Microtonal music is music using microtones—intervals 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.
Microtonal music can refer to all music which contains intervals smaller than the conventional contemporary Western semitone. The term usually refers to music containing very small intervals but can include any tuning that differs from the western 12-tone equal temperament. Traditional Indian systems of 22 śruti; Indonesian gamelan music; Thai, Burmese, and African music, and music using just intonation, meantone temperament or other alternative tunings may be considered microtonal (Griffiths and Lindley 1980; Griffiths, Lindley, and Zannos 2001). Microtonal variation of intervals is standard practice in the African-American musical forms of spirituals, blues and jazz (Cook and Pople 2004, 124–26).
Many microtonal equal divisions of the octave have been proposed, usually (but not always) in order to achieve approximation to the intervals of just intonation (Griffiths and Lindley 1980; Griffiths, Lindley, and Zannos 2001).
Terminology other than "microtonal" is used by theorists and composers. Ivan Wyschnegradsky used the term ultra-chromatic for intervals smaller than the semitone and infra-chromatic for intervals larger than the semitone (Wyschnegradsky 1972, 84–87). Ivor Darreg proposed the term xenharmonic. (See xenharmonic music).
The Hellenic civilizations of ancient Greece left fragmentary records of their music—e.g. the Delphic Hymns. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining 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).
The Italian Renaissance composer and theorist Nicola Vicentino (1511–1576) worked with microtonal intervals and built a keyboard with 36 keys to the octave known as the archicembalo. While theoretically an interpretation of ancient Greek tetrachordal theory, in effect Vicentino presented a circulating system of quarter-comma meantone, maintaining major thirds tuned in just intonation in all keys (Barbour 1951, 117–18).
Jacques Fromental Halévy composed a quarter-tone work for soli, choir and orchestra entitled "Prométhée enchaîné" in 1849.
Alexander John Ellis, who in the 1880s produced a translation of Helmholtz's On the Sensations of Tone, proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings (Helmholtz 1885, 514–27). Ellis also studied the tunings of non-Western cultures and, in a report to the Royal Society, stated that they did not use either equal divisions of the octave or just intonation intervals (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 non-Western tunings and rhythms. Some scholars have ascribed Debussy's subsequent innovative use of the whole-tone (six equal pitches per octave) tuning in such compositions as the Fantaisie for piano and orchestra and the Toccata from the suite Pour le piano to his exposure to the Balinese gamelan at the Paris exposition (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.
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 (continuing to build his handcrafted orchestra of microtonal just intonation instruments), and Eivind Groven.
Digital synthesizers from the Yamaha TX81Z (1987) on and inexpensive software synthesizers have contributed to the ease and popularity of exploring microtonal music.
Microtonalism in electronic music
Electronic music facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems (Griffiths, Lindley, and Zannos 2001). In 1954, Karlheinz Stockhausen built his electronic Studie II on an 81-step scale starting from 100 Hz with the interval of 51/25 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, and Zannos 2001).
In 1979–80 Easley Blackwood composed a set of Twelve Microtonal Etudes for Electronic Music Media, a cycle that explores all of the equal temperaments from 13 notes to the octave through 24 notes to the octave, including 15-ET and 19-ET (Blackwood and Kust 2005,[page needed]) "The project," he wrote, "was to explore the tonal and modal behavior of all [of these] equal tunings…, devise a notation for each tuning, and write a composition in each tuning to illustrate good chord progressions and the practical application of the notation" (Blackwood n.d.).
In 1986, Wendy Carlos experimented with many microtonal systems including just intonation, using alternate tuning scales she invented for the album Beauty In the Beast. "This whole formal discovery came a few weeks after I had completed the album, Beauty in the Beast, which is wholly in new tunings and timbres" (Carlos 1989–96).
Microtonalism in rock music
A form of microtone known as the blue note is an integral part of rock music and one of its predecessors, the blues. The blue notes, located on the third, fifth, and seventh notes of a diatonic major scale, are flattened by a variable microtone (Ferguson 1999, 20).
