View source for Microtonality

{{short description|Use in music of microtones (intervals smaller than a semitone)}}
{{For|sounds on the time scale shorter than musical notes|microsound}}
{{Redirect|Microtone|the slicing tool|Microtome}}
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|content=<score>{ \new Staff \with{ \magnifyStaff #2 \omit Score.TimeSignature } { \fixed c' <c disih g aisih>1 } }</score>
|caption=Composer Charles Ives chose the chord above as a good candidate for a "fundamental" chord in the quarter tone scale, akin not to the tonic but to the major chord of traditional tonality<ref>{{cite book | last = Boatwright | first = Howard | year = 1971 | chapter = Ives' Quarter-Tone Impressions | title = Perspectives on American Composers | editor1-first = Benjamin | editor1-last = Boretz | editor2-first = Edward T. | editor2-last = Cone | pages = 8–9 | location = Princeton | publisher = Princeton University Press | isbn = 978-0-393-02155-4}}</ref><br>[[File:Ives fundamental chord (quarter tones).ogg]]<br>[[File:Ives quarter tone fundamental chord arp.mid]]<br>Two examples of an Ives fundamental chord with quarter tones
}}

'''Microtonality''' is the use in music of microtones — [[interval (music)|intervals]] smaller than a [[semitone]], also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western [[Equal temperament#Twelve-tone equal temperament|tuning of twelve equal intervals per octave]]. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in [[equal temperament]].

==Terminology==

=== Microtone ===
{{Image frame
|content=<score>{ \new Staff \with{ \magnifyStaff #2 \omit Score.TimeSignature } \fixed c' { beh bes \tweak Accidental.stencil #ly:text-interface::print \tweak Accidental.text \markup { \musicglyph #"accidentals.flatflat.slash" } beseh beseh! bih bis bisih } }</score>
|caption=[[Quarter tone]] [[Accidental (music)|accidentals]] residing outside the Western [[semitone]]: <br>quarter tone flat, [[flat (music)|flat]], (two variants of) three quarter tones flat;<br>quarter tone sharp, [[Sharp (music)|sharp]], three quarter tones sharp
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''Microtonal music'' can refer to any music containing microtones. The words "microtone" and "microtonal" were coined before 1912 by [[Maud MacCarthy (Omananda Puri)|Maud MacCarthy Mann]] in order to avoid the misnomer "[[quarter tone]]" when speaking of the [[Shruti (music)|srutis]] of Indian music.<ref>{{cite journal | last = Mann | first = Maud (MacCarthy) | date = 16 January 1912 | title = Some Indian Conceptions of Music |journal=Proceedings of the Musical Association, 38th Session (1911–1912) | page = 44}}</ref> Prior to this time the term "quarter tone" was used, confusingly, not only for an interval actually half the size of a semitone, but also for all intervals (considerably) smaller than a semitone.<ref>{{cite journal | author-link = Alexander John Ellis | last = Ellis | first = Alexander J. | date = 25 May 1877 | title = On the Measurement and Settlement of Musical Pitch |journal=[[Journal of the Society of Arts]]| volume = 25 | number = 1279 | page = 665}}</ref><ref>{{cite journal | last = Meyer | first = Max | date = July–October 1903 | title = Experimental Studies in the Psychology of Music |journal=[[American Journal of Psychology]]| volume = 14 | number = 3–4 | pages = 192–214| doi = 10.2307/1412315 | jstor = 1412315 }}</ref> It may have been even slightly earlier, perhaps as early as 1895, that the Mexican composer [[Julián Carrillo]], writing in Spanish or French, coined the terms ''microtono''/''micro-ton'' and ''microtonalismo''/''micro-tonalité''.<ref name=Donval-2006-p119>{{cite book | last = Donval | first = Serge | date = 2006 | title = Histoire de l'acoustique musicale | location = Courlay | publisher = Fuzeau | isbn = 978-2-84169-152-4 | type = paperback | page = 119}}</ref>

In French, the usual term is the somewhat more self-explanatory ''micro-intervalle'', and French sources give the equivalent German and English terms as ''Mikrointervall'' (or ''Kleinintervall'') and ''micro interval'' (or ''microtone''), respectively.<ref>{{cite encyclopedia | author-link = Gilbert Amy | last = Amy | first = Gilbert | date = 1961 | contribution = Micro-intervalle | encyclopedia = Encyclopédie de la musique | editor-first = François | editor-last = Michel | others = in collaboration with [[François Lesure]] and Vladimir Fèdorov | location = Paris | publisher = Fasquelle}}</ref><ref>{{cite encyclopedia | url = https://books.google.com/books?id=qQcTAQAAMAAJ&q=%22micro-intervalle%22 | entry = Micro-intervalle | encyclopedia = Nouveau Larousse encyclopédique | edition = Second | editor-first = Yves | editor-last = Garnier | volume = 2: Kondratiev-Zythum | page = 1011 | location = Paris | publisher = Larousse | isbn = 978-2-03-153132-6| title = Nouveau Larousse encyclopédique: Kondratiev-Zythum | year = 1998 }}</ref><ref>{{cite book | last = Wallon | first = Simone | year = 1980 | title = L'allemand musicologique | series = Guides Musicologiques | location = Paris | publisher = Editions Beauchesne | isbn = 2-7010-1011-X | page = 13}}</ref><ref>{{cite book | last = Whitfield | first = Charles | year = 1989 | title = L'anglais musicologique: l'anglais des musiciens | series = Guides Musicologiques | location = Paris | publisher = Editions Beauchesne | isbn = 2-7010-1181-7 | page = 13}}</ref> "Microinterval" is a frequent alternative in English, especially in translations of writings by French authors and in discussion of music by French composers.<ref>{{cite journal | last1 = Battier | first1 = Marc | first2 = Thierry | last2 = Lacino | date = 1984 | title = Simulation and Extrapolation of Instrumental Sounds Using Direct Synthesis at IRCAM (''A Propos'' of ''Resonance'') | journal = Contemporary Music Review | volume = 1 (Musical Thought at IRCAM, edited by Tod Machover) | pages = 77–82| doi = 10.1080/07494468400640081 | hdl = 2027/spo.bbp2372.1982.033 | hdl-access = free }}</ref><ref>{{cite journal | last = Boulez | first = Pierre | year = 1958 | title = At the Ends of Fruitful Land ... | translator-first = Alexander | translator-last = Goehr | journal = [[Die Reihe]] | volume = 1, Electronic Music | edition = English | pages = 22–23}}</ref><ref>{{cite book | last = Rae | first = Caroline | year = 2013 | contribution = Messiaen and Ohana: Parallel Preoccupations or Anxiety of Influence? | title = Messiaen Perspectives 2: Techniques, Influence and Reception | editor1-first = Robert | editor1-last = Fallon | editor2-first = Christopher | editor2-last = Dingle | pages = 164, 174n40 | location = Farnham | publisher = Ashgate Publishing, Ltd. | isbn = 978-1-4094-2696-7}}</ref> In English, the two terms "microtone" and "microinterval" are synonymous.<ref>{{cite book | last = Maclagan | first = Susan J. | year = 2009 | title = A Dictionary for the Modern Flutist | location = Lanham, MS, and Plymouth | publisher = Scarecrow Press, Inc. | isbn = 978-0-8108-6711-6 | page = 109}}</ref> The English analogue of the related French term, ''micro-intervalité'', however, is rare or nonexistent, normally being translated as "microtonality"; in French, the terms ''micro-ton'', ''microtonal'' (or ''micro-tonal''), and ''microtonalité'' are also sometimes used, occasionally mixed in the same passage with ''micro-intervale'' and ''micro-intervalité''.<ref name=Donval-2006-p119 /><ref>Donval (2006), p. 183.</ref><ref>{{cite book | author-link = :fr:Franck Jedrzejewski | last = Jedrzejewski | first = Franck | year = 2014 | title = Dictionnaire des musiques microtonales: 1892–2013 | trans-title = Dictionary of Microtonal Musics: 1892–2013 | language = fr | location = Paris | publisher = L'Harmattan | isbn = 978-2-343-03540-6 | pages = [[List of Latin phrases (P)#passim|passim]]}}</ref><ref>{{cite book | last = Rigoni | first = Michel | year = 1998 | title = Karlheinz Stockhausen: ... un vaisseau lancé vers le ciel | language = fr | edition = Second, revised, corrected, and enlarged | series = Musique de notre temps: compositeurs | location = Lillebonne | publisher = Millénaire III Éditions | isbn = 978-2-911906-02-2 | page = 314}}</ref>

[[Ezra Sims]], in the article "Microtone" in the second edition of the ''[[Harvard Dictionary of Music]]'' defines "microtone" as "an interval smaller than a semitone",<ref>{{cite book | last = Apel | first = Will | year = 1974 | title = The Harvard Dictionary of Music | edition = Second | location = Cambridge, Massachusetts, USA | publisher = Harvard University Press | page = 527}}</ref> which corresponds with [[Aristoxenus]]'s use of the term ''[[diesis]]''.<ref>{{cite book | last = Richter | first = Lukas | year = 2001 | chapter = Diesis (ii) | title = [[The New Grove Dictionary of Music and Musicians]] | edition = Second | editor1-first = Stanley | editor1-last = Sadie | editor1-link = Stanley Sadie | editor2-first = John | editor2-last = Tyrrel | editor2-link = John Tyrrell (musicologist) | location = London | publisher = Macmillan Publishers}}</ref> However, the unsigned article "Comma, Schisma" in the same reference source calls [[Comma (music)|comma]], [[schisma]], and [[diaschisma]] "microintervals" but not "microtones",<ref>Apel (1974), p. 188.</ref> and in the fourth edition of the same reference (which retains Sims's article on "Microtone") a new "Comma, Schisma" article by André Barbera calls them simply "intervals".<ref>{{cite book | last = Barbera | first = André | year = 2003 | chapter = Comma, Schisma | title = Harvard Dictionary of Music | edition = Fourth | editor-first = Don Michael | editor-last = Randel | page = 193 | location = Cambridge, Massachusetts, USA | publisher = The Belknap Press of Harvard University Press | isbn = 978-0-674-01163-2}}</ref> In the second edition of ''[[The New Grove Dictionary of Music and Musicians]]'', [[Paul Griffiths (writer)|Paul Griffiths]], [[Mark Lindley]], and Ioannis Zannos define "microtone" as a musical rather than an acoustical entity: "any musical interval or difference of pitch distinctly smaller than a semitone", including "the tiny [[enharmonic]] melodic intervals of [[ancient Greece]], the several divisions of the [[octave]] into more than 12 parts, and various discrepancies among the intervals of [[just intonation]] or between a sharp and its enharmonically paired flat in various forms of [[mean-tone temperament]]", as well as the Indian [[Shruti (music)|sruti]], and small intervals used in [[Byzantine chant]], [[Arabic music#Characteristics of Arabic music|Arabic music theory]] from the 10th century onward, and similarly for [[Persian traditional music]] and [[Turkish music]] and various other Near Eastern musical traditions,<ref name="Griffiths-Lindley-Zannos-2001">{{cite book | last1 = Griffiths | first1 = Paul | first2 = Mark | last2 = Lindley | first3 = Ioannis | last3 = Zannos | year = 2001 | chapter = Microtone | title = [[The New Grove Dictionary of Music and Musicians]] | edition = Second | editor1-first = Stanley | editor1-last = Sadie | editor2-link = John Tyrrell (musicologist) | editor2-first = John | editor2-last = Tyrrell | location = London | publisher = Macmillan Publishers}}</ref> but do not actually name the "mathematical" terms schisma, comma, and diaschisma.

