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Microtonal music

Microtonal music is music using microtonesintervals of less than an 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

Microtonal music may 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. By this definition, the following systems are microtonal: a diatonic scale in any meantone tuning; much Indonesian gamelan music; and Thai, Burmese, and African music which use 7 tones in each (approximate) octave. Hence, the term "microtonal" is used to describe music using intervals not found in 12-tone equal temperament, so these musics, as well as musics using just intonation, meantone temperament, or other alternative tunings may be considered microtonal.
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 (and many of those inspired by him) 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 ξένος, foreign, and Greek ξενία, hospitable) for any scale other than 12-tone equal tempered scale. (See xenharmonic music).
In any case, it should be debated whether microtone opposes macrotone (in the same way microeconomics opposes macroeconomics), or if it is used in the scientific way of measurement units, which is surely exaggerated: a micro-x is a unit of the proportion of 1 to 10-6 of x (such as µm, micrometre, micrometer or micron). Maybe the word minitones would be more appropriate, but has not been used until now.

Usage

One reason microtonalists explore alternate tunings is that each unique even or uneven division of the octave or non-octave or octave+fifth etc. gives a new world of intervallic connections and thereby new musical content. Just-intonation scales like 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 partial (Partch 1979, 93, 119-137). Some like the 19 tone or 31 tone equal scales may be used close to diatonic scales, but extend them considerably. Other divisions of the octave do not support the diatonic basis for Western musical notation and tonal theory, but have other equally viable intervallic relationships.

History

The earliest music of which a written record exists anywhere on earth appears to be the Hurrian Hymn (Fink 1988; Dumbrill 2000,). This music may have been microtonal, though interpretation of the Hurrian records has been disputed (West 1994).

The Hellenic civilizations of ancient Greece also left fragmentary records of their music—c.f., the Delphic Hymns. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining tetrachords, 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 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 Antiphonarium Codex Montpellier suggests that it records microtonal tunings, probably the Greek enharmonic (Mandelbaum 1961, ). In his opinion, this indicates that microtonal tunings survived and were commonly used late into the medieval period.

Meantone tunings date from the early 1490s, as scholars such as Richard Taruskin and Patrizio Barbieri have pointed out. Since the time of Pietro Aron's treatise (Aron 1523), meantone tuning became extremely common and was considered to represent "correct" tuning throughout Europe until 1750 and in England and Spain until 1850. Such meantone tunings sound similar to, but more harmonious than, conventional Western tunings of 12 equal pitches per octave, when performed on an instrument limited to 12 pitches per octave, as long as the composer restricts him/herself 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.) Some early composers, however, deliberately wandered far afield from the root note of meantone tunings, producing highly microtonal effects in typical renditions of their music. One prominent example is "Ut, Re, Mi, Fa, Sol, La" by the British virginal composer John Bull (composed sometime between the 1580s and 1610, and included in the Fitzwilliam Virginal Book). Such extensive modulation in meantone tuning on a 12-note-per octave instrument sounds "wolf" fifths and other exotic musical intervals not found in contemporary Western music using 12 equal pitches per octave.

It was quite common in the heyday of meantone tuning to find keyboards with "split" keys or special organ stops, often allowing 13-16 pitches per octave of meantone tuning. In this way music by Handel and many other composers could be played in meantone tuning, maintaining smooth harmony and conventional-sounding melody even as the music modulated to distant keys. Teachers of string instruments, including Leopold Mozart, and of wind instruments, including Quantz, expected their students to distinguish all enharmonic pairs of pitches (like F# and Gb) in their playing, with the sharpened version of one diatonic tone being played lower than the flattened version of the next diatonic tone up. So composers in the meantone era who restricted their harmonic compass were doing so largely because they were writing for keyboard or an ensemble that included a keyboard.

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 5-limit thirds and sixths of the diatonic scale than can be found on modern 12-tone instruments. Several French composers of the 17th century made use of this fact by designing keyboards for 19 equal intervals to the octave, which could be played in all keys with no "wolf" intervals. 17th-century Dutch scientist and musician Christiaan Huygens promoted the use of 31-equal, which also allows meantone in all keys without "wolves", but with better approximations of 7-limit intervals than in 19-equal. Huygens advocated the use of the just seventh, with pitch ratio 7/4. This interval is very well approximated in 31-equal. In the 20th century, a Dutch school of microtonalists arose around Adriaan Fokker, which sought to use the novel resources of Huygens' 31-tone system as fundamental features of new musical forms, and not merely according to their established functions in common-practice tonality. Many Dutch composers were associated with this school, including Fokker himself under a pseudonym; the best-known was probably Henk Badings.

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.

The Italian 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. However Vicentino's experiments were primarily motivated by his research (as he saw it) on the ancient Greek genera, and by his desire to have beatless intervals (when played with near-harmonic-series timbres) available within chromatic compositions.

Johann Kuhnau's composition "Der Kampf zwischen David und Goliath," composed around 1700 in meantone, makes prominent and aggressive use of the exotic intervals available in meantone—specifically, the "wolf" fifth. The effect of contrasting lightly tempered fifths with the dissonant "wolf" fifth depends on the audible microtonal distinction between the intervals.

Composers such as Beethoven and Schubert made extensive use of the enharmonic modulation cycles possible only in a closed tuning of 12 pitches per octave, and not open-ended tunings like meantone. This led to the demise of meantone thinking in most of Europe by the outset of the Romantic period. Microtonality was not completely lost, however, as some string teachers began to advocate "expressive intonation" in which the enharmonic distinctions of meantone were often reversed, i.e., the sharpened version of one diatonic tone often played higher than the flattened version of the next diatonic tone up.

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.

By the 1910s and 1920s, a fad emerged for quarter tones (24 equal pitches per octave), 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. 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).

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.

