Microtonal music or microtonality is the use in music of microtones— intervals smaller than a

semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls between the keys of a piano tuned in

equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...

. In ''Revising the musical equal temperament,'' Haye Hinrichsen defines equal temperament as “the frequency ratios of all intervals are invariant under transposition (translational shifts along the keyboard), i.e., to be constant. The standard twelve-tone ''equal temperament'' (ET), which was originally invented in ancient China and rediscovered in Europe in the 16th century, is determined by two additional conditions. Firstly the octave is divided into twelve semitones. Secondly the octave, the most fundamental of all intervals, is postulated to be pure (beatless), as described by the frequency ratio 2:1.”

Terminology

Microtone

''Microtonal music'' can refer to any music containing microtones. The words "microtone" and "microtonal" were coined before 1912 by Maud MacCarthy Mann in order to avoid the misnomer "

quarter tone A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, ...

" when speaking of the srutis 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 composer

Julián Carrillo Julián Carrillo Trujillo (January 28, 1875 – September 9, 1965) was a Mexican composer,Camp, Roderic Ai (1995). "Carrillo (Flores), Nabor" on ''Mexican Political Biographies, 1935–1993: Third Edition'', p. 121. . conductor, violin ...

, writing in Spanish or French, coined the terms ''microtono''/''micro-ton'' and ''microtonalismo''/''micro-tonalité''. In French, the usual term is the somewhat more self-explanatory ''micro-intervalle'', and French sources give the equivalent German and English terms as ''Mikrointervall'' (or ''Kleinintervall'') and ''micro interval'' (or ''microtone''), respectively. "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, ''micro-intervalité'', however, is rare or nonexistent, normally being translated as "microtonality"; in French, the terms ''micro-ton'', ''microtonal'' (or ''micro-tonal''), and ''microtonalité'' are also sometimes used, occasionally mixed in the same passage with ''micro-intervale'' and ''micro-intervalité''.

Ezra Sims Ezra Sims (January 16, 1928 in Birmingham, Alabama — January 30, 2015 in Boston, Massachusetts) was one of the pioneers in the field of microtonal composition. He invented a system of notation that was adopted by many microtonal composers after ...

, in the article "Microtone" in the second edition of the ''

Harvard Dictionary of Music ''The Harvard Dictionary of Music'' is a standard music reference book published by the Belknap Press of Harvard University Press. The first edition, titled ''Harvard Dictionary of Music'', was published in 1944, and was edited by Willi Apel. ...

'' defines "microtone" as "an interval smaller than a semitone", which corresponds with

Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have bee ...

's use of the term '' diesis''. However, the unsigned article "Comma, Schisma" in the same reference source calls

comma The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline o ...

, schisma and diaschisma "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 ''

The New Grove Dictionary of Music and Musicians ''The New Grove Dictionary of Music and Musicians'' is an encyclopedic dictionary of music and musicians. Along with the German-language ''Die Musik in Geschichte und Gegenwart'', it is one of the largest reference works on the history and the ...

'', Paul Griffiths, Mark Lindley, and Ioannis Zannos define "microtone" as a musical rather than an acoustical entity: "any musical interval or difference of pitch distinctly smaller than a semitone", including "the tiny

enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written ...

melodic intervals of

ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...

, the several divisions of the

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

into more than 12 parts, and various discrepancies among the intervals of

just intonation In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and ...

or between a sharp and its enharmonically paired flat in various forms of mean-tone temperament", as well as the Indian sruti, and small intervals used in

Byzantine chant Byzantine music (Greek: Βυζαντινή μουσική) is the music of the Byzantine Empire. Originally it consisted of songs and hymns composed to Greek texts used for courtly ceremonials, during festivals, or as paraliturgical and liturgical ...

