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Wikipedia

Microtonal music

January 26, 2023

For sounds on the time scale shorter than musical notes, see microsound.
"Microtone" redirects here. For the slicing tool, see Microtome.

Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls between the keys of a piano tuned in equal temperament.

Composer Charles Ives chose the chord above as a good candidate for a "fundamental" chord in the quarter tone scale, akin not to the tonic but to the major chord of traditional tonality[1]
Two examples of an Ives fundamental chord with quarter tones

Terminology

Microtone

 
Quarter tone accidentals residing outside the Western semitone:
quarter tone sharp, sharp, three quarter tones sharp;
quarter tone flat, flat, (two variants of) three quarter tones flat

Microtonal music can refer to any music containing microtones. The words "microtone" and "microtonal" were coined before 1912 by Maud MacCarthy Mann in order to avoid the misnomer "quarter tone" when speaking of the srutis of Indian music.[2] Prior to this time the term "quarter tone" was used, confusingly, not only for an interval actually half the size of a semitone, but also for all intervals (considerably) smaller than a semitone.[3][4] It may have been even slightly earlier, perhaps as early as 1895, that the Mexican composer Julián Carrillo, writing in Spanish or French, coined the terms microtono/micro-ton and microtonalismo/micro-tonalité.[5]

In French, the usual term is the somewhat more self-explanatory micro-intervalle, and French sources give the equivalent German and English terms as Mikrointervall (or Kleinintervall) and micro interval (or microtone), respectively.[6][7][8][9] "Microinterval" is a frequent alternative in English, especially in translations of writings by French authors and in discussion of music by French composers.[10][11][12] In English, the two terms "microtone" and "microinterval" are synonymous.[13] The English analogue of the related French term, micro-intervalité, however, is rare or nonexistent, normally being translated as "microtonality"; in French, the terms micro-ton, microtonal (or micro-tonal), and microtonalité are also sometimes used, occasionally mixed in the same passage with micro-intervale and micro-intervalité.[5][14][15][16]

Ezra Sims, in the article "Microtone" in the second edition of the Harvard Dictionary of Music defines "microtone" as "an interval smaller than a semitone",[17] which corresponds with Aristoxenus's use of the term diesis.[18] However, the unsigned article "Comma, Schisma" in the same reference source calls comma, schisma and diaschisma "microintervals" but not "microtones",[19] and in the fourth edition of the same reference (which retains Sims's article on "Microtone") a new "Comma, Schisma" article by André Barbera calls them simply "intervals".[20] In the second edition of The New Grove Dictionary of Music and Musicians, Paul Griffiths, Mark Lindley, and Ioannis Zannos define "microtone" as a musical rather than an acoustical entity: "any musical interval or difference of pitch distinctly smaller than a semitone", including "the tiny enharmonic melodic intervals of ancient Greece, the several divisions of the octave into more than 12 parts, and various discrepancies among the intervals of just intonation or between a sharp and its enharmonically paired flat in various forms of mean-tone temperament", as well as the Indian sruti, and small intervals used in Byzantine chant, Arabic music theory from the 10th century onward, and similarly for Persian traditional music and Turkish music and various other Near Eastern musical traditions,[21] but do not actually name the "mathematical" terms schisma, comma, and diaschisma.

"Microtone" is also sometimes used to refer to individual notes, "microtonal pitches" added to and distinct from the familiar twelve notes of the chromatic scale,[22] as "enharmonic microtones",[23] for example.

In English the word "microtonality" is mentioned in 1946 by Rudi Blesh who related it to microtonal inflexions of the so-called "blues scales".[24] In Court B. Cutting's 2019 Microtonal Analysis of “Blues Notes” and the Blues Scale, he states that academic studies of the early blues concur that its pitch scale has within it three microtonal “blue notes” not found in 12 tone equal temperament intonation.[25] It was used still earlier by W. McNaught with reference to developments in "modernism" in a 1939 record review of the Columbia History of Music, Vol. 5.[26] In German the term Mikrotonalität came into use at least by 1958,[27][28] though "Mikrointervall" is still common today in contexts where very small intervals of early European tradition (diesis, comma, etc.) are described, as e.g. in the new Geschichte der Musiktheorie[29] while "Mikroton" seems to prevail in discussions of the avant-garde music and music of Eastern traditions.[citation needed] The term "microinterval" is used alongside "microtone" by American musicologist Margo Schulter in her articles on medieval music.[30][31]

Microtonal

The term "microtonal music" usually refers to music containing very small intervals but can include any tuning that differs from Western twelve-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.[32][21] Microtonal variation of intervals is standard practice in the African-American musical forms of spirituals, blues and jazz.[33]

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.[32][21]

Terminology other than "microtonal" has been used or proposed by some theorists and composers. In 1914, A. H. Fox Strangways objected that "'heterotone' would be a better name for śruti than the usual translation 'microtone'".[34] Modern Indian researchers yet write: "microtonal intervals called shrutis".[35] In Germany, Austria, and Czechoslovakia in the 1910s and 1920s the usual term continued to be Viertelton-Musik (quarter tone music[36][page needed]), and the type of intervallic structure found in such music was called the Vierteltonsystem,[37][38] which was (in the mentioned region) regarded as the main term for referring to music with microintervals, though as early as 1908 Georg Capellan had qualified his use of "quarter tone" with the alternative term "Bruchtonstufen (Viertel- und Dritteltöne)" (fractional degrees (quarter and third tones)).[39] Despite the inclusion of other fractions of a whole tone, this music continued to be described under the heading "Vierteltonmusik" until at least the 1990s, for example in the twelfth edition of the Riemann Musiklexikon,[40] and in the second edition of the popular Brockhaus Riemann Musiklexikon.[41]

Ivan Wyschnegradsky used the term ultra-chromatic for intervals smaller than the semitone and infra-chromatic for intervals larger than the semitone;[42] this same term has been used since 1934 by ethnomusicologist Victor Belaiev (Belyaev) in his studies of Azerbaijan and Turkish traditional music.[43][44][45] A similar term, subchromatic, has been used by theorist Marek Žabka.[46] Ivor Darreg proposed[when?][citation needed] the term xenharmonic; see xenharmonic music. The Austrian composer Franz Richter Herf and the music theorist Rolf Maedel, Herf's colleague at the Salzburg Mozarteum, preferred using the Greek word ekmelic when referring to "all the pitches lying outside the traditional twelve-tone system".[47] Some authors in Russia[48][49][50][51][52][53] and some musicology dissertations[54][55][56][57][58][59] disseminate the term микрохроматика (microchromatics), coined in the 1970s by Yuri Kholopov,[60] to describe a kind of 'intervallic genus' (интервальный род) for all possible microtonal structures, both ancient (as enharmonic genus—γένος ἐναρμόνιον—of Greeks) and modern (as quarter tone scales of Alois Haba); this generalization term allowed also to avoid derivatives such as микротональность (microtonality, which could be understood in Russian as a sub-tonality, which is subordinate to the dominating tonality, especially in the context of European music of the 19th century) and микротоника (microtonic, "a barely perceptible tonic"; see a clarification in Kholopov [2000][61]). Another Russian authors use more international adjective 'microtonal' and rendered it in Russian as 'микротоновый', but not 'microtonality' ('микротональность').[62][63][64][65] However, the terms 'микротональность'[66] and 'микротоника'[67] are also used. Some authors writing in French have adopted the term "micro-intervallique" to describe such music.[68][69] Italian musicologist Luca Conti dedicated two his monographs to microtonalismo,[70][71] which is the usual term in Italian, and also in Spanish (e.g., as found in the title of Rué [2000][72]). The analogous English form, "microtonalism", is also found occasionally instead of "microtonality", e.g., "At the time when serialism and neoclassicism were still incipient a third movement emerged: microtonalism".[73]

The term "macrotonal" has been used for intervals wider than twelve-tone equal temperament,[74][better source needed] or where there are "fewer than twelve notes per octave", though "this term is not very satisfactory and is used only because there seems to be no other".[75] The term "macrotonal" has also been used for musical form.[76]

Examples of this can be found in various places, ranging from Claude Debussy's impressionistic harmonies to Aaron Copland's chords of stacked fifths, to John Luther Adams' Clouds of Forgetting, Clouds of Unknowing (1995), which gradually expands stacked-interval chords ranging from minor 2nds to major 7thsm. Louis Andriessen's De Staat (1972–1976) contains a number of "augmented" modes that are based on Greek scales but are asymmetrical to the octave.[77]

History

 
Greek Dorian mode (enharmonic genus) on E, divided into two tetrachords.