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).

Prominent microtonal composers of the 1960s and 1970s include John Eaton (who created his own microtonal synthesizer, the Syn Ket, to produce microtonal intervals), Ivor Darreg again (who augmented his home-built orchestra of instruments to include guitars refretted in equal temperaments 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, and 31, as well as the magalyra series of sub-contrabass steel guitar instruments), Harry Partch, Easley Blackwood (who composed and performed the well-known Twelve Microtonal Etudes for Electronic Music Media with compositions in every equal division of the octave from 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and 24 equal pitches per octave) and Augusto Novaro, the Mexican microtonal theorist who composed studies in 15 equal, among others. Barbara Benary also formed Gamelan Son of Lion around this period, and Lou Harrison was instrumental in creating American gamelan orchestras at Mills College. 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; see also the parisian ensemble "L'itinéraire". György Ligeti in Hamburg strongly promoted microtonality and used it in several of his works.

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 rock music

Greg Ginn, guitarist of American hardcore punk band Black Flag, made use of microtonal intervals. An example of a song containing microtonal music is "Damaged II," from 1981's Damaged LP. Another is "Police Story," most versions of which end in a cadence played a quarter-tone sharp.

Elliott Sharp's groups Carbon, Tectonics and Terraplen make extensive use of just intonation microtonality to intensely dissonant and vibrant effect. Los Angeles guitarist Rod Poole has produced a number of rock-oriented xenharmonic CDs.

The band Crash Worship made use of Ivor Darreg's megalyra subcontrabass microtonal instrument for both xenharmonic and industrial noise purposes.

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.

Elaine Walker of Zia has released several albums making use of the Bohlen-Pierce scale and other equal temperaments such as the 19tet and 10tet. Zia performs on electronic instruments that specifically do not reference the standard 12 tone tuning.

Jonny Greenwood, of the alternative rock band Radiohead, has experimented with microtonal music in both his solo material and his work with the band; for instance, the song Climbing Up the Walls, from the band's 1997 album OK Computer, includes a recording of sixteen violins playing quarter tones apart from each other to create a droning, atonal 'white noise' effect.

Other rock artists using microtonality in their work include Glenn Branca (who has created a number of symphonic works for ensembles of microtonally tuned electric guitars) and Jon and Brad Catler (who play microtonal electric guitar and electric bass guitar).

Microtonality often appears to occur in popular rock music in contexts where it is not notated or explicitly described as microtonal, but is nonetheless quite audible. Examples include the guitar introduction to the The Doors' song "The End", the extremely microtonal vocal line in Sinéad O'Connor's songs -- most notably on "Nothing Compares 2 U," -- and in the microtonal bass lines in songs like Siouxsie and the Banshees' "Israel." 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."

Explicitly microtonal jazz has also made a niche for itself as, for example, in the playing of trumpeter Don Ellis, who used a quartertone trumpet built to his specifications, woodwind player Joe Maneri, who has mapped what he calls the "virtual pitch continuum" onto the intervals of 72-tone equal temperament, and in albums released by percussionist Emil Richards, Lothar and the Hand People, the xenharmonic intonational inflexions of John Coltrane, and many others.

Microtonalism in Electronica

In 1953, Karlheinz Stockhausen builds his electronic Studie II on an equal division of 25 parts of the 5th harmonic (51/25). 1986's Beauty In the Beast saw Wendy Carlos experimenting with many microtonal systems including just intonation, using alternate tuning scales she invented for the album.

See also

Western microtonal pioneers

Pioneers of modern Western microtonal music include:

  • Henry Ward Poole (keyboard designs, 1825–1890)
  • Charles Ives (U.S.A., 1874–1954, quartertones)
  • Julián Carrillo (Mexico, 1875–1965) many different equal temperaments, look here or here (mostly Spanish but some English too)
  • Béla Bartók (Hungary, 1881–1945, rare uses of quartertones)
  • George Enescu (Romania, France, 1881–1955) (in 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 and Stimmung, microtonal instrumental and vocal writing throughout Licht)
  • 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)
  • Krzyztof Penderecki (Poland, b. 1933, quartertones)
  • 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

Microtonal researchers

Bibliography

  • 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. Online edition of the 1529 text . 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. New York: Routledge.
  • 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.
  • Barlow, Clarence (ed.). 2001. "The Ratio Book." (Documentation of the Ratio Symposium Royal Conservatory The Hague 14-16 December 1992). Feedback Papers 43.
  • Burns, Edward M. 1999. "Intervals, Scales, and Tuning." In The Psychology of Music, second edition, ed. Diana Deutsch,. San Diego: Academic Press. ISBN 0-12-213564-4.
  • 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
  • Ellis, Alexander J. 1884. "Tonometrical Observations on Some Existing Non-Harmonic Musical Scales". Proceedings of the Royal Society of London 37:368–85.
  • Fink, Robert. 1988. "The Oldest Song in the World". Archaeologia Musicalis 2, no. 2:98–100.
  • 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.
  • Jedrzejewsky, Franck. 2003. Dictionnaire des musiques microtonales [Dictionary of Microtonal Musics]. Paris: L'Harmattan. ISBN 2-7475-5576-3.
  • 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.
  • Mandelbaum, M. Joel. 1961. "Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament. ". Ph.D. thesis. Bloomington: Indiana University.
  • Partch, Harry. 1979. Genesis of a Music, 2nd edition. New York: Da Capo Press. ISBN 0-306-80106-X.
  • 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, Martin Litchfield. 1994. "The Babylonian Musical Notation and the Hurrian Melodic Texts". Music and Letters 75, no. 2 (May): 161–79.
  • Wyschnegradsky, Ivan. 1972. “L'Ultrachromatisme et les espaces non octaviants”. La Revue Musicale nos. 290–91:71-141.

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