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Quarter tone

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"24 equal temperament" redirects here. For other uses, seeArab tone system.
Quarter tone on C

Aquarter toneis a pitch halfway between the usual notes of achromatic scaleor anintervalabout half as wide (orally, or logarithmically) as asemitone,which itself is half awhole tone.Quarter tones divide the octave by 50centseach, and have 24 different pitches.

Trumpetwith 3 normal valves and a quartering on the extension valve (right)

Quarter tones have their roots in the music of the Middle East and more specifically inPersian traditional music.[1]However, the first evidenced proposal of theequally-temperedquarter tone scale, or24 equal temperament,was made by 19th-century music theorists Heinrich Richter in 1823[2]andMikhail Mishaqaabout 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 Wyschnegradsky,Iannis Xenakis,andSeppe Gebruers(SeeList of quarter tone pieces.)

Types[edit]

Equal-tempered tuning systems[edit]

Composer Charles Ives chose the four-note chord above (C–Dthree quarter sharp–G–Athree quarter sharp) as good possibility for a "fundamental" chord in the quarter-tone scale, akin not to the tonic but to the major chord of traditional tonality.[4]
Neutral second on C
8-tet scale on C
Major second on C
The "subminor seventh":Bthree quarter flat=Ahalf sharp,19 quarter tones. It approximates theharmonic seventh,B7♭.Maneri-Sims notation:B♭

The termquarter tonecan 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 called24-tone equal temperament(24-TET), the quarter tone is 50cents,or a frequency ratio of24√2or approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). In this scale the quarter tone is the smalleststep.A semitone is thus made of two steps, and three steps make athree-quarter toneorneutral second,half of aminor third.The 8-TET scale is composed of three-quarter tones. Four steps make a whole tone.

Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems.22-TETcontains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas53-TEThas an interval of 45.28 cents, slightly smaller.72-TETalso has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. The smallest interval in31 equal temperament(the "diesis" of 38.71 cents) is half achromatic semitone,one-third of adiatonic semitoneand one-fifth of a whole tone, so it may function as a quarter tone, a fifth-toneora sixth-tone.

Just intonation tuning systems[edit]

Injust intonationthe quarter tone can be represented by theseptimal quarter tone,36:35 (48.77 cents), or by theundecimal quarter tone(i.e. thethirty-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 aminor third(6:5) andseptimal minor third(7:6).

ComposerBen Johnston,to accommodate thejustseptimal quarter tone, uses a small "7" (7) as an accidental to indicate a note is lowered 49 cents, or an upside down "7"(7 upside-down) 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]TheManeri-Sims notationsystem designed for72-etuses the accidentalsandfor a quarter tone (36:35 or 48.77 cents) up and down.

Playing quarter tones[edit]

Quarter tone clarinetby Fritz Schüller

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 thatcannotplay quarter tones (except by using special techniques—see below) include:

  • Most standard or unmodified non-electronic keyboard instruments, such aspianos,organs,andaccordions
  • Frettedstring instrumentssuch asguitars,bass guitars,andukuleles(though on these it is possible to play quarter tones bypitch-bending,with special tunings, or with customized necks)
  • Pitched percussion instruments,if standard techniques are used, and if the instruments are not tunable
  • Westernwind instrumentsthat 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 theirembouchure,to play at leastsomequarter tones, if not a wholescale)
    • Valved brass instruments (trumpet,tuba) (though, as with woodwinds, embouchure manipulation, as well asharmonictones that fall closer to quarter-tones than half-tones, make quarter-tone scales possible; thehorntechnique of adjusting pitch with the right hand in the bell makes this instrument an exception)
  • Harmonica(although note bending is a common technique)

Conventional musical instruments thatcanplay quarter tones include

Other instruments can be used to play quarter tones when usingaudio signal processingeffects such aspitch 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[edit]

See also:Persian traditional music,Arabic music,andArab tone system

Many Persiandastgahand Arabicmaqamatcontain intervals of three-quarter tone size; a short list of these follows.[8]