The Hellenic civilizations of ancient Greece left fragmentary records of their music, such as the Delphic Hymns. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining 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 equal intervals called dieses (single "diesis", δίεσις); 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).[78] Theoretics usually described several diatonic and chromatic genera (some as chroai, "coloration" of one specific intervallic type), but the enarmonic genus was always the only one (argumented as one with the smallest intervals possible).

 
Vicentino's archicembalo in cents

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.[79]

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.[80]

In 1760 the French flautist Charles de Lusse [de] published a treatise, L'Art de la flute traversiere, all surviving copies of which conclude with a composition (possibly added a year or two after the actual publication of the volume) incorporating several quarter tones, titled Air à la grecque, accompanied by explanatory notes tying it to the realization of the Greek enharmonic genus and a chart of quarter tone fingerings for the entire range of the one-keyed flute. Shortly afterward, in a letter published in the Mercure de France in September 1764, the celebrated flautist Pierre-Gabriel Buffardin mentioned this piece and expressed an interest in quarter tones for the flute.[81][82]

Jacques Fromental Halévy composed a cantata "Prométhée enchaîné" for a solo voice, choir and orchestra (premiered in 1849), where in one movement (Choeur des Océanides) he used quarter tones, to imitate the enharmonic genus of Greeks.

In the 1910s and 1920s, quarter tones (24 equal pitches per octave) received attention from such composers as Charles Ives, Julián Carrillo, Alois Hába, Ivan Wyschnegradsky, and Mildred Couper.

Alexander John Ellis, who in the 1880s produced a translation of Hermann Helmholtz's On the Sensations of Tone, proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings.[83] Ellis also studied the tunings of non-Western cultures and, in a report to the Royal Society, stated that they used neither equal divisions of the octave nor just intonation intervals.[84] Ellis inspired Harry Partch immensely.[85]

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,[86] 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".[87] 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 Helmholtz's writings.[88] Emil Berliner's introduction of the phonograph in the 1890s allowed much non-Western music to be recorded and heard by Western composers, further spurring the use of non-12-equal tunings.[citation needed]

Major microtonal composers of the 1920s and 1930s include Alois Hába (quarter tones, or 24 equal pitches per octave, and sixth tones), Julián Carrillo (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).[89]

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.

Microtonality in electronic music

Electronic music facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems.[21] 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,[90] and in Gesang der Jünglinge (1955–56) he used various scales, ranging from seven up to sixty equal divisions of the octave.[91] In 1955, Ernst Krenek used 13 equal-tempered intervals per octave in his Whitsun oratorio, Spiritus intelligentiae, sanctus.[21]

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.[92][full citation needed][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".[93][full citation needed]

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".[94]

In 2016, electronic music composed with arbitrary microtonal scales was explored on the album Radionics Radio: An Album of Musical Radionic Thought Frequencies by British composer Daniel Wilson, who derived his compositions' tunings from frequency-runs submitted by users of a custom-built web application replicating radionics-based electronic soundmaking equipment used by Oxford's De La Warr Laboratories in the late 1940s, thereby supposedly embodying thoughts and concepts within the tunings.[95]

Finnish artist Aleksi Perälä (Rephlex) works exclusively in a microtonal system known as the Colundi sequence.[96][97]

Limitations of some synthesizers

The General MIDI Specification does not directly support microtonal music, because each note-on and note-off message only represents one chromatic tone. However, microtonal scales can be emulated using pitch bending, such as in LilyPond's implementation.[98]

Although some synthesizers allow the creation of customized microtonal scales, this solution does not allow compositions to be transposed. For example, if each B note is raised one quarter tone, then the "raised 7th" would only affect a C major scale.

Microtonality in rock music

 
Album cover of Live in Sydney '21 by Australian band King Gizzard & the Lizard Wizard, featuring a custom built microtonal electric guitar.

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.[99] Joe Monzo has made a microtonal analysis of the song "Drunken Hearted Man",[100] written and recorded by the delta blues musician Robert Johnson.[101]

Musicians such as Jon Catler have incorporated microtonal guitars like 31-tone equal tempered guitar and a 62-tone just intonation guitar in blues and jazz rock music.[102]

English rock band Radiohead has used microtonal string arrangements in its music, such as on "How to Disappear Completely" from the album Kid A.[101]

American band Secret Chiefs 3 has been making its own custom "microtonal" instruments since the mid 1990s. The proprietary tuning system they use in their Ishraqiyun aspect is ratio-based, not equal temperament. The band's leader Trey Spruance, also of Mr. Bungle challenges the terminology of "microtonality" as a development that instead of liberating tonal sensibility to a universe of diverse possibilities, both new and historical, instead mainly serves to reinforce the idea that the universal standard for "tone" is the (western) semitone.[103]

Australian band King Gizzard and the Lizard Wizard utilises microtonal instruments, including custom microtonal guitars modified to play in 24-TET tuning. Tracks with these instruments appear on their 2017 albums Flying Microtonal Banana[104] and Gumboot Soup, their 2020 album K.G, and their 2021 album L.W.[105]

American band Dollshot used quarter tones and other microtonal intervals in their album Lalande.[106]

American instrumental trio Consider the Source employs microtonal instruments in their music.[citation needed]