"Microtone" is also sometimes used to refer to individual notes, "microtonal pitches" added to and distinct from the familiar twelve notes of the chromatic scale,<ref>{{cite book | last = Von Gunden | first = Heidi | year = 1986 | title = The Music of Ben Johnston | location = Metuchen (New Jersey, USA) and London (England) | publisher = The Scarecrow Press, Inc. | isbn = 0-8108-1907-4 | page = 59}}</ref> as "enharmonic microtones",<ref>{{cite book | last = Barbieri | first = Patrizio | year = 2008 | title = Enharmonic instruments and music 1470–1900 | location = Latina, Italy | publisher = Il Levante Libreria Editrice | isbn = 978-88-95203-14-0 | page = 139}}</ref> for example.

In English the word "microtonality" is mentioned in 1946 by [[Rudi Blesh]] who related it to microtonal inflexions of the so-called "[[blues scale]]s".<ref>{{cite book | author-link = Rudi Blesh | last = Blesh | first = Rudi | year = 1946 | title = Shining Trumpets: A History of Jazz | location = New York | publisher = Alfred A. Knopf | page = 234}}</ref> In Court B. Cutting's 2019 ''Microtonal Analysis of “Blues Notes” and the Blues Scale'', he states that academic studies of the early blues concur that its pitch scale has within it three microtonal “blue notes” not found in 12 tone equal temperament intonation.<ref>{{Cite journal |last=Cutting |first=Court B|date=2019-01-17 |title=Microtonal Analysis of "Blue Notes" and the Blues Scale |url=http://emusicology.org/article/view/6316 |journal=[[Empirical Musicology Review]]|volume=13 |issue=1–2 |page=84 |doi=10.18061/emr.v13i1-2.6316 |issn=1559-5749|doi-access=free }}</ref> It was used still earlier by [[William Gray McNaught|W. McNaught]] with reference to developments in "modernism" in a 1939 record review of the ''Columbia History of Music, Vol. 5''.<ref>{{cite journal | last = McNaught | first = W. | date = February 1939 | title = Gramophone Notes |journal=[[The Musical Times]]| volume = 80 | number = 1152 | pages = 102–104| doi = 10.2307/923814 | jstor = 923814 }}</ref> In German the term ''Mikrotonalität'' came into use at least by 1958,<ref>{{cite book | last = Prieberg | first = Fred K. | date = 1958 | title = Lexikon der Neuen Musik | location = Freiburg im Breisgau and Munich | publisher = K. Alber | page = 288}}</ref><ref>{{cite book | last = Prieberg | first = Fred K. | date = 1960 | title = Musica ex machina: über das Verhältnis von Musik und Technik | location = Berlin, Frankfurt, and Vienna | publisher = Verlag Ullstein | pages = 29–32, 210–212, ''[[List of Latin phrases (I)|inter alia]]''}}</ref> though "Mikrointervall" is still common today in contexts where very small intervals of early European tradition (diesis, comma, etc.) are described, as e.g. in the new ''Geschichte der Musiktheorie''<ref>{{cite book | last = Zaminer | first = Frieder | date = 2006 | chapter = Harmonik und Musiktheorie im alten Griechenland | title = Geschichte der Musiktheorie, Vol. 2 | editor1-link = Thomas Ertelt | editor1-first = Thomas | editor1-last = Ertelt | editor2-link = Heinz von Loesch | editor2-first = Heinz | editor2-last = von Loesch | editor3-first = Frieder | editor3-last = Zaminer | location = Darmstadt | publisher = Wissenschaftliche Buchgesellschaft | isbn = 3-534-01202-X | page = 94}}</ref> while "Mikroton" seems to prevail in discussions of the [[avant-garde music]] and music of Eastern traditions.{{citation needed|date=August 2019}}<!-- search results on Google overwhelming dominated by commercial links to Mikroton Recordings --> The term "microinterval" is used alongside "microtone" by American musicologist Margo Schulter in her articles on [[medieval music]].<ref>{{cite web | url = http://www.medieval.org/emfaq/harmony/pyth.html | last = Schulter | first = Margo | date = 10 June 1998 | title = Pythagorean Tuning and Medieval Polyphony | publisher = Medieval Music and Arts Foundation | editor-first = Todd | editor-last = McComb | access-date = 2 February 2016}}</ref><ref>{{cite web | url = http://www.medieval.org/emfaq/harmony/marchetmf.html | last = Schulter | first = Margo | date = 2 March 2001 | title = Xenharmonic Excursion to Padua, 1318: Marchettus, the Cadential Diesis, and Neo-Gothic Tunings | publisher = Medieval Music and Arts Foundation | editor-first = Todd | editor-last = McComb | access-date = 2 February 2016}}</ref>

=== Microtonal ===
The term "microtonal music" usually refers to music containing very small intervals but can include any tuning that differs from Western twelve-tone [[equal temperament]]. Traditional Indian systems of 22 [[Śruti (music)|śruti]]; Indonesian [[gamelan|gamelan music]]; Thai, Burmese, and African music, and music using [[just intonation]], [[meantone temperament]] or other alternative tunings may be considered microtonal.<ref name="Griffiths-Lindley-1980">{{cite book | author1-link = Paul Griffiths (writer) | last1 = Griffiths | first1 = Paul | author2-link = Mark Lindley | first2 = Mark | last2 = Lindley | year = 1980 | chapter = Microtone | title = [[The New Grove Dictionary of Music and Musicians]] | editor-first = Stanley | editor-last = Sadie | editor-link = Stanley Sadie | volume = 12 | pages = 279–280 | location = London | publisher = Macmillan Publishers | isbn = 1-56159-174-2}}</ref><ref name="Griffiths-Lindley-Zannos-2001"/> Microtonal variation of intervals is standard practice in the African-American musical forms of [[spirituals]], [[blues]], and [[jazz]].<ref>{{cite book | last1 = Cook | first1 = Nicholas | first2 = Anthony | last2 = Pople | year = 2004 | title = The Cambridge History of Twentieth-Century Music | location = Cambridge and New York| publisher = Cambridge University Press | isbn = 0-521-66256-7 | pages = 124–126}}</ref>

Many microtonal equal divisions of the octave have been proposed, usually (but not always) in order to achieve approximation to the intervals of [[just intonation]].<ref name="Griffiths-Lindley-1980"/><ref name="Griffiths-Lindley-Zannos-2001"/>

Terminology other than "microtonal" has been used or proposed by some theorists and composers. In 1914, [[A. H. Fox Strangways]] objected that "'heterotone' would be a better name for śruti than the usual translation 'microtone'".<ref>{{cite book | last = Strangways | first = A. H. Fox | year = 1914 | url = https://archive.org/details/musicofhindostan025091mbp | title = The Music of Hindostan | location = Oxford | publisher = Clarendon Press | page = 127n1}}</ref> Modern Indian researchers yet write: "microtonal intervals called shrutis".<ref>{{citation | last1 = Datta | first1 = Asoke Kumar | first2 = Ranjan | last2 = Sengupta | first3 = Nityananda | last3 = Dey | first4 = Dipali | last4 = Nag | date = 2006 | title = Experimental Analysis of Shrutis from Performances in Hindustani Music | location = Kolkata | publisher = ITC Sangeet Research Academy | isbn = 81-903818-0-6 | page = 18}}</ref> In Germany, Austria, and Czechoslovakia in the 1910s and 1920s the usual term continued to be ''Viertelton-Musik'' (quarter tone music<ref>{{cite book | last = Möllendorff | first = Willy von | date = 1917 | title = Musik mit Vierteltönen | location = Leipzig | publisher = Verlag F. E. C. Leuckart|lccn=22022338|oclc=5842096 }}</ref>{{Page needed|date=July 2015}}<!--The mere fact that this book uses "Viertelton" in the title is not sufficient to verify that it was the usual term in Germany, Austria, and Czechoslovakia.-->), and the type of intervallic structure found in such music was called the ''Vierteltonsystem'',<ref>{{cite journal | last = Hába | first = Alois | date = 1921 | title = Harmonische Grundlagen des Vierteltonsystems | journal = Melos | volume = 3 | pages = 201–209}}</ref><ref>{{cite journal | last = Hába | first = Alois | date = 1922 | title = Vývoj hudební tvorby a theorie vzhledem k diatonice, chromatice a čtvrttónové soustavě | journal = Listy hudební matice| volume = 1 | pages = 35–40, 51–57}}</ref> which was (in the mentioned region) regarded as the main term for referring to music with microintervals, though as early as 1908 Georg Capellan had qualified his use of "quarter tone" with the alternative term "Bruchtonstufen (Viertel- und Dritteltöne)" (fractional degrees (quarter and third tones)).<ref>{{cite book | last = Capellen | first = Georg | date = 1908 | title = Fortschrittliche Harmonie- und Melodielehre | location = Leipzig | publisher = C. F. Kahnt Nachfolger | page = 184}}</ref> Despite the inclusion of other fractions of a whole tone, this music continued to be described under the heading "Vierteltonmusik" until at least the 1990s, for example in the twelfth edition of the ''[[Riemann Musiklexikon]]'',<ref>{{cite book | last = Riemann | first = Hugo | date = 1967 | chapter = Vierteltonmusik | title = [[Riemann Musiklexikon]]: Volume 3, Sachteil | edition = Twelfth fully revised | editor1-link = Wilibald Gurlitt | editor1-first = Wilibald | editor1-last = Gurlitt | editor2-link = Hans Heinrich Eggebrecht | editor2-first = Hans Heinrich | editor2-last = Eggebrecht | location = Mainz | publisher = B. Schott's Söhne | pages = 1032–1033}}</ref> and in the second edition of the popular ''Brockhaus Riemann Musiklexikon''.<ref>{{cite book | editor1-first = Carl | editor1-last = Dahlhaus | editor2-link = Hans Heinrich Eggebrecht | editor2-first = Hans Heinrich | editor2-last = Eggebrecht | editor3-first = Kurt | editor3-last = Oehl | date = 1995 | title = Brockhaus Riemann Musiklexikon in vier Bänden und einem Ergänzungsband, Volume 4 | trans-title = Brockhaus Riemann Music Lexicon in Four Volumes and a Supplementary Volume | edition = Second | location = Mainz | publisher = Atlantis-Schott Musikbuch-Verlag | page = 304}}</ref>