  1. Bayati(بیاتی): D Ehalf flatF G A B♭C D
    \relative c' { \time 8/4 \omit Staff.TimeSignature d4 eeh f g a bes c d \bar "|" }
  2. Rast(راست):
    C D Ehalf flatF G A Bhalf flatC (ascending)
    C B♭A G F Ehalf flatD C (descending)
    \relative c' { \time 8/4 \omit Staff.TimeSignature c4 d eeh f g a beh c \bar "|" }
  3. Saba(صبا): D Ehalf flatF G♭A B♭C D
    \relative c' { \time 8/4 \omit Staff.TimeSignature d4 eeh f ges a bes c d \bar "|" }
  4. Sigah(سه گاه): Ehalf flatF G A Bhalf flatC D Ehalf flat
    \relative c' { \time 8/4 \omit Staff.TimeSignature eeh f g a beh c d eeh \bar "|" }
  5. ‘Ajam(عجم)
  6. Hoseyni

The Islamic philosopher and scientistAl-Farabidescribed a number of intervals in his work in music, including a number of quarter tones.

Assyrian/Syriac Church Music Scale:[9]

  1. Qadmoyo (Bayati)
  2. Trayono (Hussayni)
  3. Tlithoyo (Segah)
  4. Rbiʿoyo (Rast)
  5. Hmishoyo
  6. Shtithoyo (ʿAjam)
  7. Shbiʿoyo
  8. Tminoyo

Quarter-tone scale[edit]

Known asgadwalin Arabic,[8]thequarter-tone scalewas 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 toMishaqawho wrote a book devoted to the topic[11]but made clear that his teacher, Sheikh Muhammad al-Attar (1764–1828), was one among many already familiar with the concept.[12]

\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 atheoreticalconstruct 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 bySafi al-Din al-Urmawiin the thirteenth century.[12]

19-Limit just intonation intervals approximated in 24TET

ComposerCharles Iveschose the chord C–Dhalf sharp–F–Ghalf sharp–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 Western music[edit]

The bass descent ofNancy Sinatra's version of "These Boots Are Made for Walkin'  "includes quarter tone descents.[13] Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, USA.[14][15] Another quartertone metal album was issued by the Swedish band Massive Audio Nerve.[16] Australianpsychedelic rockbandKing Gizzard & the Lizard Wizard's albumsFlying Microtonal Banana,K.G.,andL.W.heavily emphasize quarter-tones and used a custom-built guitar in 24TETtuning.[17] Jazz violinist / violistMat Maneri,in conjunction with his fatherJoe Maneri,made a crossover fusion album,Pentagon(2005),[18]that featured experiments in hip hop with quarter tone pianos, as well as electric organ andmellotrontextures, along with distorted trombone, in a post-Bitches Brew type of mixedjazz/rock.[19]

Later,Seppe Gebruersstarted playing and improvising with two pianos tuned a quarter-tone apart. In 2019 he started a research project at theRoyal Conservatory of Ghent,titled 'Unexplored possibilities of contemporary improvisation and the influence of microtonality in the creation process'.[20] With two pianos tuned a quarter tone apart Gebruers recorded 'The Room: Time & Space' (2018) in a trio formation with drummerPaul Lovensand bassistHugo Anthunes.In his solo project 'Playing with standards' (album release January 2023), Gebruers plays with famous songs including jazz standards. WithPaul LyttonandNils Vermeulenhe forms a 'Playing with standards' trio.

Ancient Greek tetrachords[edit]

Theenharmonic genusof theGreektetrachordconsisted of aditoneor an approximatemajor third,and asemitone,which was divided into twomicrotones.Aristoxenos,Didymosand 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).[21][22]

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

Interval size in equal temperament[edit]

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

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

Moving from12-TETto 24-TET allows the better approximation of a number of intervals. Intervals matched particularly closely include theneutral second,neutral third,and (11:8) ratio, or the 11th harmonic. Theseptimal minor thirdandseptimal major thirdare 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.