In the West

Western microtonal pioneers

Modern Western microtonal composers

Western microtonal researchers

See also

References

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Further reading

  • Adèr, Lidiâ Olegovna [Адэр, Лидия Олеговна]. 2011a. "Микротоновая идея: Истоки и предпосылки" [The Concept of Microtonality: Its Origin and Background]. Научный журнал Санкт-Петербургской консерватории [Opera musicologica: Naučnyj žurnal Sankt-Peterburgskoj konservatorii] 3–4, nos. 8–9:114–134.
  • Adèr, Lidiâ Olegovna [Адэр, Лидия Олеговна]. 2011b. "Микротоновый инструментарий—первые шаги от утопии к практике" [Microtonal Instruments: The First Steps from Utopia to Practice]. In Временник Зубовского института: Инструментализм в истории культуры [Instrumentalism in the history of culture], edited by Evgenia Vladimirovna Hazdan, 52–65. Vremennik Zubovskogo instituta 7. St. Petersburg: Rossijskij Institut Istorii Iskusstv.
  • 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 (in 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, 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. 215–264. 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)
  • Colonna, Fabio. 1618. La sambuca lincea, overo Dell'istromento musico perfetto. Naples: C. Vitale. Facsimile reprint of a copy containing manuscript critical annotations by Scipione Stella (1618–1624), with an introduction by Patrizio Barbieri. Musurgiana 24. Lucca, Italy: Libreria Musicale Italiana, 1991.
  • Daniels, Arthur Michael. 1965. "Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas". Journal of Music Theory 9, no. 1 (Spring): 2–51.
  • 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.
  • Fritsch, Johannes G. 2007. "Allgemeine Harmonik, Tonsysteme, Mikrotonalität: Ein geschichtlicher Überblick". In Orientierungen: Wege im Pluralismus der Gegenwartsmusik, edited by Jörn Peter Hiekel, 107–122. Veröffentlichungen des Instituts für Neue Musik und Musikerziehung Darmstadt 47. Mainz: Schott Musik International. ISBN 978-3-7957-1837-4.
  • Gilmore, Bob. 1998. Harry Partch: A Biography. New Haven: Yale University Press. ISBN 0-300-06521-3.
  • Haas, Georg Friedrich. 2007. "Mikrotonalität und spektrale Musik seit 1980". In Orientierungen: Wege im Pluralismus der Gegenwartsmusik, edited by Jörn Peter Hiekel, 123–129. Veröffentlichungen des Instituts für Neue Musik und Musikerziehung Darmstadt 47. Mainz: Schott Musik International. ISBN 978-3-7957-1837-4.
  • Hába, Alois. 1927. Neue Harmonielehre des diatonischen, chromatischen Viertel-, Drittel-, Sechstel- und Zwölftel-tonsystems. Leipzig: Kistner & Siegel.
  • Johnston, Ben. 2006. 'Maximum Clarity' and other writings on music, ed. B. Gilmore. Urbana and Chicago: University of Illinois Press.
  • Kotschy, Johannes. 2008. "Mikrotonalität: Eine Zeiterscheinung?" Österreichische Musikzeitschrift 63, no. 7 (July): 8–15.
  • Landman, Yuri. [2008]. "Third Bridge Helix: From Experimental Punk to Ancient Chinese Music and the Universal Physical Laws of Consonance". (accessed 6 December 2008).
  • Landman, Yuri. n.d. "" on Hypercustom.com (accessed 31 March 2009).
  • Leedy, Douglas. 1991. "A Venerable Temperament Rediscovered". Perspectives of New Music 29, no. 2 (Summer): 202–211.
  • Lindley, Mark. 2001b. "Temperaments". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Mandelbaum, M. Joel. 1961. "Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament". Ph.D. thesis. Bloomington: Indiana University.
  • Mosch, Ulrich. 2008. "Ultrachromatik und Mikrotonalität: Hans Zenders Grundlegung einer neuen Harmonik". In Hans Zender: Vielstimmig in sich, edited by Werner Grünzweig, Anouk Jeschke, and Jörn Peter Hiekel, 61–76. Archive zur Musik des 20. Jahrhunderts, No. 12. Hofheim:Wolke. ISBN 978-3-936000-25-2.
  • Noyze, Dave, and Richard D. James.. 2014. "". Noyzelab Blogspot.com.au (Monday, 10 November)
  • Stahnke, Manfred. 2010. "About Backyards and Limbos: Microtonality Revisited". In Concepts, Experiments and Fieldwork: Studies in Systematic Musicology and Ethnomusicology, edited by Rolf Bader, Christiane Neuhaus, and Ulrich Morgenstern, with a prefaceby Achim Reichel, 297–314. Frankfurt am Main and New York: Peter Lang. ISBN 978-3-631-58902-1.
  • Vitale, Raoul. 1982. "La Musique suméro-accadienne: gamme et notation musicale". Ugarit-Forschungen 14: 241–263.
  • Werntz, Julia. 2001. "Adding Pitches: Some New Thoughts, Ten Years after Perspectives of New Music's 'Forum: Microtonality Today'". Perspectives of New Music 39, no. 2 (Summer): 159–210.
  • Wood, James. 1986. "Microtonality: Aesthetics and Practicality". The Musical Times 127, no. 1719 (June): 328–330.
  • Wyschnegradsky, Ivan. 1937. "La musique à quarts de ton et sa réalisation pratique". La Revue Musicale no. 171:26–33.
  • Zweifel, Paul. 1996. "Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach". Perspectives of New Music 34, no. 1 (Winter): 140–161.

External links

 
Wikimedia Commons has media related to Microtonal music.
  • Microtonal music at Curlie
  • Aikin, Jim. 2003.
  • 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. "". (Accessed 19 August 2008)
  • Wilson, Erv. "Wilson Archives of papers on microtonal theory"
  • Listen – Xenharmonic Wiki – links to microtonal composers and compositions
  • Projects – Xenharmonic Wiki – links to microtonal projects around the world
  • Offtonic Microtonal Synthesizer, a browser-based synth to explore microtonal tunings with a QWERTY keyboard
  • MidiPro.org 2020-11-23 at the Wayback Machine allows any sound card or synthesizer to play 48 microtones per octave, each separated by 1/8 step

