Microtonal music
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**Microtonal music** is [[music]] using microtones—[[musical interval|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>half-sharp, [[Sharp (music)|sharp]], sharp-and-a-half;<BR>half-flat, [[flat (music)|flat]], flat-and-a-half, another variant of flat-and-a-half]]
''Microtonal music'' can refer to all music which contains intervals smaller than the conventional contemporary Western [[semitone]]. The term implies music containing very small intervals but can include any tuning that differs from the western 12-tone [[equal temperament]]. The following systems are considered to be microtonal: the traditional [[Carnatic Music|Carnatic]] system of 22 [[Śruti (music)|śruti]]; much Indonesian [[gamelan|gamelan music]]; Thai, Burmese, and African music using seven tones in each (approximate) octave; and [[blues]] and/or [[rock music]] which makes extensive use of [[blue notes]]. Also, music using [[just intonation]], [[meantone temperament]], or other alternative tunings may be considered microtonal.<br />
Other terminology has been used (and is still used today) by theorists and composers. ''Micro-intervals'' is commonly used to speak about intervals smaller than the [[semitone]], and sometimes ''macro-intervals'' for non-multiples of the [[semitone]] greater than it. [[Ivan Wyschnegradsky]] used the term ''ultra-chromatic'' for micro-intervals and ''infra-chromatic'' for macro-intervals (Wyschnegradsky 1972, 84-87). [[Ivor Darreg]] proposed the term ''xenharmonic'' (from the [[Greek language|Greek]] ''ξένος'', ''foreign'', and [[Greek language|Greek]] ''ξενία'', ''hospitable'') for any scale other than the 12-tone equal-tempered scale. (See [[Xenharmony|xenharmonic]] music).
==Usage==
One reason composers of microtonal music explore alternate tunings is that each unique division of the octave or [[pseudo-octave]] creates new interval relationships and thereby new sound possibilities. Just-intonation scales such as [[Harry Partch's 43-tone scale|Partch's 43 tone unequal scale]] start with the (non-tempered) diatonic Western scale, and many of them extend it, in Partch's case up to the 11th [[overtone|partial]] (Partch 1979, 93, 119–37). Some microtonal scales, like the [[19 equal temperament|19 tone]] or [[31 equal temperament|31 tone]] equal-tempered scales, contain intervals that are close to those within diatonic scales. Other equal divisions of the octave, such as 15-, 16-, and 17-tone, may also support a diatonic basis for Western musical notation and tonal theory, and have other viable intervallic relationships (Blackwood 1991). For example, although 19-note equal tuning provides the same diatonic chordal relations as are found in 12-note equal tuning, the available chromatic progressions are quite different, because of the closed circle of nineteen fifths, as opposed to twelve. In 12-note equal tuning, a modulating sequence in successive descending minor thirds will return to its starting point at the fourth transposed repetition, but in 19-note tuning the initial chord is not found until the nineteenth transposed repetition, creating a rather confounding but not disagreeable effect (Blackwood 1991, 171).
=History=
{{Essay-like|date=April 2008}}
The earliest music of which a written record exists anywhere on earth appears to be the [[Hurrian]] Hymn (Fink 1988; Dumbrill 2000, {{Page needed|date=March 2009}}). The clay tablets were discovered in the ancient city of [[Ugarit]] on the Mediterranean coast of [[Syria]]. The first modern recording of this music was made by Anne Draffkorn Kilmer and Richard L. Crocker in 1976 (Kilmer, Crocker, and Brown 1976). This music may have been microtonal, even though, while interpretation of many aspects of the Hurrian records has been disputed (West 1994), expert opinion overwhelmingly favors some variety of diatonic, Pythagorean tuning (Duchesne-Guillemin 1975, 1977, 1980, 1984; Kilmer 1965, 1971, 1974, 1976; Vitale 1982; West 1994; Wulstan 1968).
The Hellenic civilizations of ancient Greece also left fragmentary records of their music—c.f., the [[Delphic Hymn]]s. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining [[tetrachord]]s, recognizing three 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]]) (West 1992, 160–72).
[[Joel Mandelbaum]] has argued in his PhD thesis that scholarship done on the [[Antiphonary of St. Benigne, Dijon|Antiphonarium Codex Montpellier]] suggests that it records microtonal tunings, probably the Greek enharmonic (Mandelbaum 1961, {{Page needed|date=April 2008}}<!--This dissertation has 461 pages in it, surely Mandelbaum does not spread his demonstration of Montpellier over all of them.-->). In his opinion, this indicates that microtonal tunings survived and were commonly used late into the medieval period.
Meantone tunings sound similar to, but more harmonious than, the later Western tuning of 12 equal semitones per octave, when performed on an instrument limited to 12 pitches per octave, as long as the music is restricted to a narrow compass of musical keys close to the root note of the tuning (i.e., if the meantone tuning is tuned starting with C, the keys close to C major will sound like a more harmonious take on conventional Western music; distant keys, however, like Eb minor, will contain highly audibly exotic and sometimes discordant musical intervals.){{Citation needed|date=November 2009}} Such extensive modulation in meantone tuning on a 12-note-per octave instrument sounds "wolf" fifths and other exotic musical intervals not found in music using 12 equal pitches per octave.
Many tunings of meantone temperament can be made to close, in practice, using a manageable number of notes per octave. The 1/3-comma and 1/4-comma meantones close very nearly in 19 and 31 tones per octave, respectively, with better approximations to the [[Limit (music)|5-limit]] thirds and sixths of the diatonic scale than can be found on modern 12-tone instruments.
<!-- 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, making use of audibly microtonal intervals like the 63-cent interval of 1/19 of an octave (Lindley 2001a).
The Italian [[Renaissance music|Renaissance]] composer and theorist [[Nicola Vicentino]] (1511–1576) experimented with microintervals and built a keyboard with 36 keys to the octave, known as the [[archicembalo]].{{Citation needed|date=March 2010}} However Vicentino's experiments were primarily motivated by his research (as he saw it) on the ancient Greek [[genus (music)|genera]], and by his desire to have beatless intervals (when played with near-harmonic-series timbres) available within chromatic compositions.{{Citation needed|date=March 2010}}
[[Jacques Fromental Halévy]] composed a quarter-tone work for soli, choir and orchestra "Prométhée enchaîné" in 1849, and European composers produced an ever-increasing number of microtonal compositions as the 19th century waned and the 20th century began.{{Citation needed|date=March 2010}}
By the 1910s and 1920s, a fad emerged for [[quarter tone]]s (24 equal pitches per octave),{{Citation needed|date=March 2010}} inspiring composers as [[Charles Ives]], [[Julián Carrillo]], [[Alois Hába]], [[Ivan Wyschnegradsky]], and [[Mildred Couper]]. Such was the popularity of 24 equal during the late teens and 1920s, for example, that [[Erwin Schulhoff]] gave classes in quarter-tone composition at the [[Prague Conservatory]].{{Citation needed|date=March 2010}} [[Béla Bartók]] came late, and only sporadically, to quartertones (e.g. in his Sonata for violin solo, which uses quarter tones in an essential manner).{{Citation needed|date=March 2010}}
[[Alexander John Ellis]], who in the 1880s produced a translation with extensive footnotes and appendices to Helmholtz's ''On the Sensations of Tone'', proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings (Helmholtz 1885, 514–27). Ellis also studied the tunings of non-Western cultures and, in a report to the Royal Society, determined that they did not use either equal divisions of the octave or just intonation intervals (Ellis 1884). Ellis inspired [[Harry Partch]] immensely (Partch 1979, vii).
During the Exposition Universelle of 1889, [[Claude Debussy]] heard a Balinese gamelan performance and was exposed to their non-Western tunings and rhythms. Some scholars have ascribed Debussy's subsequent innovative use of the whole-tone (6 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 (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" (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'', ''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 (Don 1991, 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.
While experimenting with his violin in 1895, [[Julian Carrillo]] (1875–1965) discovered the sixteenths of tone, i.e., sixteen clearly different sounds between the pitches of G and A emitted by the fourth violin string. He named his discovery ''[[Sonido 13]]'' (the thirteenth sound) and wrote on music theory and the physics of music. He invented a simple numerical musical notation that can represent scales based on any division of the octave, like thirds, fourths, quarters, fifths, sixths, sevenths, and so on (even if Carrillo wrote, most of the time, for quarters, eights, and sixteenths combined, the notation is able to represent any imaginable subdivision). He invented new musical instruments, and adapted others to produce microintervals. He composed a large amount of microtonal music and recorded about 30 of his compositions.{{Citation needed|date=March 2010}}
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) (Partch 1979, 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 again (continuing to build his handcrafted orchestra of microtonal just intonation instruments) and Ivor Darreg (who built the first fully retunable electronic synthesizer capable of any division of the octave, just or equal or non-just non-equal).{{Citation needed|date=March 2010}}
Barbara Benary also formed Gamelan Son of Lion around this period, and [[Lou Harrison]] was instrumental in creating American gamelan orchestras at [[Mills College]].{{Citation needed|date=November 2009}} In Europe, the "Spectralists" in Paris created their first works from 1973 on with an extensive use of microtonal harmony. The main composers were [[Hugues Dufourt]], [[Gérard Grisey]], [[Tristan Murail]] and [[Michael Levinas]]{{Citation needed|date=November 2009}}; see also the Parisian ensemble "L'itinéraire".