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 Sonatas for Solo Violin, Op. 27)
- 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)
- 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 example of serial music with quartertones in his pieces Visage Nuptial and Polyphonie X, but soon after abandoning microtonal elements)
- Karlheinz Stockhausen (Germany, 1928–2007, in his electronic works many microtonal concepts, non-octaving scales in Studie II, just intonation in Gruppen 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)
- Carlton Gamer (U.S.A, born 1929, 7-tone, 19-tone, 22-tone, 31-tone equal temperament)
- Alvin Lucier (U.S.A., b. 1931)
- Joel Mandelbaum (U.S.A., b. 1932)
- Krzysztof Penderecki (Poland, b. 1933, quartertones)
- Easley Blackwood (b. 1933)
- Alain Bancquart(France, b.1934) (quarter tones and 16th tones)
- James Tenney (U.S.A., 1934–2006, just intonation, 72-tone equal temperament)
- Terry Riley (U.S.A., b. 1935, just intonation)
- La Monte Young (U.S.A., b. 1935, just intonation)
- John Corigliano (U.S.A., b. 1938, quarter tones)
- Douglas Leedy (b. 1938, just intonation, meantone)
- Wendy Carlos (U.S.A., b. 1939, non-octaving scales)
- Bruce Mather (Canada, b.1939, different equal temperaments, following Wyschnegradsky)
- Brian Ferneyhough (Great Britain, b. 1943, quartertones, 31ET in Unity Capsule for solo flute,1976)
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)
- Glenn Branca (b. 1948)
- Claude Vivier (1948–1983)
- Dean Drummond (b. 1949) (Harry Partch's instruments currently in his possession)
- Greg Schiemer (b. 1949)
- Lasse Thoresen (b. 1949)
- Warren Burt (b. 1949)
- Manfred Stahnke (b. 1951)
- Rhys Chatham (b. 1952)
- Kraig Grady (b. 1952) (invented acoustic instruments in just intonation & recurrent sequences)
- David First (b. 1953)
- Georg Friedrich Haas (b. 1953)
- James Wood (b. 1953)
- Pascale Criton (b. 1954) (different equal temperaments, most particularly very dense ETs such as the 96ET)
- Paul Dirmeikis (b. 1954)
- Stephen James Taylor (b. 1954)
- Pascal Dusapin (b. 1955) (different equal temperaments, notably the 48ET)
- Kyle Gann (b. 1955)
- Johnny Reinhard (b. 1956) (different equal temperaments, just intonation, polymicrotonally)
- Eric Mandat (b. 1957)
- Erling Wold (b. 1958)
- Michael Bach Bachtischa (b. 1958)
- Lucio Garau (b. 1959)
- Martin Smolka (b. 1959)
- Georg Hajdu (b. 1960)
- William Susman (b. 1960)
- François Paris (b. 1961)
- Daniel James Wolf (b. 1961)
- Harold Fortuin (b. 1964)
- Marc Sabat (b. 1965)
- Georges Lentz (b. 1965)
- Jeffrey Ching (b. 1965) (quartertones, ancient Chinese tunings, e.g. circle-of-fifths and just intonation)
- Geoff Smith (b. 1966)
- Trey Spruance (b. 1969)
- Richard David James, aka Aphex Twin (b. 1971)
- Paweł Mykietyn (b. 1971)
- Yitzhak Yedid (b. 1971)
- Adam Silverman (b. 1973)
- Yuri Landman (b. 1973)
- Kristoffer Zegers (b. 1973)
- Saman Samadi (b. 1984)
- Michael Waller (b. 1985)
- Christiaan Huygens (1629–1695)
- Julián Carrillo (1875–1965)
- Adriaan Daniël Fokker (1887–1972)
- Ivan Wyschnegradsky (1893–1979)
- Alois Hába (1893–1973)
- Harry Partch (1901–1974)
- Alain Daniélou (1907–1994)
- Jean-Etienne Marie (1917–1989)
- Erv Wilson (b. 1928)
- Carlton Gamer (b. 1929)
- Joel Mandelbaum (b. 1932)
- James Tenney (1934–2006)
- Clarence Barlow (b. 1945)
- Gene Ward Smith (b. 1947)
- Valeri Brainin (b. 1948)
- Jacques Dudon (b. 1951)
- William Sethares (b. 1955)
- Georg Hajdu (b. 1960)
- Bob Gilmore (b. 1961)
- Marc Sabat (b. 1965)
- Anon. n.d. "[untitled]".[full citation needed]
- Barbour, J. Murray. 1951. Tuning and Temperament: A Historical Survey. East Lansing: Michigan State College Press. Reprinted [n.p.]: Dover, 2004. ISBN 0-486-43406-0 (pbk).
- Blackwood, Easley. n.d. Liner notes to "Blackwood: Microtonal Compositions". CDR018. N.p.: Cedille Records.[full citation needed]
- Blackwood, Easley, and Jeffrey Kust. 2005. Easley Blackwood: Microtonal Compositions, second edition. n.p.: Cedille. (First edition 1996.)[full citation needed]
- 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.
- Carlos, Wendy. 1989–96. "Three Asymmetric Divisions of the Octave". wendycarlos.com (Accessed March 28, 2009).
- Cook, Nicholas, and Anthony Pople. 2004 The Cambridge History of Twentieth-Century Music. Cambridge and New York: Cambridge University Press. ISBN 0-521-66256-7.
- Couture, François. n.d. "Jon Catler: Evolution for Electric Guitar and Orchestra". AllMusic (Accessed 3 April 2013).
- 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.