[[Ivan Wyschnegradsky]] used the term ''ultra-chromatic'' for intervals smaller than the semitone and ''infra-chromatic'' for intervals larger than the semitone;<ref>{{cite journal | last = Wyschnegradsky | first = Ivan | date = 1972 | title = L'Ultrachromatisme et les espaces non octaviants |journal=[[La Revue musicale]]| number = 290–91 | pages = 84–87}}</ref> this same term has been used since 1934 by ethnomusicologist Victor Belaiev (Belyaev) in his studies of Azerbaijan and Turkish traditional music.<ref>{{cite book | last = Belyaev | first = ((Victor M. [Беляев, В. М.])) | year = 1971 | chapter = Азербайджанская народная песня (1960) | trans-chapter = Azerbaijan Folk Songs | editor-first = Victor | editor-last = Belyaev | title = О музыкальном фольклоре и древней письменности | trans-title = On Musical Folklore and Ancient Literature | location = Moscow | publisher = Sov'etskii Kompozitor | pages = 108–156}}</ref><ref>{{cite book | last = Belyaev | first = ((Victor M. [Беляев, В. М.])) | year = 1971 | chapter = Турецкая музыка (1934) | trans-chapter = Turkish Music | editor-first = Victor | editor-last = Belyaev | title = О музыкальном фольклоре и древней письменности | trans-title = On Musical Folklore and Ancient Literature | location = Moscow | publisher = Sov'etskii Kompozitor | pages = 163–176}}</ref><ref>{{cite journal | first = Victor | last = Belaiev | title = Turkish Music [abridged English version]|journal=[[The Musical Quarterly]]| volume = 21 | number = 3 | date = July 1935 | pages = 356–367| doi = 10.1093/mq/XXI.3.356 }}</ref> A similar term, ''subchromatic'', has been used by theorist Marek Žabka.<ref>{{cite journal | last = Žabka | first = Marek | date = Fall 2014 | title = Dancing with the Scales: Subchromatic Generated Tone Systems |journal=[[Journal of Music Theory]]| volume = 58 | number = 2 | pages = 179–233| doi = 10.1215/00222909-2781769 }}</ref> [[Ivor Darreg]] proposed the term ''xenharmonic'' in March 1966;<ref>{{Cite web |title=Web archive of Xenharmonic Bulletin No. 1 - Xenarmonia A' (March 1966) |url=http://www.tonalsoft.com/sonic-arts/darreg/xallianc.htm |access-date=2024-12-24 |website=www.tonalsoft.com}}</ref> see [[Xenharmony|xenharmonic]] music. The [[Austria]]n composer {{ill|Franz Richter Herf|de}} and the music theorist Rolf Maedel, Herf's colleague at the [[Mozarteum University of Salzburg|Salzburg Mozarteum]], preferred using the Greek word ''ekmelic'' when referring to "all the pitches lying outside the traditional twelve-tone system".<ref>{{cite journal | last = Hesse | first = Horst-Peter | date = Winter 1991 | title = Breaking into a New World of Sound: Reflections on the Austrian Composer Franz Richter Herf (1920–1989) |journal=[[Perspectives of New Music]]| volume = 29 | number = 1 | pages = 212–235| doi = 10.2307/833077 | jstor = 833077 }}</ref> Some authors in Russia<ref>{{cite encyclopedia | year = 1990 | lang = ru | contribution = Микрохроматика | trans-contribution = Mikrochromatika / Microchromatics | title = Музыкальный энциклопедический словарь | trans-title = Musical Encyclopedic Dictionary | page = 344 | location = Moscow | publisher = Sov'etskaya Entsiklopediya}}</ref><ref>{{cite encyclopedia | year = 2007 | lang = ru | contribution = Микрохроматические интервалы | trans-contribution = Mikrochromaticheskie Intervali / Microchromatic Intervals | title = Музыкальный словарь Гроува | trans-title = Grove Music Dictionary | edition = Second | page = 563 | location = Moscow | publisher = Praktika}}</ref><ref>{{cite book | last = Akopyan | first = Levon | language = ru | title = Музыка ХХ века. Энциклопедический словарь | trans-title = Music of the Twentieth Century: An Academic Dictionary | pages = 353–354 | location = Moscow | publisher = Praktika}}</ref><ref>{{cite book | editor-last = Tsenova | editor-first = ((V. S. [Ценова, В. С.])) | year = 2007 | title = Теория современной композиции | trans-title = The Theory of Modern Composition | language = ru | location = Moscow | publisher = Muzyka | pages = 65, 123, 152 etc.}}</ref><ref>{{citation | first1 = Y. [Ю. ХОЛОПОВ] | last1 = Kholopov | first2 = L. [л. КИРИЛЛИНА] | last2 = Kirillina | first3 = T. [Т. КЮРЕГЯН] | last3 = Kyuregyan | first4 = G. [г. ЛЫЖОВ] | last4 = Lyzhov | first5 = R. [Р. ПОСПЕЛОВА] | last5 = Pospelova | first6 = V. [В. ЦЕНОВА] | last6 = Tsenova | year = 2006 | title = Музыкально-теоретические системы | trans-title = Musical-Theoretical Systems | language = ru | location = Moscow | publisher = Kompozitor | pages = 86 etc. | url = http://www.kholopov.ru/mts-kholopov%20(etc).pdf }}</ref><ref>{{citation | last = Kholopov | first = Yuri N. [ю.н.холопов] | year = 2003 | title = Гармония. Теоретический курс | trans-title = Harmony: Theoretical Course | language = ru | location = St Petersburg | publisher = Lan | isbn = 5-8114-0516-2 | pages = 172 etc. | url = http://www.kholopov.ru/harmony/kholopov-harm-theor.pdf }}</ref> and some musicology dissertations<ref>{{cite thesis |last= Klishin |first= A. G. |date= 2010 |title= Проблемы музыкального строя в начале Нового времени | trans-title = Problems of Musical Structure in the Early Modern Era |type= PhD diss. | location = Moscow |publisher= [[Moscow Conservatory]] }}</ref><ref>{{cite thesis |last= Gurenko |first= N.A. [Гуренко Н.А] |date= 2010 |title= Микрохроматика И. Вышнеградского: История, теория, практика освоения | trans-title = The Microchomatics of I. Wyschnegradsky: History, Theory, Practice, Development |type= PhD diss. |publisher= [[Urals Mussorgsky State Conservatoire]] }}</ref><ref>{{cite thesis |last= Polunina |first= E. N. [Полунина Е.Н.] |date= 2010 |title= Микрохроматика в музыкальном искусстве позднего Возрождения | trans-title = Microchromatics in Music of the Late Renaissance |type= PhD diss. | location = Vladivostok |publisher= Far East State Academy of Arts }}</ref><ref>{{cite thesis |last= Rovner |first= A. A. |date= 2010 |title= Сергей Протопопов: композиторское творчество и теоретические работы | trans-title = Sergey Protopopov: composer's output and theoretical works |type= PhD diss. | location = Moscow |publisher= [[Moscow Conservatory]] }}</ref><ref>{{cite thesis |last= Nikoltsev |first= I. D. |date= 2013 |title= Микрохроматика в системе современного музыкального мышления | trans-title = Microchomatics in Contemporary Musical Thought |type= PhD diss. | location = Moscow |publisher= [[Moscow Conservatory]] }}</ref><ref>More references can be located on the ''disserCat'' website, at {{cite web | url = http://www.dissercat.com/search?keys=%D0%BC%D0%B8%D0%BA%D1%80%D0%BE%D1%85%D1%80%D0%BE%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 | title = Поиск диссертаций | trans-title = Search for dissertations}}</ref> disseminate the term [[:ru:Микрохроматика|''микрохроматика'']] (microchromatics), coined in the 1970s by [[Yuri Kholopov]],<ref>{{cite encyclopedia | author-link = Yuri Kholopov | last = Kholopov | first = Yuri Nikolaevich [Холопов Ю.Н.] | date = 1976 | chapter = Микрохроматика | trans-chapter = Microchromatics | title = Музыкальная энциклопедия | trans-title = Musical Encyclopedia | volume = 3 | pages = 587–589 | location = Moscow | publisher = Bolshaya Sovetskaya Entsiklopedia [Great Soviet Encyclopedia]}}</ref> to describe a kind of 'intervallic genus' ([[:ru:Роды интервальных систем|интервальный род]]) for all possible microtonal structures, both ancient (as enharmonic genus—γένος ἐναρμόνιον—of Greeks) and modern (as quarter tone scales of [[Alois Haba]]); this generalization term allowed also to avoid derivatives such as ''микротональность'' (microtonality, which could be understood in Russian as a sub-[[tonality]], which is subordinate to the dominating tonality, especially in the context of European music of the 19th century) and ''микротоника'' (microtonic, "a barely perceptible [[tonic (music)|tonic]]"; see a clarification in Kholopov [2000]<ref>{{cite book | author-link = Yuri Kholopov | last = Kholopov | first = Y. N. [Холопов Ю.Н.] | date = 2000 | chapter = Микро и последствия | trans-chapter = Micro and consequences | title = Музыкальное образование в контексте культуры | trans-title = Music education in the cultural context | pages = 27–38 | location = Moscow | publisher = Gnessins Music Academy}}</ref>). Other Russian authors use the more international adjective 'microtonal' and have rendered it in Russian as 'микротоновый', but not 'microtonality' ('микротональность').<ref>{{cite book | last = Kogut | first = Gennady. A. | date = 2005 | title = Микротоновая музыка | trans-title = Microtonal Music | language = ru | location = Kyiv | publisher = Naukova Dumka | isbn = 966-00-0604-7}}</ref><ref>{{cite thesis | last = Adèr | first = ((Lidiâ Olegovna [Адэр, Лидия Олеговна])) | date = 2013 | title = Микротоновая музыка в Европе и России в 1900–1920–е годы | trans-title = Microtonic music in Europe and Russia in the 1900s–1920s | type = Non-doctoral diss. | location = St. Petersburg | publisher = [[Saint Petersburg Conservatory|Gosudarstvennaâ Konservatoriâ imeni N.A. Rimskogo-Korsakova]]}}</ref><ref>{{cite journal | last1 = Pavlenko | first1 = Sergej Vasil'evič | first2 = Igor' | last2 = Kefalidi | first3 = Viktor Alekseevič | last3 = Ekimovskij | date = 2002 | title = Микротоновые элементы: Беседа | trans-title = Microtonal Elements: A Conversation | journal = Музыкальная Академия [Muzykal'naâ akademiâ] | volume = 2 | pages = 21–24}}</ref><ref>{{Cite web|url=https://www.dissercat.com/search?q=%D0%BC%D0%B8%D0%BA%D1%80%D0%BE%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D1%8B%D0%B9&year=&cat= |title=Поиск диссертаций: микротоновый – Результат поиска, документов найдено: 14 | trans-title = Dissertation search: микротоновый – Search result, documents found: 14 |website=disserCat | access-date = 14 December 2020}}</ref> However, the terms 'микротональность'<ref>{{Cite web|url=https://www.dissercat.com/search?q=%D0%BC%D0%B8%D0%BA%D1%80%D0%BE%D1%82%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C&year=&cat= |title=Поиск диссертаций: микротональность – Результат поиска, документов найдено: 1 | trans-title = Dissertation search: микротональность – Search result, documents found: 1 |website=disserCat | access-date = 14 December 2020}}</ref> and 'микротоника'<ref>{{Cite web|url=https://www.dissercat.com/search?q=%D0%BC%D0%B8%D0%BA%D1%80%D0%BE%D1%82%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0&year=&cat= |title=Поиск диссертаций: микротоника – Результат поиска, документов найдено: 1 | trans-title = Dissertation search: микротоника – Search result, documents found: 1 |website=disserCat | access-date = 14 December 2020}}</ref> are also used. Some authors writing in French have adopted the term "micro-intervallique" to describe such music.<ref>{{cite book | last = Criton | first = Pascale | date = 2010 | chapter = Variabilité et multiplicité acoustique | trans-chapter = Variability and acoustic multiplicity | title = Manières de faire des sons | trans-title = Ways of making sounds | language = fr | editor1-link = Antonia Soulez | editor1-first = Antonia | editor1-last = Soulez | editor2-first = Horacio | editor2-last = Vaggione | pages = 119–133 | series = Musique-philosophie | location = Paris | publisher = L'Harmattan | isbn = 978-2-296-12959-7}}</ref><ref>{{cite book | author-link = :fr:Franck Jedrzejewski | last = Jedrzejewski | first = Franck | year = 2004 | contribution = Alois Hába et l'expérimentation micro-intervallique | title = L'attraction et la nécessité: Musique tchèque et culture française au XXe siècle | editor1-first = Xavier | editor1-last = Galmiche | editor2-first = Lenka | editor2-last = Stránská | pages = 169–175 | location = Paris | publisher = [[Paris-Sorbonne University|Université Paris-Sorbonne (Paris IV)]] | isbn = 978-80-86385-27-3}}</ref> Italian musicologist Luca Conti dedicated two of his monographs to ''microtonalismo'',<ref>{{citation | last = Conti | first = Luca | date = 2005 | title = Suoni di una terra incognita: il microtonalismo in Nord America (1900–1940) | trans-title = Sounds of an unknown land: microtonalism in North America (1900–1940) | language = it | location = Lucca | publisher = Libreria musicale italiana}}</ref><ref>{{citation | last = Conti | first = Luca | date = 2008 | title = Ultracromatiche sensazioni: il microtonalismo in Europa (1840–1940) | trans-title = Ultrachromatic sensations: microtonalism in Europe (1840–1940) | language = it | location = Lucca | publisher = Libreria musicale italiana}}</ref> which is the usual term in Italian, and also in Spanish (e.g., as found in the title of Rué [2000]<ref>{{cite journal | last = Rué | first = Roberto | date = 2000 | title = Diatonismo, cromatismo y microtonalismo: Una interpretación estructuralista | trans-title = Diatonism, chromaticism and microtonalism: A structuralist interpretation | language = es | journal = Música e investigación: Revista del Instituto Nacional de Musicología "Carlos Vega" | trans-journal = Music and research: Magazine of the National Institute of Musicology "Carlos Vega" | volume = 4 | number = 7–8 | pages = 39–53}}</ref>). The analogous English form, "microtonalism", is also found occasionally instead of "microtonality", e.g., "At the time when serialism and neoclassicism were still incipient a third movement emerged: microtonalism".<ref>{{cite journal | last = Chou | first = Wen-chung | date = April 1971 | title = Asian Concepts and Twentieth-Century Western Composers |journal=[[The Musical Quarterly]]| volume = 57 | number = 2 | pages = 211–229}}</ref>