January 26, 2023
microtonal, music, sounds, time, scale, shorter, than, musical, notes, microsound, microtone, redirects, here, slicing, tool, microtome, microtonality, music, microtones, intervals, smaller, than, semitone, also, called, microintervals, also, extended, include. For sounds on the time scale shorter than musical notes see microsound Microtone redirects here For the slicing tool see Microtome Microtonal music or microtonality is the use in music of microtones intervals smaller than a semitone also called microintervals It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave In other words a microtone may be thought of as a note that falls between the keys of a piano tuned in equal temperament Composer Charles Ives chose the chord above as a good candidate for a fundamental chord in the quarter tone scale akin not to the tonic but to the major chord of traditional tonality 1 source source source source source Two examples of an Ives fundamental chord with quarter tones Contents 1 Terminology 1 1 Microtone 1 2 Microtonal 2 History 3 Microtonality in electronic music 3 1 Limitations of some synthesizers 4 Microtonality in rock music 5 In the West 5 1 Western microtonal pioneers 5 2 Modern Western microtonal composers 5 3 Western microtonal researchers 6 See also 7 References 8 Further reading 9 External linksTerminology EditMicrotone Edit Quarter tone accidentals residing outside the Western semitone quarter tone sharp sharp three quarter tones sharp quarter tone flat flat two variants of three quarter tones flat Microtonal music can refer to any music containing microtones The words microtone and microtonal were coined before 1912 by Maud MacCarthy Mann in order to avoid the misnomer quarter tone when speaking of the srutis of Indian music 2 Prior to this time the term quarter tone was used confusingly not only for an interval actually half the size of a semitone but also for all intervals considerably smaller than a semitone 3 4 It may have been even slightly earlier perhaps as early as 1895 that the Mexican composer Julian Carrillo writing in Spanish or French coined the terms microtono micro ton and microtonalismo micro tonalite 5 In French the usual term is the somewhat more self explanatory micro intervalle and French sources give the equivalent German and English terms as Mikrointervall or Kleinintervall and micro interval or microtone respectively 6 7 8 9 Microinterval is a frequent alternative in English especially in translations of writings by French authors and in discussion of music by French composers 10 11 12 In English the two terms microtone and microinterval are synonymous 13 The English analogue of the related French term micro intervalite however is rare or nonexistent normally being translated as microtonality in French the terms micro ton microtonal or micro tonal and microtonalite are also sometimes used occasionally mixed in the same passage with micro intervale and micro intervalite 5 14 15 16 Ezra Sims in the article Microtone in the second edition of the Harvard Dictionary of Music defines microtone as an interval smaller than a semitone 17 which corresponds with Aristoxenus s use of the term diesis 18 However the unsigned article Comma Schisma in the same reference source calls comma schisma and diaschisma microintervals but not microtones 19 and in the fourth edition of the same reference which retains Sims s article on Microtone a new Comma Schisma article by Andre Barbera calls them simply intervals 20 In the second edition of The New Grove Dictionary of Music and Musicians Paul Griffiths Mark Lindley and Ioannis Zannos define microtone as a musical rather than an acoustical entity any musical interval or difference of pitch distinctly smaller than a semitone including the tiny enharmonic melodic intervals of ancient Greece the several divisions of the octave into more than 12 parts and various discrepancies among the intervals of just intonation or between a sharp and its enharmonically paired flat in various forms of mean tone temperament as well as the Indian sruti and small intervals used in Byzantine chant Arabic music theory from the 10th century onward and similarly for Persian traditional music and Turkish music and various other Near Eastern musical traditions 21 but do not actually name the mathematical terms schisma comma and diaschisma Microtone is also sometimes used to refer to individual notes microtonal pitches added to and distinct from the familiar twelve notes of the chromatic scale 22 as enharmonic microtones 23 for example In English the word microtonality is mentioned in 1946 by Rudi Blesh who related it to microtonal inflexions of the so called blues scales 24 In Court B Cutting s 2019 Microtonal Analysis of Blues Notes and the Blues Scale he states that academic studies of the early blues concur that its pitch scale has within it three microtonal blue notes not found in 12 tone equal temperament intonation 25 It was used still earlier by W McNaught with reference to developments in modernism in a 1939 record review of the Columbia History of Music Vol 5 26 In German the term Mikrotonalitat came into use at least by 1958 27 28 though Mikrointervall is still common today in contexts where very small intervals of early European tradition diesis comma etc are described as e g in the new Geschichte der Musiktheorie 29 while Mikroton seems to prevail in discussions of the avant garde music and music of Eastern traditions citation needed The term microinterval is used alongside microtone by American musicologist Margo Schulter in her articles on medieval music 30 31 Microtonal Edit The term microtonal music usually refers to music containing very small intervals but can include any tuning that differs from Western twelve tone equal temperament Traditional Indian systems of 22 sruti Indonesian gamelan music Thai Burmese and African music and music using just intonation meantone temperament or other alternative tunings may be considered microtonal 32 21 Microtonal variation of intervals is standard practice in the African American musical forms of spirituals blues and jazz 33 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 32 21 Terminology other than microtonal has been used or proposed by some theorists and composers In 1914 A H Fox Strangways objected that heterotone would be a better name for sruti than the usual translation microtone 34 Modern Indian researchers yet write microtonal intervals called shrutis 35 In Germany Austria and Czechoslovakia in the 1910s and 1920s the usual term continued to be Viertelton Musik quarter tone music 36 page needed and the type of intervallic structure found in such music was called the Vierteltonsystem 37 38 which was in the mentioned region regarded as the main term for referring to music with microintervals though as early as 1908 Georg Capellan had qualified his use of quarter tone with the alternative term Bruchtonstufen Viertel und Dritteltone fractional degrees quarter and third tones 39 Despite the inclusion of other fractions of a whole tone this music continued to be described under the heading Vierteltonmusik until at least the 1990s for example in the twelfth edition of the Riemann Musiklexikon 40 and in the second edition of the popular Brockhaus Riemann Musiklexikon 41 Ivan Wyschnegradsky used the term ultra chromatic for intervals smaller than the semitone and infra chromatic for intervals larger than the semitone 42 this same term has been used since 1934 by ethnomusicologist Victor Belaiev Belyaev in his studies of Azerbaijan and Turkish traditional music 43 44 45 A similar term subchromatic has been used by theorist Marek Zabka 46 Ivor Darreg proposed when citation needed the term xenharmonic see xenharmonic music The Austrian composer Franz Richter Herf and the music theorist Rolf Maedel Herf s colleague at the Salzburg Mozarteum preferred using the Greek word ekmelic when referring to all the pitches lying outside the traditional twelve tone system 47 Some authors in Russia 48 49 50 51 52 53 and some musicology dissertations 54 55 56 57 58 59 disseminate the term mikrohromatika microchromatics coined in the 1970s by Yuri Kholopov 60 to describe a kind of intervallic genus intervalnyj rod for all possible microtonal structures both ancient as enharmonic genus genos ἐnarmonion of Greeks and modern as quarter tone scales of Alois Haba this generalization term allowed also to avoid derivatives such as mikrotonalnost microtonality which could be understood in Russian as a sub tonality which is subordinate to the dominating tonality especially in the context of European music of the 19th century and mikrotonika microtonic a barely perceptible tonic see a clarification in Kholopov 2000 61 Another Russian authors use more international adjective microtonal