Examine individual changes

'{{distinguish|Microsound}} [[Image:Ives quarter tone fundamental chord.png|thumb|right|250px|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 {{harv|Boatwright|1971|loc=8–9}}. {{Audio|Ives fundamental chord (quarter tones).ogg|Play}} or {{Audio|Ives quarter tone fundamental chord arp.mid|play}}]] '''Microtonal music''' is music using microtones—[[interval (music)|intervals]] of less than an [[equal temperament|equally spaced]] [[semitone]]. Microtonal music can also refer to music which uses intervals not found in the Western system of 12 equal intervals to the octave. ==Terminology== [[Image:partial accidentals.svg|right|frame|[[Quarter-tone]] [[Accidental (music)|accidentals]] residing outside the Western [[semitone]]: <BR>quarter tone sharp, [[Sharp (music)|sharp]], three quarter tones sharp;<BR>quarter tone flat, [[flat (music)|flat]], (two variants of) three quarter tones flat]] ''Microtonal music'' can refer to all music which contains intervals smaller than the conventional contemporary Western [[semitone]]. The term usually refers to music containing very small intervals but can include any tuning that differs from the western 12-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 ({{harvnb|Griffiths and Lindley|1980}}; {{harvnb|Griffiths, Lindley, and Zannos|2001}}). Microtonal variation of intervals is standard practice in the African-American musical forms of spirituals, blues and jazz {{harv|Cook and Pople|2004|loc=124–26}}. 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 ({{harvnb|Griffiths and Lindley|1980}}; {{harvnb|Griffiths, Lindley, and Zannos|2001}}). Terminology other than "microtonal" is used by theorists and composers. [[Ivan Wyschnegradsky]] used the term ''ultra-chromatic'' for intervals smaller than the semitone and ''infra-chromatic'' for intervals larger than the semitone {{harv|Wyschnegradsky 1972|loc=84–87}}. [[Ivor Darreg]] proposed the term ''xenharmonic''. (See [[Xenharmony|xenharmonic]] music). ==History== [[Image:Greek Dorian enharmonic genus.png|thumb|300px|Greek Dorian mode ([[Genus (music)#Enharmonic|enharmonic genus]]) on E, divided into two tetrachords. {{audio|Greek Dorian mode on E, enharmonic genus.mid|Play}}]] The Hellenic civilizations of ancient Greece left fragmentary records of their music—e.g. 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 [[Cent (music)|cents]], less than half of the contemporary Western [[semitone]] of 100 cents. In the ancient Greek enharmonic genus, the tetrachord contained a semitone of varying sizes (approximately 100 cents) divided into two such smaller, microtonal, intervals; in conjunction with a larger interval of roughly 400 cents, these intervals comprised the perfect fourth (approximately 498 cents, or the ratio of 4/3 in [[just intonation]]) {{harv|West|1992|loc=160–72}}. <!-- Image with inadequate rationale removed: [[Image:Tonraum30.11-14 1.jpg|thumb|right|A reproduction of Vicentino's archicembalo]] -->[[Guillaume Costeley]]'s "Chromatic Chanson", "Seigneur Dieu ta pitié" of 1558 used 1/3 comma meantone and explored the full compass of 19 pitches in the octave. {{harv|Lindley|2001a}}. 