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 (Griffiths, Lindley, & Zannos 2001). In 1954, [[Karlheinz Stockhausen]] built his electronic ''Studie II'' on an 81-step scale starting from 100 Hz with the interval of 5<sup>1/25</sup> between steps (Stockhausen 1964, 37), and in ''[[Gesang der Jünglinge]]'' (1955–56) he used various scales, ranging from seven up to sixty equal divisions of the octave (Decroupet and Ungeheuer 1998, 105, 116, 119–21). In 1955, [[Ernst Krenek]] used 13 equal-tempered intervals per octave in his Whitsun oratorio, ''Spiritus intelligentiae, sanctus'' (Griffiths, Lindley, & Zannos 2001).
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" (Carlos 1989–96).
=Microtonalism in rock music=
A form of microtone known as the [[blue note]] is an integral part of [[rock music]] and its predecessor, [[blues]]. The blue notes, located on the third, fifth, and seventh notes of a diatonic major scale, are flattened by an inexact amount, generally less than a semitone.{{Citation needed|date=November 2009}} The flattened fifth is also known as the sharpened fourth (Ferguson 1999, 20).
The band [[Cipher (New Wave band)|Cipher]] (Los Angeles-late 70s to mid 80s) played in a 7-limit 22-tone scale of [[Erv Wilson]]. The intonation was done under the guidance of Jose Garcia who refretted all the guitars and bass. Co-composer, Marsha Mann, who was the lead singer and lyricist for the band, also sang in the same tuning.{{Citation needed|date=November 2009}} They appeared on [[New Wave Theater]].{{Citation needed|date=November 2009}} Cipher is listed and pictured (above The Clash) in the 1985 illustrated encyclopedia, 'Who's New Wave in Music', by David Blanco, who refers to them as a 'microtonal dance band'.
Also part of the L.A. punk scene was [[Kraig Grady]] who played extensively both as a solo act (on [[pump organ]] and [[hammered dulcimer]]) and as a member of bands such as the string ensemble Fat and Fucked Up and Brad Laner’s large ensemble Debt of Nature. Grady's instruments were retuned to his 7-limit Centaur tuning.{{Citation needed|date=November 2009}}
The Japanese band [[Syzygys]] (Hitomi Shimizu and Hiromi Nishida) have released two albums utilizing the 43-tone scale of Harry Partch, using a modified reed organ (Syzygys 2007).
Zia{{Who|date=October 2010}}<!--Is this a person, or a band, or what? There is a very long disambiguation page for this name, but nothing on it seems to fit here. The reference at the end of the sentence is to something spelled the same way, but in all caps, like an acronym.--> has released several albums making use of the [[Bohlen–Pierce scale]] and other equal temperaments such as the [[19 equal temperament|19tet]] and 10tet. Zia performs on electronic instruments that specifically do not reference the standard 12-tone tuning (ZIA [2006]).
The November 2004 WSES Official Newsletter for Acoustics, Science, and Technology of Music mentions that "bands from [[Sonic Youth]] to [[Art Rock Circus]] have written music with non-standard and microtonal guitar tunings." Sonic Youth uses [[scordatura|alternate tuned guitars]] with several strings tuned slightly different from each other, creating a [[Beat (acoustics)|beating]] sound. The [[3rd Bridge|third bridge]] technique led to the microtonal scale used on the [[Yuri Landman]]'s [[Moodswinger]] and his clarification based on this scale about the physical consonant paradox present in [[experimental rock]] (Landman 2008). [[These Are Powers]] modified their bass guitar into a microtonal adjusted instrument based on the changed [[musical scale]] of the bass guitar (Carr 2008). Because the fretboard isn't representing the [[12TET]] anymore because of the preparation, the chord combinations and tone progressions form an altered [[microtonal]] spectrum. The Japanese multi-instrumentalist and [[experimental musical instrument]] builder [[Yuichi Onoue]] developed an 24-TET [[quarter tone]] tuning on his guitar as well as a deeply scaloped electric guitar for microtonal playing techniques (Landman [n.d.]).
=See also=
* [[3rd Bridge]]
* [[Arab tone system]] and [[Arabic maqam|maqam]]
* [[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]]
===Western microtonal pioneers===
Pioneers of modern Western microtonal music include:
* [[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'' in quartertone tuning, natural harmonics in his Horn Trio, later just intonation in his solo concertos)
* [[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 attempt 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)
* [[Alvin Lucier]] (U.S.A., b. 1931)
* [[Joel Mandelbaum]] (U.S.A., b. 1932)
* [[Krzysztof Penderecki]] (Poland, b. 1933, quartertones)
* [[Easley Blackwood (musician)|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)
* [[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)
=Recent microtonal composers=
* [[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)
* [[Warren Burt]] (b. 1949)
* [[Manfred Stahnke]] (b. 1951)
* [[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)
* [[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)
* [[Georg Hajdu]] (b. 1960)
* [[William Susman]] (b. 1960)
* [[Daniel James Wolf]] (b. 1961)
* [[François Paris]] (b.1961)
* [[Rod Poole]] (b.1962 - d.2007)
* [[Harold Fortuin]] (b. 1964)
* [[Marc Sabat]] (b. 1965)
* [[Georges Lentz]] (b. 1965)
* [[Geoff Smith (British musician)|Geoff Smith]] (b. 1966)
* [[Yitzhak Yedid]] (b.1971)
* [[Aphex Twin|Richard D. James]] (b. 1971)
* [[Adam Silverman]] (b. 1973)
* [[Yuri Landman]] (b. 1973)
* [[Kristoffer Zegers]] (b. 1973)
* [[Gregg Rossetti]] (b. 1982)
=Microtonal researchers=
* [[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)
* [[Joel Mandelbaum]] (b. 1932)
* [[James Tenney]] (1934–2006)
* [[Clarence Barlow]] (b. 1945)
* [[Valeri Brainin]] (b. 1948)
* [[Jacques Dudon]] (b. 1951)
* [[William Sethares]] (b. 1955)
* [[Georg Hajdu]] (b. 1960)
* [[Bob Gilmore]] (b. 1961)
* [[Marc Sabat]] (b. 1965)
=References=
*[[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.
*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.
*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 3039100882
*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
*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.
*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.
*[[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.
*Blackwood, Easley. 1985. ''The Structure of Recognizable Diatonic Tunings''. Princeton: Princeton University Press. ISBN 0691091293
*Blackwood, Easley. 1991. "Modes and Chord Progressions in Equal Tunings". ''Perspectives of New Music'' 29, no. 2 (Summer): 166–200.
*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.
*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.
*[[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).
* Carr, Vanessa. 2008. "[http://www.vancarr.com/?p=42 These Are Ghost Punks]". Vanessa Carr’s website (29 February). (Accessed 2 April 2009)
* 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.
* Duchesne-Guillemin, Marcelle. "Les Problemes de la notation hourrite". ''Revue d'Assyriologie'' 69 (1975), 159-73,
* Duchesne-Guillemin, Marcelle. 1980. "Sur la restitution de la musique hourrite". ''Revue de musicologie'' 66: 5-26.
* Duchesne-Guillemin, Marcelle. 1977. ''Dechaffrement de la musique babylonienne'' (Accademia dei Lincei, Quaderno 236), Rome, 1977;
* Duchesne-Guillemin, Marcelle. 1984. ''[http://128.97.6.202/attach/duchesne-guillermin%201984%20the%20discovery%20of%20mesopotamian%20music.pdf A Hurrian Musical Score from Ugarit]''. Sources from the Ancient Near East 2, fascicle 2. Malibu: Undena Publications. ISBN 0-89003-158-4
*Don, Gary. 2001. "Brilliant Colors Provocatively Mixed: Overtone Structures in the Music of Debussy". ''Music Theory Spectrum'' 23, no. 1 (Spring): 61–73.
*Dumbrill, Richard J. 2000. ''The Musicology and Organology of the Ancient Near East'', second edition. London: Tadema Press. ISBN 0953363309
*[[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.
*[[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 0786642858.
*Fink, Robert. 1988. "The Oldest Song in the World". ''Archaeologia Musicalis'' 2, no. 2:98–100.
*Gilmore, Bob. 1998. ''Harry Partch: A Biography''. New Haven: Yale University Press. ISBN 0300065213.
*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. London: Macmillan Publishers; New York: Grove's Dictionaries of Music.
*[[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.
*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.
*Howat, Roy. 2001. "Debussy, (Achille-)Claude: 10, 'Musical Language'". ''The New Grove Dictionary of Music and Musicians'', ed. S. Sadie and J. Tyrrell. London: Macmillan.
*Jedrzejewski, Franck. 2003. ''Dictionnaire des musiques microtonales'' [Dictionary of Microtonal Musics]. Paris: L'Harmattan. ISBN 2-7475-5576-3.
* Johnston, Ben, 2006. '''Maximum Clarity' and other writings on music'', ed. B. Gilmore. Urbana and Chicago: University of Illinois Press.
* Kilmer, Anne Draffkorn. 1965. "The Strings of Musical Instruments: their Names, Numbers, and Significance". ''Studies in Honor of Benno Landsberger'' = ''Assyriological Studies'' 16: 261–68.
