instrument can be used to perform quarter tones, if two players and two identical instruments, with one tuned a quarter tone higher, are used. As this requires neither a special instrument nor special techniques, much quarter toned music is written for pairs of pianos, violins, harps, etc. The retuning of the instrument, and then returning it to its former pitch, is easy for violins, harder for harps, and slow and relatively expensive for pianos.

The following deals with the ability of single instruments to produce quarter tones. In Western instruments, this means "in addition to the usual 12-tone system".

Because many musical instruments manufactured today (2018) 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 that cannot play quarter tones (except by using special techniques—see below) include:

Most standard or unmodified non-electronic keyboard instruments, such as pianos, organs, and accordions
Fretted string instruments such as guitars, bass guitars, and ukuleles (though on these it is possible to play quarter tones by pitch-bending, with special tunings, or with customized necks)
Pitched percussion instruments, if standard techniques are used, and if the instruments are not tunable
Western wind instruments that use keys or valves
- Woodwind instruments, such as clarinets, saxophones, flutes, and oboes (though with many of these, it is still possible using non-standard techniques such as special fingerings or by the player manipulating their embouchure, to play at least some quarter tones, if not a whole scale)
- Valved brass instruments (trumpet, tuba) (though, as with woodwinds, embouchure manipulation, as well as harmonic tones that fall closer to quarter-tones than half-tones, make quarter-tone scales possible; the horn technique of adjusting pitch with the right hand in the bell makes this instrument an exception)

Conventional musical instruments that can play quarter tones include

Electronic instruments:
- Synthesizers, using either special keyboard controllers or continuous-pitch controllers such as fingerboard controllers, or when controlled by a sequencer capable of outputting quarter-tone control signals.
- Theremins and other continuously pitched instruments
Fretless string instruments, such as the violin family, fretless guitars, fretless electric basses, ouds, and members of the huqin family of instruments.
String instruments with movable frets (such as the sitar)
Specially fretted string instruments (such as the Turkish bağlama).
Fretted string instruments specially tuned to quarter tones
Pedal steel guitar
Wind instruments whose main means of tone-control is a slide, such as trombones, the tromboon invented by P. D. Q. Bach, the slide trumpet and the slide whistle
Specially keyed woodwind instruments. A quarter tone clarinet was built by Fritz Schüller (1883–1977) of Markneukirchen, and a quarter tone mechanism for flutes by Eva Kingma.
Valved brass instruments with extra, quarter-tone valves, and natural brass instruments that play through the 11th and 13th partials of the harmonic series
Kazoo
Pitched percussion instruments, when tuning permits (e.g., timpani), or using special techniques

Other instruments can be used to play quarter tones when using audio signal processing effects such as pitch shifting.

Quarter-tone pianos have been built, which consist essentially of two pianos with two keyboards stacked one above the other in a single case, one tuned a quarter tone higher than the other.^{[citation needed]}

Music of the Middle East

Many Persian dastgah and Arabic maqamat contain intervals of three-quarter tone size; a short list of these follows.^[7]

Bayati (بیاتی): D E F G A B♭ C D
$\relative c' { \time 8/4 \omit Staff.TimeSignature d4 eeh f g a bes c d \bar "|" }$
Rast (راست):
C D E F G A B C (ascending)

C B♭ A G F E D C (descending)

$\relative c' { \time 8/4 \omit Staff.TimeSignature c4 d eeh f g a beh c \bar "|" }$
Saba (صبا): D E F G♭ A B♭ C D
$\relative c' { \time 8/4 \omit Staff.TimeSignature d4 eeh f ges a bes c d \bar "|" }$
Sigah (سه گاه): E F G A B C D E
$\relative c' { \time 8/4 \omit Staff.TimeSignature eeh f g a beh c d eeh \bar "|" }$
‘Ajam (عجم)
Hoseyni

The Islamic philosopher and scientist Al-Farabi described a number of intervals in his work in music, including a number of quarter tones.

Assyrian/Syriac Church Music Scale:^[8]

Qadmoyo (Bayati)
Trayono (Hussayni)
Tlithoyo (Segah)
Rbiʿoyo (Rast)
Hmishoyo
Shtithoyo (ʿAjam)
Shbiʿoyo
Tminoyo

Quarter-tone scale

Known as gadwal in Arabic,^[9] 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.^[10] The invention of the scale is attributed to Mikhail Mishaqa whose work Essay on the Art of Music for the Emir Shihāb (al-Risāla al-shihābiyya fi 'l-ṣināʿa al-mūsīqiyya) 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.^[11]