, Arabic music theory from the 10th century onward, and similarly for

Persian traditional music Persian traditional music or Iranian traditional music, also known as Persian classical music or Iranian classical music, refers to the classical music of Iran (also known as ''Persia''). It consists of characteristics developed through the cou ...

and

Turkish music The music of Turkey includes mainly Turkic and Byzantine elements as well as partial influences ranging from Ottoman music, Middle Eastern music and Music of Southeastern Europe, as well as references to more modern European and American popul ...

and various other Near Eastern musical traditions, but do not actually name the "mathematical" terms schisma, comma, and diaschisma. "Microtone" is also sometimes used to refer to individual notes, "microtonal pitches" added to and distinct from the familiar twelve notes of the chromatic scale, as "enharmonic microtones", for example. In English the word "microtonality" is mentioned in 1946 by

Rudi Blesh Rudolph Pickett Blesh (January 21, 1899 – August 25, 1985) was an American jazz critic and enthusiast. Biography Blesh studied at Dartmouth College and held jobs writing jazz reviews for the '' San Francisco Chronicle'' and the ''New Yo ...

who related it to microtonal inflexions of the so-called "

blues scale Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spiritual (music), spirituals, work songs, field hollers, Ring shout, shouts, chants, and rhymed simple narra ...

s". In Court B. Cutting's 2019 ''Microtonal Analysis of “Blues Notes” and the Blues Scale'', he states that academic studies of the early blues concur that its pitch scale has within it three microtonal “blue notes” not found in 12 tone equal temperament intonation. It was used still earlier by W. McNaught with reference to developments in "modernism" in a 1939 record review of the ''Columbia History of Music, Vol. 5''. In German the term ''Mikrotonalität'' 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 ''Geschichte der Musiktheorie'' while "Mikroton" seems to prevail in discussions of the

avant-garde music Avant-garde music is music that is considered to be at the forefront of innovation in its field, with the term "avant-garde" implying a critique of existing aesthetic conventions, rejection of the status quo in favor of unique or original eleme ...

and music of Eastern traditions. The term "microinterval" is used alongside "microtone" by American musicologist Margo Schulter in her articles on

medieval music Medieval music encompasses the sacred and secular music of Western Europe during the Middle Ages, from approximately the 6th to 15th centuries. It is the first and longest major era of Western classical music and followed by the Renaissance ...

Microtonal

The term "microtonal music" usually refers to music containing very small intervals but can include any tuning that differs from Western twelve-tone

. Traditional Indian systems of 22

śruti ''Shruti'' ( sa, श्रुति, , ) in Sanskrit means "that which is heard" and refers to the body of most authoritative, ancient religious texts comprising the central canon of Hinduism. Manusmriti states: ''Śrutistu vedo vijñeyaḥ'' ( ...

; Indonesian gamelan music; Thai, Burmese, and African music, and music using

, meantone temperament or other alternative tunings may be considered microtonal. Microtonal variation of intervals is standard practice in the African-American musical forms of

spirituals Spirituals (also known as Negro spirituals, African American spirituals, Black spirituals, or spiritual music) is a genre of Christian music that is associated with Black Americans, which merged sub-Saharan African cultural heritage with the ...

, blues and

jazz Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a majo ...

. Many microtonal equal divisions of the octave have been proposed, usually (but not always) in order to achieve approximation to the intervals of

. Terminology other than "microtonal" has been used or proposed by some theorists and composers. In 1914, A. H. Fox Strangways objected that "'heterotone' would be a better name for śruti than the usual translation 'microtone'". 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 ''Viertelton-Musik'' (quarter tone music), and the type of intervallic structure found in such music was called the ''Vierteltonsystem'', 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 '' Riemann Musiklexikon'', and in the second edition of the popular ''Brockhaus Riemann Musiklexikon''. Ivan Wyschnegradsky used the term ''ultra-chromatic'' for intervals smaller than the semitone and ''infra-chromatic'' 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, ''subchromatic'', has been used by theorist Marek Žabka. Ivor Darreg proposed the term ''xenharmonic''; see xenharmonic music. The

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

n composer Franz Richter Herf and the music theorist Rolf Maedel, Herf's colleague at the Salzburg Mozarteum, preferred using the Greek word ''ekmelic'' when referring to "all the pitches lying outside the traditional twelve-tone system". Some authors in Russia and some musicology dissertations disseminate the term ''микрохроматика'' (microchromatics), coined in the 1970s by Yuri Kholopov, to describe a kind of 'intervallic genus' ( интервальный род) for all possible microtonal structures, both ancient (as enharmonic genus—γένος ἐναρμόνιον—of Greeks) and modern (as quarter tone scales of Alois Haba); this generalization term allowed also to avoid derivatives such as ''микротональность'' (microtonality, which could be understood in Russian as a sub-

tonality Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is cal ...