and rendered it in Russian as mikrotonovyj but not microtonality mikrotonalnost 62 63 64 65 However the terms mikrotonalnost 66 and mikrotonika 67 are also used Some authors writing in French have adopted the term micro intervallique to describe such music 68 69 Italian musicologist Luca Conti dedicated two his monographs to microtonalismo 70 71 which is the usual term in Italian and also in Spanish e g as found in the title of Rue 2000 72 The analogous English form microtonalism is also found occasionally instead of microtonality e g At the time when serialism and neoclassicism were still incipient a third movement emerged microtonalism 73 The term macrotonal has been used for intervals wider than twelve tone equal temperament 74 better source needed or where there are fewer than twelve notes per octave though this term is not very satisfactory and is used only because there seems to be no other 75 The term macrotonal has also been used for musical form 76 Examples of this can be found in various places ranging from Claude Debussy s impressionistic harmonies to Aaron Copland s chords of stacked fifths to John Luther Adams Clouds of Forgetting Clouds of Unknowing 1995 which gradually expands stacked interval chords ranging from minor 2nds to major 7thsm Louis Andriessen s De Staat 1972 1976 contains a number of augmented modes that are based on Greek scales but are asymmetrical to the octave 77 History Edit source source source Greek Dorian mode enharmonic genus on E divided into two tetrachords The Hellenic civilizations of ancient Greece left fragmentary records of their music such as the Delphic Hymns The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining 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 equal intervals called dieses single diesis diesis 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 78 Theoretics usually described several diatonic and chromatic genera some as chroai coloration of one specific intervallic type but the enarmonic genus was always the only one argumented as one with the smallest intervals possible Vicentino s archicembalo in cents Guillaume Costeley s Chromatic Chanson Seigneur Dieu ta pitie of 1558 used 1 3 comma meantone and explored the full compass of 19 pitches in the octave 79 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 80 In 1760 the French flautist Charles de Lusse de published a treatise L Art de la flute traversiere all surviving copies of which conclude with a composition possibly added a year or two after the actual publication of the volume incorporating several quarter tones titled Air a la grecque accompanied by explanatory notes tying it to the realization of the Greek enharmonic genus and a chart of quarter tone fingerings for the entire range of the one keyed flute Shortly afterward in a letter published in the Mercure de France in September 1764 the celebrated flautist Pierre Gabriel Buffardin mentioned this piece and expressed an interest in quarter tones for the flute 81 82 Jacques Fromental Halevy composed a cantata Promethee enchaine for a solo voice choir and orchestra premiered in 1849 where in one movement Choeur des Oceanides he used quarter tones to imitate the enharmonic genus of Greeks In the 1910s and 1920s quarter tones 24 equal pitches per octave received attention from such composers as Charles Ives Julian Carrillo Alois Haba Ivan Wyschnegradsky and Mildred Couper Alexander John Ellis who in the 1880s produced a translation of Hermann Helmholtz s On the Sensations of Tone proposed an elaborate set of exotic just intonation tunings and non harmonic tunings 83 Ellis also studied the tunings of non Western cultures and in a report to the Royal Society stated that they used neither equal divisions of the octave nor just intonation intervals 84 Ellis inspired Harry Partch immensely 85 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 86 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 87 Still others have argued that Debussy s works like L isle joyeuse La cathedrale engloutie Prelude a l apres midi d un faune La mer Pagodes Danseuses de Delphes and Cloches a travers les feuilles are marked by a more basic interest in the microtonal intervals found between the higher members of the overtone series under the influence of Helmholtz s writings 88 Emil Berliner s introduction of the phonograph in the 1890s allowed much non Western music to be recorded and heard by Western composers further spurring the use of non 12 equal tunings citation needed Major microtonal composers of the 1920s and 1930s include Alois Haba quarter tones or 24 equal pitches per octave and sixth tones Julian Carrillo 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 89 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 Microtonality in electronic music EditElectronic music facilitates the use of any kind of microtonal tuning and sidesteps the need to develop new notational systems 21 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 90 and in Gesang der Junglinge 1955 56 he used various scales ranging from seven up to sixty equal divisions of the octave 91 In 1955 Ernst Krenek used 13 equal tempered intervals per octave in his Whitsun oratorio Spiritus intelligentiae sanctus 21 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 92 full citation needed 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 93 full citation needed 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 94 In 2016 electronic music composed with arbitrary microtonal scales was explored on the album Radionics Radio An Album of Musical Radionic Thought Frequencies by British composer Daniel Wilson who derived his compositions tunings from frequency runs submitted by users of a custom built web application replicating radionics based electronic soundmaking equipment used by Oxford s De La Warr Laboratories in the late 1940s thereby supposedly embodying thoughts and concepts within the tunings 95 Finnish artist Aleksi Perala Rephlex works exclusively in a microtonal system known as the Colundi sequence 96 97 Limitations of some synthesizers Edit The General MIDI Specification does not directly support microtonal music because each note on and note off message only represents one chromatic tone However microtonal scales can be emulated using pitch bending such as in LilyPond s implementation 98 Although some synthesizers allow the creation of customized microtonal scales this solution does not allow compositions to be transposed For example if each B note is raised one quarter tone then the raised 7th would only affect a C major scale Microtonality in rock music Edit Album cover of Live in Sydney 21 by Australian band King Gizzard amp the Lizard Wizard featuring a custom built microtonal electric guitar 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 99 Joe Monzo has made a microtonal analysis of the song Drunken Hearted Man 100 written and recorded by the delta blues musician Robert Johnson 101 Musicians such as Jon Catler have incorporated microtonal guitars like 31 tone equal tempered guitar and a 62 tone just intonation guitar in blues and jazz rock music 102 English rock band Radiohead has used microtonal string arrangements in its music such as on How to Disappear Completely from the album Kid A 101 American band Secret Chiefs 3 has been making its own custom microtonal instruments since the mid 1990s The proprietary tuning system they use in their Ishraqiyun aspect is ratio based not equal temperament The band s leader Trey Spruance also of Mr Bungle challenges the terminology of microtonality as a development that instead of liberating tonal sensibility to a universe of diverse possibilities both new and historical instead mainly serves to reinforce the idea that the universal standard for tone is the western semitone 103 Australian band King Gizzard and the Lizard Wizard utilises microtonal instruments including custom microtonal guitars modified to play in 24 TET tuning Tracks with these instruments appear on their 2017 albums Flying Microtonal Banana 104 and Gumboot Soup their 2020 album K G and their 2021 album L W 105 American band Dollshot used quarter tones and other microtonal intervals in their album Lalande 106 American instrumental trio Consider the Source employs microtonal instruments in their music citation needed In the West EditThis section needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed July 2016 Learn how and when to remove this template message Western microtonal pioneers Edit Henry Ward Poole keyboard designs 1825 1890 Eugene Ysaye Belgium U S A 1858 1931 used quarter tones in several of the Sonatas for Solo Violin Op 27 Ferruccio Busoni Italy Germany 1866 1924 Experimented with microtones including third tones Charles Ives U S A 1874 1954 quarter tones Julian Carrillo Mexico 1875 