423:, 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)). 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
5664:
5659:
624:
7103:
7113:
521:"; see a clarification in Kholopov ). Other Russian authors use the more international adjective 'microtonal' and have rendered it in Russian as 'микротоновый', but not 'microtonality' ('микротональность'). However, the terms 'микротональность' and 'микротоника' are also used. Some authors writing in French have adopted the term "micro-intervallique" to describe such music. Italian musicologist Luca Conti dedicated two of his monographs to
1123:
112:
525:, which is the usual term in Italian, and also in Spanish (e.g., as found in the title of Rué ). 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".
774:
to his exposure to the
Balinese gamelan at the Paris exposition, 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
528:
The term "macrotonal" has been used for intervals wider than twelve-tone equal temperament, 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". The term "macrotonal" has also been used for musical
202:), respectively. "Microinterval" is a frequent alternative in English, especially in translations of writings by French authors and in discussion of music by French composers. In English, the two terms "microtone" and "microinterval" are synonymous. The English analogue of the related French term,
615:
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
158:
of Indian music. 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. It may have been even slightly earlier, perhaps as early as 1895, that the
Mexican
998:
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. Joe Monzo has made a microtonal analysis of the song "Drunken
Hearted Man", written and recorded by the delta blues musician
4919:
Adèr, Lidiâ Olegovna . 2011b. "Микротоновый инструментарий—первые шаги от утопии к практике" . In Временник Зубовского института: Инструментализм в истории культуры , edited by
Evgenia Vladimirovna Hazdan, 52–65. Vremennik Zubovskogo instituta 7. St. Petersburg: Rossijskij Institut Istorii
4267:
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
1056:
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.
579:
66:
414:
objected that "'heterotone' would be a better name for śruti than the usual translation 'microtone'". Modern Indian researchers yet write: "microtonal intervals called shrutis". In
Germany, Austria, and Czechoslovakia in the 1910s and 1920s the usual term continued to be
606:
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
4995:. 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.
571:
907:. "The project," he wrote, "was to explore the tonal and modal behavior of all 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".
580:
57:
981:
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.
67:
47:
620:). 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).
264:"microintervals" but not "microtones", 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". In the second edition of
683:, 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
498:
761:
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
336:, 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. It was used still earlier by
4932:. 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
321:"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, as "enharmonic microtones", for example.
2210: – mathematical characterization of the harmonic complexity of music; way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale
55:
447:
for intervals larger than the semitone; this same term has been used since 1934 by ethnomusicologist Victor
Belaiev (Belyaev) in his studies of Azerbaijan and Turkish traditional music. A similar term,
348:
came into use at least by 1958, 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
828:(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),
56:
970:
1.0 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
278:, 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
3856:
51:
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
4763:
4009:
Rué, Roberto (2000). "Diatonismo, cromatismo y microtonalismo: Una interpretación estructuralista" [Diatonism, chromaticism and microtonalism: A structuralist interpretation].
813:
577:
64:
679:, 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
821:'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.
4967:
Chromatische und enharmonische Musik und Musikinstrumente des 16. und 17. Jahrhunderts/Chromatic and Enharmonic Music and Musical Instruments in the 16th and 17th Centuries
4969:. Schweizer Jahrbuch für Musikwissenschaft/Annales suisses de musicologie/Annuario svizzero di musicologia 22, edited by Joseph Willimann. Bern: Verlag Peter Lang AG.
738:, proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings. Ellis also studied the tunings of non-Western cultures and, in a report to the
578:
5000:
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
817:
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.
487:
when referring to "all the pitches lying outside the traditional twelve-tone system". Some authors in Russia and some musicology dissertations disseminate the term
65:
3812:
Pavlenko, Sergej Vasil'evič; Kefalidi, Igor'; Ekimovskij, Viktor Alekseevič (2002). "Микротоновые элементы: Беседа" [Microtonal Elements: A Conversation].
3831:
836:(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).
5174:, edited by Jörn Peter Hiekel, 123–129. Veröffentlichungen des Instituts für Neue Musik und Musikerziehung Darmstadt 47. Mainz: Schott Musik International.
3702:
5399:". 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)
3881:
2130:
1585:
1360:
488:
469:
388:
or other alternative tunings may be considered microtonal. Microtonal variation of intervals is standard practice in the African-American musical forms of
2689:. Musique de notre temps: compositeurs (in French) (Second, revised, corrected, and enlarged ed.). Lillebonne: Millénaire III Éditions. p. 314.
6001:
5312:, edited by Rolf Bader, Christiane Neuhaus, and Ulrich Morgenstern, with a prefaceby Achim Reichel, 297–314. Frankfurt am Main and New York: Peter Lang.
894:
4936:, Venice: Bernardino & Matheo de Vitali, 1529. Facsimile reprint, Bibliotheca musica Bononiensis, sezione 2., n. 10. Bologna: Forni Editori, 1969.
4794:
665:
4947:, Venice: Marchio Stessa, 1539. Facsimile edition, edited by Georg Frey. Kassel: Bärenreiter, 1970. Fourth edition, Venice, 1562. English edition, as
4430:
Decroupet, Pascal; Ungeheuer, Elena (Winter 1998). "Through the Sensory Looking-Glass: The Aesthetic and Serial Foundations of Gesang der Jünglinge".
1905:
775:
many bell- and gong-like sonorities and brilliant exploitation of the piano's natural resonance". Still others have argued that Debussy's works like
368:
The term "microtonal music" usually refers to music containing very small intervals but can include any tuning that differs from Western twelve-tone
4845:
356:
and music of Eastern traditions. The term "microinterval" is used alongside "microtone" by American musicologist Margo Schulter in her articles on
4914:
Adèr, Lidiâ Olegovna . 2011a. "Микротоновая идея: Истоки и предпосылки" . Научный журнал Санкт-Петербургской консерватории 3–4, nos. 8–9:114–134.
653:. While theoretically an interpretation of ancient Greek tetrachordal theory, in effect Vicentino presented a circulating system of quarter-comma
3093:
2799:
2735:
1767:
403:
Many microtonal equal divisions of the octave have been proposed, usually (but not always) in order to achieve approximation to the intervals of
266:
4951:, translated by Peter Bergquist. 3 vols. Colorado College Music Press Translations, no. 4. Colorado Springs: Colorado College Music Press, 1970.
789:
5222:
501:) for all possible microtonal structures, both ancient (as enharmonic genus—γένος ἐναρμόνιον—of Greeks) and modern (as quarter tone scales of
4771:
3414:
Hesse, Horst-Peter (Winter 1991). "Breaking into a New World of Sound: Reflections on the Austrian Composer Franz Richter Herf (1920–1989)".
2590:
Rae, Caroline (2013). "Messiaen and Ohana: Parallel Preoccupations or Anxiety of Influence?". In Fallon, Robert; Dingle, Christopher (eds.).
5297:
6129:
4820:
6695:
764:
5416:
1214:
5987:
5485:
4937:
4283:
1218:
318:
and various other Near Eastern musical traditions, but do not actually name the "mathematical" terms schisma, comma, and diaschisma.
5334:
Werntz, Julia. 2001. "Adding Pitches: Some New Thoughts, Ten Years after Perspectives of New Music's 'Forum: Microtonality Today'".
6061:
5390:
1635:
843:(31 equal tones per octave), Partch (continuing to build his handcrafted orchestra of microtonal just intonation instruments), and
4691:
1357:(France, 1919–1989, many different equal temperaments: 18ET, 24ET, 30ET, 36ET, 48ET, 96ET most particularly and polymicrotonality)
6194:
5974:
5403:
4234:: A Quarter-tone Piece for Flute in the Historical Context of the Enharmonic Genre in Eighteenth-century French Music and Theory
88:, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western
5137:, 107–122. Veröffentlichungen des Instituts für Neue Musik und Musikerziehung Darmstadt 47. Mainz: Schott Musik International.
3318:
Belyaev, Victor M. (1971). "Азербайджанская народная песня (1960)" [Azerbaijan Folk Songs]. In Belyaev, Victor (ed.).
1192:
5317:
5288:
5179:
5142:
4117:
4092:
3955:
3923:
2848:
2768:
2694:
2669:
2624:
2599:
2532:
Battier, Marc; Lacino, Thierry (1984). "Simulation and Extrapolation of Instrumental Sounds Using Direct Synthesis at IRCAM (
2466:
2413:
2309:
1042:
has been making its own custom "microtonal" instruments since the mid 1990s. The proprietary tuning system they use in their
3618:
854:(1987) on and inexpensive software synthesizers have contributed to the ease and popularity of exploring microtonal music.
899:
a cycle that explores all of the equal temperaments from 13 notes to the octave through 24 notes to the octave, including
697:
composed a cantata "Prométhée enchaîné" for a solo voice, choir and orchestra (premiered in 1849), where in one movement (
6204:
5588:
5232:
5220:. . "Third Bridge Helix: From Experimental Punk to Ancient Chinese Music and the Universal Physical Laws of Consonance".
4722:
865:
facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems. In 1954,
5012:(ed.). 2001. "The Ratio Book." (Documentation of the Ratio Symposium Royal Conservatory The Hague 14–16 December 1992).
513:, which is subordinate to the dominating tonality, especially in the context of European music of the 19th century) and
1140:
1061:
5086:
Daniels, Arthur Michael. 1965. "Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas".
5081:(1618–1624), with an introduction by Patrizio Barbieri. Musurgiana 24. Lucca, Italy: Libreria Musicale Italiana, 1991.
4747:
560:(1972–1976) contains a number of "augmented" modes that are based on Greek scales but are asymmetrical to the octave.
5159:
5109:
5056:
5030:
4974:
4648:
4324:
4213:
4186:
4168:
4157:
3906:
Criton, Pascale (2010). "Variabilité et multiplicité acoustique" [Variability and acoustic multiplicity]. In
3773:
3571:
3169:
3127:
3102:
3015:
2823:
2516:
2491:
1899:
1162:
4053:
7147:
6573:
4750:
4603:
4247:
Reilly, Edward R.; Solum, John (Spring 1992). "De Lusse, Buffardin, and an Eighteenth-Century Quarter Tone Piece".
480:
89:
4358:
Howat, Roy (2001). "Debussy, (Achille-)Claude: §10, 'Musical Language'". In Sadie, Stanley; Tyrrell, John (eds.).
6688:
6167:
5864:
5097:
2251:
1312:
4846:
https://www.native-instruments.com/fileadmin/userlib/legacy/userlib_kontakt/1355701044_File_12389_53.shadow-.zip
4208:(Reprinted : Dover, 2004 ed.). East Lansing, Michigan, USA: Michigan State College Press. pp. 117–18.
1029:
has used microtonal string arrangements in their music, such as on "How to Disappear Completely" from the album
598:. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining
146:
can refer to any music containing microtones. The words "microtone" and "microtonal" were coined before 1912 by
5478:
2366:
2345:
1857:
1144:
147:
4373:
Don, Gary (Spring 2001). "Brilliant Colors Provocatively Mixed: Overtone Structures in the Music of Debussy".
3218:
Hába, Alois (1922). "Vývoj hudební tvorby a theorie vzhledem k diatonice, chromatice a čtvrttónové soustavě".
2763:(Fourth ed.). Cambridge, Massachusetts, USA: The Belknap Press of Harvard University Press. p. 193.
2452:
704:
In the 1910s and 1920s, quarter tones (24 equal pitches per octave) received attention from such composers as
634:'s "Chromatic Chanson", "Seigneur Dieu ta pitié" of 1558 used 1/3 comma meantone (which almost exactly equals
6974:
6352:
3798:
750:
5271:
Mosch, Ulrich. 2008. "Ultrachromatik und Mikrotonalität: Hans Zenders Grundlegung einer neuen Harmonik". In
5004:, edited by Diego L. González, Domenico Stanzial, and Davide Bonsi. 2 vols. Venice: Fondazione Giorgio Cini.
3942:(2004). "Alois Hába et l'expérimentation micro-intervallique". In Galmiche, Xavier; Stránská, Lenka (eds.).
2661:
742:, stated that they used neither equal divisions of the octave nor just intonation intervals. Ellis inspired
92:. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in
7142:
6054:
4490:
4343:(2001). "Debussy, (Achille-)Claude: §7, 'Models and Influences'". In Sadie, Stanley; Tyrrell, John (eds.).
307:
2300:
Boatwright, Howard (1971). "Ives' Quarter-Tone Impressions". In Boretz, Benjamin; Cone, Edward T. (eds.).
649:(1511–1576) worked with microtonal intervals and built a keyboard with 36 keys to the octave known as the
7024:
6713:
6290:
5969:
2888:
2794:
2730:
1779:
881:(1955–56) he used various scales, ranging from seven up to sixty equal divisions of the octave. In 1955,
570:
238:
111:
46:
5189:
Neue Harmonielehre des diatonischen, chromatischen Viertel-, Drittel-, Sechstel- und Zwölftel-tonsystems
5002:
Musical Sounds from Past Millennia: Proceedings of the International Symposium on Musical Acoustics 2001
4897:
3337:
Belyaev, Victor M. (1971). "Турецкая музыка (1934)" [Turkish Music]. In Belyaev, Victor (ed.).
1392:
in quarter tone tuning, natural harmonics in his Horn Trio, later just intonation in his solo concertos)
832:(third tones, quarter tones, sixth tones and twelfth tones, non octaving scales) and the early works of
694:
410:
Terminology other than "microtonal" has been used or proposed by some theorists and composers. In 1914,
7106:
6681:
6134:
5994:
5737:
5613:
5508:
1791:
17:
4281:
Ellis, Alexander J. (1884). "Tonometrical Observations on Some Existing Non-Harmonic Musical Scales".
783:
206:, however, is rare or nonexistent, normally being translated as "microtonality"; in French, the terms
6119:
5946:
5934:
5471:
4432:
3947:
3416:
2983:
2196:
2179:
311:
4956:
Barbieri, Patrizio. 1989. "An Unknown 15th-Century French Manuscript on Organ Building and Tuning".
3470:"Микрохроматические интервалы" [Mikrochromaticheskie Intervali / Microchromatic Intervals].
6403:
5638:
4702:
on 23 September 2015. Transcript from an audio recording of the broadcast on Citizen Insane website
4553:
3279:
3257:
1875:
1070:
688:
5380:
2010:
594:
The Hellenic civilizations of ancient Greece left fragmentary records of their music, such as the
7094:
6539:
6373:
6199:
6124:
6047:
5896:
5767:
5578:
5460:
allows any sound card or synthesizer to play 48 microtones per octave, each separated by 1/8 step
5453:
5088:
4934:
Toscanello in musica... nuovamente stampato con laggiunta da lui fatta et con diligentia corretto
4236:(DMA diss.). Iowa City, Iowa, USA: The University of Iowa. pp. iii, 1, 9–10, 52–55, 116–119.