, which is subordinate to the dominating tonality, especially in the context of European music of the 19th century) and ''микротоника'' (microtonic, "a barely perceptible tonic"; see a clarification in Kholopov 000. Another Russian authors use more international adjective 'microtonal' and 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 his monographs to ''microtonalismo'', which is the usual term in Italian, and also in Spanish (e.g., as found in the title of Rué 000. 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". 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 form. Examples of this can be found in various places, ranging from

Claude Debussy (Achille) Claude Debussy (; 22 August 1862 – 25 March 1918) was a French composer. He is sometimes seen as the first Impressionism in music, Impressionist composer, although he vigorously rejected the term. He was among the most infl ...

's impressionistic harmonies to

Aaron Copland Aaron Copland (, ; November 14, 1900December 2, 1990) was an American composer, composition teacher, writer, and later a conductor of his own and other American music. Copland was referred to by his peers and critics as "the Dean of American Com ...

's chords of stacked fifths, to John Luther Adams' ''Clouds of Forgetting'', ''Clouds of Unknowing'' (1995), which gradually expands stacked-interval chords ranging from minor 2nds to major 7thsm.

Louis Andriessen Louis Joseph Andriessen (; 6 June 1939 – 1 July 2021) was a Dutch composer, pianist and academic teacher. Considered the most influential Dutch composer of his generation, he was a central proponent of The Hague school of composition. Although ...

's ''De Staat'' (1972–1976) contains a number of "augmented" modes that are based on Greek scales but are asymmetrical to the octave.

History

The Hellenic civilizations of ancient Greece left fragmentary records of their music, such as the

Delphic Hymns The Delphic Hymns are two musical compositions from Ancient Greece, which survive in substantial fragments. They were long regarded as being dated circa 138 BC and 128 BC, respectively, but recent scholarship has shown it likely they wer ...

. The ancient Greeks approached the creation of different musical intervals and modes by dividing and combining

tetrachord In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency pr ...

s, recognizing three

genera Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial ...

of tetrachords: the enharmonic, the chromatic, and the diatonic. Ancient Greek intervals were of many different sizes, including microtones. The enharmonic genus in particular featured intervals of a distinctly "microtonal" nature, which were sometimes smaller than 50 cents, less than half of the contemporary Western

of 100 cents. In the ancient Greek enharmonic genus, the tetrachord contained a semitone of varying sizes (approximately 100 cents) divided into two equal intervals called dieses (single "diesis", δίεσις); in conjunction with a larger interval of roughly 400 cents, these intervals comprised the perfect fourth (approximately 498 cents, or the ratio of 4/3 in

). 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). Archicembalo en Cents

Guillaume Costeley Guillaume Costeley ronounced Cotelay(1530, possibly 1531 – 28 January 1606) was a French composer of the Renaissance. He was the court organist to Charles IX of France and famous for his numerous ''chansons'', which were representative of the ...

's "Chromatic Chanson", "Seigneur Dieu ta pitié" of 1558 used 1/3 comma meantone and explored the full compass of 19 pitches in the octave. The Italian

Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass id ...

composer and theorist Nicola Vicentino (1511–1576) worked with microtonal intervals and built a keyboard with 36 keys to the octave known as the archicembalo. While theoretically an interpretation of ancient Greek tetrachordal theory, in effect Vicentino presented a circulating system of quarter-comma meantone, maintaining major thirds tuned in

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

Jacques Fromental Halévy Ancient and noble French family names, Jacques, Jacq, or James are believed to originate from the Middle Ages in the historic northwest Brittany region in France, and have since spread around the world over the centuries. To date, there are over ...

composed a cantata "Prométhée enchaîné" for a solo voice, choir and orchestra (premiered in 1849), where in one movement (''Choeur des Océanides'') he used quarter tones, to imitate the enharmonic genus of Greeks. In the 1910s and 1920s, quarter tones (24 equal pitches per octave) received attention from such composers as Charles Ives,

Alois Hába Alois Hába (21 June 1893 – 18 November 1973) was a Czech composer, music theorist and teacher. He belongs to the important discoverers in modern classical music, and major composers of microtonal music, especially using the quarter-tone sc ...