1965 many different equal temperaments look here or here mostly Spanish but some English too Bela Bartok Hungary 1881 1945 rare uses of quarter tones 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 quarter tones on the violin in Myths Op 30 1915 Percy Grainger Australia 1882 1961 particularly works for his free music machine Edgard Varese France U S A 1883 1965 Mordecai Sandberg Romania Austria Palestine USA Canada 1897 1973 Luigi Russolo Italy 1885 1947 used quarter tones and eighth tones on the Intonarumori noise instruments Mildred Couper U S A 1887 1974 quarter tones Alois Haba Czechoslovakia 1893 1973 quarter tones and other equal temperaments Ivan Wyschnegradsky U S S R Russia France 1893 1979 quarter tones twelfth tones and other equal temperaments Harry Partch U S A 1901 1974 just intonation including a system of 43 unequal tones to the octave Eivind Groven Norway 1901 1977 53ET Henk Badings The Netherlands 1907 1987 31ET Maurice Ohana France 1913 1992 third tones 18ET and quarter tones 24ET most particularly Giacinto Scelsi Italy 1905 1988 intuitive linear tone deviations quarter tones 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 de nl Austria 1920 1989 72 equal temperament ekmelic music Iannis Xenakis Greece France 1922 2001 quarter and third tones most particularly occasionally eighth tones Gyorgy Ligeti Hungary 1923 2006 Ramifications in quarter tone tuning natural harmonics in his Horn Trio later just intonation in his solo concertos Luigi Nono Italy 1924 1990 quarter tones eighth tones and 16th tones Claude Ballif France 1924 2004 quarter tones Tui St George Tucker 1924 2004 Pierre Boulez France 1925 2016 first example of serial music with quarter tones in his pieces Le 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 occasional microtonal instrumental and vocal writing throughout Licht Ben Johnston U S A 1926 2019 extended just intonation Joe Maneri U S A 1927 2009 Ezra Sims U S A 1928 2015 72 tone equal temperament Erv Wilson 1928 2016 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 1933 2020 quarter tones 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 quarter tones 31ET in Unity Capsule for solo flute 1976 quarter tones and eighth tones in La Chute d Icare 1988 Jukka Tiensuu Finland b 1948 quarter tones non equal temperament tunings Modern Western microtonal composers Edit Clarence Barlow b 1945 Gerard Grisey 1946 1998 spectral approach to microintervals quarter tones eighth tones Max Mereaux b 1946 Tristan Murail b 1947 spectral approach to microintervals quarter tones eighth tones Glenn Branca b 1948 Elizabeth Brown b 1953 Claude Vivier 1948 1983 Dean Drummond 1949 2013 Greg Schiemer b 1949 Lasse Thoresen b 1949 Warren Burt b 1949 Manfred Stahnke b 1951 James Erber b 1951 quarter tones Rhys Chatham b 1952 Kraig Grady b 1952 invented acoustic instruments in just intonation amp 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 Dave Soldier b 1956 Eric Mandat b 1957 Erling Wold b 1958 Michael Bach Bachtischa b 1958 Lucio Garau b 1959 Michael Harrison b 1959 just intonation Martin Smolka b 1959 Richard Barrett b 1959 Georg Hajdu b 1960 William Susman b 1960 Francois Paris b 1961 Franklin Cox b 1961 quarter tones twelfth tones extended just intonation Daniel James Wolf b 1961 Claus Steffen Mahnkopf b 1962 quarter tones eight tones Harold Fortuin b 1964 Marc Sabat b 1965 extended JI up to 23 limit Georges Lentz b 1965 Jeffrey Ching b 1965 quarter tones ancient Chinese tunings e g circle of fifths and just intonation Geoff Smith b 1966 Trey Spruance b 1969 Elaine Walker b 1969 Richard David James aka Aphex Twin b 1971 Pawel Mykietyn b 1971 Yitzhak Yedid b 1971 Fabio Costa composer conductor b 1971 Sander Germanus b 1972 Yuri Landman b 1973 Kristoffer Zegers b 1973 Karola Obermueller b 1977 Martin Suckling b 1981 Saman Samadi b 1984 Taylor Brook b 1985 Michael Waller b 1985 Sean Archibald aka Sevish b 1988 Seppe Gebruers aka Ultrachromatic Clocktower b 1990 Robin Haigh b 1993 Jacob Collier b 1994 Western microtonal researchers Edit Mordecai Sandberg 1897 1973 Christiaan Huygens 1629 1695 Julian Carrillo 1875 1965 Adriaan Daniel Fokker 1887 1972 Ivan Wyschnegradsky 1893 1979 Joseph Yasser 1893 1981 Alois Haba 1893 1973 Harry Partch 1901 1974 Alain Danielou 1907 1994 Jean Etienne Marie 1917 1989 Erv Wilson 1928 2016 Carlton Gamer b 1929 Joel Mandelbaum b 1932 James Tenney 1934 2006 Tom Ze b 1936 Clarence Barlow b 1945 Valeri Brainin b 1948 Jacques Dudon b 1951 William Sethares b 1955 Georg Hajdu b 1960 Bob Gilmore 1961 2015 Marc Sabat b 1965 See also EditSonido 13 3rd bridge Arab tone system and maqam Bohlen Pierce scale Continuum Fingerboard Fokker periodicity blocks Genus music Harmony Huygens Fokker Foundation Just intonation Limit music Microtuner MIDI tuning standard Music of India Musical scale Musical tuning Partch s 43 tone scale Quarter tone Raga ScalaReferences Edit Boatwright Howard 1971 Boretz Benjamin Cone Edward T eds Ives Quarter Tone Impressions Perspectives on American Composers Princeton Princeton University Press pp 8 9 Mann Maud MacCarthy 16 January 1912 Some Indian Conceptions of Music Proceedings of the Musical Association 38th Session 1911 1912 44 Ellis Alexander J 25 May 1877 On the Measurement and Settlement of Musical Pitch Journal of the Society of Arts 25 1279 665 Meyer Max July October 1903 Experimental Studies in the Psychology of Music American Journal of Psychology 14 3 4 192 214 doi 10 2307 1412315 JSTOR 1412315 a b Donval Serge 2006 Histoire de l acoustique musicale paperback Courlay Fuzeau p 119 ISBN 978 2 84169 152 4 Amy Gilbert 1961 Micro intervalle In Michel Francois ed Encyclopedie de la musique in collaboration with Francois Lesure and Vladimir Fedorov Paris Fasquelle Garnier Yves ed 1998 Micro intervalle Nouveau Larousse encyclopedique Kondratiev Zythum Nouveau Larousse encyclopedique Vol 2 Kondratiev Zythum Second ed Paris Larousse p 1011 ISBN 978 2 03 153132 6 Wallon Simone 1980 L allemand musicologique Guides Musicologiques Paris Editions Beauchesne p 13 ISBN 2 7010 1011 X Whitfield Charles 1989 L anglais musicologique l anglais des musiciens Guides Musicologiques Paris Editions Beauchesne p 13 ISBN 2 7010 1181 7 Battier Marc Lacino Thierry 1984 Simulation and Extrapolation of Instrumental Sounds Using Direct Synthesis at IRCAM A Propos of Resonance Contemporary Music Review 1 Musical Thought at IRCAM edited by Tod Machover 77 82 doi 10 1080 07494468400640081 hdl 2027 spo bbp2372 1982 033 Boulez Pierre 1958 Translated by Goehr Alexander At the Ends of Fruitful Land Die Reihe English ed 1 Electronic Music 22 23 Rae Caroline 2013 Messiaen and Ohana Parallel Preoccupations or Anxiety of Influence In Fallon Robert Dingle Christopher eds Messiaen Perspectives 2 Techniques Influence and Reception Farnham Ashgate Publishing Ltd pp 164 174n40 ISBN 978 1 4094 2696 7 Maclagan Susan J 2009 A Dictionary for the Modern Flutist Lanham MS and Plymouth Scarecrow Press Inc p 109 ISBN 978 0 8108 6711 6 Donval 2006 p 183 Jedrzejewski Franck in French 2014 Dictionnaire des musiques microtonales 1892 2013 Dictionary of Microtonal Musics 1892 2013 in French Paris L Harmattan pp passim ISBN 978 2 343 03540 6 Rigoni Michel 1998 Karlheinz Stockhausen un vaisseau lance vers le ciel Musique de notre temps compositeurs in French Second revised corrected and enlarged ed Lillebonne Millenaire III Editions p 314 ISBN 978 2 911906 02 2 Apel Will 1974 The Harvard Dictionary of Music Second ed Cambridge Massachusetts USA Harvard University Press p 527 Richter Lukas 2001 Diesis ii In Sadie Stanley Tyrrel John eds The New Grove Dictionary of Music and Musicians Second ed London Macmillan Publishers Apel 1974 p 188 Barbera Andre 2003 Comma Schisma In Randel Don Michael ed Harvard Dictionary of Music Fourth ed Cambridge Massachusetts USA The Belknap Press of Harvard University Press p 193 ISBN 978 0 674 01163 2 a b c d e Griffiths Paul Lindley Mark Zannos Ioannis 2001 Microtone In Sadie Stanley Tyrrell John eds The New Grove Dictionary of Music and Musicians Second ed London Macmillan Publishers Von Gunden Heidi 1986 The Music of Ben Johnston Metuchen New Jersey USA and London England The Scarecrow Press Inc p 59 ISBN 0 8108 1907 4 Barbieri Patrizio 2008 Enharmonic instruments and music 1470 1900 Latina Italy Il Levante Libreria Editrice p 139 ISBN 978 88 95203 14 0 Blesh Rudi 1946 Shining Trumpets A History of Jazz New York Alfred A Knopf p 234 Cutting Court B 2019 01 17 Microtonal Analysis of Blue Notes and the Blues Scale Empirical Musicology Review 13 1 2 84 doi 10 18061 emr v13i1 2 6316 ISSN 1559 5749 McNaught W February 1939 Gramophone Notes The Musical Times 80 1152 102 104 doi 10 2307 923814 JSTOR 923814 Prieberg Fred K 1958 Lexikon der Neuen Musik Freiburg im Breisgau and Munich K Alber p 288 Prieberg Fred K 1960 