The term "macrotonal" has been used for intervals wider than twelve-tone equal temperament,<ref>{{cite web | date = n.d. | url = http://xenharmonic.wikispaces.com/Macrotonal | archive-url = https://archive.today/20160714151212/http://xenharmonic.wikispaces.com/Macrotonal | url-status = dead | archive-date = July 14, 2016 | title = Macrotonal | work = Xenharmonic Wiki blog at macrospaces.com | access-date = 3 February 2016 }}</ref>{{better source needed|date=December 2020}} or where there are "fewer than twelve notes per octave", though "this term is not very satisfactory and is used only because there seems to be no other".<ref>{{cite book | last = Pressing | first = Jeff | date = 1992 | title = Synthesizer Performance and Real-time Techniques | location = Madison | publisher = A-R Editions | isbn = 978-0-89579-257-0 | page = 239}}</ref> The term "macrotonal" has also been used for musical form.<ref>{{cite book | last1 = Spring | first1 = Glenn | first2 = Jere | last2 = Hutcheson | date = 2013 | title = Musical Form and Analysis: Time, Pattern, Proportion | location = Long Grove | publisher = Waveland Press, Inc. | isbn = 978-1-4786-0722-9 | page = 82}}</ref>

Examples of this can be found in various places, ranging from [[Claude Debussy]]'s impressionistic harmonies to [[Aaron Copland]]'s chords of stacked fifths, to [[John Luther Adams]]' ''Clouds of Forgetting'', ''Clouds of Unknowing'' (1995), which gradually expands stacked-interval chords ranging from minor 2nds to major 7thsm. [[Louis Andriessen]]'s ''De Staat'' (1972–1976) contains a number of "augmented" modes that are based on Greek scales but are asymmetrical to the octave.<ref>{{citation | last = Adlington | first = Robert | date = 2004 | title = Louis Andriessen, De Staat | location = Hants, UK | publisher = Ashgate Publishing | page = 88}}
</ref>

==History==
{{Image frame|width=280
|content=<score>{ \omit Score.TimeSignature \relative c' { \override NoteHead.duration-log = #0 \hide Stem e feh geses a b ceh deses e } }</score>
|caption=[[File:Greek Dorian mode on E, enharmonic genus.mid]]<br>Greek Dorian mode ([[Genus (music)#Enharmonic|enharmonic genus]]) on E, divided into two tetrachords.
}}

The Hellenic civilizations of ancient Greece left fragmentary records of their music, such as the [[Delphic Hymns]]. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining [[tetrachord]]s, recognizing three [[Genus (music)|genera]] of tetrachords: the enharmonic, the chromatic, and the diatonic. Ancient Greek intervals were of many different sizes, including microtones. The enharmonic genus in particular featured intervals of a distinctly "microtonal" nature, which were sometimes smaller than 50&nbsp;[[cent (music)|cents]], less than half of the contemporary [[Occidental culture|Western]] [[semitone]] of 100&nbsp;cents. In the ancient Greek [[enharmonic scale|enharmonic genus]], the tetrachord contained a semitone of varying sizes (approximately 100&nbsp;cents) divided into two equal intervals called [[diesis|dieses]] (single "diesis", {{math|δίεσις}}); in conjunction with a larger interval of roughly 400&nbsp;cents, these intervals comprised the perfect fourth (approximately 498&nbsp;cents, or the frequency ratio of {{small|{{sfrac| 4 | 3 }}}} in [[just intonation]]).<ref>{{cite book | last = West | first = Martin Litchfield | year = 1992 | title = Ancient Greek Music | location = Oxford, UK | publisher = Clarendon Press | isbn = 0-19-814897-6 | pages = 160–172}} (paperback {{ISBN|0-19-814975-1}})</ref> Theoretics usually described several diatonic and chromatic genera (some as chroai, "coloration" of one specific intervallic type), but the enarmonic genus was always the only one (argumented as one with the smallest intervals possible).

[[File:Archicembalo en Cents.jpg|thumb|upright=1.5|Vicentino's archicembalo in cents]]
[[Guillaume Costeley]]'s "Chromatic Chanson", "Seigneur Dieu ta pitié" of 1558 used {{nobr|{{small|{{sfrac| 1 | 3 }}}} comma}} [[meantone temperament|meantone]] (which almost exactly equals [[19 equal temperament]]) and explored the full compass of 19&nbsp;pitches in the octave.<ref>{{cite encyclopedia | last = Lindley | first = Mark | year = 2001 | title = Mean-tone | encyclopedia = [[The New Grove Dictionary of Music and Musicians]] | edition = 2nd | editor1-first = Stanley | editor1-last = Sadie | editor1-link = Stanley Sadie | editor2-first = John | editor2-last = Tyrrell | editor2-link = John Tyrrell (professor of music) | location = London, UK | publisher = Macmillan Publishers }}
</ref>

The Italian [[Renaissance music|Renaissance]] composer and theorist [[Nicola Vicentino]] (1511–1576) worked with microtonal intervals and built a keyboard with 36 keys to the octave known as the [[archicembalo]]. While theoretically an interpretation of ancient Greek tetrachordal theory, in effect Vicentino presented a circulating system of quarter-comma [[meantone]], maintaining major thirds tuned in [[just intonation]] in all keys.<ref>{{cite book | last = Barbour | first = J. Murray | year = 2004 |orig-year = 1951 | title = Tuning and Temperament: A historical survey | location = East Lansing, MI (1951) / Mineola, NY (2004) | publisher = Michigan State College Press (1951) / Dover Books (2004) | edition = reprint | isbn = 0-486-43406-0 | pages = 117–118 }}</ref>

In 1760 the French flautist {{Interlanguage link|Charles de Lusse|lt=|de||WD=}} published a treatise, ''L'Art de la flute traversiere'', all surviving copies of which conclude with a composition (possibly added a year or two after the actual publication of the volume) incorporating several quarter tones, titled ''Air à la grecque'', accompanied by explanatory notes tying it to the realization of the Greek enharmonic genus and a chart of quarter tone fingerings for the entire range of the one-keyed flute. Shortly afterward, in a letter published in the ''Mercure de France'' in September&nbsp;1764, the celebrated flautist [[Pierre-Gabriel Buffardin]] mentioned this piece and expressed an interest in quarter tones for the flute.<ref>{{cite thesis | last = Koenig | first = Laura Jeanne | year = 1995 | title = Air à la grecque | quote = A quarter-tone piece for flute in the historical context of the enharmonic benre in eighteenth-century French music and theory | degree = [[Doctor of Musical Arts|DMA]] | location = Iowa City, IA | publisher = The University of Iowa | pages = {{math|''iii''}}, 1, 9–10, 52–55, 116–119}}</ref><ref>{{cite journal | last1 = Reilly | first1 = Edward R. | first2 = John | last2 = Solum | date = Spring 1992 | title = De Lusse, Buffardin, and an eighteenth-century quarter tone piece | journal = Historical Performance | pages = 19–23 }}</ref>

[[Jacques Fromental Halévy]] composed a cantata "Prométhée enchaîné" for a solo voice, choir and orchestra (premiered in 1849), where in one movement (''Choeur des Océanides'') he used quarter tones, to imitate the enharmonic genus of Greeks.

In the 1910s and 1920s, quarter tones received attention from such composers as [[Charles Ives]], [[Julián Carrillo]], [[Alois Hába]], [[Ivan Wyschnegradsky]], and [[Mildred Couper]].

[[Alexander John Ellis]], who in the 1880s produced a translation of [[Hermann Helmholtz]]'s ''On the Sensations of Tone'', proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings.<ref>{{cite book | author-link1 = Hermann von Helmholtz | last1 = von&nbsp;Helmholtz | first1 = Hermann | year = 1885 | title = On the Sensations of Tone as a Physiological Basis for the Theory of Music | title-link = On the Sensations of Tone | edition = 2nd |quote=Second English edition, translated, thoroughly revised and corrected, rendered conformable to the fourth (and last) German edition of 1877, with numerous additional notes and a new additional appendix bringing down information to 1885, and especially adapted to the use of music students |first2=Alexander J. |last2=Ellis | author2-link= Alexander John Ellis | location = London, UK | publisher = Longmans, Green | pages = 514–527 |language=en }} <!-- Ellis was not just an editor: He added extensive appendices with new material, expanding details beyond Helmholtz. --></ref> Ellis also studied the tunings of [[non-Western music|non-Western cultures]] and, in a report to the [[Royal Society]], stated that they used neither equal divisions of the octave nor just intonation intervals.<ref>{{cite journal | last = Ellis | first = Alexander J. | author-link = Alexander J. Ellis | year = 1884 | title = Tonometrical observations on some existing non-harmonic musical scales |journal=[[Proceedings of the Royal Society of London]] | volume = 37 | pages = 368–385 | bibcode = 1884RSPS...37..368E }}</ref> Ellis inspired [[Harry Partch]] immensely.<ref>{{cite book | last = Partch | first = Harry | author-link = Harry Partch | year = 1979 | title = [[Genesis of a Music]] | edition = 2nd | location = New York, NY | publisher = Da Capo Press | isbn = 0-306-80106-X | page = {{mvar|vii}} }}</ref>