3527:
Kholopov, Y. ; Kirillina, L. ; Kyuregyan, T. ; Lyzhov, G. ; Pospelova, R. ; Tsenova, V. (2006),
3387:
3080:
2164:
1463:
1380:(Greece, France, 1922–2001, quarter and third tones most particularly, occasionally eighth tones)
1305:(U.S.S.R. (Russia), France, 1893–1979, quarter tones, twelfth tones and other equal temperaments)
1133:
939:, who derived his compositions' tunings from frequency-runs submitted by users of a custom-built
271:
3056:"Xenharmonic Excursion to Padua, 1318: Marchettus, the Cadential Diesis, and Neo-Gothic Tunings"
877:
552:(1995), which gradually expands stacked-interval chords ranging from minor 2nds to major 7thsm.
7137:
7116:
7075:
6395:
6358:
6348:
6157:
5593:
5364:
Zweifel, Paul. 1996. "Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach".
5077:. Naples: C. Vitale. Facsimile reprint of a copy containing manuscript critical annotations by
4579:"Igloo Magazine :: Aleksi Perälä (Ovuca) :: The original harmony of Human and Nature"
3939:
2649:
1953:
1827:
1388:
419:(quarter tone music), and the type of intervallic structure found in such music was called the
4268:
information to 1885, and especially adapted to the use of music students by Alexander J. Ellis
1438:(Germany, 1928–2007, in his electronic works many microtonal concepts, non-octaving scales in
931:
In 2016, electronic music composed with arbitrary microtonal scales was explored on the album
7059:
6598:
6391:
5713:
5543:
5129:. 2007. "Allgemeine Harmonik, Tonsysteme, Mikrotonalität: Ein geschichtlicher Überblick". In
4861:
4375:
4262:
4034:
3358:
2173:
1854:(b. 1965) (quarter tones, ancient Chinese tunings, e.g. circle-of-fifths and just intonation)
1707:
1618:
1511:
1444:
1435:
1407:
1395:
1369:
1365:
866:
840:
474:
337:
295:
4965:
Barbieri, Patrizio. 2002. "The Evolution of Open-Chain Enharmonic Keyboards c1480–1650". In
6566:
6399:
6344:
6326:
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6316:
6311:
6306:
6301:
6296:
6281:
6276:
6271:
6266:
6261:
6256:
6023:
5846:
5841:
5836:
5831:
5826:
5821:
5816:
5806:
5801:
5796:
5791:
5786:
5518:
5167:
4986:, second edition, edited by Robert Palmieri and Margaret W. Palmieri,. New York: Routledge.
4683:
4292:
3262:
2340:
2222:
1725:
1716:(b. 1954) (different equal temperaments, most particularly very dense ETs such as the 96ET)
1701:
1505:
1011:
904:
900:
875:
on an 81-step scale starting from 100 Hz with the interval of 5 between steps, and in
807:
727:
635:
425:
411:
385:
5280:
5134:
4795:"'L.W.' proves King Gizzard & the Lizard Wizard can master microtonality a third time"
3385:Žabka, Marek (Fall 2014). "Dancing with the Scales: Subchromatic Generated Tone Systems".
951:
in the late 1940s, thereby supposedly embodying thoughts and concepts within the tunings.
8:
6959:
6363:
6336:
6234:
6018:
5963:
5663:
5643:
5352:
5310:
Concepts, Experiments and Fieldwork: Studies in Systematic Musicology and Ethnomusicology
5257:, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
3683:
3660:
3595:
3553:
2818:. Metuchen (New Jersey, USA) and London (England): The Scarecrow Press, Inc. p. 59.
2016:
1881:
1302:
1255:
1244:
1106:
1064:
utilises microtonal instruments, including custom microtonal guitars modified to play in
920:
829:
717:
670:
436:
5276:
4296:
4032:
Chou, Wen-chung (April 1971). "Asian Concepts and Twentieth-Century Western Composers".
3144:
2793:
Griffiths, Paul; Lindley, Mark; Zannos, Ioannis (2001). "Microtone". In Sadie, Stanley;
2714:(Second ed.). Cambridge, Massachusetts, USA: Harvard University Press. p. 527.
586:
6954:
6882:
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6214:
6209:
5940:
5658:
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4578:
4453:
4315:
3433:
3055:
2944:
2383:
2046:
1998:
1923:
1354:
1247:, and in the Third Violin Sonata, as inflections characteristic of Romanian folk music)
955:
631:
119:
5528:
4958:
The Organ Yearbook: A Journal for the Players & Historians of Keyboard Instruments
4340:
2437:
2004:
1692:(b. 1952) (invented acoustic instruments in just intonation & recurrent sequences)
1210:
709:
160:
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6867:
6752:
6704:
6647:
6407:
6368:
6243:
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5026:
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4209:
4164:
4153:
4113:
4088:
3951:
3919:
3859:[Dissertation search: микротональность – Search result, documents found: 1].
3769:
3567:
3303:
3165:
3123:
3098:
3011:
2927:
2907:
2844:
2819:
2764:
2690:
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2620:
2595:
2558:
2512:
2487:
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2409:
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1992:
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1565:
1422:
1274:
1250:
1188:
948:
777:
731:
642:
541:
369:
353:
242:
defines "microtone" as "an interval smaller than a semitone", which corresponds with
93:
6433:
5558:
2040:
1887:
1809:
252:. However, the unsigned article "Comma, Schisma" in the same reference source calls
7080:
7049:
7014:
6969:
6964:
6877:
6857:
6847:
6812:
6807:
6615:
6387:
6251:
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6139:
6104:
5916:
5869:
5718:
5628:
5553:
5513:
5494:
5126:
4665:
4624:
microtonal chords. A MIDI player that supports pitch bending will also be required.
4445:
4384:
4011:
Música e investigación: Revista del Instituto Nacional de Musicología "Carlos Vega"
3425:
3396:
3367:
3253:
3003:
2936:
2897:
2553:
2545:
2461:. Vol. 2: Kondratiev-Zythum (Second ed.). Paris: Larousse. p. 1011.
2375:
2364:
Meyer, Max (July–October 1903). "Experimental Studies in the Psychology of Music".
2151:
2106:
1863:
1240:
1224:
1198:
1182:
862:
795:
646:
553:
81:
6822:
6802:
5583:
5264:
Multiple Division Of the Octave and the Tonal Resources of the 19 Tone Temperament
4513:
4015:
Music and research: Magazine of the National Institute of Musicology "Carlos Vega"
3834:[Dissertation search: микротоновый – Search result, documents found: 14].
3528:
3032:
1606:
1383:
1333:(France, 1913–1992, third tones (18ET) and quarter tones (24ET) most particularly)
1268:
1235:
373:
6989:
6887:
6837:
6593:
6559:
6509:
6149:
5856:
5598:
5457:
5325:
Vitale, Raoul. 1982. "La Musique suméro-accadienne: gamme et notation musicale".
5305:
5078:
5009:
4844:
the 1st shadow-sky tonal nonoctave scales are available for the sampler Kontakt:
4687:
4496:
4476:
3727:]. Vol. 3. Moscow: Bolshaya Sovetskaya Entsiklopedia . pp. 587–589.
3301:
Wyschnegradsky, Ivan (1972). "L'Ultrachromatisme et les espaces non octaviants".
2269:
2201:
2088:
2064:
1929:
1743:
1671:
1600:
1541:
1517:
1499:
1339:(Italy, 1905–1988, intuitive linear tone deviations, quarter tones, eighth tones)
1336:
1201:(Italy, Germany, 1866–1924). Experimented with microtones, including third tones.
1039:
1015:
940:
924:. "This whole formal discovery came a few weeks after I had completed the album,
915:
658:
617:
404:
381:
303:
291:
4751:
https://www.trebuchet-magazine.com/secret-chiefs-3-interview-with-trey-spruance/
3944:
L'attraction et la nécessité: Musique tchèque et culture française au XXe siècle
3884:[Dissertation search: микротоника – Search result, documents found: 1].
3284:
Brockhaus Riemann Musiklexikon in vier Bänden und einem Ergänzungsband, Volume 4
2579:. 1, Electronic Music. Translated by Goehr, Alexander (English ed.): 22–23.
7039:
6999:
6984:
6913:
6908:
6817:
6767:
6187:
6162:
6109:
6070:
5980:
5693:
5648:
5538:
4061:
3907:
3857:"Поиск диссертаций: микротональность – Результат поиска, документов найдено: 1"
3615:
The Microchomatics of I. Wyschnegradsky: History, Theory, Practice, Development
3267:(Twelfth fully revised ed.). Mainz: B. Schott's Söhne. pp. 1032–1033.
2998:
Zaminer, Frieder (2006). "Harmonik und Musiktheorie im alten Griechenland". In
2245:
2231:
2094:
2076:
1965:
1959:
1947:
1833:
1803:
1731:
1719:
1713:
1659:
1623:
1535:
1377:
1290:
1262:
1000:
754:
721:
691:
mentioned this piece and expressed an interest in quarter tones for the flute.
533:
357:
299:
283:
155:
4821:"Notes from Underground: Ivan Wyschnegradsky's Manual of Quarter-Tone Harmony"
3918:]. Musique-philosophie (in French). Paris: L'Harmattan. pp. 119–133.
3290:] (Second ed.). Mainz: Atlantis-Schott Musikbuch-Verlag. p. 304.
2902:
2549:
2325:
Mann, Maud (MacCarthy) (16 January 1912). "Some Indian Conceptions of Music".
1612:
1609:(1946–1998) (spectral approach to microintervals, quarter tones, eighth tones)
7131:
7019:
6747:
6630:
6482:
6451:
6224:
6177:
6084:
5891:
5633:
5608:
4388:
4182:
3738:
3716:
3400:
3088:
2999:
2911:
2726:
2236:
2207:
2184:
2100:
2058:
2022:
1977:
1893:
1869:
1851:
1845:
1785:
1653:
1647:
1641:
1579:
1547:
1487:
1413:
1401:
1330:
1318:
1280:
1230:
1049:
844:
839:
Prominent microtonal composers or researchers of the 1940s and 1950s include
818:
770:
739:
603:
595:
537:
518:
494:
340:
with reference to developments in "modernism" in a 1939 record review of the
315:
253:
135:
6777:
5563:
5447:, a browser-based synth to explore microtonal tunings with a QWERTY keyboard
3832:"Поиск диссертаций: микротоновый – Результат поиска, документов найдено: 14"
2187: – Classification of musical scale or key in ancient Greek music theory
2028:
1626:(b. 1947) (spectral approach to microintervals, quarter tones, eighth tones)
1296:
825:
713:
7054:
7009:
6923:
6918:
6797:
6787:
6757:
6742:
6635:
6446:
6286:
6089:
5811:
5708:
5703:
5698:
5683:
5678:
5573:
5533:
5523:
5217:
4857:
4636:
4509:
4310:
3973:
Suoni di una terra incognita: il microtonalismo in Nord America (1900–1940)
3371:
3160:
Datta, Asoke Kumar; Sengupta, Ranjan; Dey, Nityananda; Nag, Dipali (2006),
3084:
2981:. Berlin, Frankfurt, and Vienna: Verlag Ullstein. pp. 29–32, 210–212,
2883:
2257:
2159:
2070:
2034:
1941:
1935:
1911:
1815:
1749:
1746:(b. 1956) (different equal temperaments, just intonation, polymicrotonally)
1683:
1629:
1559:
1553:
1523:
1493:
1428:
1417:
1342:
1324:
1308:
1204:
1088:
1082:
1076:
1065:
936:
911:
882:
851:
833:
743:
705:
650:
608:
275:
151:
129:
116:
5396:
5038:
Blackwood, Easley. 1991. "Modes and Chord Progressions in Equal Tunings".
3882:"Поиск диссертаций: микротоника – Результат поиска, документов найдено: 1"
3478:] (in Russian) (Second ed.). Moscow: Praktika. 2007. p. 563.
3459:] (in Russian). Moscow: Sov'etskaya Entsiklopediya. 1990. p. 344.
3288:
Brockhaus Riemann Music Lexicon in Four Volumes and a Supplementary Volume
294:
or between a sharp and its enharmonically paired flat in various forms of
290:
into more than 12 parts, and various discrepancies among the intervals of
6994:
6979:
6534:
6529:
6519:
6114:
6094:
5762:
5757:
5747:
5688:
5051:, second edition, ed. Diana Deutsch. 215–264. San Diego: Academic Press.
4925:
4641:
All Blues Soloing for Jazz Guitar: Scales, Licks, Concepts & Choruses
4441:
2429:
2118:
2112:
1971:
1797:
1773:
1761:
1755:
1695:
1689:
1677:
1665:
1562:(Canada, b. 1939, different equal temperaments, following Wyschnegradsky)
1529:
1348:
958:
works exclusively in a microtonal system known as the Colundi sequence.
453:
329:
243:
5283:, 61–76. Archive zur Musik des 20. Jahrhunderts, No. 12. Hofheim:Wolke.
4991:
Barbieri, Patrizio, Alessandro Barca, and conte Giordano Riccati. 1987.
3122:. Cambridge and New York: Cambridge University Press. pp. 124–126.
623:
7044:
7034:
7004:
6737:
6524:
6493:
5752:
5603:
5422:
5263:
2864:
2759:
Barbera, André (2003). "Comma, Schisma". In Randel, Don Michael (ed.).
2387:
2216:
2145:
2124:
2052:
1839:
1490:(U.S.A, 1929–2023, 7-tone, 19-tone, 22-tone, 31-tone equal temperament)
1481:
1469:
1299:(Czechoslovakia, 1893–1973, quarter tones and other equal temperaments)
1265:(Australia, 1882–1961, particularly works for his "free music machine")
1147: in this section. Unsourced material may be challenged and removed.
1053:
1044:
1007:
995:
971:
599:
502:
461:
389:
325:
279:
261:
31:
4885:
4873:
4457:
4401:
Partch (1979), pp. 119–137 (Chapter 8, "Application of the 11 Limit").
3437:
3162:
Experimental Analysis of Shrutis from Performances in Hindustani Music
2948:
505:); this generalization term allowed also to avoid derivatives such as
7029:
6949:
6832:
6514:
6468:
5906:
5623:
4898:
http://centrebombe.org/dansleciel,lebruitdel'ombre.html#nonoctave
3977:
Sounds of an unknown land: microtonalism in North America (1900–1940)
2575:
2343:(25 May 1877). "On the Measurement and Settlement of Musical Pitch".