Musica ex machina uber das Verhaltnis von Musik und Technik Berlin Frankfurt and Vienna Verlag Ullstein pp 29 32 210 212 inter alia Zaminer Frieder 2006 Harmonik und Musiktheorie im alten Griechenland In Ertelt Thomas von Loesch Heinz Zaminer Frieder eds Geschichte der Musiktheorie Vol 2 Darmstadt Wissenschaftliche Buchgesellschaft p 94 ISBN 3 534 01202 X Schulter Margo 10 June 1998 McComb Todd ed Pythagorean Tuning and Medieval Polyphony Medieval Music and Arts Foundation Retrieved 2 February 2016 Schulter Margo 2 March 2001 McComb Todd ed Xenharmonic Excursion to Padua 1318 Marchettus the Cadential Diesis and Neo Gothic Tunings Medieval Music and Arts Foundation Retrieved 2 February 2016 a b Griffiths Paul Lindley Mark 1980 Microtone In 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Gurlitt Wilibald Eggebrecht Hans Heinrich eds Riemann Musiklexikon Volume 3 Sachteil Twelfth fully revised ed Mainz B Schott s Sohne pp 1032 1033 Dahlhaus Carl Eggebrecht Hans Heinrich Oehl Kurt eds 1995 Brockhaus Riemann Musiklexikon in vier Banden und einem Erganzungsband Volume 4 Brockhaus Riemann Music Lexicon in Four Volumes and a Supplementary Volume Second ed Mainz Atlantis Schott Musikbuch Verlag p 304 Wyschnegradsky Ivan 1972 L Ultrachromatisme et les espaces non octaviants La Revue musicale 290 91 84 87 Belyaev Victor M Belyaev V M 1971 Azerbajdzhanskaya narodnaya pesnya 1960 Azerbaijan Folk Songs In Belyaev Victor ed O muzykalnom folklore i drevnej pismennosti On Musical Folklore and Ancient Literature Moscow Sov etskii Kompozitor pp 108 156 Belyaev Victor M Belyaev V M 1971 Tureckaya muzyka 1934 Turkish Music In Belyaev Victor ed O muzykalnom folklore i drevnej pismennosti On Musical Folklore and Ancient Literature Moscow Sov etskii Kompozitor pp 163 176 Belaiev Victor July 1935 Turkish Music abridged English version The Musical Quarterly 21 3 356 367 doi 10 1093 mq XXI 3 356 Zabka Marek Fall 2014 Dancing with the Scales Subchromatic Generated Tone Systems Journal of Music Theory 58 2 179 233 doi 10 1215 00222909 2781769 Hesse Horst Peter Winter 1991 Breaking into a New World of Sound Reflections on the Austrian Composer Franz Richter Herf 1920 1989 Perspectives of New Music 29 1 212 235 doi 10 2307 833077 JSTOR 833077 Mikrohromatika Mikrochromatika Microchromatics Muzykalnyj enciklopedicheskij slovar Musical Encyclopedic Dictionary in Russian Moscow Sov etskaya Entsiklopediya 1990 p 344 Mikrohromaticheskie intervaly Mikrochromaticheskie Intervali Microchromatic Intervals Muzykalnyj slovar Grouva Grove Music Dictionary in Russian Second ed Moscow Praktika 2007 p 563 Akopyan Levon Muzyka HH veka Enciklopedicheskij slovar Music of the Twentieth Century An Academic Dictionary in Russian Moscow Praktika pp 353 354 Tsenova V S Cenova V S ed 2007 Teoriya sovremennoj kompozicii The Theory of Modern Composition in Russian Moscow Muzyka pp 65 123 152 etc Kholopov Y Yu HOLOPOV Kirillina L l KIRILLINA Kyuregyan T T KYuREGYaN Lyzhov G g LYZhOV Pospelova R R POSPELOVA Tsenova V V CENOVA 2006 Muzykalno teoreticheskie sistemy Musical Theoretical Systems PDF in Russian Moscow Kompozitor pp 86 etc Kholopov Yuri N yu n holopov 2003 Garmoniya Teoreticheskij kurs Harmony Theoretical Course PDF in Russian St Petersburg Lan pp 172 etc ISBN 5 8114 0516 2 Klishin A G 2010 Problemy muzykalnogo stroya v nachale Novogo vremeni Problems of Musical Structure in the Early Modern Era PhD diss Moscow Moscow Conservatory Gurenko N A Gurenko N A 2010 Mikrohromatika I Vyshnegradskogo Istoriya teoriya praktika osvoeniya The Microchomatics of I Wyschnegradsky History Theory Practice Development PhD diss Urals Mussorgsky State Conservatoire Polunina E N Polunina E N 2010 Mikrohromatika v muzykalnom iskusstve pozdnego Vozrozhdeniya Microchromatics in Music of the Late Renaissance PhD diss Vladivostok Far East State Academy of Arts Rovner A A 2010 Sergej Protopopov kompozitorskoe tvorchestvo i teoreticheskie raboty Sergey Protopopov composer s output and theoretical works PhD diss Moscow Moscow Conservatory Nikoltsev I D 2013 Mikrohromatika v sisteme sovremennogo muzykalnogo myshleniya Microchomatics in Contemporary Musical Thought PhD diss Moscow Moscow Conservatory More references can be located on the disserCat website at Poisk dissertacij Search for dissertations Kholopov Yuri Nikolaevich Holopov Yu N 1976 Mikrohromatika Microchromatics Muzykalnaya enciklopediya Musical Encyclopedia Vol 3 Moscow Bolshaya Sovetskaya Entsiklopedia Great Soviet Encyclopedia pp 587 589 Kholopov Y N Holopov Yu N 2000 Mikro i posledstviya Micro and consequences Muzykalnoe obrazovanie v kontekste kultury Music education in the cultural context Moscow Gnessins Music Academy pp 27 38 Kogut Gennady A 2005 Mikrotonovaya muzyka Microtonal Music in Russian Kyiv Naukova Dumka ISBN 966 00 0604 7 Ader Lidia Olegovna Ader Lidiya Olegovna 2013 Mikrotonovaya muzyka v Evrope i Rossii v 1900 1920 e gody Microtonic music in Europe and Russia in the 1900s 1920s Non doctoral diss St Petersburg Gosudarstvennaa Konservatoria imeni N A Rimskogo Korsakova Pavlenko Sergej Vasil evic Kefalidi Igor Ekimovskij Viktor Alekseevic 2002 Mikrotonovye elementy Beseda Microtonal Elements A Conversation Muzykalnaya Akademiya Muzykal naa akademia 2 21 24 Poisk dissertacij mikrotonovyj Rezultat poiska dokumentov najdeno 14 Dissertation search mikrotonovyj Search result documents found 14 disserCat Retrieved 14 December 2020 Poisk dissertacij mikrotonalnost Rezultat poiska dokumentov najdeno 1 Dissertation search mikrotonalnost Search result documents found 1 disserCat Retrieved 14 December 2020 Poisk dissertacij mikrotonika Rezultat poiska dokumentov najdeno 1 Dissertation search mikrotonika Search result documents found 1 disserCat Retrieved 14 December 2020 Criton Pascale 2010 Variabilite et multiplicite acoustique Variability and acoustic multiplicity In Soulez Antonia Vaggione Horacio eds Manieres de faire des sons Ways of making sounds Musique philosophie in French Paris L Harmattan pp 119 133 ISBN 978 2 296 12959 7 Jedrzejewski Franck in French 2004 Alois Haba et l experimentation micro intervallique In Galmiche Xavier Stranska Lenka eds L attraction et la necessite Musique tcheque et culture francaise au XXe siecle Paris Universite Paris Sorbonne Paris IV pp 169 175 ISBN 978 80 86385 27 3 Conti Luca 2005 Suoni di una terra incognita il microtonalismo in Nord America 1900 1940 Sounds of an unknown land microtonalism in North America 1900 1940 in Italian Lucca Libreria musicale italiana Conti Luca 2008 Ultracromatiche sensazioni il microtonalismo in Europa 1840 1940 Ultrachromatic sensations microtonalism in Europe 1840 1940 in Italian Lucca Libreria musicale italiana Rue Roberto 2000 Diatonismo cromatismo y microtonalismo Una interpretacion estructuralista Diatonism chromaticism and microtonalism A structuralist interpretation Musica e investigacion Revista del Instituto Nacional de Musicologia Carlos Vega Music and research Magazine of the National Institute of Musicology Carlos Vega in Spanish 4 7 8 39 53 Chou Wen chung April 1971 Asian Concepts and Twentieth Century Western Composers The Musical Quarterly 57 2 211 229 Macrotonal Xenharmonic Wiki blog at macrospaces com n d Archived from the original on July 14 2016 Retrieved 3 February 2016 Pressing Jeff 1992 Synthesizer Performance and Real time Techniques Madison A R Editions p 239 ISBN 978 0 89579 257 0 Spring Glenn Hutcheson Jere 2013 Musical Form and Analysis Time Pattern Proportion Long Grove Waveland Press Inc p 82 ISBN 978 1 4786 0722 9 Adlington Robert 2004 Louis Andriessen De Staat Hants UK Ashgate Publishing p 88 West Martin Litchfield 1992 Ancient Greek Music Oxford Clarendon Press pp 160 172 ISBN 0 19 814897 6 ISBN 0 19 814975 1 paperback Lindley Mark 2001 Mean tone In Sadie Stanley Tyrrell John eds The New Grove Dictionary of Music and Musicians Second ed London Macmillan Publishers Barbour J Murray 1951 Tuning and Temperament A Historical Survey Reprinted n p Dover 2004 ed East Lansing Michigan USA Michigan State College Press pp 117 18 ISBN 0 486 43406 0 Koenig Laura Jeanne 1995 Air a la grecque A Quarter tone Piece for Flute in the Historical Context of the Enharmonic Genre in Eighteenth century French Music and Theory DMA diss Iowa City Iowa USA The University of Iowa pp iii 1 9 10 52 55 116 119 Reilly Edward R Solum John Spring 1992 De Lusse Buffardin and an Eighteenth Century Quarter Tone Piece Historical Performance 19 23 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 fourth and last German edition of 1877 with numerous additional notes and a new additional appendix bringing down information to 1885 and especially adapted to the use of music students by Alexander J Ellis London Longmans Green pp 514 527 Ellis Alexander J 1884 Tonometrical Observations on Some Existing Non Harmonic