* Kilmer, Anne Draffkorn. 1971. "The Discovery of an Ancient Mesopotamian Theory of Music". ''Proceedings of the American Philosophical Association'' 115, no. 2 (April): 131–49.
* Kilmer, Anne Draffkorn. 1974. "The Cult Song with Music from Ancient Ugarit: Another Interpretation". ''Revue d'Assyriologie'' 68:69–82.
* Kilmer, Anne Draffkorn, Richard L. Crocker, and Robert R. Brown. 1976. ''Sounds from Silence: Recent Discoveries in Ancient Near Eastern Music''. Berkeley: Bit Enki Publications. (booklet and LP record, Bit Enki Records BTNK 101, reissued [s.d.] with CD).
* [[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)
* 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)
* Leedy, Douglas. 2001. "A Venerable Temperament Rediscovered". ''Perspectives of New Music'' 29, no. 2 (Summer): 202–11.
* Lesure, François. 2001. "Debussy, (Achille-)Claude: 7, 'Models and Influences'". ''The New Grove Dictionary of Music and Musicians'', ed. S. Sadie and J. Tyrrell. London: Macmillan.
*[[Mark Lindley|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; New York: Grove's Dictionaries of Music.
*Lindley, Mark. 2001b. "Temperaments". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers; New York: Grove's Dictionaries of Music.
* Mandelbaum, M. Joel. 1961. "Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament.[http://anaphoria.com/mandelbaum.html]". Ph.D. thesis. Bloomington: Indiana University.
* [[Harry Partch|Partch, Harry]]. 1979. ''Genesis of a Music'', 2nd edition. New York: Da Capo Press. ISBN 0-306-80106-X.
* Stockhausen, Karlheinz. 1964. ''Texte'' 2: Aufsätze 1952–1962 zur musikalischen Praxis, edited and with an afterword by Dieter Schnebel. Cologne: Verlag M. DuMont Schauberg.
* Szygys (musical group). 2007. "[http://www.syzygys.jp/e_pages Szygys: A Female Duo Who Plays Microtonal Pop Music]" (webpage)
* Vitale, Raoul. 1982. "La Musique suméro-accadienne: gamme et notation musicale". ''Ugarit-Forschungen'' 14: 241–63.
* West, Martin Litchfield. 1992. ''Ancient Greek Music''. Oxford: Clarendon Press; New York: Oxford University Press. ISBN 0198148976 (cloth) ISBN 0-19-814975-1 (pbk)
* West, M[artin] L[itchfield]. 1994. "The Babylonian Musical Notation and the Hurrian Melodic Texts". ''Music and Letters'' 75, no. 2 (May): 161–79.
* Wulstan, David. 1968. "The Tuning of the Babylonian Harp", ''Iraq'' 30: 215–28.
* [[Ivan Wyschnegradsky|Wyschnegradsky, Ivan]]. 1937. "La musique à quarts de ton et sa réalisation pratique". ''La Revue Musicale'' no. 171:26–33.
* Wyschnegradsky, Ivan. 1972. “L'Ultrachromatisme et les espaces non octaviants”. ''La Revue Musicale'' nos. 290–91:71-141.
* ZIA (musical group). [2006]. [http://www.ziaspace.com/ZIA/sections/news.html ZIA homepage] (Accessed 2 April 2009)
==External links==
* 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)
* [[Open Directory Project]] [n.d.] [http://search.dmoz.org/cgi-bin/search?search=microtonal+music Microtonal 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
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<html><head><title>Microtonal music</title></head><body><!-- ws:start:WikiTextTocRule:22:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><a href="#Terminology">Terminology</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#History">History</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Microtonalism in electronic music">Microtonalism in electronic music</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Microtonalism in rock music">Microtonalism in rock music</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#See also">See also</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Recent microtonal composers">Recent microtonal composers</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Microtonal researchers">Microtonal researchers</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#References">References</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> <!-- ws:end:WikiTextTocRule:34 --><br /> <br /> <strong>Microtonal music</strong> is <a class="wiki_link" href="/music">music</a> using microtones—<a class="wiki_link" href="/musical%20interval">intervals</a> of less than an <a class="wiki_link" href="/Equal%20Temperament">equally spaced</a> <a class="wiki_link" href="/semitone">semitone</a>. Microtonal music can also refer to music which uses intervals not found in the Western system of 12 equal intervals to the octave.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Terminology"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terminology</h1> <a class="wiki_link" href="http://image.wikispaces.com/partial%20accidentals.svg">right|frame|[[Quarter-tone</a> <a class="wiki_link" href="/Accidental%20%28music%29">accidentals</a> residing outside the Western <a class="wiki_link" href="/semitone">semitone</a>: <BR>half-sharp, <a class="wiki_link" href="/Sharp%20%28music%29">sharp</a>, sharp-and-a-half;<BR>half-flat, <a class="wiki_link" href="/flat%20%28music%29">flat</a>, flat-and-a-half, another variant of flat-and-a-half]]<br /> ''Microtonal music'' can refer to all music which contains intervals smaller than the conventional contemporary Western <a class="wiki_link" href="/semitone">semitone</a>. The term implies music containing very small intervals but can include any tuning that differs from the western 12-tone <a class="wiki_link" href="/equal%20temperament">equal temperament</a>. The following systems are considered to be microtonal: the traditional <a class="wiki_link" href="/Carnatic%20Music">Carnatic</a> system of 22 <a class="wiki_link" href="/%C5%9Aruti%20%28music%29">śruti</a>; much Indonesian <a class="wiki_link" href="/gamelan">gamelan music</a>; Thai, Burmese, and African music using seven tones in each (approximate) octave; and <a class="wiki_link" href="/blues">blues</a> and/or <a class="wiki_link" href="/rock%20music">rock music</a> which makes extensive use of <a class="wiki_link" href="/blue%20notes">blue notes</a>. Also, music using <a class="wiki_link" href="/just%20intonation">just intonation</a>, <a class="wiki_link" href="/meantone%20temperament">meantone temperament</a>, or other alternative tunings may be considered microtonal.<br /><br /> Other terminology has been used (and is still used today) by theorists and composers. ''Micro-intervals'' is commonly used to speak about intervals smaller than the <a class="wiki_link" href="/semitone">semitone</a>, and sometimes ''macro-intervals'' for non-multiples of the <a class="wiki_link" href="/semitone">semitone</a> greater than it. <a class="wiki_link" href="/Ivan%20Wyschnegradsky">Ivan Wyschnegradsky</a> used the term ''ultra-chromatic'' for micro-intervals and ''infra-chromatic'' for macro-intervals (Wyschnegradsky 1972, 84-87). <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> proposed the term ''xenharmonic'' (from the <a class="wiki_link" href="/Greek%20language">Greek</a> ''ξένος'', ''foreign'', and <a class="wiki_link" href="/Greek%20language">Greek</a> ''ξενία'', ''hospitable'') for any scale other than the 12-tone equal-tempered scale. (See <a class="wiki_link" href="/Xenharmony">xenharmonic</a> music).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Terminology-Usage"></a><!-- ws:end:WikiTextHeadingRule:2 -->Usage</h2> One reason composers of microtonal music explore alternate tunings is that each unique division of the octave or <a class="wiki_link" href="/pseudo-octave">pseudo-octave</a> creates new interval relationships and thereby new sound possibilities. Just-intonation scales such as <a class="wiki_link" href="/Harry%20Partch%27s%2043-tone%20scale">Partch's 43 tone unequal scale</a> start with the (non-tempered) diatonic Western scale, and many of them extend it, in Partch's case up to the 11th <a class="wiki_link" href="/overtone">partial</a> (Partch 1979, 93, 119–37). Some microtonal scales, like the <a class="wiki_link" href="/19%20equal%20temperament">19 tone</a> or <a class="wiki_link" href="/31%20equal%20temperament">31 tone</a> equal-tempered scales, contain intervals that are close to those within diatonic scales. Other equal divisions of the octave, such as 15-, 16-, and 17-tone, may also support a diatonic basis for Western musical notation and tonal theory, and have other viable intervallic relationships (Blackwood 1991). For example, although 19-note equal tuning provides the same diatonic chordal relations as are found in 12-note equal tuning, the available chromatic progressions are quite different, because of the closed circle of nineteen fifths, as opposed to twelve. In 12-note equal tuning, a modulating sequence in successive descending minor thirds will return to its starting point at the fourth transposed repetition, but in 19-note tuning the initial chord is not found until the nineteenth transposed repetition, creating a rather confounding but not disagreeable effect (Blackwood 1991, 171).