During the [[Exposition Universelle (1889)|Exposition Universelle of 1889]], [[Claude Debussy]] heard a Balinese [[gamelan]] performance and was exposed to [[non-Western music|non-Western]] tunings and rhythms. Some scholars have ascribed Debussy's subsequent innovative use of the whole-tone (six equal pitches per octave) tuning in such compositions as the [[Fantaisie for piano and orchestra (Debussy)|''Fantaisie for piano and orchestra'']] and the Toccata from the suite ''[[Pour le piano]]'' to his exposure to the Balinese gamelan at the Paris exposition,<ref>{{cite encyclopedia | last = Lesure | first = François | author-link = François Lesure | year = 2001 | contribution = Debussy, (Achille-)Claude: §7,&nbsp;Models and influences | encyclopedia = [[The New Grove Dictionary of Music and Musicians]] | edition = 2nd | editor1-first = Stanley | editor1-last = Sadie | editor2-first = John | editor2-last = Tyrrell | location = London, UK | publisher = Macmillan Publishers }}</ref> and have asserted his rebellion at this time "against the rule of [[12 equal temperament|equal temperament]]" and that the gamelan gave him "the confidence to embark (after the 1900 world exhibition) on his fully characteristic mature piano works, with their many bell- and gong-like sonorities and brilliant exploitation of the piano's natural resonance".<ref>{{cite encyclopedia | last = Howat | first = Roy | year = 2001 | contribution = Debussy, (Achille-)Claude: §10,&nbsp;Musical language | encyclopedia = [[The New Grove Dictionary of Music and Musicians]] | edition = 2nd | editor1-first = Stanley | editor1-last = Sadie | editor2-first = John | editor2-last = Tyrrell | location = London, UK | publisher = Macmillan Publishers }}</ref> Still others have argued that Debussy's works like ''[[L'isle joyeuse]]'', ''[[La cathédrale engloutie]]'', ''[[Prélude à l'après-midi d'un faune]]'', ''[[La mer (Debussy)|La mer]]'', ''[[Pagodes]]'', ''[[Danseuses de Delphes]]'', and ''[[Cloches à travers les feuilles]]'' are marked by a more basic interest in the microtonal intervals found between the higher members of the overtone series, under the influence of Helmholtz's writings.<ref>{{cite journal | last = Don | first = Gary | date = Spring 2001 | title = Brilliant colors provocatively mixed: Overtone structures in the music of Debussy |journal=[[Music Theory Spectrum]] | volume = 23 | number = 1 | pages = 61–73 | doi = 10.1525/mts.2001.23.1.61 }}</ref> [[Emil Berliner]]'s introduction of the phonograph in the 1890s allowed much non-Western music to be recorded and heard by Western composers, further spurring the use of non-[[12 equal temperament|{{nobr|12 {{sc|EDO}}}}]] tunings.{{citation needed|date=June 2015}}

Major microtonal composers of the 1920s and 1930s include [[Alois Hába]] (quarter tones, or 24&nbsp;equal pitches per octave, and sixth tones), Julián Carrillo ([[24 equal temperament|{{nobr|24 {{sc|EDO}}}}]], 36, 48, 60, 72, and 96&nbsp;equal pitches to the octave embodied in a series of specially custom-built pianos), [[Ivan Wyschnegradsky]] (third tones, quarter tones, sixth tones and twelfth tones, non octaving scales) and the early works of [[Harry Partch]] (just intonation using frequencies at ratios of prime integers 3, 5, 7, and 11, their powers, and products of those numbers, from a central frequency of G-196).<ref>{{harvp|Partch|1979|pp=119–137}} (Chapter&nbsp;8, "Application of the 11&nbsp;limit").</ref>

Prominent microtonal composers or researchers of the 1940s and 1950s include [[Adriaan Daniel Fokker]] ([[31 equal temperament|{{nobr|31 {{sc|EDO}}}}]]), Partch (continuing to build his handcrafted orchestra of microtonal just intonation instruments), and [[Eivind Groven]].

Digital synthesizers from the [[Yamaha TX81Z]] (1987) on and inexpensive software synthesizers have contributed to the ease and popularity of exploring microtonal music.

==Microtonality in electronic music==
[[Electronic music]] facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems.<ref name="Griffiths-Lindley-Zannos-2001" /> In 1954, [[Karlheinz Stockhausen]] built his electronic ''[[Studie II]]'' on an 81-step scale starting from 100&nbsp;Hz with the interval of 5<sup>1/25</sup> between steps,<ref>{{cite book | last = Stockhausen | first = Karlheinz | year = 1964 | title = Texte 2: Aufsätze 1952–1962 zur musikalischen Praxis | trans-title = Texts 2: Essays on musical practice 1952–1962 | editor-first = Dieter | editor-last = Schnebel | location = Cologne | publisher = Verlag M. DuMont Schauberg | page = 37}}</ref> and in ''[[Gesang der Jünglinge]]'' (1955–56) he used various scales, ranging from seven up to sixty equal divisions of the octave.<ref>{{cite journal | last1 = Decroupet | first1 = Pascal | first2 = Elena | last2 = Ungeheuer | date = Winter 1998 | title = Through the Sensory Looking-Glass: The Aesthetic and Serial Foundations of Gesang der Jünglinge |translator=Jerome Kohl|translator-link=Jerome Kohl|journal=[[Perspectives of New Music]]| volume = 36 | number = 1 | pages = 105, 116, 119–121| doi = 10.2307/833578 | jstor = 833578 }}</ref> In 1955, [[Ernst Krenek]] used 13 equal-tempered intervals per octave in his Whitsun oratorio, ''Spiritus intelligentiae, sanctus''.<ref name="Griffiths-Lindley-Zannos-2001"/>

In 1979–80 Easley Blackwood composed a set of ''[[Twelve Microtonal Etudes for Electronic Music Media]],'' a cycle that explores all of the equal temperaments from 13 notes to the octave through 24 notes to the octave, including [[15 equal temperament|15-ET]] and [[19 equal temperament|19-ET]].<ref>{{citation | last1 = Blackwood | first1 = Easley | first2 = Jeffrey | last2 = Kust | year = 2005 | orig-year = 1996 | title = Easley Blackwood: Microtonal Compositions | edition = Second | publisher = [[Cedille Records]] }}</ref>{{Full citation needed|date=November 2014<!--Place of publication and ISBN needed.-->}}{{Page needed|date=November 2014}} "The project," he wrote, "was to explore the tonal and modal behavior of all [of these] equal tunings..., devise a notation for each tuning, and write a composition in each tuning to illustrate good chord progressions and the practical application of the notation".<ref>{{citation | last = Blackwood | first = Easley | date = n.d. | title = Liner notes to "Blackwood: Microtonal Compositions" [CDR018] | url = http://www.dramonline.org/albums/blackwood-microtonal-compositions/notes | publisher = [[Cedille Records]]}}</ref>{{Full citation needed|date=November 2014<!--To judge from the catalog number, presumably this is a CD rather than an LP or MP3 file, which should be specified, as well as the year of release and a place of publication, if given on the disc or accompanying booklet.-->}}

In 1986, [[Wendy Carlos]] experimented with many microtonal systems including [[just intonation]], using alternate tuning scales she invented for the album ''[[Beauty In the Beast]]''. "This whole formal discovery came a few weeks after I had completed the album, ''Beauty in the Beast'', which is wholly in new tunings and timbres".<ref>{{cite web | last = Carlos | first = Wendy | author-link = Wendy Carlos | date = 1989–1996 | url = http://www.wendycarlos.com/resources/pitch.html | title = Three Asymmetric Divisions of the Octave | work = wendycarlos.com | access-date = March 28, 2009}}</ref>

In 2016, electronic music composed with arbitrary microtonal scales was explored on the album ''Radionics Radio: An Album of Musical Radionic Thought Frequencies'' by British composer [[Meadow House|Daniel Wilson]], who derived his compositions' tunings from frequency-runs submitted by users of a custom-built [[web application]] replicating [[radionics|radionics-based]] electronic soundmaking equipment used by Oxford's [[George de la Warr|De La Warr Laboratories]] in the late 1940s, thereby supposedly embodying thoughts and concepts within the tunings.<ref>{{cite journal | last = Murphy | first = Ben | title = Making Waves | journal = Electronic Sound | date = January 2017 | number = 26 | pages = 70–75}}</ref>

Finnish artist [[Aleksi Perälä]] works exclusively in a microtonal system known as the Colundi sequence.<ref>{{Cite web |date=2019-01-10 |title="Colundi" is Music Tuned to Frequencies That Heal the Body |url=https://daily.bandcamp.com/lists/colundi-aleksi-perala-interview |access-date=2022-12-01 |website=Bandcamp Daily}}</ref><ref>{{Cite web |date=2021-11-01 |title=Igloo Magazine :: Aleksi Perälä (Ovuca) :: The original harmony of Human and Nature |url=https://igloomag.com/profiles/aleksi-perala-oct-2021 |access-date=2022-12-01 |language=en-US}}</ref>

===Limitations of some synthesizers===
The [[MIDI]] 1.0 specification does not directly support microtonal music, because each note-on and note-off message only represents one chromatic tone. However, microtonal scales can be emulated using [[pitch bend]]ing, such as in [[LilyPond]]'s implementation.<ref>{{cite web |author1=LilyPond project |author-link1=LilyPond |title=LilyPond – Notation Reference v2.21.7 (development-branch). |url=http://lilypond.org/doc/v2.21/Documentation/notation/supported-notation-for-midi |website=LilyPond |access-date=28 October 2020 |page=3.5.1 Supported notation for MIDI |language=en |quote=Microtones but ''not'' microtonal chords. A MIDI player that supports pitch bending will also be required.}}</ref>

Although some synthesizers allow the creation of customized microtonal scales, this solution does not allow compositions to be transposed. For example, if each B note is raised one quarter tone, then the "raised 7th" would only affect a C major scale.

==Microtonality in rock music==
Early microtonal guitars focused on issues with the 12-tone equal temperament system. In 1829, Thomas Perronet Thompson designed the Enharmonic Guitar that featured small holes where frets could be inserted. Later developments from Luthier René Lacôte and Paul Kochendorfer include an adjustable ebony-mounted frets and levers to simultaneously adjust multiple frets.<ref>{{Cite journal |last1=Acet |first1=Ruşen Can |last2=Başar |first2=Batuhan |last3=Çoğulu |first3=Tolgahan |last4=Çoğulu |first4=Atlas |last5=Italia |first5=Tony |last6=Keser |first6=Selçuk |date=2022-06-30 |title=New Additions to the Guitar Family: Lego and Automatic Microtonal Guitars |journal=Musicologist |language=en |volume=6 |issue=1 |pages=27–28 |doi=10.33906/musicologist.1079674 |issn=2618-5652|doi-access=free }}</ref> A form of microtone known as the [[blue note]] is an integral part of [[rock music]] and one of its predecessors, the blues. The blue notes, located on the third, fifth, and seventh notes of a diatonic major scale, are flattened by a variable microtone.<ref>{{cite book | last = Ferguson | first = Jim | author-link = Jim Ferguson | year = 1999 | title = All Blues Soloing for Jazz Guitar: Scales, Licks, Concepts & Choruses | series = Guitar Master Class | location = Pacific, Missouri, USA | publisher = Mel Bay | isbn = 0-7866-4285-8 | page = 20}}</ref> Joe Monzo has made a microtonal analysis of the song "Drunken Hearted Man",<ref>{{cite web | last = Monzo | first = Joe | date = 1998 | url = http://tonalsoft.com/monzo/rjohnson/drunken.aspx | title = A Microtonal Analysis of Robert Johnson's "Drunken Hearted Man"}}</ref> written and recorded by the delta blues musician [[Robert Johnson]].<ref name="Wilson-Penderecki-Greenwood-2012">{{cite episode | last1 = Wilson | first1 = John | first2 = Krzysztof | last2 = Penderecki | author2-link = Krzysztof Penderecki | first3 = Jonny | last3 = Greenwood | author3-link = Jonny Greenwood | title = Interview with Jonny and Krzysztof Penderecki | series = Front Row | air-date = 23 March 2012 | station = BBC Radio 4 | transcript = Transcript from an audio recording of the broadcast on Citizen Insane website | url = http://www.citizeninsane.eu/t2012-03-23BBCRadio4.htm | access-date = 21 July 2014 | url-status = dead | archive-url = https://web.archive.org/web/20150923203752/http://www.citizeninsane.eu/t2012-03-23BBCRadio4.htm | archive-date = 23 September 2015}}</ref>