$\relative c' { \cadenzaOn \omit Staff.TimeSignature \tempo 1 = 90 \set Score.tempoHideNote = ##t c1 cih cis cisih d dih dis disih e eih f fih fis fisih g gih gis gisih a aih ais aisih b bih \bar "|" c \bar "|." \break c1 ceh b beh bes beseh a aeh aes aeseh g geh ges geseh f feh e eeh ees eeseh d deh des deseh \bar "|" c \bar "|." }$

The quarter tone scale may be primarily a theoretical construct in Arabic music. The quarter tone gives musicians a "conceptual map" they can use 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 a mainstream requirement since that period.^[10]

Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, developed by Safi al-Din al-Urmawi in the thirteenth century.^[11]

Composer Charles Ives chose the chord C–D–F–G–B♭ as good possibility for a "secondary" chord in the quarter-tone scale, akin to the minor chord of traditional tonality. He considered that it may be built upon any degree of the quarter tone scale^[4] Here is the secondary "minor" and its "first inversion":

$\relative c' { \omit Staff.TimeSignature \set Score.tempoHideNote = ##t <c dih f gih bes>1 \bar "|" <c f gih bes dih>1 \bar "|." }$

In popular music

The Japanese multi-instrumentalist and experimental musical instrument builder Yuichi Onoue developed a 24-TET quarter tone tuning on his guitar.^[12] Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, USA.^[13]^[14] Another quartertone metal album was issued by the Swedish band Massive Audio Nerve.^[15] Australian psychedelic rock band King Gizzard & the Lizard Wizard's album Flying Microtonal Banana heavily emphasizes quarter-tones.^{[citation needed]} Jazz violinist/violist Mat Maneri, in conjunction with his father Joe Maneri, made a crossover fusion album, Pentagon, that featured experiments in hip hop with quarter tone pianos, as well as electric organ and mellotron textures, along with distorted trombone, in a post-Bitches Brew type of mixed Jazz/rock.^[16]

Ancient Greek tetrachords

Greek Dorian enharmonic genus: two disjunct tetrachords each of a quarter tone, quarter tone, and major third. Play

The enharmonic genus of the Greek tetrachord consisted of a ditone or an approximate major third, and a semitone, which was divided into two microtones. Aristoxenos, Didymos and others presented the semitone as being divided into two approximate quarter tone intervals of about the same size, while other ancient Greek theorists described the microtones resulting from dividing the semitone of the enharmonic genus as unequal in size (i.e., one smaller than a quarter tone and one larger).^[17]^[18]

Interval size in equal temperament

Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed by Alois Hába (neutral third, etc.) and Ivan Wyschnegradsky (major fourth, etc.):

interval name	size (steps)	size (cents)	midi	just ratio	just (cents)	midi	error (cents)
octave	24	1200	play^ⓘ	2:1	1200.00	play^ⓘ	+00.00
semidiminished octave	23	1150	play^ⓘ	35:18	1151.23	play^ⓘ	−01.23
supermajor seventh	23	1150	play^ⓘ	27:14	1137.04	play^ⓘ	+12.96
major seventh	22	1100	play^ⓘ	15:80	1088.27	play^ⓘ	+11.73
neutral seventh, major tone	21	1050	play^ⓘ	11:60	1049.36	play^ⓘ	+00.64
neutral seventh, minor tone	21	1050	play^ⓘ	20:11	1035.00	play^ⓘ	+15.00
large just minor seventh	20	1000	play^ⓘ	9:5	1017.60	play^ⓘ	−17.60
small just minor seventh	20	1000	play^ⓘ	16:90	0996.09	play^ⓘ	+03.91
supermajor sixth/subminor seventh	19	0950	play^ⓘ	7:4	0968.83	play^ⓘ	−18.83
major sixth	18	0900	play^ⓘ	5:3	0884.36	play^ⓘ	+15.64
neutral sixth	17	0850	play^ⓘ	18:11	0852.59	play^ⓘ	−02.59
minor sixth	16	0800	play^ⓘ	8:5	0813.69	play^ⓘ	−13.69
subminor sixth	15	0750	play^ⓘ	14:90	0764.92	play^ⓘ	−14.92
perfect fifth	14	0700	play^ⓘ	3:2	0701.96	play^ⓘ	−01.96
minor fifth	13	0650	play^ⓘ	16:11	0648.68	play^ⓘ	+01.32
lesser septimal tritone	12	0600	play^ⓘ	7:5	0582.51	play^ⓘ	+17.49
major fourth	11	0550	play^ⓘ	11:80	0551.32	play^ⓘ	−01.32
perfect fourth	10	0500	play^ⓘ	4:3	0498.04	play^ⓘ	+01.96
tridecimal major third	09	0450	play^ⓘ	13:10	0454.21	play^ⓘ	−04.21
septimal major third	09	0450	play^ⓘ	9:7	0435.08	play^ⓘ	+14.92
major third	08	0400	play^ⓘ	5:4	0386.31	play^ⓘ	+13.69
undecimal neutral third	07	0350	play^ⓘ	11:90	0347.41	play^ⓘ	+02.59
minor third	06	0300	play^ⓘ	6:5	0315.64	play^ⓘ	−15.64
septimal minor third	05	0250	play^ⓘ	7:6	0266.87	play^ⓘ	−16.87
tridecimal five-quarter tone	05	0250	play^ⓘ	15:13	0247.74	play^ⓘ	+02.26
septimal whole tone	05	0250	play^ⓘ	8:7	0231.17	play^ⓘ	+18.83
major second, major tone	04	0200	play^ⓘ	9:8	0203.91	play^ⓘ	−03.91
major second, minor tone	04	0200	play^ⓘ	10:90	0182.40	play^ⓘ	+17.60
neutral second, greater undecimal	03	0150	play^ⓘ	11:10	0165.00	play^ⓘ	−15.00
neutral second, lesser undecimal	03	0150	play^ⓘ	12:11	0150.64	play^ⓘ	−00.64
15:14 semitone	02	0100	play^ⓘ	15:14	0119.44	play^ⓘ	−19.44
diatonic semitone, just	02	0100	play^ⓘ	16:15	0111.73	play^ⓘ	−11.73
21:20 semitone	02	0100	play^ⓘ	21:20	0084.47	play^ⓘ	+15.53
28:27 semitone	01	0050	play^ⓘ	28:27	0062.96	play^ⓘ	−12.96
33:32 semitone	01	0050	play^ⓘ	33:32	0053.27	play^ⓘ	−3.27
unison	00	0000	play^ⓘ	1:1	0000.00	play^ⓘ	+00.00