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="History"></a><!-- ws:end:WikiTextHeadingRule:4 -->History</h1> <tt>Essay-like|date=April 2008</tt><br /> The earliest music of which a written record exists anywhere on earth appears to be the <a class="wiki_link" href="/Hurrian">Hurrian</a> Hymn (Fink 1988; Dumbrill 2000, <tt>Page needed|date=March 2009</tt>). The clay tablets were discovered in the ancient city of <a class="wiki_link" href="/Ugarit">Ugarit</a> on the Mediterranean coast of <a class="wiki_link" href="/Syria">Syria</a>. The first modern recording of this music was made by Anne Draffkorn Kilmer and Richard L. Crocker in 1976 (Kilmer, Crocker, and Brown 1976). This music may have been microtonal, even though, while interpretation of many aspects of the Hurrian records has been disputed (West 1994), expert opinion overwhelmingly favors some variety of diatonic, Pythagorean tuning (Duchesne-Guillemin 1975, 1977, 1980, 1984; Kilmer 1965, 1971, 1974, 1976; Vitale 1982; West 1994; Wulstan 1968).<br /> <br /> The Hellenic civilizations of ancient Greece also left fragmentary records of their music—c.f., the <a class="wiki_link" href="/Delphic%20Hymn">Delphic Hymn</a>s. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining <a class="wiki_link" href="/tetrachord">tetrachord</a>s, recognizing three 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 <a class="wiki_link" href="/Cent%20%28music%29">cents</a>, less than half of the contemporary Western <a class="wiki_link" href="/semitone">semitone</a> 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 <a class="wiki_link" href="/just%20intonation">just intonation</a>) (West 1992, 160–72).<br /> <br /> <a class="wiki_link" href="/Joel%20Mandelbaum">Joel Mandelbaum</a> has argued in his PhD thesis that scholarship done on the <a class="wiki_link" href="/Antiphonary%20of%20St.%20Benigne%2C%20Dijon">Antiphonarium Codex Montpellier</a> suggests that it records microtonal tunings, probably the Greek enharmonic (Mandelbaum 1961, <tt>Page needed|date=April 2008</tt><!--This dissertation has 461 pages in it, surely Mandelbaum does not spread his demonstration of Montpellier over all of them.-->). In his opinion, this indicates that microtonal tunings survived and were commonly used late into the medieval period.<br /> <br /> Meantone tunings sound similar to, but more harmonious than, the later Western tuning of 12 equal semitones per octave, when performed on an instrument limited to 12 pitches per octave, as long as the music is restricted to a narrow compass of musical keys close to the root note of the tuning (i.e., if the meantone tuning is tuned starting with C, the keys close to C major will sound like a more harmonious take on conventional Western music; distant keys, however, like Eb minor, will contain highly audibly exotic and sometimes discordant musical intervals.)<tt>Citation needed|date=November 2009</tt> Such extensive modulation in meantone tuning on a 12-note-per octave instrument sounds "wolf" fifths and other exotic musical intervals not found in music using 12 equal pitches per octave.<br /> <br /> Many tunings of meantone temperament can be made to close, in practice, using a manageable number of notes per octave. The 1/3-comma and 1/4-comma meantones close very nearly in 19 and 31 tones per octave, respectively, with better approximations to the <a class="wiki_link" href="/Limit%20%28music%29">5-limit</a> thirds and sixths of the diatonic scale than can be found on modern 12-tone instruments.<br /> <br /> <!-- Image with inadequate rationale removed: <a class="wiki_link" href="http://image.wikispaces.com/Tonraum30.11-14%201.jpg">thumb|right|A reproduction of Vicentino's archicembalo</a> --><a class="wiki_link" href="/Guillaume%20Costeley">Guillaume Costeley</a>'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, making use of audibly microtonal intervals like the 63-cent interval of 1/19 of an octave (Lindley 2001a).<br /> <br /> The Italian <a class="wiki_link" href="/Renaissance%20music">Renaissance</a> composer and theorist <a class="wiki_link" href="/Nicola%20Vicentino">Nicola Vicentino</a> (1511–1576) experimented with microintervals and built a keyboard with 36 keys to the octave, known as the <a class="wiki_link" href="/archicembalo">archicembalo</a>.<tt>Citation needed|date=March 2010</tt> However Vicentino's experiments were primarily motivated by his research (as he saw it) on the ancient Greek <a class="wiki_link" href="/genus%20%28music%29">genera</a>, and by his desire to have beatless intervals (when played with near-harmonic-series timbres) available within chromatic compositions.<tt>Citation needed|date=March 2010</tt><br /> <br /> <a class="wiki_link" href="/Jacques%20Fromental%20Hal%C3%A9vy">Jacques Fromental Halévy</a> composed a quarter-tone work for soli, choir and orchestra "Prométhée enchaîné" in 1849, and European composers produced an ever-increasing number of microtonal compositions as the 19th century waned and the 20th century began.<tt>Citation needed|date=March 2010</tt><br /> <br /> By the 1910s and 1920s, a fad emerged for <a class="wiki_link" href="/quarter%20tone">quarter tone</a>s (24 equal pitches per octave),<tt>Citation needed|date=March 2010</tt> inspiring composers as <a class="wiki_link" href="/Charles%20Ives">Charles Ives</a>, <a class="wiki_link" href="/Juli%C3%A1n%20Carrillo">Julián Carrillo</a>, <a class="wiki_link" href="/Alois%20H%C3%A1ba">Alois Hába</a>, <a class="wiki_link" href="/Ivan%20Wyschnegradsky">Ivan Wyschnegradsky</a>, and <a class="wiki_link" href="/Mildred%20Couper">Mildred Couper</a>. Such was the popularity of 24 equal during the late teens and 1920s, for example, that <a class="wiki_link" href="/Erwin%20Schulhoff">Erwin Schulhoff</a> gave classes in quarter-tone composition at the <a class="wiki_link" href="/Prague%20Conservatory">Prague Conservatory</a>.<tt>Citation needed|date=March 2010</tt> <a class="wiki_link" href="/B%C3%A9la%20Bart%C3%B3k">Béla Bartók</a> came late, and only sporadically, to quartertones (e.g. in his Sonata for violin solo, which uses quarter tones in an essential manner).<tt>Citation needed|date=March 2010</tt><br /> <br /> <a class="wiki_link" href="/Alexander%20John%20Ellis">Alexander John Ellis</a>, who in the 1880s produced a translation with extensive footnotes and appendices to Helmholtz's ''On the Sensations of Tone'', proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings (Helmholtz 1885, 514–27). Ellis also studied the tunings of non-Western cultures and, in a report to the Royal Society, determined that they did not use either equal divisions of the octave or just intonation intervals (Ellis 1884). Ellis inspired <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a> immensely (Partch 1979, vii).<br /> <br /> During the Exposition Universelle of 1889, <a class="wiki_link" href="/Claude%20Debussy">Claude Debussy</a> heard a Balinese gamelan performance and was exposed to their non-Western tunings and rhythms. Some scholars have ascribed Debussy's subsequent innovative use of the whole-tone (6 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 (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" (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'', ''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 <a class="wiki_link" href="/Hermann%20Helmholtz">Hermann Helmholtz</a>'s writings (Don 1991, 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.<br /> <br /> While experimenting with his violin in 1895, <a class="wiki_link" href="/Julian%20Carrillo">Julian Carrillo</a> (1875–1965) discovered the sixteenths of tone, i.e., sixteen clearly different sounds between the pitches of G and A emitted by the fourth violin string. He named his discovery ''<a class="wiki_link" href="/Sonido%2013">Sonido 13</a>'' (the thirteenth sound) and wrote on music theory and the physics of music. He invented a simple numerical musical notation that can represent scales based on any division of the octave, like thirds, fourths, quarters, fifths, sixths, sevenths, and so on (even if Carrillo wrote, most of the time, for quarters, eights, and sixteenths combined, the notation is able to represent any imaginable subdivision). He invented new musical instruments, and adapted others to produce microintervals. He composed a large amount of microtonal music and recorded about 30 of his compositions.