Musicians such as [[Jon Catler]] have incorporated microtonal guitars like [[31 equal temperament|31-tone equal tempered]] guitar and a 62-tone [[just intonation]] guitar in blues and [[jazz rock]] music.<ref>{{cite web | last = Couture | first = François | date = n.d. | url = http://www.allmusic.com/album/evolution-for-electric-guitar-and-orchestra-mw0000979771 | title = Jon Catler: Evolution for Electric Guitar and Orchestra | work = AllMusic | access-date = 3 April 2013}}</ref>

English rock band [[Radiohead]] has used microtonal string arrangements in their music, such as on "How to Disappear Completely" from the album ''[[Kid A]]''.<ref name="Wilson-Penderecki-Greenwood-2012"/>

American band [[Secret Chiefs 3]] has been making its own custom "microtonal" instruments since the mid 1990s. The proprietary tuning system they use in their ''[[Ishraqiyun]]'' aspect is ratio-based, not equal temperament. The band's leader [[Trey Spruance]], also of [[Mr. Bungle]], challenges the terminology of "microtonality" as a development that instead of liberating tonal sensibility to a universe of diverse possibilities, both new and historical, instead mainly serves to reinforce the idea that the universal standard for "tone" is the (western) semitone.<ref><nowiki>{{cite web | url = </nowiki>[https://music.mxdwn.com/2015/11/10/reviews/secret-chiefs-3-ishraqiyun-perichoresis/ h] https://www.trebuchet-magazine.com/secret-chiefs-3-interview-with-trey-spruance/</ref>

Australian band [[King Gizzard and the Lizard Wizard]] utilises microtonal instruments, including custom microtonal guitars modified to play in [[Quarter tone|24-TET tuning]]. Tracks with these instruments appear on their albums ''[[Flying Microtonal Banana]]'',<ref>{{cite web | url = http://www.heavenlyrecordings.com/news/2016/11/king-gizzard-announce-a-new-album-flying-microtonal-banana/ | title = King Gizzard Announce a New Album, 'Flying Microtonal Banana' | author = Heavenly Recordings | date = 11 November 2016 | work = Heavenly Records | access-date = 29 March 2017 | url-status = dead | archive-url = https://web.archive.org/web/20161211175037/http://www.heavenlyrecordings.com/news/2016/11/king-gizzard-announce-a-new-album-flying-microtonal-banana/ | archive-date = 11 December 2016}}</ref> ''[[K.G. (album)|K.G]]'', and ''[[L.W. (album)|L.W.]]''.<ref>{{cite web | url = https://www.dailycal.org/2021/03/04/l-w-proves-king-gizzard-the-lizard-wizard-can-master-microtonality-a-third-time/| title = 'L.W.' proves King Gizzard & the Lizard Wizard can master microtonality a third time | author = Pooja Bale | date = 4 April 2021 | work = The Daily Californian | access-date = 4 April 2021}}</ref>

American band [[Horse Lords]] uses [[just intonation]], playing hand-modified guitars with repositioned frets.<ref>{{Cite web |title=Horse Lords |url=https://www.discogs.com/artist/3068399-Horse-Lords |access-date=2025-01-19 |website=Discogs |language=en}}</ref>

American band [[The Mercury Tree]] began incorporating microtonality in their 2014 album ''Countenance'', using quarter tones on the song "Vestigial". In their 2016 album ''Permutations'', they continued exploring quarter tones, and the track "Ether / Ore" was composed using the [[Alpha scale|Carlos Alpha]] tuning.<ref>{{Cite AV media |url=https://www.youtube.com/watch?v=CdlMzkZRVVg |title=The Mercury Tree Live Interview: Ben Spees |date=2023-12-16 |last=Make Weird Music |access-date=2024-12-24 |via=YouTube}}</ref> Their 2018 collaborative EP with [[Cryptic Ruse]], titled ''Cryptic Tree'', utilized both [[23 equal temperament|23-TET]] and [[17 equal temperament|17-TET]]. The 2019 album ''Spidermilk'' and the 2023 album ''Self Similar'' both feature 17 notes per octave, with the latter also including tracks in [[34 equal temperament|34-TET]] and [[68 equal temperament|68-TET]].<ref>mercurytree.net</ref>

[[Ventifacts (band)|Ventifacts]], a prog-rock and folk songwriting duo between Ben Spees (of The Mercury Tree) and Damon Waitkus (of [[Jack O' the Clock]]) have made music which is exclusively microtonal. The tuning systems they use are [[free pitch]], 24-TET, 17-TET, [[22-TET]], [[10 tone equal temperament|10-TET]] and [[20 tone equal temperament|20-TET]].<ref>https://ventifacts.bandcamp.com/album/ventifacts</ref>

American band [[Dollshot]] used quarter tones and other microtonal intervals in their album ''Lalande''.<ref>{{cite web | last1 = K[aplan] | first1 = Noah | first2 = Rosie | last2 = K[aplan] | date = 2018 | url = https://nmbx.newmusicusa.org/notes-from-underground-ivan-wyschnegradskys-manual-of-quarter-tone-harmony/ | title = Notes from Underground: Ivan Wyschnegradsky's Manual of Quarter-Tone Harmony | work = New Music Box | access-date = May 15, 2018}}</ref>

American instrumental trio [[Consider the Source]] employs microtonal instruments in their music.{{Citation needed|date=July 2020}}

Australian alternative musician [[Jack Tickner]] uses a [[just intonation]] guitar in releases like his 2018 EP ''Reassuring Weight''.

==In the West==
{{more citations needed section|date=July 2016}}

===Western microtonal pioneers===
{{div col|colwidth=27em}}
* [[Henry Ward Poole]] (keyboard designs, 1825–1890)
* [[Eugène Ysaÿe]] (Belgium, U.S.A., 1858–1931, used quarter tones in several of the [[Six Sonatas for solo violin (Ysaÿe)|Sonatas for Solo Violin, Op. 27]])
* [[Ferruccio Busoni]] (Italy, Germany, 1866–1924). Experimented with microtones, including third tones.
* [[Charles Ives]] (U.S.A., 1874–1954, quarter tones)
* [[Julián Carrillo]] (Mexico, 1875–1965) many different equal temperaments
* [[Béla Bartók]] (Hungary, 1881–1945, rare uses of quarter tones)
* [[George Enescu]] (Romania, France, 1881–1955) (in ''[[Œdipe (opera)|Œdipe]]'' to suggest the [[enharmonic genus]] of [[ancient Greek music]], and in the Third Violin Sonata, as inflections characteristic of Romanian folk music)
* [[Karol Szymanowski]] (Poland, 1882–1937, used quarter tones on the violin in ''[[Myths (Szymanowski)|Myths]]'' Op. 30, 1915)
* [[Percy Grainger]] (Australia, 1882–1961, particularly works for his "free music machine")
* [[Edgard Varèse]] (France, U.S.A., 1883–1965)
* [[Mordecai Sandberg]] (Romania, Austria, Palestine, USA, Canada, 1897–1973)
* [[Luigi Russolo]] (Italy, 1885–1947, used quarter tones and eighth tones on the ''Intonarumori'', noise instruments)
* [[Mildred Couper]] (U.S.A., 1887–1974, quarter tones)
* [[Alois Hába]] (Czechoslovakia, 1893–1973, quarter tones and other equal temperaments)
* [[Ivan Wyschnegradsky]] (U.S.S.R. (Russia), France, 1893–1979, quarter tones, twelfth tones and other equal temperaments)
* [[Harry Partch]] (U.S.A., 1901–1974, just intonation, including a system of [[Harry Partch's 43-tone scale|43 unequal tones to the octave]])
* [[Eivind Groven]] (Norway, 1901–1977, 53ET)
* [[Henk Badings]] (The Netherlands, 1907–1987, 31ET)
* [[Maurice Ohana]] (France, 1913–1992, third tones (18ET) and quarter tones (24ET) most particularly)
* [[Giacinto Scelsi]] (Italy, 1905–1988, intuitive linear tone deviations, quarter tones, eighth tones)
* [[Lou Harrison]] (U.S.A., 1917–2003, just intonation)
* [[Ivor Darreg]] (U.S.A., 1917–1994)
* [[Jean-Etienne Marie]] (France, 1919–1989, many different equal temperaments: 18ET, 24ET, 30ET, 36ET, 48ET, 96ET most particularly and polymicrotonality)
* {{ill|Franz Richter Herf|de||nl}} (Austria, 1920–1989, 72-equal temperament, "ekmelic" music)
* [[Iannis Xenakis]] (Greece, France, 1922–2001, quarter and third tones most particularly, occasionally eighth tones)
* [[György Ligeti]] (Hungary, 1923–2006, ''[[Ramifications (Ligeti)|Ramifications]]'' in quarter tone tuning, natural harmonics in his Horn Trio, later just intonation in his solo concertos)
* [[Luigi Nono (composer)|Luigi Nono]] (Italy, 1924–1990, quarter tones, eighth tones and 16th tones)
* [[Claude Ballif]] (France, 1924–2004, quarter tones)
* [[Tui St. George Tucker]] (1924–2004)
* [[Pierre Boulez]] (France, 1925–2016) (first example of [[serial music]] with quarter tones in his pieces ''[[Le Visage nuptial]]'' and ''[[Polyphonie X]]'', but soon after abandoning microtonal elements)
* [[Karlheinz Stockhausen]] (Germany, 1928–2007, used and explored in his electronic works many microtonal concepts, non-octaving scales in ''Studie II'', just intonation in ''[[Gruppen (Stockhausen)|Gruppen]]'' and ''[[Stimmung]]'', occasional microtonal instrumental and vocal writing throughout ''[[Licht]]'')
* [[Ben Johnston (composer)|Ben Johnston]] (U.S.A., 1926–2019, extended just intonation)
* [[Joe Maneri]] (U.S.A., 1927–2009)
* [[Ezra Sims]] (U.S.A., 1928–2015, 72-tone equal temperament)
* [[Erv Wilson]] (1928–2016)
* [[Carlton Gamer]] (U.S.A, 1929–2023, 7-tone, 19-tone, 22-tone, 31-tone equal temperament)
* [[Alvin Lucier]] (U.S.A., b. 1931)
* [[Joel Mandelbaum]] (U.S.A., b. 1932)
* [[Krzysztof Penderecki]] (Poland, 1933–2020, quarter tones)
* [[Easley Blackwood, Jr.|Easley Blackwood]] (1933–2023)
* [[Alain Bancquart]] (France, b. 1934) (quarter tones and 16th tones)
* [[James Tenney]] (U.S.A., 1934–2006, just intonation, 72-tone equal temperament)
* [[Terry Riley]] (U.S.A., b. 1935, just intonation)
* [[La Monte Young]] (U.S.A., b. 1935, just intonation)
* [[John Corigliano]] (U.S.A., b. 1938, quarter tones)
* [[Douglas Leedy]] (b. 1938, just intonation, meantone)
* [[Wendy Carlos]] (U.S.A., b. 1939, non-octaving scales)
* [[Bruce Mather]] (Canada, b. 1939, different equal temperaments, following Wyschnegradsky)
* [[Brian Ferneyhough]] (Great Britain, b. 1943, quarter tones, 31ET in ''Unity Capsule'' for solo flute, 1976; quarter tones and eighth tones in ''La Chute d'Icare'', 1988)
* [[Jukka Tiensuu]] (Finland, b. 1948, quarter tones, non equal temperament tunings)