2278:
1737:
1475:
1026:
1019:
991:
944:
885:
used 13 equal-tempered intervals per octave in his Whitsun oratorio,
871:
233:
222:
are also sometimes used, occasionally mixed in the same passage with
186:, and French sources give the equivalent German and English terms as
38:
4677:
4675:
4643:. Guitar Master Class. Pacific, Missouri, USA: Mel Bay. p. 20.
4492:
Liner notes to "Blackwood: Microtonal Compositions" [CDR018]
3611:Микрохроматика И. Вышнеградского: История, теория, практика освоения
3199:
Hába, Alois (1921). "Harmonische Grundlagen des Vierteltonsystems".
2379:
2082:
1122:
701:) he used quarter tones, to imitate the enharmonic genus of Greeks.
6662:
6657:
6625:
6610:
5901:
5463:
5426:
5203:, ed. B. Gilmore. Urbana and Chicago: University of Illinois Press.
4599:
4449:
3992:
Ultracromatiche sensazioni: il microtonalismo in Europa (1840–1940)
3653:Сергей Протопопов: композиторское творчество и теоретические работы
3429:
2940:
1450:
1095:
975:
654:
612:
510:
123:
85:
6673:
6039:
5308:. 2010. "About Backyards and Limbos: Microtonality Revisited". In
1818:(b. 1961) (quarter tones, twelfth tones, extended just intonation)
1454:, occasional microtonal instrumental and vocal writing throughout
1191:(Belgium, U.S.A., 1858–1931, used quarter tones in several of the
6488:
6438:
5438:
5355:. 1937. "La musique à quarts de ton et sa réalisation pratique".
5343:
Wood, James. 1986. "Microtonality: Aesthetics and Practicality".
5208:
Kotschy, Johannes. 2008. "Mikrotonalität: Eine Zeiterscheinung?"
4672:
4666:"A Microtonal Analysis of Robert Johnson's "Drunken Hearted Man""
2511:. Guides Musicologiques. Paris: Editions Beauchesne. p. 13.
2486:. Guides Musicologiques. Paris: Editions Beauchesne. p. 13.
2190:
1098:
used quarter tones and other microtonal intervals in their album
933:
Radionics Radio: An Album of Musical Radionic Thought Frequencies
801:
758:
465:
377:
257:
5068:". Vanessa Carr's website (29 February). (Accessed 2 April 2009)
4818:
3741:(2000). "Микро и последствия" [Micro and consequences].
3526:
3097:. Vol. 12. London: Macmillan Publishers. pp. 279–280.
2788:
2786:
2784:
2782:
2780:
2327:
Proceedings of the Musical Association, 38th Session (1911–1912)
1582:(Finland, b. 1948, quarter tones, non equal temperament tunings)
1048:
aspect is ratio-based, not equal temperament. The band's leader
616:
perfect fourth (approximately 498 cents, or the ratio of 4/3 in
182:
In French, the usual term is the somewhat more self-explanatory
6641:
6604:
6582:
6456:
6172:
6099:
5618:
5432:
5417:
Julián Carrillo and the 13th Sound: A Microtonal Musical System
5384:
5065:
4764:"King Gizzard Announce a New Album, 'Flying Microtonal Banana'"
3640:] (PhD diss.). Vladivostok: Far East State Academy of Arts.
2619:. Lanham, MS, and Plymouth: Scarecrow Press, Inc. p. 109.
2544:. 1 (Musical Thought at IRCAM, edited by Tod Machover): 77–82.
2248: – Terms for tuning an instrument and a systems of pitches
2148: – A guitar where the bridge extends beyond its usual stop
1588:(France, b. 1961, introduces acyclic nonoctave scales in 1980)
1526:(U.S.A., 1934–2006, just intonation, 72-tone equal temperament)
287:
248:
5244:
Leedy, Douglas. 1991. "A Venerable Temperament Rediscovered".
3996:
Ultrachromatic sensations: microtonalism in Europe (1840–1940)
3516:] (in Russian). Moscow: Muzyka. pp. 65, 123, 152 etc.
3451:"Микрохроматика" [Mikrochromatika / Microchromatics].
1398:(Italy, 1924–1990, quarter tones, eighth tones and 16th tones)
1283:(Italy, 1885–1947, used quarter tones and eighth tones on the
532:
Examples of this can be found in various places, ranging from
509:(microtonality, which could be understood in Russian as a sub-
27:
Use in music of microtones (intervals smaller than a semitone)
6620:
6473:
6461:
5391:
Jim Aikin's article on alternative tuning in electronic music
5236:
3010:. Darmstadt: Wissenschaftliche Buchgesellschaft. p. 94.
2777:
1456:
1031:
638:) and explored the full compass of 19 pitches in the octave.
393:
30:
For sounds on the time scale shorter than musical notes, see
5444:
5409:
4990:
4604:"LilyPond – Notation Reference v2.21.7 (development-branch)"
4554:""Colundi" is Music Tuned to Frequencies That Heal the Body"
2979:
Musica ex machina: über das Verhältnis von Musik und Technik
2843:. Latina, Italy: Il Levante Libreria Editrice. p. 139.
2592:
Messiaen Perspectives 2: Techniques, Influence and Reception
1213:(Mexico, 1875–1965) many different equal temperaments, look
1068:. Tracks with these instruments appear on their 2017 albums
479:
and the music theorist Rolf Maedel, Herf's colleague at the
324:
In English the word "microtonality" is mentioned in 1946 by
72:
Two examples of an Ives fundamental chord with quarter tones
6478:
5170:. 2007. "Mikrotonalität und spektrale Musik seit 1980". In
5047:
Burns, Edward M. 1999. "Intervals, Scales, and Tuning." In
4993:
Acustica accordatura e temperamento nell'illuminismo Veneto
3799:
Gosudarstvennaâ Konservatoriâ imeni N.A. Rimskogo-Korsakova
3676:Микрохроматика в системе современного музыкального мышления
3634:Микрохроматика в музыкальном искусстве позднего Возрождения
2573:
Boulez, Pierre (1958). "At the Ends of Fruitful Land ...".
2263:
1374:(Austria, 1920–1989, 72-equal temperament, "ekmelic" music)
1311:(U.S.A., 1901–1974, just intonation, including a system of
967:
918:, using alternate tuning scales she invented for the album
397:
4862:
https://twitter.com/Mick_Gordon/status/1627845703505711105
3811:
3657:
Sergey Protopopov: composer's output and theoretical works
2594:. Farnham: Ashgate Publishing, Ltd. pp. 164, 174n40.
1734:(b. 1955) (different equal temperaments, notably the 48ET)
824:
Major microtonal composers of the 1920s and 1930s include
328:
who related it to microtonal inflexions of the so-called "
236:, in the article "Microtone" in the second edition of the
6551:
4982:
Barbieri, Patrizio. 2003. "Temperaments, Historical". In
4723:"Jon Catler: Evolution for Electric Guitar and Orchestra"
4681:
4319:(Second ed.). New York: Da Capo Press. p. vii.
3075:
3073:
2966:. Freiburg im Breisgau and Munich: K. Alber. p. 288.
2884:"Microtonal Analysis of "Blue Notes" and the Blues Scale"
2687:
Karlheinz Stockhausen: ... un vaisseau lancé vers le ciel
2239: – Ascending or descending sequence of musical tones
5075:
La sambuca lincea, overo Dell'istromento musico perfetto
4896:
the nonoctave polyscalar music theory published online:
3795:
Microtonic music in Europe and Russia in the 1900s–1920s
3791:Микротоновая музыка в Европе и России в 1900–1920–е годы
1572:
for solo flute, 1976; quarter tones and eighth tones in
1253:(Poland, 1882–1937, used quarter tones on the violin in
352:
while "Mikroton" seems to prevail in discussions of the
334:
Microtonal Analysis of “Blues Notes” and the Blues Scale
5172:
Orientierungen: Wege im Pluralismus der Gegenwartsmusik
5131:
Orientierungen: Wege im Pluralismus der Gegenwartsmusik
4419:]. Cologne: Verlag M. DuMont Schauberg. p. 37.
4411:
Stockhausen, Karlheinz (1964). Schnebel, Dieter (ed.).
3497:] (in Russian). Moscow: Praktika. pp. 353–354.
3345:]. Moscow: Sov'etskii Kompozitor. pp. 163–176.
3326:]. Moscow: Sov'etskii Kompozitor. pp. 108–156.
2432:(1961). "Micro-intervalle". In Michel, François (ed.).
2304:. Princeton: Princeton University Press. pp. 8–9.
2241:
Pages displaying short descriptions of redirect targets
2227:
Pages displaying short descriptions of redirect targets
5450:
5102:
The Musicology and Organology of the Ancient Near East
3749:]. Moscow: Gnessins Music Academy. pp. 27–38.
3495:
Music of the Twentieth Century: An Academic Dictionary
3277:
3070:
2792:
1593:
37:"Microtone" redirects here. For the slicing tool, see
3998:] (in Italian), Lucca: Libreria musicale italiana
3979:] (in Italian), Lucca: Libreria musicale italiana
3592:
Problems of Musical Structure in the Early Modern Era
3566:(in Russian), St Petersburg: Lan, pp. 172 etc.,
3164:, Kolkata: ITC Sangeet Research Academy, p. 18,
2266: – Melodic mode of improvisation in Indian music
1277:(Romania, Austria, Palestine, USA, Canada, 1897–1973)
5412:". (Article on alternative tuning in Peruvian music)
5117:
Fink, Robert. 1988. "The Oldest Song in the World".
4413:
Texte 2: Aufsätze 1952–1962 zur musikalischen Praxis
4110:
Musical Form and Analysis: Time, Pattern, Proportion
3719:(1976). "Микрохроматика" [Microchromatics].
3054:
Schulter, Margo (2 March 2001). McComb, Todd (ed.).
3031:
Schulter, Margo (10 June 1998). McComb, Todd (ed.).
2274:
Pages displaying wikidata descriptions as a fallback
2212:
Pages displaying wikidata descriptions as a fallback
2176: – Music performance controller and synthesizer
2169:
Pages displaying wikidata descriptions as a fallback
2156:
Pages displaying wikidata descriptions as a fallback
2154: – system for identifying tones in Arabic music
914:
experimented with many microtonal systems including
857:
380:; Thai, Burmese, and African music, and music using
6002:
Twelve Microtonal Etudes for Electronic Music Media
4761:
3588:Проблемы музыкального строя в начале Нового времени
3159:
961:
895:
Twelve Microtonal Etudes for Electronic Music Media
4429:
3541:(in Russian), Moscow: Kompozitor, pp. 86 etc.
2925:McNaught, W. (February 1939). "Gramophone Notes".
2454:Nouveau Larousse encyclopédique: Kondratiev-Zythum
2399:
2397:
947:electronic soundmaking equipment used by Oxford's
5300:". Noyzelab Blogspot.com.au (Monday, 10 November)
5266:". Ph.D. thesis. Bloomington: Indiana University.
5216:
4999:
2654:Dictionnaire des musiques microtonales: 1892–2013
1985:
163:, writing in Spanish or French, coined the terms
7129:
5435:– links to microtonal composers and compositions
4362:(Second ed.). London: Macmillan Publishers.
4347:(Second ed.). London: Macmillan Publishers.
4193:(Second ed.). London: Macmillan Publishers.
4085:Synthesizer Performance and Real-time Techniques
3638:Microchromatics in Music of the Late Renaissance
3120:The Cambridge History of Twentieth-Century Music
3079:
2803:(Second ed.). London: Macmillan Publishers.
2739:(Second ed.). London: Macmillan Publishers.
2660:] (in French). Paris: L'Harmattan. pp.
2509:L'anglais musicologique: l'anglais des musiciens
2219: – Device to test musical instrument tuning
1568:(Great Britain, b. 1943, quarter tones, 31ET in
1520:(France, b. 1934) (quarter tones and 16th tones)
1432:, but soon after abandoning microtonal elements)
1227:(Hungary, 1881–1945, rare uses of quarter tones)
310:from the 10th century onward, and similarly for
5441:– links to microtonal projects around the world
5295:
5255:The New Grove Dictionary of Music and Musicians
4692:"Interview with Jonny and Krzysztof Penderecki"
4360:The New Grove Dictionary of Music and Musicians
4345:The New Grove Dictionary of Music and Musicians
4191:The New Grove Dictionary of Music and Musicians
4112:. Long Grove: Waveland Press, Inc. p. 82.
4107:
3356:Belaiev, Victor (July 1935). "Turkish Music ".
3241:. Leipzig: C. F. Kahnt Nachfolger. p. 184.
3094:The New Grove Dictionary of Music and Musicians
2800:The New Grove Dictionary of Music and Musicians
2736:The New Grove Dictionary of Music and Musicians
2451:Garnier, Yves, ed. (1998). "Micro-intervalle".
2394:
1109:employs microtonal instruments in their music.
928:, which is wholly in new tunings and timbres".
267:The New Grove Dictionary of Music and Musicians
5427:Wilson Archives of papers on microtonal theory
5351:
5023:The Structure of Recognizable Diatonic Tunings
3680:Microchomatics in Contemporary Musical Thought
3339:О музыкальном фольклоре и древней письменности
3320:О музыкальном фольклоре и древней письменности
3300:
2225: – Specification of precise musical pitch
2204: – Musical tuning based on pure intervals
1478:(U.S.A., 1928–2015, 72-tone equal temperament)
1175:
985:
892:In 1979–80 Easley Blackwood composed a set of
6689:
6567:
6055:
5479:
5404:Dr. John Chalmers Divisions of the Tetrachord
5223:Perfect Sound Forever (online music magazine)
4470:
4417:Texts 2: Essays on musical practice 1952–1962
4152:. Oxford: Clarendon Press. pp. 160–172.
2531:
2254: – Musical scale created by Harry Partch
1466:(U.S.A., 1926–2019, extended just intonation)
730:, who in the 1880s produced a translation of
611:, less than half of the contemporary Western
497:, to describe a kind of 'intervallic genus' (
132:, (two variants of) three quarter tones flat;
6130:List of intervals in 5-limit just intonation
5201:Maximum Clarity' and other writings on music
4598:
4538:Murphy, Ben (January 2017). "Making Waves".
4270:. London: Longmans, Green. pp. 514–527.
3938:
3797:] (Non-doctoral diss.). St. Petersburg:
3743:Музыкальное образование в контексте культуры
3252:Riemann, Hugo (1967). "Vierteltonmusik". In
2648:
2272: – software to work with musical scales
443:for intervals smaller than the semitone and
5296:Noyze, Dave, and Richard D. James.. 2014. "
4610:. p. 3.5.1 Supported notation for MIDI
4508:
4410:
4246:
4206:Tuning and Temperament: A Historical Survey
4137:, Hants, UK: Ashgate Publishing, p. 88
3239:Fortschrittliche Harmonie- und Melodielehre
3183:
3033:"Pythagorean Tuning and Medieval Polyphony"
2408:(paperback). Courlay: Fuzeau. p. 119.