<tt>Citation needed|date=March 2010</tt><br /> <br /> Major microtonal composers of the 1920s and 1930s include <a class="wiki_link" href="/Alois%20H%C3%A1ba">Alois Hába</a> (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), <a class="wiki_link" href="/Ivan%20Wyschnegradsky">Ivan Wyschnegradsky</a> (third tones, quarter tones, sixth tones and twelfth tones, non octaving scales) and the early works of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a> (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) (Partch 1979, chapt. 8, "Application of the 11 Limit", 119–37).<br /> <br /> Prominent microtonal composers or researchers of the 1940s and 1950s include <a class="wiki_link" href="/Adriaan%20Daniel%20Fokker">Adriaan Daniel Fokker</a> (31 equal tones per octave), Partch again (continuing to build his handcrafted orchestra of microtonal just intonation instruments) and Ivor Darreg (who built the first fully retunable electronic synthesizer capable of any division of the octave, just or equal or non-just non-equal).<tt>Citation needed|date=March 2010</tt><br /> <br /> Barbara Benary also formed Gamelan Son of Lion around this period, and <a class="wiki_link" href="/Lou%20Harrison">Lou Harrison</a> was instrumental in creating American gamelan orchestras at <a class="wiki_link" href="/Mills%20College">Mills College</a>.<tt>Citation needed|date=November 2009</tt> In Europe, the "Spectralists" in Paris created their first works from 1973 on with an extensive use of microtonal harmony. The main composers were <a class="wiki_link" href="/Hugues%20Dufourt">Hugues Dufourt</a>, <a class="wiki_link" href="/G%C3%A9rard%20Grisey">Gérard Grisey</a>, <a class="wiki_link" href="/Tristan%20Murail">Tristan Murail</a> and <a class="wiki_link" href="/Michael%20Levinas">Michael Levinas</a><tt>Citation needed|date=November 2009</tt>; see also the Parisian ensemble "L'itinéraire".<br /> <br /> Digital synthesizers from the Yamaha TX81Z (1987) on and inexpensive software synthesizers have contributed to the ease and popularity of exploring microtonal music.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Microtonalism in electronic music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Microtonalism in electronic music</h1> Electronic music facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems (Griffiths, Lindley, & Zannos 2001). In 1954, <a class="wiki_link" href="/Karlheinz%20Stockhausen">Karlheinz Stockhausen</a> 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 (Stockhausen 1964, 37), and in ''<a class="wiki_link" href="/Gesang%20der%20J%C3%BCnglinge">Gesang der Jünglinge</a>'' (1955–56) he used various scales, ranging from seven up to sixty equal divisions of the octave (Decroupet and Ungeheuer 1998, 105, 116, 119–21). In 1955, <a class="wiki_link" href="/Ernst%20Krenek">Ernst Krenek</a> used 13 equal-tempered intervals per octave in his Whitsun oratorio, ''Spiritus intelligentiae, sanctus'' (Griffiths, Lindley, & Zannos 2001).<br /> <br /> In 1986, <a class="wiki_link" href="/Wendy%20Carlos">Wendy Carlos</a> experimented with many microtonal systems including <a class="wiki_link" href="/just%20intonation">just intonation</a>, 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" (Carlos 1989–96).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Microtonalism in rock music"></a><!-- ws:end:WikiTextHeadingRule:8 -->Microtonalism in rock music</h1> A form of microtone known as the <a class="wiki_link" href="/blue%20note">blue note</a> is an integral part of <a class="wiki_link" href="/rock%20music">rock music</a> and its predecessor, <a class="wiki_link" href="/blues">blues</a>. The blue notes, located on the third, fifth, and seventh notes of a diatonic major scale, are flattened by an inexact amount, generally less than a semitone.<tt>Citation needed|date=November 2009</tt> The flattened fifth is also known as the sharpened fourth (Ferguson 1999, 20).<br /> <br /> The band <a class="wiki_link" href="/Cipher%20%28New%20Wave%20band%29">Cipher</a> (Los Angeles-late 70s to mid 80s) played in a 7-limit 22-tone scale of <a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a>. The intonation was done under the guidance of Jose Garcia who refretted all the guitars and bass. Co-composer, Marsha Mann, who was the lead singer and lyricist for the band, also sang in the same tuning.<tt>Citation needed|date=November 2009</tt> They appeared on <a class="wiki_link" href="/New%20Wave%20Theater">New Wave Theater</a>.<tt>Citation needed|date=November 2009</tt> Cipher is listed and pictured (above The Clash) in the 1985 illustrated encyclopedia, 'Who's New Wave in Music', by David Blanco, who refers to them as a 'microtonal dance band'.<br /> <br /> Also part of the L.A. punk scene was <a class="wiki_link" href="/Kraig%20Grady">Kraig Grady</a> who played extensively both as a solo act (on <a class="wiki_link" href="/pump%20organ">pump organ</a> and <a class="wiki_link" href="/hammered%20dulcimer">hammered dulcimer</a>) and as a member of bands such as the string ensemble Fat and Fucked Up and Brad Laner’s large ensemble Debt of Nature. Grady's instruments were retuned to his 7-limit Centaur tuning.<tt>Citation needed|date=November 2009</tt><br /> <br /> The Japanese band <a class="wiki_link" href="/Syzygys">Syzygys</a> (Hitomi Shimizu and Hiromi Nishida) have released two albums utilizing the 43-tone scale of Harry Partch, using a modified reed organ (Syzygys 2007).<br /> <br /> Zia<tt>Who|date=October 2010</tt><!--Is this a person, or a band, or what? There is a very long disambiguation page for this name, but nothing on it seems to fit here. The reference at the end of the sentence is to something spelled the same way, but in all caps, like an acronym.--> has released several albums making use of the <a class="wiki_link" href="/Bohlen%E2%80%93Pierce%20scale">Bohlen–Pierce scale</a> and other equal temperaments such as the <a class="wiki_link" href="/19%20equal%20temperament">19tet</a> and 10tet. Zia performs on electronic instruments that specifically do not reference the standard 12-tone tuning (ZIA [2006]).<br /> <br /> The November 2004 WSES Official Newsletter for Acoustics, Science, and Technology of Music mentions that "bands from <a class="wiki_link" href="/Sonic%20Youth">Sonic Youth</a> to <a class="wiki_link" href="/Art%20Rock%20Circus">Art Rock Circus</a> have written music with non-standard and microtonal guitar tunings." Sonic Youth uses <a class="wiki_link" href="/scordatura">alternate tuned guitars</a> with several strings tuned slightly different from each other, creating a <a class="wiki_link" href="/Beat%20%28acoustics%29">beating</a> sound. The <a class="wiki_link" href="/3rd%20Bridge">third bridge</a> technique led to the microtonal scale used on the <a class="wiki_link" href="/Yuri%20Landman">Yuri Landman</a>'s <a class="wiki_link" href="/Moodswinger">Moodswinger</a> and his clarification based on this scale about the physical consonant paradox present in <a class="wiki_link" href="/experimental%20rock">experimental rock</a> (Landman 2008). <a class="wiki_link" href="/These%20Are%20Powers">These Are Powers</a> modified their bass guitar into a microtonal adjusted instrument based on the changed <a class="wiki_link" href="/musical%20scale">musical scale</a> of the bass guitar (Carr 2008). Because the fretboard isn't representing the <a class="wiki_link" href="/12TET">12TET</a> anymore because of the preparation, the chord combinations and tone progressions form an altered <a class="wiki_link" href="/microtonal">microtonal</a> spectrum. The Japanese multi-instrumentalist and <a class="wiki_link" href="/experimental%20musical%20instrument">experimental musical instrument</a> builder <a class="wiki_link" href="/Yuichi%20Onoue">Yuichi Onoue</a> developed an 24-TET <a class="wiki_link" href="/quarter%20tone">quarter tone</a> tuning on his guitar as well as a deeply scaloped electric guitar for microtonal playing techniques (Landman [n.d.]).