{{div col end}}

===Later Western microtonal composers===
{{div col|colwidth=27em}}
* [[Hans-Joachim Koellreutter]] (Brazil, 1915–2005)
* [[Clarence Barlow]] (1945–2023)
* [[Gérard Grisey]] (1946–1998) (spectral approach to microintervals, quarter tones, eighth tones)
* [[Max Méreaux]] (b. 1946)
* [[Michael Tilson Thomas|Michael Tilson Thomas]] (b. 1944)
* [[Tristan Murail]] (b. 1947) (spectral approach to microintervals, quarter tones, eighth tones)
* [[Glenn Branca]] (b. 1948)
* [[Elizabeth Brown (composer and performer)|Elizabeth Brown]] (b. 1953)
* [[Claude Vivier]] (1948–1983)
* [[Dean Drummond]] (1949–2013)
* [[Greg Schiemer]] (b. 1949)
* [[Lasse Thoresen]] (b. 1949)
* [[Warren Burt]] (b. 1949)
* [[Manfred Stahnke]] (b. 1951)
* [[James Erber]] (b. 1951) (quarter tones)
* [[Rhys Chatham]] (b. 1952)
* [[Kraig Grady]] (b. 1952) (invented acoustic instruments in just intonation & recurrent sequences)
* [[David First]] (b. 1953)
* [[Georg Friedrich Haas]] (b. 1953)
* [[James Wood (composer)|James Wood]] (b. 1953)
* [[Pascale Criton]] (b. 1954) (different equal temperaments, most particularly very dense ETs such as the 96ET)
* [[Paul Dirmeikis]] (b. 1954)
* [[Stephen James Taylor]] (b. 1954)
* [[Pascal Dusapin]] (b. 1955) (different equal temperaments, notably the 48ET)
* [[Kyle Gann]] (b. 1955)
* [[Johnny Reinhard]] (b. 1956) (different equal temperaments, just intonation, polymicrotonally)
* [[Dave Soldier]] (b. 1956)
* [[Eric Mandat]] (b. 1957)
* [[Erling Wold]] (b. 1958)
* [[Michael Bach (cellist, composer, visual artist)|Michael Bach Bachtischa]] (b. 1958)
* [[Lucio Garau]] (b. 1959)
* [[Michael Harrison (musician)|Michael Harrison]] (b. 1959) (just intonation)
* [[Martin Smolka]] (b. 1959)
* [[Richard Barrett (composer)|Richard Barrett]] (b. 1959)
* [[Georg Hajdu]] (b. 1960)
* [[William Susman]] (b. 1960)
* [[François Paris]] (b. 1961)
* [[Franklin Cox]] (b. 1961) (quarter tones, twelfth tones, extended just intonation)
* [[Daniel James Wolf]] (b. 1961)
* [[Claus-Steffen Mahnkopf]] (b. 1962) (quarter tones, eight tones)
* [[Harold Fortuin]] (b. 1964)
* [[Marc Sabat]] (b. 1965) (extended JI up to 23-limit)
* [[Georges Lentz]] (b. 1965)
* [[Jeffrey Ching]] (b. 1965) (quarter tones, ancient Chinese tunings, e.g. circle-of-fifths and just intonation)
* [[Geoff Smith (British musician)|Geoff Smith]] (b. 1966)
* [[Peter Thoegersen]] (b. 1967) (Polymicrotonality)
* [[Trey Spruance]] (b. 1969)
* [[Elaine Walker (composer)|Elaine Walker]] (b. 1969)
* [[Richard David James]], aka Aphex Twin (b. 1971)
* [[Sevish]] (b. 1988)
* [[Paweł Mykietyn]] (b. 1971)
* [[Yitzhak Yedid]] (b. 1971)
* [[Fabio Costa (composer, conductor)]] (b. 1971)
* [[Yuri Landman]] (b. 1973)
* [[Kristoffer Zegers]] (b. 1973)
* [[Karola Obermueller]] (b. 1977)
* [[Martin Suckling]] (b. 1981)
* [[Saman Samadi]] (b. 1984)
* [[Taylor Brook]] (b. 1985)
* [[Michael Waller]] (b. 1985)
* [[Mick Gordon (composer)|Mick Gordon]] (b. 1985)<ref>Microtonal composition for [[Atomic Heart]]: https://twitter.com/Mick_Gordon/status/1627845703505711105</ref>
* [[Sean Archibald]], aka Sevish, (b. 1988)
*[[Seppe Gebruers]] (b. 1990)<ref name="playingwithstandards.com">the quartertone pianos: http://www.playingwithstandards.com</ref>
* [[Robin Haigh]] (b. 1993)
* [[Jacob Collier]] (b. 1994)
{{div col end}}

=== Western microtonal researchers ===
{{div col|colwidth=19em}}
* [[Mordecai Sandberg]] (1897–1973)
* [[Christiaan Huygens]] (1629–1695)
* [[Julián Carrillo]] (1875–1965)
* [[Adriaan Daniël Fokker]] (1887–1972)
* [[Ivan Wyschnegradsky]] (1893–1979)
* [[Joseph Yasser]] (1893–1981)
* [[Alois Hába]] (1893–1973)
* [[Harry Partch]] (1901–1974)
* [[Alain Daniélou]] (1907–1994)
* [[Jean-Etienne Marie]] (1917–1989)
* [[Erv Wilson]] (1928–2016)
* [[Carlton Gamer]] (1929-2023)
* [[Joel Mandelbaum]] (b. 1932)
* [[James Tenney]] (1934–2006)
*[[Seppe Gebruers]] (b. 1990)<ref name="playingwithstandards.com"/>
* [[Tom Zé]] (b. 1936)
* [[Clarence Barlow]] (1945–2023)
* [[Valeri Brainin]] (b. 1948)
* [[Jacques Dudon]] (b. 1951)
* [[William Sethares]] (b. 1955)
* [[Georg Hajdu]] (b. 1960)
* [[Bob Gilmore]] (1961–2015)
* [[Marc Sabat]] (b. 1965)
* [[Mathius Shadow-Sky]] (b. 1961) <ref>the nonoctave polyscalar music theory published online: http://centrebombe.org/dansleciel,lebruitdel'ombre.html#nonoctave</ref>
{{div col end}}

==See also==
{{div col|colwidth=18em}}
* {{annotated link|3rd bridge}}
* {{annotated link|Arab tone system}} and [[Arabic maqam|maqam]]
* {{annotated link|Bohlen–Pierce scale}}
* {{annotated link|Continuum Fingerboard}}
* {{annotated link|Fokker periodicity blocks}}
* {{annotated link|Genus (music)}}
* {{annotated link|Harmony}}
* {{annotated link|Huygens-Fokker Foundation}}
* {{annotated link|Just intonation}}
* {{annotated link|Limit (music)}}
* {{annotated link|Microtuner}}
* {{annotated link|MIDI Tuning Standard|MIDI tuning standard}}
* {{annotated link|Music of India}}
* {{annotated link|Musical scale}}
* {{annotated link|Musical tuning}}
* {{annotated link|Harry Partch's 43-tone scale|Partch's 43-tone scale}}
* {{annotated link|Quarter tone}}
* {{annotated link|Raga}}
* {{annotated link|Scala (program)|Scala}}
* {{annotated link|Sonido 13}}
{{div col end}}