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 {{harv|Barbour|1951|loc=117–18}}. [[Jacques Fromental Halévy]] composed a quarter-tone work for soli, choir and orchestra entitled "Prométhée enchaîné" in 1849. In the 1910s and 1920s, [[quarter tone]]s (24 equal pitches per octave) 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 Helmholtz's ''On the Sensations of Tone'', proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings {{harv|Helmholtz|1885|loc=514–27}}. Ellis also studied the tunings of non-Western cultures and, in a report to the Royal Society, stated that they did not use either equal divisions of the octave or just intonation intervals {{harv|Ellis|1884}}. Ellis inspired [[Harry Partch]] immensely {{harv|Partch|1979|loc=vii}}. During the Exposition Universelle of 1889, [[Claude Debussy]] heard a Balinese gamelan performance and was exposed to 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]]'' and the Toccata from the suite ''[[Pour le piano]]'' to his exposure to the Balinese gamelan at the Paris exposition {{harv|Lesure|2001}}, and have asserted his rebellion at this time "against the rule of 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" {{harv|Howat|2001}}. 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 [[Hermann Helmholtz]]'s writings {{harv|Don|1991|loc=69 et passim}}. 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 tunings. Major microtonal composers of the 1920s and 1930s include [[Alois Hába]] (quarter tones, or 24 equal pitches per octave, and sixth tones), Julian Carillo (24 equal, 36, 48, 60, 72, and 96 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) {{harv|Partch|1979|loc=chapt. 8, "Application of the 11 Limit", 119–37}}. Prominent microtonal composers or researchers of the 1940s and 1950s include [[Adriaan Daniel Fokker]] (31 equal tones per octave), 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. ==Microtonalism in electronic music== Electronic music facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems {{harv|Griffiths, Lindley, and 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 5^1/25 between steps {{harv|Stockhausen|1964|loc=37}}, and in ''[[Gesang der Jünglinge]]'' (1955–56) he used various scales, ranging from seven up to sixty equal divisions of the octave {{harv|Decroupet and Ungeheuer|1998|loc=105, 116, 119–21}}. In 1955, [[Ernst Krenek]] used 13 equal-tempered intervals per octave in his Whitsun oratorio, ''Spiritus intelligentiae, sanctus'' {{harv|Griffiths, Lindley, and 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]] {{harv|Blackwood and Kust|2005|loc={{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" {{harv|Blackwood|n.d.}}. 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" {{harv|Carlos|1989–96}}. [[Aphex Twin]] has been making microtonal electronic music with software and various analog and digital synthesizers since his 1994 album, Selected Ambient Works Vol. II. {{harv|Anon.|n.d.}} ==Microtonalism in rock music== 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 {{harv|Ferguson|1999|loc=20}}. Musicians like [[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 {{harv|Couture|n.d.}}. The band [[Radiohead]] have used microtonal string arrangements in their music, such as on ''How To Disappear Completely'' from their album [[Kid A]] {{harv|Wilson, Penderecki, and Greenwood|2012}}. ==See also== {{div col|cols=4}} * [[Sonido 13]] * [[3rd bridge]] * [[Arab tone system]] and [[Arabic maqam|maqam]] * [[Bohlen–Pierce scale]] * [[Continuum Fingerboard]] * [[Fokker periodicity blocks]] * [[Genus (music)]] * [[Harmony]] * [[Just intonation]] * [[Limit (music)]] * [[Microtuner]] * [[MIDI Tuning Standard|MIDI tuning standard]] * [[Music of India]] * [[Musical scale]] * [[Musical tuning]] * [[Harry Partch's 43-tone scale|Partch's 43-tone scale]] * [[Quarter tone]] * [[Raga]] * [[Scala (program)|Scala]] {{div col end}} ===Western microtonal pioneers=== Pioneers