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:10 -->See also</h1> <ul><li><a class="wiki_link" href="/3rd%20Bridge">3rd Bridge</a></li><li><a class="wiki_link" href="/Arab%20tone%20system">Arab tone system</a> and <a class="wiki_link" href="/Arabic%20maqam">maqam</a></li><li><a class="wiki_link" href="/Fokker%20periodicity%20blocks">Fokker periodicity blocks</a></li><li><a class="wiki_link" href="/Genus%20%28music%29">Genus (music)</a></li><li><a class="wiki_link" href="/Harmony">Harmony</a></li><li><a class="wiki_link" href="/Just%20intonation">Just intonation</a></li><li><a class="wiki_link" href="/Limit%20%28music%29">Limit (music)</a></li><li><a class="wiki_link" href="/Microtuner">Microtuner</a></li><li><a class="wiki_link" href="/MIDI%20Tuning%20Standard">MIDI tuning standard</a></li><li><a class="wiki_link" href="/Music%20of%20India">Music of India</a></li><li><a class="wiki_link" href="/Musical%20scale">Musical scale</a></li><li><a class="wiki_link" href="/Musical%20tuning">Musical tuning</a></li><li><a class="wiki_link" href="/Harry%20Partch%27s%2043-tone%20scale">Partch's 43-tone scale</a></li><li><a class="wiki_link" href="/Quarter%20tone">Quarter tone</a></li><li><a class="wiki_link" href="/Raga">Raga</a></li><li><a class="wiki_link" href="/Scala%20%28program%29">Scala</a></li></ul><br /> <!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="See also--Western microtonal pioneers"></a><!-- ws:end:WikiTextHeadingRule:12 -->Western microtonal pioneers</h3> Pioneers of modern Western microtonal music include:<br /> <ul><li><a class="wiki_link" href="/Henry%20Ward%20Poole">Henry Ward Poole</a> (keyboard designs, 1825–1890)</li></ul><br /> <ul><li><a class="wiki_link" href="/Eug%C3%A8ne%20Ysa%C3%BFe">Eugène Ysaÿe</a> (Belgium, U.S.A., 1858–1931, used quarter tones in several of the <a class="wiki_link" href="/6%20Sonatas%20for%20Solo%20Violin%2C%20Op.%2027%20%28Ysa%C3%BFe%29">Sonatas for Solo Violin, Op. 27</a>)</li><li><a class="wiki_link" href="/Charles%20Ives">Charles Ives</a> (U.S.A., 1874–1954, quartertones)</li><li><a class="wiki_link" href="/Juli%C3%A1n%20Carrillo">Julián Carrillo</a> (Mexico, 1875–1965) many different equal temperaments, look [<!-- ws:start:WikiTextUrlRule:723:http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html --><a class="wiki_link_ext" href="http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html" rel="nofollow">http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html</a><!-- ws:end:WikiTextUrlRule:723 --> here] or [<!-- ws:start:WikiTextUrlRule:724:http://paginas.tol.itesm.mx/campus/L00280370/julian.html --><a class="wiki_link_ext" href="http://paginas.tol.itesm.mx/campus/L00280370/julian.html" rel="nofollow">http://paginas.tol.itesm.mx/campus/L00280370/julian.html</a><!-- ws:end:WikiTextUrlRule:724 --> here] (mostly Spanish but some English too)</li><li><a class="wiki_link" href="/B%C3%A9la%20Bart%C3%B3k">Béla Bartók</a> (Hungary, 1881–1945, rare uses of quartertones)</li><li><a class="wiki_link" href="/George%20Enescu">George Enescu</a> (Romania, France, 1881–1955) (in ''<a class="wiki_link" href="/%C5%92dipe%20%28opera%29">Œdipe</a>'' to suggest the <a class="wiki_link" href="/enharmonic%20genus">enharmonic genus</a> of <a class="wiki_link" href="/ancient%20Greek%20music">ancient Greek music</a>, and in the Third Violin Sonata, as inflections characteristic of Romanian folk music)</li><li><a class="wiki_link" href="/Karol%20Szymanowski">Karol Szymanowski</a> (Poland, 1882–1937, used quartertones on the violin in ''Myths'' Op. 30, 1915)</li><li><a class="wiki_link" href="/Percy%20Grainger">Percy Grainger</a> (Australia, 1882–1961, particularly works for his "free music machine")</li><li><a class="wiki_link" href="/Edgard%20Var%C3%A8se">Edgard Varèse</a> (France, U.S.A., 1883–1965, quartertones)</li><li><a class="wiki_link" href="/Luigi%20Russolo">Luigi Russolo</a> (Italy, 1885–1947, used quartertones and eighth tones on the ''Intonarumori'', noise instruments)</li><li><a class="wiki_link" href="/Mildred%20Couper">Mildred Couper</a> (U.S.A., 1887–1974, quartertones)</li><li><a class="wiki_link" href="/Alois%20H%C3%A1ba">Alois Hába</a> (Czechoslovakia, 1893–1973, quartertones and other equal temperaments)</li><li><a class="wiki_link" href="/Ivan%20Wyschnegradsky">Ivan Wyschnegradsky</a> (U.S.S.R. (Russia), France, 1893–1979, quartertones, twelfth tones and other equal temperaments)</li><li><a class="wiki_link" href="/Harry%20Partch">Harry Partch</a> (U.S.A., 1901–1974, just intonation)</li><li><a class="wiki_link" href="/Eivind%20Groven">Eivind Groven</a> (Norway, 1901–1977, 53ET)</li><li><a class="wiki_link" href="/Henk%20Badings">Henk Badings</a> (The Netherlands, 1907–1987, 31ET)</li><li><a class="wiki_link" href="/Maurice%20Ohana">Maurice Ohana</a> (France, 1913–1992, third tones (18-equal) temperament and quarter tones (24ET) most particularly)</li><li><a class="wiki_link" href="/Giacinto%20Scelsi">Giacinto Scelsi</a> (Italy, 1905–1988, intuitive linear tone deviations, quartertones, eighth tones)</li><li><a class="wiki_link" href="/Lou%20Harrison">Lou Harrison</a> (U.S.A., 1917–2003, just intonation)</li><li><a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> (U.S.A., 1917–1994)</li><li><a class="wiki_link" href="/Jean-Etienne%20Marie">Jean-Etienne Marie</a> (France, 1919–1989, many different equal temperaments: 18ET, 24ET, 30ET, 36ET, 48ET, 96ET most particularly and polymicrotonality)</li><li><a class="wiki_link" href="/Franz%20Richter%20Herf">Franz Richter Herf</a> (Austria, 1920–1989, 72-equal temperament, "ekmelic" music)</li><li><a class="wiki_link" href="/Iannis%20Xenakis">Iannis Xenakis</a> (Greece, France, 1922–2001, quarter and third tones most particularly, occasionally eighth tones)</li><li><a class="wiki_link" href="/Gy%C3%B6rgy%20Ligeti">György Ligeti</a> (Hungary, 1923–2006, ''Ramifications'' in quartertone tuning, natural harmonics in his Horn Trio, later just intonation in his solo concertos)</li><li><a class="wiki_link" href="/Luigi%20Nono">Luigi Nono</a> (Italy, 1924–1990, quartetones, eighth tones and 16th tones)</li><li><a class="wiki_link" href="/Claude%20Ballif">Claude Ballif</a> (France, 1924–2004, quartertones)</li><li><a class="wiki_link" href="/Tui%20St.%20George%20Tucker">Tui St. George Tucker</a> (1924–2004)</li><li><a class="wiki_link" href="/Pierre%20Boulez">Pierre Boulez</a> (France, b. 1925) (first attempt of <a class="wiki_link" href="/serial%20music">serial music</a> with quartertones in his pieces ''Visage Nuptial'' and "Polyphonie X", but soon after abandoning microtonal elements)</li><li><a class="wiki_link" href="/Karlheinz%20Stockhausen">Karlheinz Stockhausen</a> (Germany, 1928–2007, in his electronic works many microtonal concepts, non-octaving scales in ''Studie II'', just intonation in ''<a class="wiki_link" href="/Gruppen%20%28Stockhausen%29">Gruppen</a>'' and ''<a class="wiki_link" href="/Stimmung">Stimmung</a>'', microtonal instrumental and vocal writing throughout ''<a class="wiki_link" href="/Licht">Licht</a>'')</li><li><a class="wiki_link" href="/Ben%20Johnston%20%28composer%29">Ben Johnston</a> (U.S.A., b. 1926, extended just intonation)</li><li><a class="wiki_link" href="/Ezra%20Sims">Ezra Sims</a> (U.S.A., b. 1928, 72-tone equal temperament)</li><li><a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a> (b. 1928)</li><li><a class="wiki_link" href="/Alvin%20Lucier">Alvin Lucier</a> (U.S.A., b. 1931)</li><li><a class="wiki_link" href="/Joel%20Mandelbaum">Joel Mandelbaum</a> (U.S.A., b. 1932)</li><li><a class="wiki_link" href="/Krzysztof%20Penderecki">Krzysztof Penderecki</a> (Poland, b. 1933, quartertones)</li><li><a class="wiki_link" href="/Easley%20Blackwood%20%28musician%29">Easley Blackwood</a> (b. 1933)</li><li><a class="wiki_link" href="/Alain%20Bancquart">Alain Bancquart</a>(France, b.1934) (quarter tones and 16th tones)</li><li><a class="wiki_link" href="/James%20Tenney">James Tenney</a> (U.S.A., 1934–2006, just intonation, 72-tone equal temperament)</li><li><a class="wiki_link" href="/Terry%20Riley">Terry Riley</a> (U.S.A., b. 1935, just intonation)</li><li><a class="wiki_link" href="/La%20Monte%20Young">La Monte Young</a> (U.S.A., b. 1935, just intonation)</li><li><a class="wiki_link" href="/Douglas%20Leedy">Douglas Leedy</a> (b. 1938, just intonation, meantone)</li><li><a class="wiki_link" href="/Wendy%20Carlos">Wendy Carlos</a> (U.S.A., b. 1939, non-octaving scales)</li><li><a class="wiki_link" href="/Bruce%20Mather">Bruce Mather</a> (Canada, b.1939, different equal temperaments, following Wyschnegradsky)</li><li><a class="wiki_link" href="/Brian%20Ferneyhough">Brian Ferneyhough</a> (Great Britain, b. 1943, quartertones, 31ET in ''Unity Capsule'' for solo flute,1976)</li></ul><br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Recent microtonal composers"></a><!