==References==
{{Reflist}}

==Further reading==
{{div col|colwidth=45em}}
* {{wikicite|ref={{harvid| Adèr |2011a}}|reference=Adèr, Lidiâ Olegovna [Адэр, Лидия Олеговна]. 2011a. "Микротоновая идея: Истоки и предпосылки" [The Concept of Microtonality: Its Origin and Background]. Научный журнал Санкт-Петербургской консерватории [Opera musicologica: Naučnyj žurnal Sankt-Peterburgskoj konservatorii] 3–4, nos. 8–9:114–134.}}
* {{wikicite|ref={{harvid| Adèr |2011b}}|reference=Adèr, Lidiâ Olegovna [Адэр, Лидия Олеговна]. 2011b. "Микротоновый инструментарий—первые шаги от утопии к практике" [Microtonal Instruments: The First Steps from Utopia to Practice]. In Временник Зубовского института: Инструментализм в истории культуры [Instrumentalism in the history of culture], edited by Evgenia Vladimirovna Hazdan, 52–65. Vremennik Zubovskogo instituta 7. St. Petersburg: Rossijskij Institut Istorii Iskusstv.}}
* {{wikicite|ref={{harvid|Aron|1523}}|reference=[[Pietro Aron|Aron, Pietro]]. 1523. ''Thoscanello de la musica''. Venice: Bernardino et Mattheo de Vitali. Facsimile edition, Monuments of music and music literature in facsimile: Second series, Music literature 69. New York: Broude Brothers, 1969. Second edition, as ''Toscanello in musica... nuovamente stampato con laggiunta da lui fatta et con diligentia corretto'', Venice: Bernardino & Matheo de Vitali, 1529. Facsimile reprint, Bibliotheca musica Bononiensis, sezione 2., n. 10. Bologna: Forni Editori, 1969. [http://euromusicology.cs.uu.nl:6334/dynaweb/tmiweb/a/aartos/@Generic__BookView;cs=default;ts=default Online edition of the 1529 text] {{in lang|it}}. Third edition, as ''Toscanello in musica'', Venice: Marchio Stessa, 1539. Facsimile edition, edited by Georg Frey. Kassel: Bärenreiter, 1970. Fourth edition, Venice, 1562. English edition, as ''Toscanello in music'', translated by Peter Bergquist. 3 vols. Colorado College Music Press Translations, no. 4. Colorado Springs: Colorado College Music Press, 1970.}}
* {{wikicite|ref={{harvid|Barbieri|1989}}|reference=Barbieri, Patrizio. 1989. "An Unknown 15th-Century French Manuscript on Organ Building and Tuning". ''The Organ Yearbook: A Journal for the Players & Historians of Keyboard Instruments'' 20.}}
* {{wikicite|ref={{harvid|Barbieri|2002}}|reference=Barbieri, Patrizio. 2002. "The Evolution of Open-Chain Enharmonic Keyboards c1480–1650". In ''Chromatische und enharmonische Musik und Musikinstrumente des 16. und 17. Jahrhunderts/Chromatic and Enharmonic Music and Musical Instruments in the 16th and 17th Centuries''. Schweizer Jahrbuch für Musikwissenschaft/Annales suisses de musicologie/Annuario svizzero di musicologia 22, edited by Joseph Willimann. Bern: Verlag Peter Lang AG. {{ISBN|3-03910-088-2}}.}}
* {{wikicite|ref={{harvid|Barbieri|2003}}|reference=Barbieri, Patrizio. 2003. "Temperaments, Historical". In ''Piano: An Encyclopedia'', second edition, edited by Robert Palmieri and Margaret W. Palmieri,{{Page needed|date=February 2011}}<!--Inclusive page numbers of Barbieri's article.-->. New York: Routledge.}}
* {{wikicite|ref={{harvid|Barbieri, Barca, and Riccati|1987}}|reference=Barbieri, Patrizio, Alessandro Barca, and conte Giordano Riccati. 1987. ''Acustica accordatura e temperamento nell'illuminismo Veneto''. Pubblicazioni del Corso superiore di paleografia e semiografia musicale dall'umanesimo al barocco, Serie I: Studi e testi 5; Pubblicazioni del Corso superiore di paleografia e semiografia musicale dall'umanesimo al barocco, Documenti 2. Rome: Edizioni Torre d'Orfeo.}}
* {{wikicite|ref={{harvid|Barbieri and Duca|2001}}|reference=Barbieri, Patrizio, and Lindoro Massimo del Duca. 2001. "Late-Renaissance Quarter-tone Compositions (1555–1618): The Performance of the ETS-31 with a DSP System". In ''Musical Sounds from Past Millennia: Proceedings of the International Symposium on Musical Acoustics 2001'', edited by Diego L. González, Domenico Stanzial, and Davide Bonsi. 2 vols. Venice: Fondazione Giorgio Cini.}}
* {{wikicite|ref={{harvid|Barlow|2001}}|reference=[[Clarence Barlow|Barlow, Clarence]] (ed.). 2001. "The Ratio Book." (Documentation of the Ratio Symposium Royal Conservatory The Hague 14–16 December 1992). ''Feedback Papers'' 43.}}
* {{wikicite|ref={{harvid|Blackwood|1985}}|reference=Blackwood, Easley. 1985. ''The Structure of Recognizable Diatonic Tunings''. Princeton: Princeton University Press. {{ISBN|0-691-09129-3}}.}}
* {{wikicite|ref={{harvid|Blackwood|1991}}|reference=Blackwood, Easley. 1991. "Modes and Chord Progressions in Equal Tunings". ''Perspectives of New Music'' 29, no. 2 (Summer): 166–200.}}
* {{wikicite|ref={{harvid|Burns|1999}}|reference=Burns, Edward M. 1999. "Intervals, Scales, and Tuning." In ''The Psychology of Music'', second edition, ed. Diana Deutsch. 215–264. San Diego: Academic Press. {{ISBN|0-12-213564-4}}.}}
* {{wikicite|ref={{harvid|Carr|2008}}|reference=Carr, Vanessa. 2008. "[http://www.vancarr.com/?p=42 These Are Ghost Punks]". Vanessa Carr's website (29 February). (Accessed 2 April 2009)}}
* {{wikicite|ref={{harvid|Colonna|1618}}|reference=Colonna, Fabio. 1618. ''La sambuca lincea, overo Dell'istromento musico perfetto''. Naples: C. Vitale. Facsimile reprint of a copy containing manuscript critical annotations by [[Scipione Stella]] (1618–1624), with an introduction by Patrizio Barbieri. Musurgiana 24. Lucca, Italy: Libreria Musicale Italiana, 1991.}}
* {{wikicite|ref={{harvid|Daniels|1965}}|reference=Daniels, Arthur Michael. 1965. "Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas". ''[[Journal of Music Theory]]'' 9, no. 1 (Spring): 2–51.}}
* {{wikicite|ref={{harvid|Dumbrill|2000}}|reference=[[Richard Dumbrill (musicologist)|Dumbrill, Richard J.]] 2000. ''The Musicology and Organology of the Ancient Near East'', second edition. London: Tadema Press. {{ISBN|0-9533633-0-9}}.}}
* {{wikicite|ref={{harvid|Fink|1988}}|reference=Fink, Robert. 1988. "The Oldest Song in the World". ''Archaeologia Musicalis'' 2, no. 2:98–100.}}
* {{wikicite|ref={{harvid|Fritsch|2007}}|reference=[[Johannes Fritsch|Fritsch, Johannes G]]. 2007. "Allgemeine Harmonik, Tonsysteme, Mikrotonalität: Ein geschichtlicher Überblick". In ''Orientierungen: Wege im Pluralismus der Gegenwartsmusik'', edited by [[Jörn Peter Hiekel]], 107–122. Veröffentlichungen des Instituts für Neue Musik und Musikerziehung Darmstadt 47. Mainz: Schott Musik International. {{ISBN|978-3-7957-1837-4}}.}}
* {{wikicite|ref={{harvid|Gilmore|1998}}|reference=Gilmore, Bob. 1998. ''Harry Partch: A Biography''. New Haven: Yale University Press. {{ISBN|0-300-06521-3}}.}}
* {{wikicite|ref={{harvid|Haas|2007}}|reference=[[Georg Friedrich Haas|Haas, Georg Friedrich]]. 2007. "Mikrotonalität und spektrale Musik seit 1980". In ''Orientierungen: Wege im Pluralismus der Gegenwartsmusik'', edited by Jörn Peter Hiekel, 123–129. Veröffentlichungen des Instituts für Neue Musik und Musikerziehung Darmstadt 47. Mainz: Schott Musik International. {{ISBN|978-3-7957-1837-4}}.}}
* {{wikicite|ref={{harvid|Hába|1927}}|reference=Hába, Alois. 1927. ''Neue Harmonielehre des diatonischen, chromatischen Viertel-, Drittel-, Sechstel- und Zwölftel-tonsystems''. Leipzig: Kistner & Siegel.}}
* {{wikicite|ref={{harvid|Johnston|2006}}|reference=Johnston, Ben. 2006. ''{{'}}Maximum Clarity' and other writings on music'', ed. B. Gilmore. Urbana and Chicago: University of Illinois Press.}}
* {{wikicite|ref={{harvid|Kotschy|2008}}|reference=Kotschy, Johannes. 2008. "Mikrotonalität: Eine Zeiterscheinung?" ''Österreichische Musikzeitschrift'' 63, no. 7 (July): 8–15.}}
* {{wikicite|ref={{harvid|Landman|[2008]}}|reference=[[Yuri Landman|Landman, Yuri]]. [2008]. "Third Bridge Helix: From Experimental Punk to Ancient Chinese Music and the Universal Physical Laws of Consonance". ''[https://web.archive.org/web/20120824020439/http://www.furious.com/perfect/experimentalstringinstruments.html Perfect Sound Forever (online music magazine)]'' (accessed 6 December 2008).}}
* {{wikicite|ref={{harvid|Landman|n.d.}}|reference=Landman, Yuri. n.d. "[https://web.archive.org/web/20151108182752/http://www.hypercustom.com/yuichionoue.html Yuichi Onoue's Kaisatsuko]" on [http://www.hypercustom.com Hypercustom.com] (accessed 31 March 2009).}}
* {{wikicite|ref={{harvid|Leedy|1991}}|reference=Leedy, Douglas. 1991. "A Venerable Temperament Rediscovered". ''Perspectives of New Music'' 29, no. 2 (Summer): 202–211.}}
* {{wikicite|ref={{harvid|Lindley|2001b}}|reference=Lindley, Mark. 2001b. "Temperaments". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}}
* {{wikicite|ref={{harvid|Mandelbaum|1961}}|reference=Mandelbaum, M. Joel. 1961. "[http://anaphoria.com/mandelbaum.html Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament]". Ph.D. thesis. Bloomington: Indiana University.}}
* {{wikicite|ref={{harvid|Mosch|2008}}|reference=Mosch, Ulrich. 2008. "Ultrachromatik und Mikrotonalität: Hans Zenders Grundlegung einer neuen Harmonik". In ''Hans Zender: Vielstimmig in sich'', edited by [[Werner Grünzweig]], Anouk Jeschke, and [[Jörn Peter Hiekel]], 61–76. Archive zur Musik des 20. Jahrhunderts, No. 12. Hofheim:Wolke. {{ISBN|978-3-936000-25-2}}.}}
* {{wikicite|ref={{harvid|Noyze and James|2014}}|reference=Noyze, Dave, and Richard D. James.. 2014. "[https://web.archive.org/web/20141112205122/http://noyzelab.blogspot.com.au/2014/11/syrobonkers-part2.html Aphex Twin Syrobonkers! Interview: Part 2]". Noyzelab Blogspot.com.au (Monday, 10 November)}}
* {{wikicite|ref={{harvid|Stahnke|2010}}|reference=[[Manfred Stahnke|Stahnke, Manfred]]. 2010. "About Backyards and Limbos: Microtonality Revisited". In ''Concepts, Experiments and Fieldwork: Studies in Systematic Musicology and Ethnomusicology'', edited by Rolf Bader, Christiane Neuhaus, and Ulrich Morgenstern, with a prefaceby Achim Reichel, 297–314. Frankfurt am Main and New York: Peter Lang. {{ISBN|978-3-631-58902-1}}.}}
* {{wikicite|ref={{harvid|Vitale|1982}}|reference=Vitale, Raoul. 1982. "La Musique suméro-accadienne: gamme et notation musicale". ''Ugarit-Forschungen'' 14: 241–263.}}
* {{wikicite|ref={{harvid|Werntz|2001}}|reference=Werntz, Julia. 2001. "Adding Pitches: Some New Thoughts, Ten Years after Perspectives of New Music's 'Forum: Microtonality Today'". ''Perspectives of New Music'' 39, no. 2 (Summer): 159–210.}}
* {{wikicite|ref={{harvid|Wood|1986}}|reference=Wood, James. 1986. "Microtonality: Aesthetics and Practicality". ''The Musical Times'' 127, no. 1719 (June): 328–330.}}
* {{wikicite|ref={{harvid|Wyschnegradsky|1937}}|reference=[[Ivan Wyschnegradsky|Wyschnegradsky, Ivan]]. 1937. "La musique à quarts de ton et sa réalisation pratique". ''La Revue Musicale'' no. 171:26–33.}}
* {{wikicite|ref={{harvid|Zweifel|1996}}|reference=Zweifel, Paul. 1996. "Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach". ''Perspectives of New Music'' 34, no. 1 (Winter): 140–161.}}
{{div col end}}

==External links==
{{commons category|Microtonal music}}
* Aikin, Jim. 2003. [https://web.archive.org/web/20080515230851/http://emusician.com/tutorials/emusic_playing_cracks/ Jim Aikin's article on alternative tuning in electronic music]
* Anon. [n.d.]. "[http://www.hoasm.org/IVO/Vicentino.html Nicola Vicentino (1511–1576)]". IVO: Sacred Music in the Italian Cinquecento outside Venice and Rome, edited by Chris Whent. Here Of A Sunday Morning website. (Accessed 19 August 2008)
* Chalmers, John. [http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html Dr. John Chalmers Divisions of the Tetrachord]
* Loli, Charles. 2008. " [http://microtonalismo.com Microtonalismo]". (Article on alternative tuning in Peruvian music)
* Solís Winkler, Ernesto. 2004. "[https://web.archive.org/web/20060901232520/http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html Julián Carrillo and the 13th Sound: A Microtonal Musical System]". (Accessed 19 August 2008)
* [[Erv Wilson|Wilson, Erv]]. "[http://anaphoria.com/wilson.html Wilson Archives of papers on microtonal theory]"
* [https://en.xen.wiki/w/Listen Listen – Xenharmonic Wiki] – links to microtonal composers and compositions
* [https://en.xen.wiki/w/Projects Projects – Xenharmonic Wiki] – links to microtonal projects around the world
* [http://offtonic.com/synth Offtonic Microtonal Synthesizer], a browser-based synth to explore microtonal tunings with a QWERTY keyboard
* [https://MidiPro.org MidiPro.org] {{Webarchive|url=https://web.archive.org/web/20201123184038/http://midipro.org/ |date=2020-11-23 }} allows any sound card or synthesizer to play 48 microtones per octave, each separated by 1/8 step

{{Microtonal music|state=expanded}}
{{Musical tuning}}
{{Timbre}}
{{Modernism (music)}}
{{Authority control}}

[[Category:Microtonality|Music]]
[[Category:Ancient Greek music]]
[[Category:Post-tonal music theory]]