of modern Western microtonal music include: {{div col|cols=3}} * [[Henry Ward Poole]] (keyboard designs, 1825–1890) * [[Eugène Ysaÿe]] (Belgium, U.S.A., 1858–1931, used quarter tones in several of the [[6 Sonatas for Solo Violin, Op. 27 (Ysaÿe)|Sonatas for Solo Violin, Op. 27]]) * [[Charles Ives]] (U.S.A., 1874–1954, quartertones) * [[Julián Carrillo]] (Mexico, 1875–1965) many different equal temperaments, look [http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html here] or [http://paginas.tol.itesm.mx/campus/L00280370/julian.html here] (mostly Spanish but some English too) * [[Béla Bartók]] (Hungary, 1881–1945, rare uses of quartertones) * [[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 quartertones on the violin in ''Myths'' Op. 30, 1915) * [[Percy Grainger]] (Australia, 1882–1961, particularly works for his "free music machine") * [[Edgard Varèse]] (France, U.S.A., 1883–1965, quartertones) * [[Luigi Russolo]] (Italy, 1885–1947, used quartertones and eighth tones on the ''Intonarumori'', noise instruments) * [[Mildred Couper]] (U.S.A., 1887–1974, quartertones) * [[Alois Hába]] (Czechoslovakia, 1893–1973, quartertones and other equal temperaments) * [[Ivan Wyschnegradsky]] (U.S.S.R. (Russia), France, 1893–1979, quartertones, twelfth tones and other equal temperaments) * [[Harry Partch]] (U.S.A., 1901–1974, just intonation) * [[Eivind Groven]] (Norway, 1901–1977, 53ET) * [[Henk Badings]] (The Netherlands, 1907–1987, 31ET) * [[Maurice Ohana]] (France, 1913–1992, third tones (18-equal) temperament and quarter tones (24ET) most particularly) * [[Giacinto Scelsi]] (Italy, 1905–1988, intuitive linear tone deviations, quartertones, 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) * [[Franz Richter Herf]] (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 quartertone tuning, natural harmonics in his Horn Trio, later just intonation in his solo concertos) * [[Luigi Nono (composer)|Luigi Nono]] (Italy, 1924–1990, quartetones, eighth tones and 16th tones) * [[Claude Ballif]] (France, 1924–2004, quartertones) * [[Tui St. George Tucker]] (1924–2004) * [[Pierre Boulez]] (France, b. 1925) (first example of [[serial music]] with quartertones in his pieces ''Visage Nuptial'' and ''Polyphonie X'', but soon after abandoning microtonal elements) * [[Karlheinz Stockhausen]] (Germany, 1928–2007, in his electronic works many microtonal concepts, non-octaving scales in ''Studie II'', just intonation in ''[[Gruppen (Stockhausen)|Gruppen]]'' and ''[[Stimmung]]'', microtonal instrumental and vocal writing throughout ''[[Licht]]'') * [[Ben Johnston (composer)|Ben Johnston]] (U.S.A., b. 1926, extended just intonation) * [[Ezra Sims]] (U.S.A., b. 1928, 72-tone equal temperament) * [[Erv Wilson]] (b. 1928) * [[Carlton Gamer]] (U.S.A, born 1929, 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, b. 1933, quartertones) * [[Easley Blackwood, Jr.|Easley Blackwood]] (b. 1933) * [[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, quartertones, 31ET in ''Unity Capsule'' for solo flute,1976) {{div col end}} ===Recent microtonal composers=== {{div col|cols=3}} * [[Clarence Barlow]] (b. 1945) * [[Gérard Grisey]] (1946–1998) (spectral approach to microintervals, quartertones, eighth tones) * [[Max Méreaux]] (b. 1946) * [[Tristan Murail]] (b. 1947) (spectral approach to microintervals, quartertones, eighth tones) * [[Claude Vivier]] (1948–1983) * [[Glenn Branca]] (b. 1948) * [[Dean Drummond]] (b. 1949) (Harry Partch's instruments currently in his possession) * [[Lasse Thoresen]] (b. 1949) * [[Greg