-- ws:end:WikiTextHeadingRule:14 -->Recent microtonal composers</h1> <ul><li><a class="wiki_link" href="/Clarence%20Barlow">Clarence Barlow</a> (b. 1945)</li><li><a class="wiki_link" href="/G%C3%A9rard%20Grisey">Gérard Grisey</a> (1946–1998) (spectral approach to microintervals, quartertones, eighth tones)</li><li><a class="wiki_link" href="/Max%20M%C3%A9reaux">Max Méreaux</a> (b. 1946)</li><li><a class="wiki_link" href="/Tristan%20Murail">Tristan Murail</a> (b. 1947) (spectral approach to microintervals, quartertones, eighth tones)</li><li><a class="wiki_link" href="/Claude%20Vivier">Claude Vivier</a> (1948–1983)</li><li><a class="wiki_link" href="/Glenn%20Branca">Glenn Branca</a> (b. 1948)</li><li><a class="wiki_link" href="/Dean%20Drummond">Dean Drummond</a> (b. 1949) (Harry Partch's instruments currently in his possession)</li><li><a class="wiki_link" href="/Lasse%20Thoresen">Lasse Thoresen</a> (b. 1949)</li><li><a class="wiki_link" href="/Warren%20Burt">Warren Burt</a> (b. 1949)</li><li><a class="wiki_link" href="/Manfred%20Stahnke">Manfred Stahnke</a> (b. 1951)</li><li><a class="wiki_link" href="/Kraig%20Grady">Kraig Grady</a> (b. 1952) (invented acoustic instruments in just intonation & recurrent sequences)</li><li><a class="wiki_link" href="/David%20First">David First</a> (b. 1953)</li><li><a class="wiki_link" href="/Georg%20Friedrich%20Haas">Georg Friedrich Haas</a> (b. 1953)</li><li><a class="wiki_link" href="/James%20Wood%20%28composer%29">James Wood</a> (b. 1953)</li><li><a class="wiki_link" href="/Paul%20Dirmeikis">Paul Dirmeikis</a> (b.1954)</li><li><a class="wiki_link" href="/Pascale%20Criton">Pascale Criton</a> (b. 1954) (different equal temperaments, most particularly very dense ETs such as the 96ET)</li><li><a class="wiki_link" href="/Stephen%20James%20Taylor">Stephen James Taylor</a> (b. 1954)</li><li><a class="wiki_link" href="/Kyle%20Gann">Kyle Gann</a> (b. 1955)</li><li><a class="wiki_link" href="/Pascal%20Dusapin">Pascal Dusapin</a> (b. 1955) (different equal temperaments, notably the 48ET)</li><li><a class="wiki_link" href="/Johnny%20Reinhard">Johnny Reinhard</a> (b. 1956) (different equal temperaments, just intonation, polymicrotonally)</li><li><a class="wiki_link" href="/Eric%20Mandat">Eric Mandat</a> (b. 1957)</li><li><a class="wiki_link" href="/Erling%20Wold">Erling Wold</a> (b. 1958)</li><li><a class="wiki_link" href="/Michael%20Bach%20%28cellist%2C%20composer%2C%20visual%20artist%29"> Michael Bach Bachtischa</a> (b. 1958)</li><li><a class="wiki_link" href="/Martin%20Smolka">Martin Smolka</a> (b. 1959)</li><li><a class="wiki_link" href="/Georg%20Hajdu">Georg Hajdu</a> (b. 1960)</li><li><a class="wiki_link" href="/William%20Susman">William Susman</a> (b. 1960)</li><li><a class="wiki_link" href="/Daniel%20James%20Wolf">Daniel James Wolf</a> (b. 1961)</li><li><a class="wiki_link" href="/Fran%C3%A7ois%20Paris">François Paris</a> (b.1961)</li><li><a class="wiki_link" href="/Rod%20Poole">Rod Poole</a> (b.1962 - d.2007)</li><li><a class="wiki_link" href="/Harold%20Fortuin">Harold Fortuin</a> (b. 1964)</li><li><a class="wiki_link" href="/Marc%20Sabat">Marc Sabat</a> (b. 1965)</li><li><a class="wiki_link" href="/Georges%20Lentz">Georges Lentz</a> (b. 1965)</li><li><a class="wiki_link" href="/Geoff%20Smith%20%28British%20musician%29">Geoff Smith</a> (b. 1966)</li><li><a class="wiki_link" href="/Yitzhak%20Yedid">Yitzhak Yedid</a> (b.1971)</li><li><a class="wiki_link" href="/Aphex%20Twin">Richard D. James</a> (b. 1971)</li><li><a class="wiki_link" href="/Adam%20Silverman">Adam Silverman</a> (b. 1973)</li><li><a class="wiki_link" href="/Yuri%20Landman">Yuri Landman</a> (b. 1973)</li><li><a class="wiki_link" href="/Kristoffer%20Zegers">Kristoffer Zegers</a> (b. 1973)</li><li><a class="wiki_link" href="/Gregg%20Rossetti">Gregg Rossetti</a> (b. 1982)</li></ul><br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Microtonal researchers"></a><!-- ws:end:WikiTextHeadingRule:16 -->Microtonal researchers</h1> <ul><li><a class="wiki_link" href="/Christiaan%20Huygens">Christiaan Huygens</a> (1629–1695)</li><li><a class="wiki_link" href="/Juli%C3%A1n%20Carrillo">Julián Carrillo</a> (1875–1965)</li><li><a class="wiki_link" href="/Adriaan%20Dani%C3%ABl%20Fokker">Adriaan Daniël Fokker</a> (1887–1972)</li><li><a class="wiki_link" href="/Ivan%20Wyschnegradsky">Ivan Wyschnegradsky</a> (1893–1979)</li><li><a class="wiki_link" href="/Alois%20H%C3%A1ba">Alois Hába</a> (1893–1973)</li><li><a class="wiki_link" href="/Harry%20Partch">Harry Partch</a> (1901–1974)</li><li><a class="wiki_link" href="/Alain%20Dani%C3%A9lou">Alain Daniélou</a> (1907–1994)</li><li><a class="wiki_link" href="/Jean-Etienne%20Marie">Jean-Etienne Marie</a> (1917–1989)</li><li><a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a> (b. 1928)</li><li><a class="wiki_link" href="/Joel%20Mandelbaum">Joel Mandelbaum</a> (b. 1932)</li><li><a class="wiki_link" href="/James%20Tenney">James Tenney</a> (1934–2006)</li><li><a class="wiki_link" href="/Clarence%20Barlow">Clarence Barlow</a> (b. 1945)</li><li><a class="wiki_link" href="/Valeri%20Brainin">Valeri Brainin</a> (b. 1948)</li><li><a class="wiki_link" href="/Jacques%20Dudon">Jacques Dudon</a> (b. 1951)</li><li><a class="wiki_link" href="/William%20Sethares">William Sethares</a> (b. 1955)</li><li><a class="wiki_link" href="/Georg%20Hajdu">Georg Hajdu</a> (b. 1960)</li><li><a class="wiki_link" href="/Bob%20Gilmore">Bob Gilmore</a> (b. 1961)</li><li><a class="wiki_link" href="/Marc%20Sabat">Marc Sabat</a> (b. 1965)</li></ul><br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="References"></a><!-- ws:end:WikiTextHeadingRule:18 -->References</h1> *<a class="wiki_link" href="/Pietro%20Aron">Aron, Pietro</a>. 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. [<!-- ws:start:WikiTextUrlRule:725:http://euromusicology.cs.uu.nl:6334/dynaweb/tmiweb/a/aartos/@Generic --><a class="wiki_link_ext" href="http://euromusicology.cs.uu.nl:6334/dynaweb/tmiweb/a/aartos/@Generic" rel="nofollow">http://euromusicology.cs.uu.nl:6334/dynaweb/tmiweb/a/aartos/@Generic</a><!-- ws:end:WikiTextUrlRule:725 -->__BookView;cs=default;ts=default Online edition of the 1529 text] <tt>it icon</tt>. 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.<br /> *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.<br /> *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 3039100882<br /> *Barbieri, Patrizio. 2003. "Temperaments, Historical". In ''Piano: An Encyclopedia'', second edition, edited by Robert Palmieri and Margaret W. Palmieri,<tt>Page needed|date=February 2011</tt><!--Inclusive page numbers of Barbieri's article.-->. New York: Routledge.<br /> *Barbieri, Patrizio. 2008. ''[<!-- ws:start:WikiTextUrlRule:726:http://www.patriziobarbieri.it/1.htm --><a class="wiki_link_ext" href="http://www.patriziobarbieri.it/1.htm" rel="nofollow">http://www.patriziobarbieri.it/1.htm</a><!-- ws:end:WikiTextUrlRule:726 --> Enharmonic instruments and music, 1470-1900]''. Latina: Il Levante Libreria Editrice. ISBN 978-88-95203-14-0<br /> *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.<br /> *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.<br /> *<a class="wiki_link" href="/Clarence%20Barlow">Barlow, Clarence</a> (ed.). 2001. "The Ratio Book." (Documentation of the Ratio Symposium Royal Conservatory The Hague 14–16 December 1992). ''Feedback Papers'' 43.<br /> *Blackwood, Easley. 1985. ''The Structure of Recognizable Diatonic Tunings''. Princeton: Princeton University Press. ISBN 0691091293<br /> *Blackwood, Easley. 1991. "Modes and Chord Progressions in Equal Tunings". ''Perspectives of New Music'' 29, no. 2 (Summer): 166–200.<br /> *Boatwright, Howard. 1971. "Ives' Quarter-Tone Impressions". 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"[<!-- ws:start:WikiTextUrlRule:729:http://www.vancarr.com/?p=42 --><a class="wiki_link_ext" href="http://www.vancarr.com/?p=42" rel="nofollow">http://www.vancarr.com/?p=42</a><!-- ws:end:WikiTextUrlRule:729 --> These Are Ghost Punks]". Vanessa Carr’s website (29 February). (Accessed 2 April 2009)</li><li>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.</li><li>Duchesne-Guillemin, Marcelle. "Les Problemes de la notation hourrite". ''Revue d'Assyriologie'' 69 (1975), 159-73,</li><li>Duchesne-Guillemin, Marcelle. 1980. "Sur la restitution de la musique hourrite". ''Revue de musicologie'' 66: 5-26.</li><li>Duchesne-Guillemin, Marcelle. 1977. ''Dechaffrement de la musique babylonienne'' (Accademia dei Lincei, Quaderno 236), Rome, 1977;</li><li>Duchesne-Guillemin, Marcelle. 