Editing Microtonality (section)

==History==
{{Image frame|width=280
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|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.
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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 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 }}
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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-link = Hermann von Helmholtz | last = von&nbsp;Helmholtz | first = 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 |lang=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.