Schiemer]] (b. 1949) * [[Warren Burt]] (b. 1949) * [[Manfred Stahnke]] (b. 1951) * [[Kraig Grady]] (b. 1952) (invented acoustic instruments in just intonation & recurrent sequences) * [[Rhys Chatham]] (b. 1952) * [[David First]] (b. 1953) * [[Georg Friedrich Haas]] (b. 1953) * [[James Wood (composer)|James Wood]] (b. 1953) * [[Paul Dirmeikis]] (b. 1954) * [[Pascale Criton]] (b. 1954) (different equal temperaments, most particularly very dense ETs such as the 96ET) * [[Stephen James Taylor]] (b. 1954) * [[Kyle Gann]] (b. 1955) * [[Pascal Dusapin]] (b. 1955) (different equal temperaments, notably the 48ET) * [[Johnny Reinhard]] (b. 1956) (different equal temperaments, just intonation, polymicrotonally) * [[Eric Mandat]] (b. 1957) * [[Erling Wold]] (b. 1958) * [[Michael Bach (cellist, composer, visual artist) | Michael Bach Bachtischa]] (b. 1958) * [[Martin Smolka]] (b. 1959) * [[Lucio Garau]] (b. 1959) * [[Georg Hajdu]] (b. 1960) * [[William Susman]] (b. 1960) * [[Daniel James Wolf]] (b. 1961) * [[François Paris]] (b. 1961) * [[Harold Fortuin]] (b. 1964) * [[Marc Sabat]] (b. 1965) * [[Georges Lentz]] (b. 1965) * [[Jeffrey Ching]] (b. 1965) (quartertones, ancient Chinese tunings, e.g. circle-of-fifths and just intonation) * [[Geoff Smith (British musician)|Geoff Smith]] (b. 1966) * [[Trey Spruance]] (b. 1969) * [[Yitzhak Yedid]] (b. 1971) * [[Paweł Mykietyn]] (b. 1971) * [[Adam Silverman]] (b. 1973) * [[Yuri Landman]] (b. 1973) * [[Kristoffer Zegers]] (b. 1973) * [[Saman Samadi]] (b. 1984) * [[Michael Waller]] (b. 1985) {{div col end}} ===Microtonal researchers=== {{div col|cols=4}} * [[Christiaan Huygens]] (1629–1695) * [[Julián Carrillo]] (1875–1965) * [[Adriaan Daniël Fokker]] (1887–1972) * [[Ivan Wyschnegradsky]] (1893–1979) * [[Alois Hába]] (1893–1973) * [[Harry Partch]] (1901–1974) * [[Alain Daniélou]] (1907–1994) * [[Jean-Etienne Marie]] (1917–1989) * [[Erv Wilson]] (b. 1928) * [[Carlton Gamer]] (b. 1929) * [[Joel Mandelbaum]] (b. 1932) * [[James Tenney]] (1934–2006) * [[Clarence Barlow]] (b. 1945) * [[Gene Ward Smith]] (b. 1947) * [[Valeri Brainin]] (b. 1948) * [[Jacques Dudon]] (b. 1951) * [[William Sethares]] (b. 1955) * [[Georg Hajdu]] (b. 1960) * [[Bob Gilmore]] (b. 1961) * [[Marc Sabat]] (b. 1965) {{div col end}} ==References== {{Refbegin|2}} * {{wikicite|ref={{harvid|Anon.|n.d.}}|reference=Anon. n.d. "[http://web.archive.org/web/20141112205122/http://noyzelab.blogspot.com.au/2014/11/syrobonkers-part2.html <nowiki>[</nowiki>untitled<nowiki>]</nowiki>]". {{Full|date=December 2014}}}} * {{wikicite|ref={{harvid|Barbour|1951}}|reference=Barbour, J. Murray. 1951. ''Tuning and Temperament: A Historical Survey''. East Lansing: Michigan State College Press. Reprinted [n.p.]: Dover, 2004. ISBN 0-486-43406-0 (pbk).}} * {{wikicite|ref={{harvid|n.d.}}|reference=Blackwood, Easley. n.d. Liner notes to [http://www.dramonline.org/albums/blackwood-microtonal-compositions/notes "Blackwood: Microtonal Compositions"]. CDR018. N.p.: [[Cedille Records]].{{Full|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.-->}} * {{wikicite|ref={{harvid|Blackwood and Kust|2005}}|reference=Blackwood, Easley, and Jeffrey Kust. 2005. ''Easley Blackwood: Microtonal Compositions'', second edition. n.p.: Cedille. (First edition 1996.){{Full|date=November 2014}}<!--Place of publication and ISBN needed.-->}} * {{wikicite|ref={{harvid|Boatwright|1971}}|reference=Boatwright, Howard. 1971. "Ives' Quarter-Tone Impressions". In ''Perspectives on American Composers'', edited by Benjamin Boretz and Edward T. Cone, 3–12. Princeton: Princeton University Press.