Moving from 12-TET to 24-TET allows the better approximation of a number of intervals. 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 and 13th harmonics more closely than the 7th.

References

^ Hormoz Farhat (2004). The Dastgah Concept in Persian Music. Cambridge University Press. ISBN 0-521-54206-5
^ ^a ^b Julian Rushton, "Quarter-Tone", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).
^ Touma, Habib Hassan (1996). The Music of the Arabs, p. 16. Trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.
^ ^a ^b Boatwright, Howard (1965). "Ives' Quarter-Tone Impressions", Perspectives of New Music 3, no. 2 (Spring-Summer): pp. 22–31; citations on pp. 27–28; reprinted in Perspectives on American Composers, edited by Benjamin Boretz and Edward T. Cone, pp. 3–12, New York: W. W. Norton, 1971, citation on pp. 8–9. "These two chords outlined above might be termed major and minor."
^ Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", Perspectives of New Music, Vol. 29, No. 1. (Winter, 1991), pp. 176–211.
^ ^a ^b Fonville, John (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", p.114, Perspectives of New Music, Vol. 29, No. 2, pp. 106–137.
^ Spector, Johanna (May 1970). "Classical ʿUd Music in Egypt with Special Reference to Maqamat". Ethnomusicology. 14 (2): 243–257. doi:10.2307/849799. JSTOR 00141836. ^{[dead link‍]}
^ Asaad, Gabriel (1990). Syria's Music Throughout History
^ "Classical 'Ud Music in Egypt with Special Reference to Maqamat", p.246. Johanna Spector. Ethnomusicology, Vol. 14, No. 2. (May, 1970), pp. 243–57.
^ ^a ^b Marcus, Scott (1993)."The Interface between Theory and Practice: Intonation in Arab Music", Asian Music, Vol. 24, No. 2. (Spring–Summer, 1993), pp. 39–58.
^ ^a ^b Maalouf, Shireen (2003). "Mikhiiʾil Mishiiqa: Virtual Founder of the Twenty-Four Equal Quartertone Scale", Journal of the American Oriental Society, Vol. 123, No. 4. (Oct.–Dec., 2003), pp. 835–40.
^ Yuichi Onoue on hypercustom.com Archived November 8, 2015, at the Wayback Machine
^ Jute Gyte's album Ressentiment on canthisbecalledmusic.com
^ Jute Gyte's album “Discontinuities” on jutegyte.bandcamp.com
^ Massive Audio Nerve's Album "Cancer Vulgaris" on blabbermouth.net
^ https://www.popmatters.com/manerimat-pentagon-2495996795.html
^ Chalmers, John H. Jr. (1993). Divisions of the Tetrachord. Hanover, NH: Frog Peak Music. ISBN 0-945996-04-7 Chapter 5, Page 49
^ West, Martin L. (1992). Ancient Greek Music. Oxford, UK: Oxford University Press. ISBN 0-19-814975-1.