687:in September 1764, the celebrated flautist
429:, and in the second edition of the popular
90:tuning of twelve equal intervals per octave
6696:
6682:
6574:
6560:
6062:
6048:
5486:
5472:
5261:
4792:
4514:"Three Asymmetric Divisions of the Octave"
4471:Blackwood, Easley; Kust, Jeffrey (2005) ,
4284:Proceedings of the Royal Society of London
3343:On Musical Folklore and Ancient Literature
3324:On Musical Folklore and Ancient Literature
3142:
2841:Enharmonic instruments and music 1470–1900
2813:
2658:Dictionary of Microtonal Musics: 1892–2013
2299:
1010:have incorporated microtonal guitars like
493:(microchromatics), coined in the 1970s by
5298:Aphex Twin Syrobonkers! Interview: Part 2
5037:
5025:. Princeton: Princeton University Press.
5020:
4488:
4473:Easley Blackwood: Microtonal Compositions
4261:
4132:
3768:] (in Russian). Kyiv: Naukova Dumka.
3673:
3491:Музыка ХХ века. Энциклопедический словарь
3149:. Oxford: Clarendon Press. p. 127n1.
3117:
2901:
2871:. New York: Alfred A. Knopf. p. 234.
2725:Richter, Lukas (2001). "Diesis (ii)". In
2557:
2506:
1163:Learn how and when to remove this message
452:, has been used by theorist Marek Žabka.
5252:
5195:
5104:, second edition. London: Tadema Press.
5096:
4981:
4964:
4955:
4762:Heavenly Recordings (11 November 2016).
4635:
4082:
4058:Xenharmonic Wiki blog at macrospaces.com
3737:
3715:
3631:
3551:
3236:
3053:
3030:
2976:
2961:
2924:
2838:
2614:
622:
5363:
5304:
5230:
5207:
5149:
5125:
5085:
5072:
4720:
4203:
4180:
4108:Spring, Glenn; Hutcheson, Jere (2013).
3747:Music education in the cultural context
3608:
3585:
3507:
3355:
3336:
3317:
3251:
3118:Cook, Nicholas; Pople, Anthony (2004).
2997:
2881:
2758:
2724:
2450:
2440:and Vladimir Fèdorov. Paris: Fasquelle.
14:
7130:
5333:
5324:
5253:Lindley, Mark. 2001b. "Temperaments".
5008:
4537:
4339:
4309:
4228:
4181:Lindley, Mark (2001). "Mean-tone". In
4087:. Madison: A-R Editions. p. 239.
3905:
3696:More references can be located on the
3650:
2684:
2572:
2481:
2403:
1842:(b. 1965) (extended JI up to 23-limit)
1830:(b. 1962) (quarter tones, eight tones)
1556:(U.S.A., b. 1939, non-octaving scales)
1416:(France, 1925–2016) (first example of
6677:
6555:
6043:
5467:
5270:
5243:
5046:
4918:
4913:
4663:
4357:
4280:
3989:
3970:
3759:
3453:Музыкальный энциклопедический словарь
3413:
3384:
2863:
2363:
2339:
1221:(mostly Spanish but some English too)
589:) on E, divided into two tetrachords.
5493:
5342:
5186:
5166:
5154:. New Haven: Yale University Press.
5116:
5063:
4924:
4147:
4031:
3948:Université Paris-Sorbonne (Paris IV)
3788:
3619:Urals Mussorgsky State Conservatoire
3217:
3198:
3188:. Leipzig: Verlag F. E. C. Leuckart.
3058:. Medieval Music and Arts Foundation
3035:. Medieval Music and Arts Foundation
2709:
2324:
1619:Michael Tilson Thomas (MTT) (b.1944)
1550:(b. 1938, just intonation, meantone)
1345:(U.S.A., 1917–2003, just intonation)
1145:adding citations to reliable sources
1116:
657:, maintaining major thirds tuned in
80:is the use in music of microtones —
6703:
6069:
4886:http://www.playingwithstandards.com
4874:http://www.playingwithstandards.com
4372:
4008:
3705:[Search for dissertations].
3488:
3008:Geschichte der Musiktheorie, Vol. 2
2869:Shining Trumpets: A History of Jazz
2617:A Dictionary for the Modern Flutist
2589:
2428:
1594:Modern Western microtonal composers
517:(microtonic, "a barely perceptible
372:. Traditional Indian systems of 22
24:
4906:
2302:Perspectives on American Composers
2281: – Theory of microtonal music
1538:(U.S.A., b. 1935, just intonation)
1532:(U.S.A., b. 1935, just intonation)
1508:(Poland, 1933–2020, quarter tones)
1404:(France, 1924–2004, quarter tones)
1327:(The Netherlands, 1907–1987, 31ET)
1293:(U.S.A., 1887–1974, quarter tones)
1207:(U.S.A., 1874–1954, quarter tones)
1062:King Gizzard and the Lizard Wizard
25:
7159:
5374:
2406:Histoire de l'acoustique musicale
1900:Fabio Costa (composer, conductor)
1420:with quarter tones in his pieces
1233:(Romania, France, 1881–1955) (in
990:A form of microtone known as the
858:Microtonality in electronic music
790:Prélude à l'après-midi d'un faune
765:Fantaisie for piano and orchestra
627:Vicentino's archicembalo in cents
483:, preferred using the Greek word
342:Columbia History of Music, Vol. 5
7111:
7102:
7101:
6205:Ptolemy's intense diatonic scale
5662:
5657:
5273:Hans Zender: Vielstimmig in sich
5210:Österreichische Musikzeitschrift
5191:. Leipzig: Kistner & Siegel.
4890:
4878:
4866:
4850:
4838:
4812:
4786:
4755:
4740:
4714:
4657:
4148:West, Martin Litchfield (1992).
3530:Музыкально-теоретические системы
3514:The Theory of Modern Composition
1544:(U.S.A., b. 1938, quarter tones)
1121:
962:Limitations of some synthesizers
887:Spiritus intelligentiae, sanctus
575:
540:'s chords of stacked fifths, to
536:'s impressionistic harmonies to
150:in order to avoid the misnomer "
62:
53:
5445:Offtonic Microtonal Synthesizer
5415:Solís Winkler, Ernesto. 2004. "
4938:Online edition of the 1529 text
4629:
4592:
4571:
4546:
4531:
4502:
4482:
4464:
4423:
4404:
4395:
4366:
4351:
4333:
4303:
4274:
4255:
4240:
4222:
4197:
4174:
4141:
4126:
4101:
4076:
4046:
4025:
4002:
3983:
3964:
3932:
3899:
3874:
3849:
3824:
3805:
3782:
3753:
3731:
3709:
3690:
3667:
3644:
3625:
3602:
3579:
3545:
3520:
3501:
3482:
3463:
3457:Musical Encyclopedic Dictionary
3444:
3407:
3378:
3349:
3330:
3311:
3294:
3271:
3245:
3230:
3211:
3192:
3184:Möllendorff, Willy von (1917).
3177:
3153:
3136:
3111:
3047:
3024:
2991:
2970:
2955:
2918:
2882:Cutting, Court B (2019-01-17).
2875:
2857:
2832:
2807:
2752:
2743:
2718:
2712:The Harvard Dictionary of Music
2703:
2678:
2642:
2633:
2608:
2583:
2566:
2525:
2459:Nouveau Larousse encyclopédique
1193:Sonatas for Solo Violin, Op. 27
1132:needs additional citations for
768:and the Toccata from the suite
286:, the several divisions of the
6975:Modes of limited transposition
5347:127, no. 1719 (June): 328–330.
3789:Adèr, Lidiâ Olegovna (2013).
3143:Strangways, A. H. Fox (1914).
2500:
2475:
2444:
2422:
2367:American Journal of Psychology
2357:
2346:Journal of the Society of Arts
2333:
2318:
2293:
1986:Western microtonal researchers
1313:43 unequal tones to the octave
1112:
850:Digital synthesizers from the
814:Cloches à travers les feuilles
751:Exposition Universelle of 1889
431:Brockhaus Riemann Musiklexikon
332:". In Court B. Cutting's 2019
302:, and small intervals used in
99:
13:
1:
4698:. BBC Radio 4. Archived from
4229:Koenig, Laura Jeanne (1995).
3510:Теория современной композиции
3508:Tsenova, V. S. , ed. (2007).
2286:
1866:(b. 1967) (Polymicrotonality)
1185:(keyboard designs, 1825–1890)
677:L'Art de la flute traversiere
363:
122:residing outside the Western
6168:Harry Partch's 43-tone scale
5865:Harry Partch's 43-tone scale
5419:". (Accessed 19 August 2008)
5397:Nicola Vicentino (1511–1576)
5368:34, no. 1 (Winter): 140–161.
5338:39, no. 2 (Summer): 159–210.
5262:Mandelbaum, M. Joel. 1961. "
5248:29, no. 2 (Summer): 202–211.
5042:29, no. 2 (Summer): 166–200.
3910:; Vaggione, Horacio (eds.).
3555:Гармония. Теоретический курс
664:In 1760 the French flautist
104:
7:
7025:Quartal and quintal harmony
6714:List of modernist composers
5988:Sonata for Microtonal Piano
5439:Projects – Xenharmonic Wiki
5226:(accessed 6 December 2008).
4856:Microtonal composition for
4793:Pooja Bale (4 April 2021).
4204:Barbour, J. Murray (1951).
3760:Kogut, Gennady. A. (2005).
3717:Kholopov, Yuri Nikolaevich
3682:] (PhD diss.). Moscow:
3659:] (PhD diss.). Moscow:
3594:] (PhD diss.). Moscow:
3560:Harmony: Theoretical Course
3552:Kholopov, Yuri N. (2003),
3535:Musical-Theoretical Systems
3282:; Oehl, Kurt, eds. (1995).
3006:; Zaminer, Frieder (eds.).
2889:Empirical Musicology Review
2839:Barbieri, Patrizio (2008).
2761:Harvard Dictionary of Music
2615:Maclagan, Susan J. (2009).
2507:Whitfield, Charles (1989).
2138:
1782:(b. 1959) (just intonation)
1271:(France, U.S.A., 1883–1965)
1176:Western microtonal pioneers
1105:American instrumental trio
986:Microtonality in rock music
350:Geschichte der Musiktheorie
239:Harvard Dictionary of Music
138:, three quarter tones sharp
10:
7164:
6581:
6135:List of meantone intervals
5995:Suite for Microtonal Piano
4819:K, Noah; K, Rosie (2018).
4721:Couture, François (n.d.).
4489:Blackwood, Easley (n.d.),
4135:Louis Andriessen, De Staat
4133:Adlington, Robert (2004),
3912:Manières de faire des sons
3472:Музыкальный словарь Гроува
2977:Prieberg, Fred K. (1960).
2962:Prieberg, Fred K. (1958).
2814:Von Gunden, Heidi (1986).
2434:Encyclopédie de la musique
1884:, aka Aphex Twin (b. 1971)
563:
36:
29:
7089:
7068:
6938:
6898:
6727:
6720:
6711:
6589:
6502:
6419:
6382:
6335:
6242:
6233:
6148:
6125:List of musical intervals
6120:Consonance and dissonance
6077:
6011:
5955:
5947:Huygens-Fokker Foundation
5935:Boston Microtonal Society
5925:
5882:
5855:
5777:
5736:
5727:
5671:
5655:
5501:
5433:Listen – Xenharmonic Wiki
5366:Perspectives of New Music
5336:Perspectives of New Music
5246:Perspectives of New Music
5239:(accessed 31 March 2009).
5233:Yuichi Onoue's Kaisatsuko
5152:Harry Partch: A Biography
5040:Perspectives of New Music
5021:Blackwood, Easley. 1985.
4433:Perspectives of New Music
3674:Nikoltsev, I. D. (2013).
3632:Polunina, E. N. (2010).
3417:Perspectives of New Music
3280:Eggebrecht, Hans Heinrich
3258:Eggebrecht, Hans Heinrich
2903:10.18061/emr.v13i1-2.6316
2816:The Music of Ben Johnston
2559:2027/spo.bbp2372.1982.033
2550:10.1080/07494468400640081
2542:Contemporary Music Review
2197:Huygens-Fokker Foundation
2180:Fokker periodicity blocks
1680:(b. 1951) (quarter tones)
1321:(Norway, 1901–1977, 53ET)
736:On the Sensations of Tone
312:Persian traditional music
298:", as well as the Indian
5092:9, no. 1 (Spring): 2–51.
4930:Thoscanello de la musica
4884:the quartertone pianos:
4872:the quartertone pianos:
4389:10.1525/mts.2001.23.1.61
3721:Музыкальная энциклопедия
3401:10.1215/00222909-2781769
3237:Capellen, Georg (1908).
3087:(1980). "Microtone". In
2484:L'allemand musicologique
2436:. in collaboration with
2260: – Musical interval
1071:Flying Microtonal Banana
695:Jacques Fromental Halévy
689:Pierre-Gabriel Buffardin
7148:Post-tonal music theory
5897:Otonality and Utonality
5408:Loli, Charles. 2008. "
5212:63, no. 7 (July): 8–15.
5089:Journal of Music Theory
5049:The Psychology of Music
4083:Pressing, Jeff (1992).
3609:Gurenko, N.A. (2010).
3586:Klishin, A. G. (2010).
3388:Journal of Music Theory
2964:Lexikon der Neuen Musik
2685:Rigoni, Michel (1998).
2482:Wallon, Simone (1980).
2193: – Aspect of music
1962:, aka Sevish, (b. 1988)
1768:Michael Bach Bachtischa
1086:, and their 2021 album
994:is an integral part of
949:De La Warr Laboratories
784:La cathédrale engloutie
154:" when speaking of the
7076:Second Viennese School
7069:Schools of composition
5594:Claus-Steffen Mahnkopf
5119:Archaeologia Musicalis
5073:Colonna, Fabio. 1618.
5064:Carr, Vanessa. 2008. "
4984:Piano: An Encyclopedia
4263:Helmholtz, Hermann von
4249:Historical Performance
3651:Rovner, A. A. (2010).
3476:Grove Music Dictionary
3186:Musik mit Vierteltönen
3146:The Music of Hindostan
2639:Donval (2006), p. 183.
2404:Donval, Serge (2006).
2252:Partch's 43-tone scale
1828:Claus-Steffen Mahnkopf
1012:31-tone equal tempered
675:published a treatise,
645:composer and theorist
628:
7060:Twelve-tone technique
6599:Fundamental frequency
6392:Temperament ordinaire
5770:(Bohlen–Pierce scale)
5714:Tui St. George Tucker
5279:, Anouk Jeschke, and
5231:Landman, Yuri. n.d. "
5196:Johnston, Ben. 2006.