}} * {{wikicite|ref={{harvid|Carlos|1989–96}}|reference=[[Wendy Carlos|Carlos, Wendy]]. 1989–96. "[http://www.wendycarlos.com/resources/pitch.html Three Asymmetric Divisions of the Octave]". ''[http://www.wendycarlos.com wendycarlos.com]'' (Accessed March 28, 2009).}} * {{wikicite|ref={{harvid|Cook and Pople|2004}}|reference=Cook, Nicholas, and Anthony Pople. 2004 ''The Cambridge History of Twentieth-Century Music''. Cambridge and New York: Cambridge University Press. ISBN 0-521-66256-7.}} * {{wikicite|ref={{harvid|Couture|n.d.}}|reference=Couture, François. n.d. "[http://www.allmusic.com/album/evolution-for-electric-guitar-and-orchestra-mw0000979771 Jon Catler: Evolution for Electric Guitar and Orchestra]". AllMusic (Accessed 3 April 2013).}} * {{wikicite|ref={{harvid|Decroupet and Ungeheuer|1998}}|reference=Decroupet, Pascal, and Elena Ungeheuer. 1998. "Through the Sensory Looking-Glass: The Aesthetic and Serial Foundations of Gesang der Jünglinge", translated from French by Jerome Kohl. ''Perspectives of New Music'' 36, no. 1 (Winter): 97–142.}} * {{wikicite|ref={{harvid|Don|2001}}|reference=Don, Gary. 2001. "Brilliant Colors Provocatively Mixed: Overtone Structures in the Music of Debussy". ''Music Theory Spectrum'' 23, no. 1 (Spring): 61–73.}} * {{wikicite|ref={{harvid|Ellis|1884}}|reference=[[Alexander John Ellis|Ellis, Alexander J]]. 1884. "Tonometrical Observations on Some Existing Non-Harmonic Musical Scales". ''Proceedings of the Royal Society of London'' 37:368–85.}} * {{wikicite|ref={{harvid|Ferguson|1999}}|reference=[[Jim Ferguson|Ferguson, Jim]]. 1999. ''All Blues Soloing for Jazz Guitar: Scales, Licks, Concepts & Choruses''. Santa Cruz: Guitar Master Class; Pacific, MO: Mel Bay. ISBN 0-7866-4285-8.}} * {{wikicite|ref={{harvid|Griffiths and Lindley|1980}}|reference=[[Paul Griffiths (writer)|Griffiths, Paul]], and [[Mark Lindley]]. 1980. "Microtone". ''The New Grove Dictionary of Music and Musicians'', edited by Stanley Sadie, 12:279–80. London: Macmillan Publishers. ISBN 1-56159-174-2.}} * {{wikicite|ref={{harvid|Griffiths, Lindley, and Zannos|2001}}|reference=Griffiths, Paul, Mark Lindley, and Ioannis Zannos. 2001. "Microtone". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan Publishers.}} * {{wikicite|ref={{harvid|Helmholtz|1885}}|reference=[[Hermann von Helmholtz|Helmholtz, Hermann von]]. 1885. ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'', second English edition, translated, thoroughly revised and corrected, rendered conformable to the 4th (and last) German ed. 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 by Alexander J. Ellis. London: Longmans, Green.}} * {{wikicite|ref={{harvid|Howat|2001}}|reference=Howat, Roy. 2001. "Debussy, (Achille-)Claude: §10, 'Musical Language'". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}} * {{wikicite|ref={{harvid|Lesure|2001}}|reference=Lesure, François. 2001. "Debussy, (Achille-)Claude: 7, 'Models and Influences'". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}} * {{wikicite|ref={{harvid|Lindley|2001a}}|reference=Lindley, Mark. 2001a. "Mean-tone". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (professor of music)|John Tyrrell]]. London: Macmillan Publishers.}} * {{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|Partch|1979}}|reference=[[Harry Partch|Partch, Harry]]. 1979. ''[[Genesis of a Music]]'', second edition. New York: Da Capo Press. ISBN 0-306-80106-X.}} * {{wikicite|ref={{harvid|Stockhausen|1964}}|reference=Stockhausen, Karlheinz. 