See also[edit]

References[edit]

  1. ^Hormoz Farhat(2004). The Dastgah Concept in Persian Music. Cambridge University Press.ISBN0-521-54206-5
  2. ^abJulian Rushton,"Quarter-Tone",The New Grove Dictionary of Music and Musicians,second edition, edited byStanley SadieandJohn Tyrrell(London: Macmillan, 2001).
  3. ^Touma, Habib Hassan (1996).The Music of the Arabs,p. 16. Translator: Laurie Schwartz. Portland, Oregon: Amadeus Press.ISBN0-931340-88-8.
  4. ^abBoatwright, Howard(1965). "Ives' Quarter-Tone Impressions",Perspectives of New Music3, no. 2 (Spring–Summer): pp. 22–31; citations on pp. 27–28; reprinted inPerspectives on American Composers,edited byBenjamin BoretzandEdward 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.
  6. ^abFonville, 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. ^Kingma System
  8. ^abSpector, Johanna (May 1970). "Classical ʿUd Music in Egypt with Special Reference to Maqamat".Ethnomusicology.14(2): 243–257.doi:10.2307/849799.JSTOR849799.
  9. ^Asaad, Gabriel (1990).Syria's Music Throughout History
  10. ^ab Marcus, Scott (Spring–Summer 1993). "The interface between theory and practice: Intonation in Arab music".Asian Music.24(2): 39–58.doi:10.2307/834466.JSTOR834466.
  11. ^ Mishaqa, Mikhiiʾil(c. 1840).al-Risāla al-shihābiyya fi 'l-ṣināʿa al-mūsīqiyya[Essay on the Art of Music for the Emir Shihāb] (in Arabic).
  12. ^ab Maalouf, Shireen (October–December 2003). "Mikhiiʾil Mishiiqa: Virtual founder of the twenty-four equal quartertone scale".Journal of the American Oriental Society.123(4): 835–840.doi:10.2307/3589971.JSTOR3589971.
  13. ^ Everett, Walter(2009).The Foundations of Rock.Oxford University Press. p.32.ISBN9780195310238.
  14. ^ Tremblay, Dæv (3 September 2014)."Jute Gyte –Ressentiment".canthisbecalledmusic(album review).
  15. ^ Gyte, Jute.Discontinuities.jutegyte.bandcamp(music album). (commerical site).
  16. ^ "Massive Audio Nerve's albumCancer Vulgarisin July ".blabbermouth.net.
  17. ^ Huguenor, Mike (21 August 2017)."King Gizzard & the Lizard Wizard talk new albumFlying Microtonal Banana".Guitar World (guitarworld )(interview).Retrieved2021-01-27.
  18. ^ Maneri, M.;Maneri, J.(2005).Pentagon(music album).
  19. ^ Maneri, Mat (1 December 2005)."Pentagonby Will Layman ".PopMatters(album review).
  20. ^"Seppe Gebruers - Playing with Standards".
  21. ^ Chalmers, John H., Jr. (1993).Divisions of the Tetrachord.Hanover, NH: Frog Peak Music. Chapter 5, page 49.ISBN0-945996-04-7.{{cite book}}:CS1 maint: multiple names: authors list (link)
  22. ^ West, Martin L.(1992).Ancient Greek Music.Oxford, UK: Oxford University Press.ISBN0-19-814975-1.

Further reading[edit]

  • Bartolozzi, Bruno (1967).New Sounds for Woodwind.London, UK / New York, NY: Oxford University Press.
  • Bousted, Donald (Fall 2002). "Microtonality, the recorder and the quarter-tone recorder manual".The Recorder Magazine.Vol. 22, no. 3. pp. 99–102.
  • Bousted, Donald (Fall 2005). "Next step quarter-tone resources: Melody".The Recorder Magazine.Vol. 25, no. 3. pp. 88–91.
  • Caravan, Ronald R. (1979).Preliminary Exercises and Etudes in Contemporary Techniques for Clarinet: Introductory material for the study of multiphonics, quarter tones, and timbre variation.Oswego, NY: Ethos Publications.
  • Ellis, Don(1975).Quarter Tones: A text with musical examples, exercises, and etudes.Plainview, NY: Harold Branch.
  • MacDonald, John (1822).A Treatise on the Harmonic System Arising from the Vibrations of the Aliquot Divisions of Strings.London, UK: T. Preston.
  • Möllendorff, Willi; Monzo, Joe (2001).Music with Quarter-Tones: Experiences at the bichromatic harmonium.U.S.: J. Monzo.
  • Rees, Carla (2007). "Eva Kingma and the quarter-tone flute".Pan: The Flute Magazine.26(4): 23–29.
  • Rewoldt, Todd (2000). "Altissimo quarter-tones for the alto saxophone".Saxophone Symposium.25:56–69.

External links[edit]

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