5168:Haas, Georg Friedrich
5066:These Are Ghost Punks
4799:The Daily Californian
4684:Penderecki, Krzysztof
4444:: 105, 116, 119–121.
4376:Music Theory Spectrum
4060:. n.d. Archived from
4035:The Musical Quarterly
3916:Ways of making sounds
3814:Музыкальная Академия
3359:The Musical Quarterly
2174:Continuum Fingerboard
2167: – musical scale
2011:Adriaan Daniël Fokker
1442:, just intonation in
1436:Karlheinz Stockhausen
1408:Tui St. George Tucker
1386:(Hungary, 1923–2006,
1014:guitar and a 62-tone
869:built his electronic
867:Karlheinz Stockhausen
841:Adriaan Daniel Fokker
626:
344:. In German the term
296:mean-tone temperament
282:melodic intervals of
6195:List of compositions
6024:Generalized keyboard
5519:Easley Blackwood Jr.
5353:Wyschnegradsky, Ivan
5150:Gilmore, Bob. 1998.
5098:Dumbrill, Richard J.
4945:Toscanello in musica
4943:. Third edition, as
4017:] (in Spanish).
3990:Conti, Luca (2008),
3971:Conti, Luca (2005),
3950:. pp. 169–175.
3940:Jedrzejewski, Franck
3725:Musical Encyclopedia
3372:10.1093/mq/XXI.3.356
3265:: Volume 3, Sachteil
3263:Riemann Musiklexikon
3220:Listy hudební matice
2749:Apel (1974), p. 188.
2650:Jedrzejewski, Franck
2223:MIDI tuning standard
1726:Stephen James Taylor
1702:Georg Friedrich Haas
1506:Krzysztof Penderecki
1287:, noise instruments)
1141:improve this article
1018:guitar in blues and
935:by British composer
878:Gesang der Jünglinge
808:Danseuses de Delphes
728:Alexander John Ellis
699:Choeur des Océanides
636:19 equal temperament
602:, recognizing three
546:Clouds of Forgetting
426:Riemann Musiklexikon
412:A. H. Fox Strangways
386:meantone temperament
134:quarter tone sharp,
7143:Ancient Greek music
6019:Enharmonic keyboard
5970:quarter tone pieces
5964:Beauty in the Beast
5644:Ivan Wyschnegradsky
5187:Hába, Alois. 1927.
5127:Fritsch, Johannes G
4949:Toscanello in music
4774:on 11 December 2016
4746:{{cite web | url =
4664:Monzo, Joe (1998).
4475:(Second ed.),
4440:(1). Translated by
4297:1884RSPS...37..368E
4150:Ancient Greek Music
3762:Микротоновая музыка
3703:"Поиск диссертаций"
3684:Moscow Conservatory
3661:Moscow Conservatory
3617:] (PhD diss.).
3596:Moscow Conservatory
2710:Apel, Will (1974).
2341:Ellis, Alexander J.
2165:Bohlen–Pierce scale
2017:Ivan Wyschnegradsky
1882:Richard David James
1472:(U.S.A., 1927–2009)
1351:(U.S.A., 1917–1994)
1303:Ivan Wyschnegradsky
1245:ancient Greek music
1107:Consider the Source
1080:, their 2020 album
978:'s implementation.
926:Beauty in the Beast
921:Beauty In the Beast
830:Ivan Wyschnegradsky
718:Ivan Wyschnegradsky
585:Greek Dorian mode (
550:Clouds of Unknowing
437:Ivan Wyschnegradsky
308:Arabic music theory
246:'s use of the term
148:Maud MacCarthy Mann
128:quarter tone flat,
6653:Sympathetic string
6429:Chinese musicology
6215:Scale of harmonics
6210:Pythagorean tuning
6158:Euler–Fokker genus
5941:Genesis of a Music
5569:Christiaan Huygens
5456:2020-11-23 at the
5389:Aikin, Jim. 2003.
5327:Ugarit-Forschungen
4316:Genesis of a Music
2131:Mathius Shadow-Sky
2047:Jean-Etienne Marie
1999:Christiaan Huygens
1924:Karola Obermueller
1586:Mathius Shadow-Sky
1361:Franz Richter Herf
1355:Jean-Etienne Marie
1025:English rock band
1006:Musicians such as
632:Guillaume Costeley
629:
481:Salzburg Mozarteum
470:Franz Richter Herf
456:proposed the term
7125:
7124:
6934:
6933:
6671:
6670:
6648:Spectral envelope
6549:
6548:
6415:
6414:
6037:
6036:
6029:Modernism (music)
5878:
5877:
5779:Equal temperament
5549:Brian Ferneyhough
5381:Microtone (music)
5357:La Revue Musicale
5345:The Musical Times
5318:978-3-631-58902-1
5289:978-3-936000-25-2
5281:Jörn Peter Hiekel
5180:978-3-7957-1837-4
5143:978-3-7957-1837-4
5135:Jörn Peter Hiekel
4690:(23 March 2012).
4119:978-1-4786-0722-9
4094:978-0-89579-257-0
3957:978-80-86385-27-3
3925:978-2-296-12959-7
3304:La Revue musicale
3254:Gurlitt, Wilibald
3004:von Loesch, Heinz
2935:(1152): 102–104.
2928:The Musical Times
2850:978-88-95203-14-0
2770:978-0-674-01163-2
2696:978-2-911906-02-2
2671:978-2-343-03540-6
2626:978-0-8108-6711-6
2601:978-1-4094-2696-7
2468:978-2-03-153132-6
2415:978-2-84169-152-4
2311:978-0-393-02155-4
1993:Mordecai Sandberg
1918:Kristoffer Zegers
1822:Daniel James Wolf
1566:Brian Ferneyhough
1502:(U.S.A., b. 1932)
1496:(U.S.A., b. 1931)
1423:Le Visage nuptial
1275:Mordecai Sandberg
1251:Karol Szymanowski
1173:
1172:
1165:
757:heard a Balinese
732:Hermann Helmholtz
685:Mercure de France
581:
542:John Luther Adams
370:equal temperament
354:avant-garde music
228:micro-intervalité
204:micro-intervalité
94:equal temperament
68:
58:
16:(Redirected from
7155:
7115:
7105:
7104:
7081:Darmstadt School
7015:Post-romanticism
6725:
6724:
6698:
6691:
6684:
6675:
6674:
6576:
6569:
6562:
6553:
6552:
6388:Well temperament
6374:Regular diatonic
6240:
6239:
6220:Tonality diamond
6064:
6057:
6050:
6041:
6040:
5917:Tonality diamond
5740:repeating scales
5734:
5733:
5719:Nicola Vicentino
5666:
5661:
5629:Nicola Vicentino
5554:Michael Finnissy
5495:Microtonal music
5488:
5481:
5474:
5465:
5464:
5402:Chalmers, John.
5369:
5360:
5348:
5339:
5330:
5321:
5306:Stahnke, Manfred
5301:
5292:
5277:Werner Grünzweig
5267:
5258:
5249:
5240:
5227:
5213:
5204:
5200:
5192:
5183:
5163:
5146:
5122:
5121:2, no. 2:98–100.
5113:
5093:
5082:
5069:
5060:
5043:
5034:
5017:
5010:Barlow, Clarence
5005:
4996:
4987:
4978:
4961:
4952:
4942:
4921:
4915:
4900:
4894:
4888:
4882:
4876:
4870:
4864:
4854:
4848:
4842:
4836:
4835:
4833:
4831:
4816:
4810:
4809:
4807:
4805:
4790:
4784:
4783:
4781:
4779:
4770:. Archived from
4768:Heavenly Records
4759:
4753:
4744:
4738:
4737:
4735:
4733:
4718:
4712:
4711:
4709:
4707:
4688:Greenwood, Jonny
4679:
4670:
4669:
4661:
4655:
4654:
4633:
4627:
4626:
4617:
4615:
4600:LilyPond project
4596:
4590:
4589:
4587:
4586:
4575:
4569:
4568:
4566:
4565:
4550:
4544:
4543:
4540:Electronic Sound
4535:
4529:
4528:
4526:
4524:
4506:
4500:
4499:
4486:
4480:
4479:
4468:
4462:
4461:
4427:
4421:
4420:
4408:
4402:
4399:
4393:
4392:
4370:
4364:
4363:
4355:
4349:
4348:
4341:Lesure, François
4337:
4331:
4330:
4307:
4301:
4300:
4278:
4272:
4271:
4259:
4253:
4252:
4244:
4238:
4237:
4232:Air à la grecque
4226:
4220:
4219:
4201:
4195:
4194:
4178:
4172:
4163:
4145:
4139:
4138:
4130:
4124:
4123:
4105:
4099:
4098:
4080:
4074:
4073:
4071:
4069:
4064:on July 14, 2016
4050:
4044:
4043:
4029:
4023:
4022:
4006:
4000:
3999:
3987:
3981:
3980:
3968:
3962:
3961:
3936:
3930:
3929:
3903:
3897:
3896:
3894:
3892:
3878:
3872:
3871:
3869:
3867:
3853:
3847:
3846:
3844:
3842:
3828:
3822:
3821:
3809:
3803:
3802:
3786:
3780:
3779:
3766:Microtonal Music
3757:
3751:
3750:
3739:Kholopov, Y. N.
3735:
3729:
3728:
3713:
3707:
3706:
3694:
3688:
3687:
3671:
3665:
3664:
3648:
3642:
3641:
3629:
3623:
3622:
3606:
3600:
3599:
3583:
3577:
3576:
3565:
3549:
3543:
3542:
3540:
3524:
3518:
3517:
3505:
3499:
3498:
3489:Akopyan, Levon.
3486:
3480:
3479:
3467:
3461:
3460:
3448:
3442:
3441:
3411:
3405:
3404:
3382:
3376:
3375:
3353:
3347:
3346:
3334:
3328:
3327:
3315:
3309:
3308:
3307:(290–91): 84–87.
3298:
3292:
3291:
3278:Dahlhaus, Carl;
3275:
3269:
3268:
3249:
3243:
3242:
3234:
3228:
3227:
3215:
3209:
3208:
3196:
3190:
3189:
3181:
3175:
3174:
3157:
3151:
3150:
3140:
3134:
3133:
3115:
3109:
3108:
3077:
3068:
3067:
3065:
3063:
3051:
3045:
3044:
3042:
3040:
3028:
3022:
3021:
2995:
2989:
2988:
2974:
2968:
2967:
2959:
2953:
2952:
2922:
2916:
2915:
2905:
2879:
2873:
2872:
2861:
2855:
2854:
2836:
2830:
2829:
2811:
2805:
2804:
2790:
2775:
2774:
2756:
2750:
2747:
2741:
2740:
2722:
2716:
2715:
2707:
2701:
2700:
2682:
2676:
2675:
2646:
2640:
2637:
2631:
2630:
2612:
2606:
2605:
2587:
2581:
2580:
2570:
2564:
2563:
2561:
2529:
2523:
2522:
2504:
2498:
2497:
2479:
2473:
2472:
2448:
2442:
2441:
2426:
2420:
2419:
2401:
2392:
2391:
2374:(3–4): 192–214.
2361:
2355:
2354:
2337:
2331:
2330:
2322:
2316:
2315:
2297:
2275:
2242:
2228:
2213:
2170:
2157:
2152:Arab tone system
2107:William Sethares
1864:Peter Thoegersen
1780:Michael Harrison
1574:La Chute d'Icare
1512:Easley Blackwood
1373:
1241:enharmonic genus
1199:Ferruccio Busoni
1183:Henry Ward Poole
1168:
1161:
1157:
1154:
1148:
1125:
1117:
1060:Australian band
863:Electronic music
681:Air à la grecque
674:
666:Charles de Lusse
647:Nicola Vicentino
587:enharmonic genus
583:
582:
554:Louis Andriessen
507:микротональность
499:интервальный род
478:
421:Vierteltonsystem
417:Viertelton-Musik
184:micro-intervalle
144:Microtonal music
70:
69:
60:
59:
21:
7163:
7162:
7158:
7157:
7156:
7154:
7153:
7152:
7128:
7127:
7126:
7121:
7098:
7085:
7064:
6990:New Objectivity
6943:
6941:
6930:
6894:
6716:
6707:
6705:Modernist music
6702:
6672:
6667:
6616:Microinflection
6594:Colors of noise
6585:
6580:
6550:
6545:
6542:(Bohlen–Pierce)
6510:833 cents scale
6498:
6421:
6411:
6378:
6331:
6229:
6150:Just intonation
6144:
6073:
6071:Musical tunings
6068:
6038:
6033:
6007:
5951:
5927:
5921:
5884:
5874:
5870:Double diatonic
5857:Just intonation
5851:
5773:
5739:
5729:
5723:
5667:
5653:
5599:Joel Mandelbaum
5529:Julián Carrillo
5509:Richard Barrett
5497:
5492:
5458:Wayback Machine
5377:
5372:
5237:Hypercustom.com
5198:
5079:Scipione Stella
5014:Feedback Papers
4940:
4909:
4907:Further reading
4904:
4903:
4895:
4891:
4883:
4879:
4871:
4867:
4855:
4851:
4843:
4839:
4829:
4827:
4817:
4813:
4803:
4801:
4791:
4787:
4777:
4775:
4760:
4756:
4745:
4741:
4731:
4729:
4719:
4715:
4705:
4703:
4680:
4673:
4662:
4658:
4651:
4634:
4630:
4620:Microtones but
4613:
4611:
4597:
4593:
4584:
4582:
4577:
4576:
4572:
4563:
4561:
4552:
4551:
4547:
4536:
4532:
4522:
4520:
4518:wendycarlos.com
4507:
4503:
4497:Cedille Records
4487:
4483:
4477:Cedille Records
4469:
4465:
4428:
4424:
4409:
4405:
4400:
4396:
4371:
4367:
4356:
4352:
4338:
4334:
4327:
4308:
4304:
4279:
4275:
4260:
4256:
4245:
4241:
4227:
4223:
4216:
4202:
4198:
4179:
4175:
4160:
4146:
4142:
4131:
4127:
4120:
4106:
4102:
4095:
4081:
4077:
4067:
4065:
4052:
4051:
4047:
4030:
4026:
4007:
4003:
3988:
3984:
3969:
3965:
3958:
3937:
3933:
3926:
3908:Soulez, Antonia
3904:
3900:
3890:
3888:
3880:
3879:
3875:
3865:
3863:
3855:
3854:
3850:
3840:
3838:
3830:
3829:
3825:
3810:
3806:
3787:
3783:
3776:
3758:
3754:
3736:
3732:
3714:
3710:
3701:
3695:
3691:
3672:
3668:
3649:
3645:
3630:
3626:
3607:
3603:
3584:
3580:
3574:
3563:
3550:
3546:
3538:
3525:
3521:
3506:
3502:
3487:
3483:
3469:
3468:
3464:
3450:
3449:
3445:
3412:
3408:
3383:
3379:
3354:
3350:
3335:
3331:
3316:
3312:
3299:
3295:
3276:
3272:
3250:
3246:
3235:
3231:
3226:: 35–40, 51–57.