1964. ''Texte'' 2: Aufsätze 1952–1962 zur musikalischen Praxis, edited and with an afterword by Dieter Schnebel. Cologne: Verlag M. DuMont Schauberg.}} * {{wikicite|ref={{harvid|West|1992}}|reference=West, Martin Litchfield. 1992. ''Ancient Greek Music''. Oxford: Clarendon Press; New York: Oxford University Press. ISBN 0-19-814897-6 (cloth) ISBN 0-19-814975-1 (pbk).}} * {{wikicite|ref={{harvid|Wilson, Penderecki, and Greenwood|2012}}|reference=Wilson, John, [[Krzysztof Penderecki]], and [[Jonny Greenwood]]. 2012. [http://www.citizeninsane.eu/t2012-03-23BBCRadio4.htm Interview with Jonny and Krzysztof Penderecki]. ''Front Row''. BBC Radio 4 (23 March). Transcript from an audio recording of the broadcast, Citizen Insane website (accessed 21 July 2014).}} * {{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|Wyschnegradsky|1972}}|reference=Wyschnegradsky, Ivan. 1972. “L'Ultrachromatisme et les espaces non octaviants”. ''La Revue Musicale'' nos. 290–91:71-141.}} {{Refend}} ==Further reading== {{Refbegin|2}} * {{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] {{it icon}}. 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. *Barbieri, Patrizio. 2008. ''[http://www.patriziobarbieri.it/1.htm Enharmonic instruments and music, 1470-1900]''. Latina: Il Levante Libreria Editrice. ISBN 978-88-95203-14-0.}} * {{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. 215–64. 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|Dumbrill|2000}}|reference=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|Gilmore|1998}}|reference=Gilmore, Bob. 1998. ''Harry Partch: A Biography''. New Haven: Yale University Press. ISBN 0-300-06521-3.}} * {{wikicite|ref={{harvid|Hesse|1991}}|reference=Hesse, Horst-Peter. 1991. "Breaking into a New World of Sound: Reflections on the Austrian Composer Franz Richter Herf (1920–1989)". ''Perspectives of New Music'' 29, no. 1 (Winter): 212–35.}} * {{wikicite|ref={{harvid|Jedrzejewski|2003}}|reference=Jedrzejewski, Franck. 2003. ''Dictionnaire des musiques microtonales'' [Dictionary of Microtonal Musics]. Paris: L'Harmattan. ISBN 2-7475-5576-3.}} * {{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|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". ''[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. "[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|2001}}|reference=Leedy, Douglas. 2001. "A Venerable Temperament Rediscovered". ''Perspectives of New Music'' 29, no. 2 (Summer): 202–11.}} * {{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|Vitale|1982}}|reference=Vitale, Raoul. 1982. "La Musique suméro-accadienne: gamme et notation musicale". ''Ugarit-Forschungen'' 14: 241–63.}} {{Refend}} ==External links== {{commons category|Microtonal music}} *{{DMOZ|Arts/Music/Theory/Tuning_Systems/Microtonal/}} * Aikin, Jim. 2003. [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. "[http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html Julian 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]" * [http://xenharmonic.wikispaces.com/MicrotonalListeningList Links to microtonal composers] at [[Xenharmonic]] Wiki * [http://xenharmonic.wikispaces.com/Projects Links to microtonal projects around the world] at [[Xenharmonic]] Wiki * [http://offtonic.com/synth Offtonic Microtonal Synthesizer], a browser-based synth to explore microtonal tunings with a QWERTY keyboard {{Musical tuning}} {{Timbre}} {{Microtonal music}} {{Modernism (music)}} {{DEFAULTSORT:Microtonal Music}} [[Category:Microtonality]] [[Category:Ancient Greek music]] [[Category:Post-tonal music theory]]'