External links

"quarter-tone / 24-edo", TonalSoft.com.

[1] Hormoz Farhat (2004). The Dastgah Concept in Persian Music. Cambridge University Press. ISBN 0-521-54206-5

[JR-2] Julian Rushton, "Quarter-Tone", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).

[3] Touma, Habib Hassan (1996). The Music of the Arabs, p. 16. Trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.

[Boatwright-4] Boatwright, Howard (1965). "Ives' Quarter-Tone Impressions", Perspectives of New Music 3, no. 2 (Spring-Summer): pp. 22–31; citations on pp. 27–28; reprinted in Perspectives on American Composers, edited by Benjamin Boretz and Edward T. Cone, pp. 3–12, New York: W. W. Norton, 1971, citation on pp. 8–9. "These two chords outlined above might be termed major and minor."

[5] Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", Perspectives of New Music, Vol. 29, No. 1. (Winter, 1991), pp. 176–211.

[Fonville-6] Fonville, John (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", p.114, Perspectives of New Music, Vol. 29, No. 2, pp. 106–137.

[7] Spector, Johanna (May 1970). "Classical ʿUd Music in Egypt with Special Reference to Maqamat". Ethnomusicology. 14 (2): 243–257. doi:10.2307/849799. JSTOR 00141836. ^{[dead link‍]}

[8] Asaad, Gabriel (1990). Syria's Music Throughout History

[9] "Classical 'Ud Music in Egypt with Special Reference to Maqamat", p.246. Johanna Spector. Ethnomusicology, Vol. 14, No. 2. (May, 1970), pp. 243–57.

[Marcus-10] Marcus, Scott (1993)."The Interface between Theory and Practice: Intonation in Arab Music", Asian Music, Vol. 24, No. 2. (Spring–Summer, 1993), pp. 39–58.

[Maalouf-11] Maalouf, Shireen (2003). "Mikhiiʾil Mishiiqa: Virtual Founder of the Twenty-Four Equal Quartertone Scale", Journal of the American Oriental Society, Vol. 123, No. 4. (Oct.–Dec., 2003), pp. 835–40.

[12] Yuichi Onoue on hypercustom.com Archived November 8, 2015, at the Wayback Machine

[13] Jute Gyte's album Ressentiment on canthisbecalledmusic.com

[14] Jute Gyte's album “Discontinuities” on jutegyte.bandcamp.com

[15] Massive Audio Nerve's Album "Cancer Vulgaris" on blabbermouth.net

[16] ttps://www.popmatters.com/manerimat-pentagon-2495996795.html

[Chalmers-Divisions-5-49-17] Chalmers, John H. Jr. (1993). Divisions of the Tetrachord. Hanover, NH: Frog Peak Music. ISBN 0-945996-04-7 Chapter 5, Page 49

[West1992-18] West, Martin L. (1992). Ancient Greek Music. Oxford, UK: Oxford University Press. ISBN 0-19-814975-1.

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@@ Line 108: / Line 108: @@
 Known as ''gadwal'' in Arabic,<ref>"Classical 'Ud Music in Egypt with Special Reference to Maqamat", p.246. Johanna Spector. ''Ethnomusicology'', Vol. 14, No. 2. (May, 1970), pp. 243–57.</ref> 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.<ref name="Marcus">Marcus, Scott (1993)."The Interface between Theory and Practice: Intonation in Arab Music", ''Asian Music'', Vol. 24, No. 2. (Spring–Summer, 1993), pp. 39–58.</ref> The invention of the scale is attributed to [[Mikhail Mishaqa]] whose work ''Essay on the Art of Music for the Emir Shihāb (al-Risāla al-shihābiyya fi 'l-ṣināʿa al-mūsīqiyya)'' 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.<ref name="Maalouf">Maalouf, Shireen (2003). "Mikhiiʾil Mishiiqa: Virtual Founder of the Twenty-Four Equal Quartertone Scale", ''Journal of the American Oriental Society'', Vol. 123, No. 4. (Oct.–Dec., 2003), pp. 835–40.</ref>
-<score vorbis="1">
+<score %vorbis="1"%%T257066%>
 \relative c' {
 \cadenzaOn \omit Staff.TimeSignature
@@ Line 122: / Line 122: @@
 Composer Charles Ives chose the chord C–D{{music|t}}–F–G{{music|t}}–B{{music|b}} as good possibility for a "secondary" chord in the quarter-tone scale, akin to the minor chord of traditional tonality. He considered that it may be built upon any degree of the quarter tone scale<ref name="Boatwright"/> Here is the secondary "minor" and its "first inversion":
-<score vorbis="1">
+<score %vorbis="1"%%T257066%>
 \relative c' {
 \omit Staff.TimeSignature