1984. ''[<!-- ws:start:WikiTextUrlRule:730:http://128.97.6.202/attach/duchesne-guillermin%201984%20the%20discovery%20of%20mesopotamian%20music.pdf --><a class="wiki_link_ext" href="http://128.97.6.202/attach/duchesne-guillermin%201984%20the%20discovery%20of%20mesopotamian%20music.pdf" rel="nofollow">http://128.97.6.202/attach/duchesne-guillermin%201984%20the%20discovery%20of%20mesopotamian%20music.pdf</a><!-- ws:end:WikiTextUrlRule:730 --> A Hurrian Musical Score from Ugarit]''. Sources from the Ancient Near East 2, fascicle 2. Malibu: Undena Publications. ISBN 0-89003-158-4</li></ul>*Don, Gary. 2001. "Brilliant Colors Provocatively Mixed: Overtone Structures in the Music of Debussy". ''Music Theory Spectrum'' 23, no. 1 (Spring): 61–73.<br /> *Dumbrill, Richard J. 2000. ''The Musicology and Organology of the Ancient Near East'', second edition. London: Tadema Press. ISBN 0953363309<br /> *<a class="wiki_link" href="/Alexander%20John%20Ellis">Ellis, Alexander J</a>. 1884. "Tonometrical Observations on Some Existing Non-Harmonic Musical Scales". ''Proceedings of the Royal Society of London'' 37:368–85.<br /> *<a class="wiki_link" href="/Jim%20Ferguson">Ferguson, Jim</a>. 1999. ''All Blues Soloing for Jazz Guitar: Scales, Licks, Concepts & Choruses''. Santa Cruz: Guitar Master Class; Pacific, MO: Mel Bay. ISBN 0786642858.<br /> *Fink, Robert. 1988. "The Oldest Song in the World". ''Archaeologia Musicalis'' 2, no. 2:98–100.<br /> *Gilmore, Bob. 1998. ''Harry Partch: A Biography''. New Haven: Yale University Press. ISBN 0300065213.<br /> *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. London: Macmillan Publishers; New York: Grove's Dictionaries of Music.<br /> *<a class="wiki_link" href="/Hermann%20von%20Helmholtz">Helmholtz, Hermann von</a>. 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.<br /> *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.<br /> *Howat, Roy. 2001. "Debussy, (Achille-)Claude: 10, 'Musical Language'". ''The New Grove Dictionary of Music and Musicians'', ed. S. Sadie and J. Tyrrell. London: Macmillan.<br /> *Jedrzejewski, Franck. 2003. ''Dictionnaire des musiques microtonales'' [Dictionary of Microtonal Musics]. Paris: L'Harmattan. ISBN 2-7475-5576-3.<br /> <ul><li>Johnston, Ben, 2006. 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"Third Bridge Helix: From Experimental Punk to Ancient Chinese Music and the Universal Physical Laws of Consonance". ''[<!-- ws:start:WikiTextUrlRule:731:http://www.furious.com/perfect/experimentalstringinstruments.html --><a class="wiki_link_ext" href="http://www.furious.com/perfect/experimentalstringinstruments.html" rel="nofollow">http://www.furious.com/perfect/experimentalstringinstruments.html</a><!-- ws:end:WikiTextUrlRule:731 --> Perfect Sound Forever (online music magazine)]''. (Accessed 6 December 2008)</li><li>Landman, Yuri. [n.d.] "[<!-- ws:start:WikiTextUrlRule:732:http://www.hypercustom.com/yuichionoue.html --><a class="wiki_link_ext" href="http://www.hypercustom.com/yuichionoue.html" rel="nofollow">http://www.hypercustom.com/yuichionoue.html</a><!-- ws:end:WikiTextUrlRule:732 --> Yuichi Onoue’s Kaisatsuko]" on [<!-- ws:start:WikiTextUrlRule:733:http://www.hypercustom.com --><a class="wiki_link_ext" href="http://www.hypercustom.com" rel="nofollow">http://www.hypercustom.com</a><!-- ws:end:WikiTextUrlRule:733 --> Hypercustom.com]. (Accessed 31 March 2009)</li><li>Leedy, Douglas. 2001. "A Venerable Temperament Rediscovered". ''Perspectives of New Music'' 29, no. 2 (Summer): 202–11.</li><li>Lesure, François. 2001. "Debussy, (Achille-)Claude: 7, 'Models and Influences'". ''The New Grove Dictionary of Music and Musicians'', ed. S. Sadie and J. Tyrrell. London: Macmillan.</li></ul>*<a class="wiki_link" href="/Mark%20Lindley">Lindley, Mark</a>. 2001a. "Mean-tone". 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[<!-- ws:start:WikiTextUrlRule:736:http://www.ziaspace.com/ZIA/sections/news.html --><a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/sections/news.html" rel="nofollow">http://www.ziaspace.com/ZIA/sections/news.html</a><!-- ws:end:WikiTextUrlRule:736 --> ZIA homepage] (Accessed 2 April 2009)</li></ul><br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="References-External links"></a><!-- ws:end:WikiTextHeadingRule:20 -->External links</h2> <ul><li>Aikin, Jim. 2003. [<!-- ws:start:WikiTextUrlRule:737:http://emusician.com/tutorials/emusic_playing_cracks/ --><a class="wiki_link_ext" href="http://emusician.com/tutorials/emusic_playing_cracks/" rel="nofollow">http://emusician.com/tutorials/emusic_playing_cracks/</a><!-- ws:end:WikiTextUrlRule:737 --> Jim Aikin's article on alternative tuning in electronic music]</li><li>Anon. [n.d.]. "[<!-- ws:start:WikiTextUrlRule:738:http://www.hoasm.org/IVO/Vicentino.html --><a class="wiki_link_ext" href="http://www.hoasm.org/IVO/Vicentino.html" rel="nofollow">http://www.hoasm.org/IVO/Vicentino.html</a><!-- ws:end:WikiTextUrlRule:738 --> 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)</li><li>Chalmers, John. [<!-- ws:start:WikiTextUrlRule:739:http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html --><a class="wiki_link_ext" href="http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html" rel="nofollow">http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html</a><!-- ws:end:WikiTextUrlRule:739 --> Dr. John Chalmers Divisions of the Tetrachord]</li><li>Loli, Charles. 2008. " [<!-- ws:start:WikiTextUrlRule:740:http://microtonalismo.com --><a class="wiki_link_ext" href="http://microtonalismo.com" rel="nofollow">http://microtonalismo.com</a><!-- ws:end:WikiTextUrlRule:740 --> Microtonalismo]". (Article on alternative tuning in Peruvian music)</li><li><a class="wiki_link" href="/Open%20Directory%20Project">Open Directory Project</a> [n.d.] [<!-- ws:start:WikiTextUrlRule:741:http://search.dmoz.org/cgi-bin/search?search=microtonal+music --><a class="wiki_link_ext" href="http://search.dmoz.org/cgi-bin/search?search=microtonal+music" rel="nofollow">http://search.dmoz.org/cgi-bin/search?search=microtonal+music</a><!-- ws:end:WikiTextUrlRule:741 --> Microtonal Music]</li><li>Solís Winkler, Ernesto. 2004. "[<!-- ws:start:WikiTextUrlRule:742:http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html --><a class="wiki_link_ext" href="http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html" rel="nofollow">http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html</a><!-- ws:end:WikiTextUrlRule:742 --> Julian Carrillo and the 13th Sound: A Microtonal Musical System]". (Accessed 19 August 2008)</li></ul>*<a class="wiki_link" href="/Erv%20Wilson">Wilson, Erv</a>. "[<!-- ws:start:WikiTextUrlRule:743:http://anaphoria.com/wilson.html --><a class="wiki_link_ext" href="http://anaphoria.com/wilson.html" rel="nofollow">http://anaphoria.com/wilson.html</a><!-- ws:end:WikiTextUrlRule:743 --> Wilson Archives of papers on microtonal theory]"<br /> <ul><li>[<!-- ws:start:WikiTextUrlRule:744:http://xenharmonic.wikispaces.com/MicrotonalListeningList --><a href="http://xenharmonic.wikispaces.com/MicrotonalListeningList">http://xenharmonic.wikispaces.com/MicrotonalListeningList</a><!-- ws:end:WikiTextUrlRule:744 --> Links to microtonal composers] at <a class="wiki_link" href="/Xenharmonic">Xenharmonic</a> Wiki</li><li>[<!-- ws:start:WikiTextUrlRule:745:http://xenharmonic.wikispaces.com/Projects --><a href="http://xenharmonic.wikispaces.com/Projects">http://xenharmonic.wikispaces.com/Projects</a><!-- ws:end:WikiTextUrlRule:745 --> Links to microtonal projects around the world] at <a class="wiki_link" href="/Xenharmonic">Xenharmonic</a> Wiki</li></ul><br /> <tt>Timbre</tt><br /> <br /> <tt>DEFAULTSORT:Microtonal Music</tt><br /> <a class="wiki_link" href="http://category.wikispaces.com/Musical%20tuning">Category/Musical tuning</a><br /> <a class="wiki_link" href="http://category.wikispaces.com/Music%20theory">Category/Music theory</a><br /> <a class="wiki_link" href="http://category.wikispaces.com/Post-tonal%20music%20theory">Category/Post-tonal music theory</a><br /> <br /> [[ca:Microtonalisme]]<br /> [[cs:Mikrotonální hudba]]<br /> [[de:Mikrotonale Musik]]<br /> [[et:Mikrotonaalsus]]<br /> [[es:Microtonalismo]]<br /> [[fr:Micro-intervalle]]<br /> [[he:מוזיקה מיקרוטונאלית]]<br /> [[nl:Microtonale muziek]]<br /> [[ja:微分音]]<br /> [[pl:Muzyka mikrotonowa]]<br /> [[pt:Música microtonal]]<br /> [[ru:Микрохроматика]]<br /> [[sv:Mikrotonal musik]]<br /> [[uk:Мікрохроматика]]<br /> [[zh:微分音音樂]]</body></html>