- Don, Gary. 2001. "Brilliant Colors Provocatively Mixed: Overtone Structures in the Music of Debussy". Music Theory Spectrum 23, no. 1 (Spring): 61–73.
- Ellis, Alexander J. 1884. "Tonometrical Observations on Some Existing Non-Harmonic Musical Scales". Proceedings of the Royal Society of London 37:368–85.
- Ferguson, Jim. 1999. All Blues Soloing for Jazz Guitar: Scales, Licks, Concepts & Choruses. Santa Cruz: Guitar Master Class; Pacific, MO: Mel Bay. ISBN 0-7866-4285-8.
- Griffiths, Paul, and Mark Lindley. 1980. "Microtone". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie, 12:279–80. London: Macmillan Publishers. ISBN 1-56159-174-2.
- 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.
- 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.
- Howat, Roy. 2001. "Debussy, (Achille-)Claude: §10, 'Musical Language'". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Lesure, François. 2001. "Debussy, (Achille-)Claude: 7, 'Models and Influences'". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Lindley, Mark. 2001a. "Mean-tone". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Lindley, Mark. 2001b. "Temperaments". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Partch, Harry. 1979. Genesis of a Music, second 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.
- West, Martin Litchfield. 1992. Ancient Greek Music. Oxford: Clarendon Press; New York: Oxford University Press. ISBN 0-19-814897-6 (cloth) ISBN 0-19-814975-1 (pbk).
- Wilson, John, Krzysztof Penderecki, and Jonny Greenwood. 2012. Interview with Jonny and Krzysztof Penderecki. Front Row. BBC Radio 4 (23 March). Transcript from an audio recording of the broadcast, Citizen Insane website (accessed 21 July 2014).
- 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.
- 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 (Italian). 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 3-03910-088-2.
- Barbieri, Patrizio. 2003. "Temperaments, Historical". In Piano: An Encyclopedia, second edition, edited by Robert Palmieri and Margaret W. Palmieri,[page needed]. New York: Routledge.
- Barbieri, Patrizio. 2008. 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.
- 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 0-691-09129-3.
- Blackwood, Easley. 1991. "Modes and Chord Progressions in Equal Tunings". Perspectives of New Music 29, no. 2 (Summer): 166–200.
- 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.
- Carr, Vanessa. 2008. "These Are Ghost Punks". Vanessa Carr’s website (29 February). (Accessed 2 April 2009)
- Dumbrill, Richard J. 2000. The Musicology and Organology of the Ancient Near East, second edition. London: Tadema Press. ISBN 0-9533633-0-9.
- 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 0-300-06521-3.
- 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.
- Jedrzejewski, Franck. 2003. Dictionnaire des musiques microtonales [Dictionary of Microtonal Musics]. Paris: L'Harmattan. ISBN 2-7475-5576-3.
- Jedrzejewski, Franck. 2014. Dictionnaire des musiques microtonales. Nouvelle édition revue et augmentée (1892-2013) [Dictionary of Microtonal Musics]. Paris: L'Harmattan. ISBN 978-2343035406.
- Johnston, Ben. 2006. 'Maximum Clarity' and other writings on music, ed. B. Gilmore. Urbana and Chicago: University of Illinois Press.
- Landman, Yuri. . "Third Bridge Helix: From Experimental Punk to Ancient Chinese Music and the Universal Physical Laws of Consonance". Perfect Sound Forever (online music magazine) (accessed 6 December 2008).
- Landman, Yuri. n.d. "Yuichi Onoue’s Kaisatsuko" on Hypercustom.com (accessed 31 March 2009).
- Leedy, Douglas. 2001. "A Venerable Temperament Rediscovered". Perspectives of New Music 29, no. 2 (Summer): 202–11.
- Mandelbaum, M. Joel. 1961. "Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament". Ph.D. thesis. Bloomington: Indiana University.
- Vitale, Raoul. 1982. "La Musique suméro-accadienne: gamme et notation musicale". Ugarit-Forschungen 14: 241–63.
|Wikimedia Commons has media related to Microtonal music.|
- Microtonal music at DMOZ
- Aikin, Jim. 2003. Jim Aikin's article on alternative tuning in electronic music
- Anon. [n.d.]. "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. Dr. John Chalmers Divisions of the Tetrachord
- Loli, Charles. 2008. " Microtonalismo". (Article on alternative tuning in Peruvian music)
- Solís Winkler, Ernesto. 2004. "Julian Carrillo and the 13th Sound: A Microtonal Musical System". (Accessed 19 August 2008)
- Wilson, Erv. "Wilson Archives of papers on microtonal theory"
- Links to microtonal composers at Xenharmonic Wiki
- Links to microtonal projects around the world at Xenharmonic Wiki
- Offtonic Microtonal Synthesizer, a browser-based synth to explore microtonal tunings with a QWERTY keyboard