, Ivan Wyschnegradsky, and Mildred Couper. Alexander John Ellis, who in the 1880s produced a translation of Hermann Helmholtz's ''On the Sensations of Tone'', proposed an elaborate set of exotic just intonation tunings and non-harmonic tunings. Ellis also studied the tunings of non-Western cultures and, in a report to the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

, stated that they used neither equal divisions of the octave nor just intonation intervals. Ellis inspired

Harry Partch Harry Partch (June 24, 1901 – September 3, 1974) was an American composer, music theorist, and creator of unique musical instruments. He composed using scales of unequal intervals in just intonation, and was one of the first 20th-century co ...

immensely. During the Exposition Universelle of 1889,

heard a Balinese

gamelan Gamelan () ( jv, ꦒꦩꦼꦭꦤ꧀, su, ᮌᮙᮨᮜᮔ᮪, ban, ᬕᬫᭂᬮᬦ᭄) is the traditional ensemble music of the Javanese, Sundanese, and Balinese peoples of Indonesia, made up predominantly of percussive instruments. ...

performance and was exposed to non-Western tunings and rhythms. Some scholars have ascribed Debussy's subsequent innovative use of the whole-tone (six equal pitches per octave) tuning in such compositions as the '' Fantaisie for piano and orchestra'' and the Toccata from the suite '' Pour le piano'' to his exposure to the Balinese gamelan at the Paris exposition, and have asserted his rebellion at this time "against the rule of equal temperament" and that the gamelan gave him "the confidence to embark (after the 1900 world exhibition) on his fully characteristic mature piano works, with their many bell- and gong-like sonorities and brilliant exploitation of the piano's natural resonance". Still others have argued that Debussy's works like ''

L'isle joyeuse L'isle joyeuse, L. 106 (The Joyful Island) is a piece for solo piano by Claude Debussy composed in 1904. According to Jim Samson (1977), the "central relationship in the work is that between material based on the whole-tone scale, the lydian ...

'', '' La cathédrale engloutie'', ''

Prélude à l'après-midi d'un faune ''Prélude à l'après-midi d'un faune'' ( L. 86), known in English as ''Prelude to the Afternoon of a Faun'', is a symphonic poem for orchestra by Claude Debussy, approximately 10 minutes in duration. It was composed in 1894 and first performed ...

'', ''

La mer La Mer may refer to: * ''La mer'' (Debussy), an orchestral composition by Claude Debussy * "La Mer" (song), a 1946 song by Charles Trenet *La Mer (horse) La Mer was a thoroughbred racehorse, who raced from 1976 to 1979. La Mer was sired by Co ...

'', ''

Pagodes ''Estampes'' ("Prints"), L.100, is a composition for solo piano by Claude Debussy. It was finished in 1903. The first performance of the work was given by Ricardo Viñes at the Société Nationale de Musique in Paris. This three-movement piano ...

'', '' Danseuses de Delphes'', and ''

Cloches à travers les feuilles Cloche (French for "bell") or la cloche (French for "the bell") may refer to: * Armoured cloche, bell-shaped turrets of the Maginot Line * ''Battement en cloche'', a classical ballet movement * Bell (instrument), especially in music directions * ...

'' 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. Emil Berliner's introduction of the phonograph in the 1890s allowed much non-Western music to be recorded and heard by Western composers, further spurring the use of non-12-equal tunings. Major microtonal composers of the 1920s and 1930s include

(quarter tones, or 24 equal pitches per octave, and sixth tones), Julián Carrillo (24 equal, 36, 48, 60, 72, and 96 equal pitches to the octave embodied in a series of specially custom-built pianos), Ivan Wyschnegradsky (third tones, quarter tones, sixth tones and twelfth tones, non octaving scales) and the early works of

(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). Prominent microtonal composers or researchers of the 1940s and 1950s include Adriaan Daniel Fokker (31 equal tones per octave), Partch (continuing to build his handcrafted orchestra of microtonal just intonation instruments), and Eivind Groven. Digital synthesizers from the Yamaha TX81Z (1987) on and inexpensive software synthesizers have contributed to the ease and popularity of exploring microtonal music.

Microtonality in electronic music

Electronic music Electronic music is a Music genre, genre of music that employs electronic musical instruments, digital instruments, or electronics, circuitry-based music technology in its creation. It includes both music made using electronic and electromech ...

facilitates the use of any kind of microtonal tuning, and sidesteps the need to develop new notational systems. In 1954,

Karlheinz Stockhausen Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groundb ...

built his electronic ''

Stud