3216:
3212:
3197:
3193:
3182:
3178:
3172:
3158:
3154:
3141:
3137:
3130:
3116:
3112:
3105:
3081:Griffiths, Paul
3078:
3071:
3061:
3059:
3052:
3048:
3038:
3036:
3029:
3025:
3018:
2996:
2992:
2975:
2971:
2960:
2956:
2923:
2919:
2880:
2876:
2862:
2858:
2851:
2837:
2833:
2826:
2812:
2808:
2791:
2778:
2771:
2757:
2753:
2748:
2744:
2723:
2719:
2708:
2704:
2697:
2683:
2679:
2672:
2647:
2643:
2638:
2634:
2627:
2613:
2609:
2602:
2588:
2584:
2571:
2567:
2530:
2526:
2519:
2505:
2501:
2494:
2480:
2476:
2469:
2449:
2445:
2438:François Lesure
2427:
2423:
2416:
2402:
2395:
2380:10.2307/1412315
2362:
2358:
2338:
2334:
2323:
2319:
2312:
2298:
2294:
2289:
2284:
2273:
2240:
2226:
2211:
2202:Just intonation
2168:
2155:
2141:
2136:
2089:Clarence Barlow
2065:Joel Mandelbaum
2005:Julián Carrillo
1988:
1983:
1930:Martin Suckling
1906:Sander Germanus
1792:Richard Barrett
1744:Johnny Reinhard
1672:Manfred Stahnke
1636:Elizabeth Brown
1601:Clarence Barlow
1596:
1591:
1542:John Corigliano
1518:Alain Bancquart
1500:Joel Mandelbaum
1363:
1337:Giacinto Scelsi
1239:to suggest the
1211:Julián Carrillo
1178:
1169:
1158:
1152:
1149:
1138:
1126:
1115:
1040:Secret Chiefs 3
1016:just intonation
988:
964:
954:Finnish artist
945:radionics-based
941:web application
916:just intonation
860:
710:Julián Carrillo
668:
659:just intonation
618:just intonation
592:
591:
590:
584:
576:
573:
572:
566:
472:
445:infra-chromatic
441:ultra-chromatic
405:just intonation
382:just intonation
366:
304:Byzantine chant
292:just intonation
224:micro-intervale
161:Julián Carrillo
141:
140:
139:
133:
127:
114:
113:
107:
102:
84:smaller than a
75:
74:
73:
71:
63:
61:
54:
52:
49:
48:
42:
35:
28:
23:
22:
15:
12:
11:
5:
7161:
7151:
7150:
7145:
7140:
7123:
7122:
7120:
7119:
7109:
7095:Romantic music
7091:
7090:
7087:
7086:
7084:
7083:
7078:
7072:
7070:
7066:
7065:
7063:
7062:
7057:
7052:
7047:
7042:
7037:
7032:
7027:
7022:
7017:
7012:
7007:
7002:
7000:Pandiatonicism
6997:
6992:
6987:
6985:New Complexity
6982:
6977:
6972:
6967:
6962:
6957:
6952:
6946:
6944:
6939:
6936:
6935:
6932:
6931:
6929:
6928:
6927:
6926:
6921:
6916:
6911:
6905:United States
6902:
6900:
6896:
6895:
6893:
6892:
6891:
6890:
6885:
6880:
6872:
6871:
6870:
6862:
6861:
6860:
6852:
6851:
6850:
6842:
6841:
6840:
6835:
6827:
6826:
6825:
6820:
6815:
6810:
6805:
6800:
6792:
6791:
6790:
6782:
6781:
6780:
6772:
6771:
6770:
6762:
6761:
6760:
6755:
6750:
6745:
6740:
6731:
6729:
6722:
6718:
6717:
6712:
6709:
6708:
6701:
6700:
6693:
6686:
6678:
6669:
6668:
6666:
6665:
6660:
6655:
6650:
6645:
6638:
6633:
6628:
6623:
6618:
6613:
6608:
6601:
6596:
6590:
6587:
6586:
6579:
6578:
6571:
6564:
6556:
6547:
6546:
6544:
6543:
6537:
6532:
6527:
6522:
6517:
6512:
6506:
6504:
6500:
6499:
6497:
6496:
6491:
6486:
6476:
6471:
6466:
6465:
6464:
6459:
6454:
6449:
6441:
6436:
6431:
6425:
6423:
6417:
6416:
6413:
6412:
6386:
6384:
6380:
6379:
6377:
6376:
6371:
6366:
6361:
6356:
6341:
6339:
6333:
6332:
6330:
6329:
6324:
6319:
6314:
6309:
6304:
6299:
6294:
6284:
6279:
6274:
6269:
6264:
6259:
6254:
6248:
6246:
6237:
6231:
6230:
6228:
6227:
6222:
6217:
6212:
6207:
6202:
6197:
6192:
6191:
6190:
6185:
6175:
6170:
6165:
6163:Harmonic scale
6160:
6154:
6152:
6146:
6145:
6143:
6142:
6137:
6132:
6127:
6122:
6117:
6112:
6110:Interval ratio
6107:
6102:
6097:
6092:
6087:
6081:
6079:
6075:
6074:
6067:
6066:
6059:
6052:
6044:
6035:
6034:
6032:
6031:
6026:
6021:
6015:
6013:
6009:
6008:
6006:
6005:
5998:
5991:
5984:
5977:
5972:
5967:
5959:
5957:
5953:
5952:
5950:
5949:
5944:
5937:
5931:
5929:
5923:
5922:
5920:
5919:
5914:
5912:Xenharmonicity
5909:
5904:
5899:
5894:
5888:
5886:
5880:
5879:
5876:
5875:
5873:
5872:
5867:
5861:
5859:
5853:
5852:
5850:
5849:
5844:
5839:
5834:
5829:
5824:
5819:
5814:
5809:
5804:
5799:
5794:
5789:
5783:
5781:
5775:
5774:
5772:
5771:
5765:
5760:
5755:
5750:
5744:
5742:
5731:
5725:
5724:
5722:
5721:
5716:
5711:
5706:
5701:
5696:
5694:Adriaan Fokker
5691:
5686:
5681:
5675:
5673:
5669:
5668:
5656:
5654:
5652:
5651:
5649:La Monte Young
5646:
5641:
5636:
5631:
5626:
5621:
5616:
5614:John Schneider
5611:
5606:
5601:
5596:
5591:
5586:
5581:
5576:
5571:
5566:
5561:
5559:Bjørn Fongaard
5556:
5551:
5546:
5541:
5539:Mildred Couper
5536:
5531:
5526:
5521:
5516:
5511:
5505:
5503:
5499:
5498:
5491:
5490:
5483:
5476:
5468:
5462:
5461:
5448:
5442:
5436:
5430:
5420:
5413:
5410:Microtonalismo
5406:
5400:
5393:
5387:
5376:
5375:External links
5373:
5371:
5370:
5361:
5359:no. 171:26–33.
5349:
5340:
5331:
5322:
5302:
5293:
5268:
5259:
5250:
5241:
5228:
5214:
5205:
5193:
5184:
5164:
5147:
5123:
5114:
5094:
5083:
5070:
5061:
5044:
5035:
5018:
5006:
4997:
4988:
4979:
4962:
4953:
4922:
4916:
4910:
4908:
4905:
4902:
4901:
4889:
4877:
4865:
4849:
4837:
4811:
4785:
4754:
4739:
4713:
4682:Wilson, John;
4671:
4656:
4649:
4628:
4591:
4570:
4558:Bandcamp Daily
4545:
4530:
4501:
4481:
4463:
4450:10.2307/833578
4422:
4403:
4394:
4365:
4350:
4332:
4325:
4302:
4273:
4254:
4239:
4221:
4214:
4196:
4183:Sadie, Stanley
4173:
4158:
4140:
4125:
4118:
4100:
4093:
4075:
4045:
4024:
4001:
3982:
3963:
3956:
3931:
3924:
3898:
3873:
3848:
3823:
3804:
3781:
3774:
3752:
3730:
3708:
3689:
3666:
3643:
3624:
3601:
3578:
3572:
3544:
3519:
3500:
3481:
3462:
3443:
3430:10.2307/833077
3424:(1): 212–235.
3406:
3395:(2): 179–233.
3377:
3366:(3): 356–367.
3348:
3329:
3310:
3293:
3270:
3244:
3229:
3210:
3191:
3176:
3170:
3152:
3135:
3128:
3110:
3103:
3089:Sadie, Stanley
3069:
3046:
3023:
3016:
3000:Ertelt, Thomas
2990:
2969:
2954:
2941:10.2307/923814
2917:
2874:
2856:
2849:
2831:
2824:
2806:
2776:
2769:
2751:
2742:
2727:Sadie, Stanley
2717:
2702:
2695:
2677:
2670:
2641:
2632:
2625:
2607:
2600:
2582:
2565:
2524:
2517:
2499:
2492:
2474:
2467:
2443:
2421:
2414:
2393:
2356:
2332:
2317:
2310:
2291:
2290:
2288:
2285:
2283:
2282:
2276:
2267:
2261:
2255:
2249:
2246:Musical tuning
2243:
2234:
2232:Music of India
2229:
2220:
2214:
2205:
2199:
2194:
2188:
2182:
2177:
2171:
2162:
2149:
2142:
2140:
2137:
2135:
2134:
2128:
2122:
2116:
2110:
2104:
2098:
2095:Valeri Brainin
2092:
2086:
2080:
2077:Seppe Gebruers
2074:
2068:
2062:
2056:
2050:
2044:
2041:Alain Daniélou
2038:
2032:
2026:
2020:
2014:
2008:
2002:
1996:
1989:
1987:
1984:
1982:
1981:
1975:
1969:
1966:Seppe Gebruers
1963:
1960:Sean Archibald
1957:
1951:
1948:Michael Waller
1945:
1939:
1933:
1927:
1921:
1915:
1909:
1903:
1897:
1891:
1888:Paweł Mykietyn
1885:
1879:
1873:
1867:
1861:
1855:
1849:
1843:
1837:
1834:Harold Fortuin
1831:
1825:
1819:
1813:
1810:François Paris
1807:
1804:William Susman
1801:
1795:
1789:
1783:
1777:
1771:
1765:
1759:
1753:
1747:
1741:
1735:
1732:Pascal Dusapin
1729:
1723:
1720:Paul Dirmeikis
1717:
1714:Pascale Criton
1711:
1705:
1699:
1693:
1687:
1681:
1675:
1669:
1663:
1660:Lasse Thoresen
1657:
1651:
1645:
1639:
1633:
1627:
1624:Tristan Murail
1621:
1616:
1610:
1604:
1597:
1595:
1592:
1590:
1589:
1583:
1577:
1563:
1557:
1551:
1545:
1539:
1536:La Monte Young
1533:
1527:
1521:
1515:
1509:
1503:
1497:
1491:
1485:
1479:
1473:
1467:
1461:
1433:
1411:
1405:
1399:
1393:
1381:
1378:Iannis Xenakis
1375:
1358:
1352:
1346:
1340:
1334:
1328:
1322:
1316:
1306:
1300:
1294:
1291:Mildred Couper
1288:
1278:
1272:
1266:
1263:Percy Grainger
1260:
1248:
1228:
1222:
1208:
1202:
1196:
1186:
1179:
1177:
1174:
1171:
1170:
1129:
1127:
1120:
1114:
1111:
1094:American band
1038:American band
1001:Robert Johnson
987:
984:
963:
960:
859:
856:
778:L'isle joyeuse
755:Claude Debussy
722:Mildred Couper
574:
569:
568:
567:
565:
562:
534:Claude Debussy
523:microtonalismo
490:микрохроматика
439:used the term
365:
362:
358:medieval music
346:Mikrotonalität
284:ancient Greece
272:Paul Griffiths
196:micro interval
192:Kleinintervall
188:Mikrointervall
177:micro-tonalité
173:microtonalismo
115:
110:
109:
108:
106:
103:
101:
98:
50:
45:
44:
43:
26:
9:
6:
4:
3:
2:
7160:
7149:
7146:
7144:
7141:
7139:
7138:Microtonality
7136:
7135:
7133:
7118:
7114:
7110:
7108:
7100:
7099:
7097:
7096:
7088:
7082:
7079:
7077:
7074:
7073:
7071:
7067:
7061:
7058:
7056:
7053:
7051:
7048:
7046:
7043:
7041:
7038:
7036:
7033:
7031:
7028:
7026:
7023:
7021:
7018:
7016:
7013:
7011:
7008:
7006:
7003:
7001:
6998:
6996:
6993:
6991:
6988:
6986:
6983:
6981:
6978:
6976:
6973:
6971:
6968:
6966:
6963:
6961:
6960:Expressionism
6958:
6956:
6953:
6951:
6948:
6947:
6945:
6937:
6925:
6922:
6920:
6917:
6915:
6912:
6910:
6907:
6906:
6904:
6903:
6901:
6897:
6889:
6886:
6884:
6881:
6879:
6876:
6875:
6873:
6869:
6866:
6865:
6863:
6859:
6856:
6855:
6853:
6849:
6846:
6845:
6843:
6839:
6836:
6834:
6831:
6830:
6828:
6824:
6821:
6819:
6816:
6814:
6811:
6809:
6806:
6804:
6801:
6799:
6796:
6795:
6793:
6789:
6786:
6785:
6783:
6779:
6776:
6775:
6773:
6769:
6766:
6765:
6763:
6759:
6756:
6754:
6751:
6749:
6746:
6744:
6741:
6739:
6736:
6735:
6733:
6732:
6730:
6726:
6723:
6719:
6715:
6710:
6706:
6699:
6694:
6692:
6687:
6685:
6680:
6679:
6676:
6664:
6661:
6659:
6656:
6654:
6651:
6649:
6646:
6644:
6643:
6639:
6637:
6634:
6632:
6629:
6627:
6624:
6622:
6619:
6617:
6614:
6612:
6609:
6607:
6606:
6602:
6600:
6597:
6595:
6592:
6591:
6588:
6584:
6577:
6572:
6570:
6565:
6563:
6558:
6557:
6554:
6541:
6538:
6536:
6533:
6531:
6528:
6526:
6523:
6521:
6518:
6516:
6513:
6511:
6508:
6507:
6505:
6501:
6495:
6492:
6490:
6487:
6484:
6483:Carnatic raga
6480:
6477:
6475:
6472:
6470:
6467:
6463:
6460:
6458:
6455:
6453:
6452:Turkish makam
6450:
6448:
6445:
6444:
6442:
6440:
6437:
6435:
6432:
6430:
6427:
6426:
6424:
6418:
6409:
6405:
6401:
6397:
6393:
6389:
6385:
6381:
6375:
6372:
6370:
6367:
6365:
6362:
6360:
6357:
6354:
6350:
6349:quarter-comma
6346:
6343:
6342:
6340:
6338:
6334:
6328:
6325:
6323:
6320:
6318:
6315:
6313:
6310:
6308:
6305:
6303:
6300:
6298:
6295:
6292:
6288:
6285:
6283:
6280:
6278:
6275:
6273:
6270:
6268:
6265:
6263:
6260:
6258:
6255:
6253:
6250:
6249:
6247:
6245:
6241:
6238:
6236:
6232:
6226:
6225:Tonality flux
6223:
6221:
6218:
6216:
6213:
6211:
6208:
6206:
6203:
6201:
6198:
6196:
6193:
6189:
6186:
6184:
6181:
6180:
6179:
6176:
6174:
6171:
6169:
6166:
6164:
6161:
6159:
6156:
6155:
6153:
6151:
6147:
6141:
6138:
6136:
6133:
6131:
6128:
6126:
6123:
6121:
6118:
6116:
6113:
6111:
6108:
6106:
6103:
6101:
6098:
6096:
6093:
6091:
6088:
6086:
6083:
6082:
6080:
6076:
6072:
6065:
6060:
6058:
6053:
6051:
6046:
6045:
6042:
6030:
6027:
6025:
6022:
6020:
6017:
6016:
6014:
6010:
6004:
6003:
5999:
5997:
5996:
5992:
5990:
5989:
5985:
5983:
5982:
5978:
5976:
5973:
5971:
5968:
5966:
5965:
5961:
5960:
5958:
5954:
5948:
5945:
5943:
5942:
5938:
5936:
5933:
5932:
5930:
5924:
5918:
5915:
5913:
5910:
5908:
5905:
5903:
5900:
5898:
5895:
5893:
5890:
5889:
5887:
5881:
5871:
5868:
5866:
5863:
5862:
5860:
5858:
5854:
5848:
5845:
5843:
5840:
5838:
5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5803:
5800:
5798:
5795:
5793:
5790:
5788:
5785:
5784:
5782:
5780:
5776:
5769:
5766:
5764:
5761:
5759:
5756:
5754:
5751:
5749:
5746:
5745:
5743:
5741:
5735:
5732:
5726:
5720:
5717:
5715:
5712:
5710:
5707:
5705:
5702:
5700:
5697:
5695:
5692:
5690:
5687:
5685:
5682:
5680:
5677:
5676:
5674:
5670:
5665:
5660:
5650:
5647:
5645:
5642:
5640:
5639:Elaine Walker
5637:
5635:
5634:Claude Vivier
5632:
5630:
5627:
5625:
5622:
5620:
5617:
5615:
5612:
5610:
5609:Roger Redgate
5607:
5605:
5602:
5600:
5597:
5595:
5592:
5590:
5589:Stu Mackenzie
5587:
5585:
5584:György Ligeti
5582:
5580:
5577:
5575:
5572:
5570:
5567:
5565:
5562:
5560:
5557:
5555:
5552:
5550:
5547:
5545:
5542:
5540:
5537:
5535:
5532:
5530:
5527:
5525:
5522:
5520:
5517:
5515:
5512:
5510:
5507:
5506:
5504:
5500:
5496:
5489:
5484:
5482:
5477:
5475:
5470:
5469:
5466:
5459:
5455:
5452:
5449:
5446:
5443:
5440:
5437:
5434:
5431:
5428:
5424:
5421:
5418:
5414:
5411:
5407:
5405:
5401:
5398:
5394:
5392:
5388:
5386:
5382:
5379:
5378:
5367:
5362:
5358:
5354:
5350:
5346:
5341:
5337:
5332:
5328:
5323:
5319:
5315:
5311:
5307:
5303:
5299:
5294:
5290:
5286:
5282:
5278:
5274:
5269:
5265:
5260:
5256:
5251:
5247:
5242:
5238:
5234:
5229:
5225:
5224:
5219:
5218:Landman, Yuri
5215:
5211:
5206:
5202:
5194:
5190:
5185:
5181:
5177:
5173:
5169:
5165:
5161:
5160:0-300-06521-3
5157:
5153:
5148:
5144:
5140:
5136:
5132:
5128:
5124:
5120:
5115:
5111:
5110:0-9533633-0-9
5107:
5103:
5099:
5095:
5091:
5090:
5084:
5080:
5076:
5071:
5067:
5062:
5058:
5057:0-12-213564-4
5054:
5050:
5045:
5041:
5036:
5032:
5031:0-691-09129-3
5028:
5024:
5019:
5015:
5011:
5007:
5003:
4998:
4994:
4989:
4985:
4980:
4976:
4975:3-03910-088-2
4972:
4968:
4963:
4959:
4954:
4950:
4946:
4939:
4935:
4931:
4927:
4923:
4917:
4912:
4911:
4899:
4893:
4887:
4881:
4875:
4869:
4863:
4859:
4853:
4847:
4841:
4826:
4825:New Music Box
4822:
4815:
4800:
4796:
4789:
4773:
4769:
4765:
4758:
4752:
4749:
4743:
4728:
4724:
4717:
4701:
4697:
4693:
4689:
4685:
4678:
4676:
4667:
4660:
4652:
4650:0-7866-4285-8
4646:
4642:
4638:
4637:Ferguson, Jim
4632:
4625:
4623:
4609:
4605:
4601:
4595:
4580:
4574:
4559:
4555:
4549:
4541:
4534:
4519:
4515:
4512:(1989–1996).
4511:
4510:Carlos, Wendy
4505:
4498:
4494:
4493:
4485:
4478:
4474:
4467:
4459:
4455:
4451:
4447:
4443:
4439:
4435:
4434:
4426:
4418:
4414:
4407:
4398:
4390:
4386:
4382:
4378:
4377:
4369:
4361:
4354:
4346:
4342:
4336:
4328:
4326:0-306-80106-X
4322:
4318:
4317:
4312:
4311:Partch, Harry
4306:
4298:
4294:
4290:
4286:
4285:
4277:
4269:
4264:
4258:
4250:
4243:
4235:
4231:
4225:
4217:
4215:0-486-43406-0
4211:
4207:
4200:
4192:
4188:
4187:Tyrrell, John
4184:
4177:
4170:
4169:0-19-814975-1
4166:
4161:
4159:0-19-814897-6
4155:
4151:
4144:
4136:
4129:
4121:
4115:
4111:
4104:
4096:
4090:
4086:
4079:
4063:
4059:
4055:
4049:
4042:(2): 211–229.
4041:
4037:
4036:
4028:
4021:(7–8): 39–53.
4020:
4016:
4012:
4005:
3997:
3993:
3986:
3978:
3974:
3967:
3959:
3953:
3949:
3945:
3941:
3935:
3927:
3921:
3917:
3913:
3909:
3902:
3887:
3883:
3877:
3862:
3858:
3852:
3837:
3833:
3827:
3819:
3815:
3808:
3800:
3796:
3792:
3785:
3777:
3775:966-00-0604-7
3771:
3767:
3763:
3756:
3748:
3744:
3740:
3734:
3726:
3722:
3718:
3712:
3704:
3699:
3693:
3685:
3681:
3677:
3670:
3662:
3658:
3654:
3647:
3639:
3635:
3628:
3620:
3616:
3612:
3605:
3597:
3593:
3589:
3582:
3575:
3573:5-8114-0516-2
3569:
3561:
3557:
3556:
3548:
3536:
3532:
3531:
3523:
3515:
3511:
3504:
3496:
3492:
3485:
3477:
3473:
3466:
3458:
3454:
3447:
3439:
3435:
3431:
3427:
3423:
3419:
3418:
3410:
3402:
3398:
3394:
3390:
3389:
3381:
3373:
3369:
3365:
3361:
3360:
3352:
3344:
3340:
3333:
3325:
3321:
3314:
3306:
3305:
3297:
3289:
3285:
3281:
3274:
3266:
3264:
3259:
3255:
3248:
3240:
3233:
3225:
3221:
3214:
3206:
3202:
3195:
3187:
3180:
3173:
3171:81-903818-0-6
3167:
3163:
3156:
3148:
3147:
3139:
3131:
3129:0-521-66256-7
3125:
3121:
3114:
3106:
3104:1-56159-174-2
3100:
3096:
3095:
3090:
3086:
3085:Lindley, Mark
3082:
3076:
3074:
3057:
3050:
3034:
3027:
3019:
3017:3-534-01202-X
3013:
3009:
3005:
3001:
2994:
2986:
2985:
2980:
2973:
2965:
2958:
2950:
2946:
2942:
2938:
2934:
2930:
2929:
2921:
2913:
2909:
2904:
2899:
2895:
2891:
2890:
2885:
2878:
2870:
2866:
2860:
2852:
2846:
2842:
2835:
2827:
2825:0-8108-1907-4
2821:
2817:
2810:
2802:
2801:
2796:
2795:Tyrrell, John
2789:
2787:
2785:
2783:
2781:
2772:
2766:
2762:
2755:
2746:
2738:
2737:
2732:
2728:
2721:
2713:
2706:
2698:
2692:
2688:
2681:
2673:
2667:
2663:
2659:
2655:
2651:
2645:
2636:
2628:
2622:
2618:
2611:
2603:
2597:
2593:
2586:
2578:
2577:
2569:
2560:
2555:
2551:
2547:
2543:
2539:
2535:
2528:
2520:
2518:2-7010-1181-7
2514:
2510:
2503:
2495:
2493:2-7010-1011-X
2489:
2485:
2478:
2470:
2464:
2460:
2456:
2455:
2447:
2439:
2435:
2431:
2425:
2417:
2411:
2407:
2400:
2398:
2389:
2385:
2381:
2377:
2373:
2369:
2368:
2360:
2352:
2348:
2347:
2342:
2336:
2328:
2321:
2313:
2307:
2303:
2296:
2292:
2280:
2277:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2250:
2247:
2244:
2238:
2237:Musical scale
2235:
2233:
2230:
2224:
2221:
2218:
2215:
2209:
2208:Limit (music)
2206:
2203:
2200:
2198:
2195:
2192:
2189:
2186:
2185:Genus (music)
2183:
2181:
2178:
2175:
2172:
2166:
2163:
2161:
2153:
2150:
2147:
2144:
2143:
2132:
2129:
2126:
2123:
2120:
2117:
2114:
2111:
2108:
2105:
2102:
2101:Jacques Dudon
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2072:
2069:
2066:
2063:
2060:
2059:Carlton Gamer
2057:
2054:
2051:
2048:
2045:
2042:
2039:
2036:
2033:
2030:
2027:
2024:
2023:Joseph Yasser
2021:
2018:
2015:
2012:
2009:
2006:
2003:
2000:
1997:
1994:
1991:
1990:
1979:
1978:Jacob Collier
1976:
1973:
1970:
1967:
1964:
1961:
1958:
1955:
1952:
1949:
1946:
1943:
1940:
1937:
1934:
1931:
1928:
1925:
1922:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1895:
1894:Yitzhak Yedid
1892:
1889:
1886:
1883:
1880:
1877:
1876:Elaine Walker
1874:
1871:
1870:Trey Spruance
1868:
1865:
1862:
1859:
1856:
1853:
1852:Jeffrey Ching
1850:
1847:
1846:Georges Lentz
1844:
1841:
1838:
1835:
1832:
1829:
1826:
1823:
1820:
1817:
1814:
1811:
1808:
1805:
1802:
1799:
1796:
1793:
1790:
1787:
1786:Martin Smolka
1784:
1781:
1778:
1775:
1772:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1748:
1745:
1742:
1739:
1736:
1733:
1730:
1727:
1724:
1721:
1718:
1715:
1712:
1709:
1706:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1682:
1679:
1676:
1673:
1670:
1667:
1664:
1661:
1658:
1655:
1654:Greg Schiemer
1652:
1649:
1648:Dean Drummond
1646:
1643:
1642:Claude Vivier
1640:
1637:
1634:
1631:
1628:
1625:
1622:
1620:
1617:
1614:
1611:
1608:
1607:Gérard Grisey
1605:
1602:
1599:
1598:
1587:
1584:
1581:
1580:Jukka Tiensuu
1578:
1575:
1571:
1570:Unity Capsule
1567:
1564:
1561:
1558:
1555:
1552:
1549:
1548:Douglas Leedy
1546:
1543:
1540:
1537:
1534:
1531:
1528:
1525:
1522:
1519:
1516:
1513:
1510:
1507:
1504:
1501:
1498:
1495:
1492:
1489:
1488:Carlton Gamer
1486:
1483:
1480:
1477:
1474:
1471:
1468:
1465:
1462:
1459:
1458:
1453:
1452:
1447:
1446:
1441:
1437:
1434:
1431:
1430:
1425:
1424:
1419:
1415:
1414:Pierre Boulez
1412:
1409:
1406:
1403:
1402:Claude Ballif
1400:
1397:
1394:
1391:
1390:
1389:Ramifications
1385:
1384:György Ligeti
1382:
1379:
1376:
1371:
1367:
1362:
1359:
1356:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1332:
1331:Maurice Ohana
1329:
1326:
1323:
1320:
1319:Eivind Groven
1317:
1314:
1310:
1307:
1304:
1301:
1298:
1295:
1292:
1289:
1286:
1282:
1281:Luigi Russolo
1279:
1276:
1273:
1270:
1269:Edgard Varèse
1267:
1264:
1261:
1259:Op. 30, 1915)
1258:
1257:
1252:
1249:
1246:
1242:
1238:
1237:
1232:
1231:George Enescu
1229:
1226:
1223:
1220:
1216:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1190:
1187:
1184:
1181:
1180:
1167:
1164:
1156:
1146:
1142:
1136:
1135:
1130:This section
1128:
1124:
1119:
1118:
1110:
1108:
1103:
1101:
1097:
1092:
1091:
1090:
1085:
1084:
1079:
1078:
1073:
1072:
1067:
1066:24-TET tuning
1063:
1058:
1055:
1051:
1050:Trey Spruance
1047:
1046:
1041:
1036:
1034:
1033:
1028:
1023:
1021:
1017:
1013:
1009:
1004:
1002:
997:
993:
983:
979:
977:
974:, such as in
973:
972:pitch bending
969:
959:
957:
956:Aleksi Perälä
952:
950:
946:
942:
938:
937:Daniel Wilson
934:
929:
927:
923:
922:
917:
913:
908:
906:
902:
898:
896:
890:
888:
884:
880:
879:
874:
873:
868:
864:
855:
853:
848:
846:
845:Eivind Groven
842:
837:
835:
831:
827:
822:
820:
819:Emil Berliner
816:
815:
810:
809:
804:
803:
798:
797:
792:
791:
786:
785:
780:
779:
773:
772:
771:Pour le piano
767:
766:
760:
756:
752:
747:
745:
741:
740:Royal Society
737:
733:
729:
725:
723:
719:
715:
711:
707:
702:
700:
696:
692:
690:
686:
682:
678:
672:
667:
662:
661:in all keys.