Musical Scales Proceedings of the Royal Society of London 37 368 385 Bibcode 1884RSPS 37 368E Partch Harry 1979 Genesis of a Music Second ed New York Da Capo Press p vii ISBN 0 306 80106 X Lesure Francois 2001 Debussy Achille Claude 7 Models and Influences In Sadie Stanley Tyrrell John eds The New Grove Dictionary of Music and Musicians Second ed London Macmillan Publishers Howat Roy 2001 Debussy Achille Claude 10 Musical Language In Sadie Stanley Tyrrell John eds The New Grove Dictionary of Music and Musicians Second ed London Macmillan Publishers Don Gary Spring 2001 Brilliant Colors Provocatively Mixed Overtone Structures in the Music of Debussy Music Theory Spectrum 23 1 61 73 doi 10 1525 mts 2001 23 1 61 Partch 1979 pp 119 137 Chapter 8 Application of the 11 Limit Stockhausen Karlheinz 1964 Schnebel Dieter ed Texte 2 Aufsatze 1952 1962 zur musikalischen Praxis Texts 2 Essays on musical practice 1952 1962 Cologne Verlag M DuMont Schauberg p 37 Decroupet Pascal Ungeheuer Elena Winter 1998 Translated by Jerome Kohl Through the Sensory Looking Glass The Aesthetic and Serial Foundations of Gesang der Junglinge Perspectives of New Music 36 1 105 116 119 121 doi 10 2307 833578 JSTOR 833578 Blackwood Easley Kust Jeffrey 2005 1996 Easley Blackwood Microtonal Compositions Second ed Cedille Records Blackwood Easley n d Liner notes to Blackwood Microtonal Compositions CDR018 Cedille Records Carlos Wendy 1989 1996 Three Asymmetric Divisions of the Octave wendycarlos com Retrieved March 28 2009 Murphy Ben January 2017 Making Waves Electronic Sound 26 70 75 Colundi is Music Tuned to Frequencies That Heal the Body Bandcamp Daily 2019 01 10 Retrieved 2022 12 01 Igloo Magazine Aleksi Perala Ovuca The original harmony of Human and Nature 2021 11 01 Retrieved 2022 12 01 LilyPond project LilyPond Notation Reference v2 21 7 development branch LilyPond p 3 5 1 Supported notation for MIDI Retrieved 28 October 2020 Microtones but not microtonal chords A MIDI player that supports pitch bending will also be required Ferguson Jim 1999 All Blues Soloing for Jazz Guitar Scales Licks Concepts amp Choruses Guitar Master Class Pacific Missouri USA Mel Bay p 20 ISBN 0 7866 4285 8 Monzo Joe 1998 A Microtonal Analysis of Robert Johnson s Drunken Hearted Man a b Wilson John Penderecki Krzysztof Greenwood Jonny 23 March 2012 Interview with Jonny and Krzysztof Penderecki Front Row BBC Radio 4 Archived from the original on 23 September 2015 Transcript from an audio recording of the broadcast on Citizen Insane website Retrieved 21 July 2014 Couture Francois n d Jon Catler Evolution for Electric Guitar and Orchestra AllMusic Retrieved 3 April 2013 cite web url h https www trebuchet magazine com secret chiefs 3 interview with trey spruance Heavenly Recordings 11 November 2016 King Gizzard Announce a New Album Flying Microtonal Banana Heavenly Records Archived from the original on 11 December 2016 Retrieved 29 March 2017 Pooja Bale 4 April 2021 L W proves King Gizzard amp the Lizard Wizard can master microtonality a third time The Daily Californian Retrieved 4 April 2021 K aplan Noah K aplan Rosie 2018 Notes from Underground Ivan Wyschnegradsky s Manual of Quarter Tone Harmony New Music Box Retrieved May 15 2018 Further reading EditAder Lidia Olegovna Ader Lidiya Olegovna 2011a Mikrotonovaya ideya Istoki i predposylki The Concept of Microtonality Its Origin and Background Nauchnyj zhurnal Sankt Peterburgskoj konservatorii Opera musicologica Naucnyj zurnal Sankt Peterburgskoj konservatorii 3 4 nos 8 9 114 134 Ader Lidia Olegovna Ader Lidiya Olegovna 2011b Mikrotonovyj instrumentarij pervye shagi ot utopii k praktike Microtonal Instruments The First Steps from Utopia to Practice In Vremennik Zubovskogo instituta Instrumentalizm v istorii kultury Instrumentalism in the history of culture edited by Evgenia Vladimirovna Hazdan 52 65 Vremennik Zubovskogo instituta 7 St Petersburg Rossijskij Institut Istorii Iskusstv 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 amp Matheo de Vitali 1529 Facsimile reprint Bibliotheca musica Bononiensis sezione 2 n 10 Bologna Forni Editori 1969 Online edition of the 1529 text in Italian Third edition as Toscanello in musica Venice Marchio Stessa 1539 Facsimile edition edited by Georg Frey Kassel Barenreiter 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 amp 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 fur 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 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 Gonzalez 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 215 264 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 Colonna Fabio 1618 La sambuca lincea overo Dell istromento musico perfetto Naples C Vitale Facsimile reprint of a copy containing manuscript critical annotations by Scipione Stella 1618 1624 with an introduction by Patrizio Barbieri Musurgiana 24 Lucca Italy Libreria Musicale Italiana 1991 Daniels Arthur Michael 1965 Microtonality and Mean Tone Temperament in the Harmonic System of Francisco Salinas Journal of Music Theory 9 no 1 Spring 2 51 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 Fritsch Johannes G 2007 Allgemeine Harmonik Tonsysteme Mikrotonalitat Ein geschichtlicher Uberblick In Orientierungen Wege im Pluralismus der Gegenwartsmusik edited by Jorn Peter Hiekel 107 122 Veroffentlichungen des Instituts fur Neue Musik und Musikerziehung Darmstadt 47 Mainz Schott Musik International ISBN 978 3 7957 1837 4 Gilmore Bob 1998 Harry Partch A Biography New Haven Yale University Press ISBN 0 300 06521 3 Haas Georg Friedrich 2007 Mikrotonalitat und spektrale Musik seit 1980 In Orientierungen Wege im Pluralismus der Gegenwartsmusik edited by Jorn Peter Hiekel 123 129 Veroffentlichungen des Instituts fur Neue Musik und Musikerziehung Darmstadt 47 Mainz Schott Musik International ISBN 978 3 7957 1837 4 Haba Alois 1927 Neue Harmonielehre des diatonischen chromatischen Viertel Drittel Sechstel und Zwolftel tonsystems Leipzig Kistner amp Siegel Johnston Ben 2006 Maximum Clarity and other writings on music ed B Gilmore Urbana and Chicago University of Illinois Press Kotschy Johannes 2008 Mikrotonalitat Eine Zeiterscheinung Osterreichische Musikzeitschrift 63 no 7 July 8 15 Landman Yuri 2008 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 1991 A Venerable Temperament Rediscovered Perspectives of New Music 29 no 2 Summer 202 211 Lindley Mark 2001b Temperaments The New Grove Dictionary of Music and Musicians second edition edited by Stanley Sadie and John Tyrrell London Macmillan Publishers Mandelbaum M Joel 1961 Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament Ph D thesis Bloomington Indiana University Mosch Ulrich 2008 Ultrachromatik und Mikrotonalitat Hans Zenders Grundlegung einer neuen Harmonik In Hans Zender Vielstimmig in sich edited by Werner Grunzweig Anouk Jeschke and Jorn Peter Hiekel 61 76 Archive zur Musik des 20 Jahrhunderts No 12 Hofheim Wolke ISBN 978 3 936000 25 2 Noyze Dave and Richard D James 2014 Aphex Twin Syrobonkers Interview Part 2 Noyzelab Blogspot com au Monday 10 November Stahnke Manfred 2010 About Backyards and Limbos Microtonality Revisited In Concepts Experiments and Fieldwork Studies in Systematic Musicology and Ethnomusicology edited by Rolf Bader Christiane Neuhaus and Ulrich Morgenstern with a prefaceby Achim Reichel 297 314 Frankfurt am Main and New York Peter Lang ISBN 978 3 631 58902 1 Vitale Raoul 1982 La Musique sumero accadienne gamme et notation musicale Ugarit Forschungen 14 241 263 Werntz Julia 2001 Adding Pitches Some New Thoughts Ten Years after Perspectives of New Music s Forum Microtonality Today Perspectives of New Music 39 no 2 Summer 159 210 Wood James 1986 Microtonality Aesthetics and Practicality The Musical Times 127 no 1719 June 328 330 Wyschnegradsky Ivan 1937 La musique a quarts de ton et sa realisation pratique La Revue Musicale no 171 26 33 Zweifel Paul 1996 Generalized Diatonic and Pentatonic Scales A Group Theoretic Approach Perspectives of New Music 34 no 1 Winter 140 161 External links Edit Wikimedia Commons has media related to Microtonal music Microtonal music at Curlie 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 Solis 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 Listen Xenharmonic Wiki links to microtonal composers and compositions Projects Xenharmonic Wiki links to microtonal projects around the world Offtonic Microtonal Synthesizer a browser based synth to explore microtonal tunings with a QWERTY keyboard MidiPro org Archived 2020 11 23 at the Wayback Machine allows any sound card or synthesizer to play 48 microtones per octave each separated by 1 8 step Retrieved from https en wikipedia org w index php title Microtonal music amp oldid 1133749361, wikipedia, wiki, book, books, library,

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