660:
656:
652:
648:
644:
639:
637:
633:
625:
621:
619:
614:
610:
605:
601:
597:
596:Delphic Hymns
588:
561:
559:
555:
551:
547:
543:
539:
538:Aaron Copland
535:
530:
526:
524:
520:
516:
512:
508:
504:
500:
496:
495:Yuri Kholopov
492:
491:
486:
482:
476:
471:
467:
463:
459:
455:
451:
446:
442:
438:
434:
432:
428:
427:
422:
418:
413:
408:
406:
401:
399:
395:
391:
387:
383:
379:
378:gamelan music
376:; Indonesian
375:
371:
361:
359:
355:
351:
347:
343:
339:
335:
331:
327:
322:
319:
317:
316:Turkish music
313:
309:
305:
301:
297:
293:
289:
285:
281:
277:
273:
269:
268:
263:
259:
255:
251:
250:
245:
241:
240:
235:
231:
229:
225:
221:
220:microtonalité
217:
213:
209:
205:
201:
197:
193:
189:
185:
180:
178:
174:
170:
166:
162:
157:
153:
149:
145:
137:
131:
125:
121:
118:
97:
95:
91:
87:
83:
79:
78:Microtonality
40:
33:
19:
7093:
7055:Tone cluster
7010:Polytonality
6955:Experimental
6640:
6636:Rustle noise
6603:
6540:Lambda scale
6447:Arabic maqam
6404:Werckmeister
6235:Temperaments
6012:Other topics
6000:
5993:
5986:
5979:
5962:
5956:Compositions
5939:
5928:publications
5883:Concepts and
5768:Lambda scale
5709:Harry Partch
5704:Yuri Landman
5699:Lou Harrison
5684:Wendy Carlos
5679:Glenn Branca
5579:Ben Johnston
5574:Charles Ives
5534:Franklin Cox
5524:Heinz Bohlen
5365:
5356:
5344:
5335:
5329:14: 241–263.
5326:
5309:
5275:, edited by
5272:
5254:
5245:
5221:
5209:
5197:
5188:
5171:
5151:
5133:, edited by
5130:
5118:
5101:
5087:
5074:
5048:
5039:
5022:
5013:
5001:
4992:
4983:
4966:
4957:
4948:
4944:
4941:(in Italian)
4933:
4929:
4926:Aron, Pietro
4892:
4880:
4868:
4858:Atomic Heart
4852:
4840:
4828:. Retrieved
4824:
4814:
4802:. Retrieved
4798:
4788:
4776:. Retrieved
4772:the original
4767:
4757:
4742:
4730:. Retrieved
4726:
4716:
4704:. Retrieved
4700:the original
4695:
4659:
4640:
4631:
4621:
4619:
4612:. Retrieved
4607:
4594:
4583:. Retrieved
4581:. 2021-11-01
4573:
4562:. Retrieved
4560:. 2019-01-10
4557:
4548:
4542:(26): 70–75.
4539:
4533:
4521:. Retrieved
4517:
4504:
4491:
4484:
4472:
4466:
4437:
4431:
4425:
4416:
4412:
4406:
4397:
4383:(1): 61–73.
4380:
4374:
4368:
4359:
4353:
4344:
4335:
4314:
4305:
4288:
4282:
4276:
4266:
4257:
4248:
4242:
4233:
4230:
4224:
4205:
4199:
4190:
4176:
4149:
4143:
4134:
4128:
4109:
4103:
4084:
4078:
4066:. Retrieved
4062:the original
4057:
4054:"Macrotonal"
4048:
4039:
4033:
4027:
4018:
4014:
4010:
4004:
3995:
3991:
3985:
3976:
3972:
3966:
3943:
3934:
3915:
3911:
3901:
3889:. Retrieved
3885:
3876:
3864:. Retrieved
3860:
3851:
3839:. Retrieved
3835:
3826:
3817:
3813:
3807:
3794:
3790:
3784:
3765:
3761:
3755:
3746:
3742:
3733:
3724:
3720:
3711:
3700:website, at
3697:
3692:
3679:
3675:
3669:
3656:
3652:
3646:
3637:
3633:
3627:
3614:
3610:
3604:
3591:
3587:
3581:
3559:
3554:
3547:
3534:
3529:
3522:
3513:
3509:
3503:
3494:
3490:
3484:
3475:
3471:
3465:
3456:
3452:
3446:
3421:
3415:
3409:
3392:
3386:
3380:
3363:
3357:
3351:
3342:
3338:
3332:
3323:
3319:
3313:
3302:
3296:
3287:
3283:
3273:
3261:
3247:
3238:
3232:
3223:
3219:
3213:
3204:
3200:
3194:
3185:
3179:
3161:
3155:
3145:
3138:
3119:
3113:
3092:
3060:. Retrieved
3049:
3037:. Retrieved
3026:
3007:
2993:
2982:
2978:
2972:
2963:
2957:
2932:
2926:
2920:
2893:
2887:
2877:
2868:
2859:
2840:
2834:
2815:
2809:
2798:
2760:
2754:
2745:
2734:
2731:Tyrrel, John
2720:
2711:
2705:
2686:
2680:
2657:
2653:
2644:
2635:
2616:
2610:
2591:
2585:
2574:
2568:
2541:
2537:
2533:
2527:
2508:
2502:
2483:
2477:
2458:
2453:
2446:
2433:
2430:Amy, Gilbert
2424:
2405:
2371:
2365:
2359:
2353:(1279): 665.
2350:
2344:
2335:
2326:
2320:
2301:
2295:
2258:Quarter tone
2071:James Tenney
2035:Harry Partch
1942:Taylor Brook
1936:Saman Samadi
1912:Yuri Landman
1816:Franklin Cox
1750:Dave Soldier
1684:Rhys Chatham
1630:Glenn Branca
1573:
1569:
1560:Bruce Mather
1554:Wendy Carlos
1524:James Tenney
1494:Alvin Lucier
1464:Ben Johnston
1455:
1449:
1443:
1439:
1429:Polyphonie X
1427:
1421:
1418:serial music
1387:
1343:Lou Harrison
1325:Henk Badings
1309:Harry Partch
1285:Intonarumori
1284:
1254:
1234:
1205:Charles Ives
1189:Eugène Ysaÿe
1159:
1150:
1139:Please help
1134:verification
1131:
1104:
1099:
1093:
1087:
1081:
1077:Gumboot Soup
1075:
1069:
1059:
1043:
1037:
1030:
1024:
1005:
989:
980:
965:
953:
943:replicating
932:
930:
925:
919:
912:Wendy Carlos
909:
893:
891:
886:
883:Ernst Krenek
876:
870:
861:
852:Yamaha TX81Z
849:
838:
834:Harry Partch
823:
812:
806:
800:
794:
788:
782:
776:
769:
763:
748:
744:Harry Partch
735:
726:
706:Charles Ives
703:
698:
693:
684:
680:
676:
663:
651:archicembalo
641:The Italian
640:
630:
593:
557:
549:
545:
531:
527:
522:
514:
506:
489:
484:
457:
450:subchromatic
449:
444:
440:
435:
430:
424:
420:
416:
409:
402:
367:
349:
345:
341:
333:
330:blues scales
323:
320:
276:Mark Lindley
265:
247:
237:
232:
227:
223:
219:
215:
211:
207:
203:
199:
195:
191:
187:
183:
181:
176:
172:
168:
164:
152:quarter tone
143:
142:
117:Quarter tone
77:
76:
7005:Polyrhythms
6980:Neotonality
6868:Szymanowski
6535:Delta scale
6530:Gamma scale
6520:Alpha scale
6422:non-Western
6420:Traditional
6115:Pitch class
6095:Millioctave
6078:Measurement
5975:just pieces
5763:Delta scale
5758:Gamma scale
5748:Alpha scale
5738:Non-octave-
5728:Tunings and
5689:Ivor Darreg
5514:Béla Bartók
5451:MidiPro.org
5423:Wilson, Erv
4442:Jerome Kohl
4291:: 368–385.
4171:(paperback)
3891:14 December
3866:14 December
3841:14 December
2896:(1–2): 84.
2865:Blesh, Rudi
2121:(1961–2015)
2119:Bob Gilmore
2113:Georg Hajdu
2091:(1945–2023)
2073:(1934–2006)
2055:(1928–2016)
2049:(1917–1989)
2043:(1907–1994)
2037:(1901–1974)
2031:(1893–1973)
2025:(1893–1981)
2019:(1893–1979)
2013:(1887–1972)
2007:(1875–1965)
2001:(1629–1695)
1995:(1897–1973)
1972:Robin Haigh
1954:Mick Gordon
1858:Geoff Smith
1798:Georg Hajdu
1774:Lucio Garau
1762:Erling Wold
1756:Eric Mandat
1696:David First
1690:Kraig Grady
1678:James Erber
1666:Warren Burt
1650:(1949–2013)
1644:(1948–1983)
1613:Max Méreaux
1603:(1945–2023)
1530:Terry Riley
1514:(1933–2023)
1484:(1928–2016)
1410:(1924–2004)
1364: [
1349:Ivor Darreg
1225:Béla Bartók
1113:In the West
749:During the
746:immensely.
669: [
643:Renaissance
600:tetrachords
515:микротоника
473: [
464:music. The
462:xenharmonic
458:xenharmonic
454:Ivor Darreg
338:W. McNaught
244:Aristoxenus
216:micro-tonal
120:accidentals
100:Terminology
7132:Categories
7050:Surrealism
7045:Stochastic
7035:Sound mass
6970:Microtonal
6942:techniques
6940:Genres and
6888:Stravinsky
6848:Skalkottas
6753:Schoenberg
6525:Beta scale
6503:Non-octave
6494:Tetrachord
6396:Kirnberger
6359:Schismatic
5926:Groups and
5885:techniques
5753:Beta scale
5604:Joe Maneri
5564:Alois Hába
5544:John Eaton
4614:28 October
4585:2022-12-01
4564:2022-12-01
4068:3 February
3207:: 201–209.
3062:2 February
3039:2 February
2984:inter alia
2287:References
2217:Microtuner
2146:3rd bridge
2133:(b. 1961)
2125:Marc Sabat
2053:Erv Wilson
2029:Alois Hába
1840:Marc Sabat
1708:James Wood
1482:Erv Wilson
1470:Joe Maneri
1396:Luigi Nono
1297:Alois Hába
1054:Mr. Bungle
1052:, also of
1045:Ishraqiyun
1008:Jon Catler
996:rock music
826:Alois Hába
714:Alois Hába
503:Alois Haba
390:spirituals
364:Microtonal
326:Rudi Blesh
280:enharmonic
262:diaschisma
212:microtonal
32:microsound
18:Microtonal
7030:Serialism
6950:Atonality
6878:Prokofiev
6721:Composers
6515:A12 scale
6469:Octoechos
6434:Shí-èr-lǜ
6383:Irregular
6200:Otonality
6140:Microtone
5907:Sonido 13
5672:Inventors
5624:Ezra Sims
5502:Composers
5395:Anon. . "
4920:Iskusstv.
4696:Front Row
4523:March 28,
3946:. Paris:
3886:disserCat
3861:disserCat
3836:disserCat
3698:disserCat
2912:1559-5749
2576:Die Reihe
2538:Resonance
2279:Sonido 13
2127:(b. 1965)
2115:(b. 1960)
2109:(b. 1955)
2103:(b. 1951)
2097:(b. 1948)
2085:(b. 1936)
2079:(b. 1990)
2067:(b. 1932)
2061:(b. 1929)
1980:(b. 1994)
1974:(b. 1993)
1968:(b. 1990)
1956:(b. 1985)
1950:(b. 1985)
1944:(b. 1985)
1938:(b. 1984)
1932:(b. 1981)
1926:(b. 1977)
1920:(b. 1973)
1914:(b. 1973)
1908:(b. 1972)
1902:(b. 1971)
1896:(b. 1971)
1890:(b. 1971)
1878:(b. 1969)
1872:(b. 1969)
1860:(b. 1966)
1848:(b. 1965)
1836:(b. 1964)
1824:(b. 1961)
1812:(b. 1961)
1806:(b. 1960)
1800:(b. 1960)
1794:(b. 1959)
1788:(b. 1959)
1776:(b. 1959)
1770:(b. 1958)
1764:(b. 1958)
1758:(b. 1957)
1752:(b. 1956)
1740:(b. 1955)
1738:Kyle Gann
1728:(b. 1954)
1722:(b. 1954)
1710:(b. 1953)
1704:(b. 1953)
1698:(b. 1953)
1686:(b. 1952)
1674:(b. 1951)
1668:(b. 1949)
1662:(b. 1949)
1656:(b. 1949)
1638:(b. 1953)
1632:(b. 1948)
1615:(b. 1946)
1476:Ezra Sims
1440:Studie II
1153:July 2016
1027:Radiohead
1020:jazz rock
992:blue note
910:In 1986,
872:Studie II
468:composer
234:Ezra Sims
208:micro-ton
200:microtone
169:micro-ton
165:microtono
159:composer
105:Microtone
82:intervals
39:Microtome
7107:Category
7040:Spectral
6965:Futurism
6899:Americas
6883:Scriabin
6854:Hungary
6829:Germany
6813:Messiaen
6808:Koechlin
6784:Finland
6774:Czechia
6768:Pousseur
6764:Belgium
6734:Austria
6663:Waveform
6658:Tonality
6626:Overtone
6611:Loudness
6400:Vallotti
6353:septimal
6345:Meantone
6105:Interval
5902:Semitone
5454:Archived
4928:. 1523.
4778:29 March
4727:AllMusic
4639:(1999).
4608:LilyPond
4313:(1979).
4265:(1885).
4251:: 19–23.
4189:(eds.).
3820:: 21–24.
3260:(eds.).
2867:(1946).
2797:(eds.).
2733:(eds.).
2652:(2014).
2534:A Propos
2139:See also
1451:Stimmung
1096:Dollshot
976:LilyPond
655:meantone
613:semitone
558:De Staat
511:tonality
466:Austrian
124:semitone
86:semitone
7092: ←
7020:Process
6909:Antheil
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