HOME

TheInfoList



OR:

Atonality in its broadest sense is music that lacks a
tonal center Tonal may refer to: * Tonal (mythology), a concept in the belief systems and traditions of Mesoamerican cultures, involving a spiritual link between a person and an animal * Tonal language, a type of language in which pitch is used to make phone ...
, or key. ''Atonality'', in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a single, central triad is not used, and the notes of the
chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...
function independently of one another. More narrowly, the term ''atonality'' describes music that does not conform to the system of tonal hierarchies that characterized
European classical music Classical music generally refers to the art music of the Western world, considered to be #Relationship to other music traditions, distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical mu ...
between the seventeenth and nineteenth centuries. "The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, as well as by the occurrence of familiar pitch combinations in unfamiliar environments". The term is also occasionally used to describe music that is neither tonal nor serial, especially the pre-
twelve-tone The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale ...
music of the
Second Viennese School The Second Viennese School () was the group of composers that comprised Arnold Schoenberg and his pupils, particularly Alban Berg and Anton Webern, and close associates in early 20th-century Vienna. Their music was initially characterized by late ...
, principally
Alban Berg Alban Maria Johannes Berg ( ; ; 9 February 1885 – 24 December 1935) was an Austrian composer of the Second Viennese School. His compositional style combined Romantic lyricism with the twelve-tone technique. Although he left a relatively sma ...
,
Arnold Schoenberg Arnold Schoenberg or Schönberg (13 September 187413 July 1951) was an Austrian and American composer, music theorist, teacher and writer. He was among the first Modernism (music), modernists who transformed the practice of harmony in 20th-centu ...
, and
Anton Webern Anton Webern (; 3 December 1883 – 15 September 1945) was an Austrian composer, conductor, and musicologist. His music was among the most radical of its milieu in its lyric poetry, lyrical, poetic concision and use of then novel atonality, aton ...
. However, "as a categorical label, 'atonal' generally means only that the piece is in the Western tradition and is not 'tonal, although there are longer periods, e.g., medieval, renaissance, and modern modal music to which this definition does not apply. "Serialism arose partly as a means of organizing more coherently the relations used in the pre-serial 'free atonal' music. ... Thus, many useful and crucial insights about even strictly serial music depend only on such basic atonal theory". Late 19th- and early 20th-century composers such as
Alexander Scriabin Alexander Nikolayevich Scriabin, scientific transliteration: ''Aleksandr Nikolaevič Skrjabin''; also transliterated variously as Skriabin, Skryabin, and (in French) Scriabine. The composer himselused the French spelling "Scriabine" which was a ...
,
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 influe ...
,
Paul Hindemith Paul Hindemith ( ; ; 16 November 189528 December 1963) was a German and American composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advo ...
,
Béla Bartók Béla Viktor János Bartók (; ; 25 March 1881 – 26 September 1945) was a Hungarian composer, pianist and ethnomusicologist. He is considered one of the most important composers of the 20th century; he and Franz Liszt are regarded as Hunga ...
,
Sergei Prokofiev Sergei Sergeyevich Prokofiev; alternative transliterations of his name include ''Sergey'' or ''Serge'', and ''Prokofief'', ''Prokofieff'', or ''Prokofyev''. , group=n ( – 5 March 1953) was a Russian composer, pianist, and conductor who l ...
,
Igor Stravinsky Igor Fyodorovich Stravinsky ( – 6 April 1971) was a Russian composer and conductor with French citizenship (from 1934) and American citizenship (from 1945). He is widely considered one of the most important and influential 20th-century c ...
, and
Edgard Varèse Edgard Victor Achille Charles Varèse (; also spelled Edgar; December 22, 1883 – November 6, 1965) was a French and American composer who spent the greater part of his career in the United States. Varèse's music emphasizes timbre and rhythm; h ...
, have written music that has been described, in full or in part, as atonal.


History

While music without a tonal center had been previously written, for example
Franz Liszt Franz Liszt (22 October 1811 – 31 July 1886) was a Hungarian composer, virtuoso pianist, conductor and teacher of the Romantic music, Romantic period. With a diverse List of compositions by Franz Liszt, body of work spanning more than six ...
's ''
Bagatelle sans tonalité ''Bagatelle sans tonalité'' ("Bagatelle without tonality", S.216a) is a piece for solo piano written by Franz Liszt in 1885. The manuscript bears the title "Fourth Mephisto Waltz" and may have been intended to replace the piece now known as the ...
'' of 1885, it is with the coming of the twentieth century that the term ''atonality'' began to be applied to pieces, particularly those written by Arnold Schoenberg and The Second Viennese School. The term "atonality" was coined in 1907 by
Joseph Marx Joseph Rupert Rudolf Marx (11 May 1882 – 3 September 1964) was an Austrian composer, teacher and critic. Life and career Marx was born in Graz and pursued studies in philosophy, art history, German studies, and music at Graz University, earnin ...
in a scholarly study of tonality, which was later expanded into his doctoral thesis. Their music arose from what was described as the "crisis of tonality" between the late nineteenth century and early twentieth century in
classical music Classical music generally refers to the art music of the Western world, considered to be #Relationship to other music traditions, distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical mu ...
. This situation had arisen over the course of the nineteenth century due to the increasing use of
ambiguous
chords Chord or chords may refer to: Art and music * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord, a chord played on a guitar, which has a particular tuning * The Chords (British band), 1970s British mod ...
, improbable
harmonic In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
inflections, and more unusual melodic and rhythmic inflections than what was possible within the styles of tonal music. The distinction between the exceptional and the normal became more and more blurred. As a result, there was a "concomitant loosening" of the synthetic bonds through which tones and harmonies had been related to one another. The connections between harmonies were uncertain even on the lowest chord-to-chord level. On higher levels, long-range harmonic relationships and implications became so tenuous, that they hardly functioned at all. At best, the felt probabilities of the style system had become obscure. At worst, they were approaching a uniformity, which provided few guides for either composition or listening.
The first phase, known as "free atonality" or "free chromaticism", involved a conscious attempt to avoid traditional
diatonic Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair ...
harmony. Works of this period include the opera ''
Wozzeck ''Wozzeck'' () is the first opera by the Austrian composer Alban Berg. Composed between 1914 and 1922, it premiered in 1925. It is based on the drama '' Woyzeck'', which German playwright Georg Büchner left incomplete at his death. Berg attende ...
'' (1917–1922) by Alban Berg and '' Pierrot lunaire'' (1912) by Schoenberg. The second phase, begun after
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
, was exemplified by attempts to create a systematic means of composing without tonality, most famously the method of composing with 12 tones or the twelve-tone technique. This period included Berg's ''
Lulu Lulu may refer to: Companies * LuLu, an early automobile manufacturer * Lulu.com, an online e-books and print self-publishing platform, distributor, and retailer * Lulu Hypermarket, a retail chain in Asia * Lululemon Athletica or simply Lulu, a C ...
'' and '' Lyric Suite'', Schoenberg's ''
Piano Concerto A piano concerto, a type of concerto, is a solo composition in the classical music genre which is composed for piano accompanied by an orchestra or other large ensemble. Piano concertos are typically virtuosic showpieces which require an advance ...
'', his oratorio '' Die Jakobsleiter'' and numerous smaller pieces, as well as his last two string quartets. Schoenberg was the major innovator of the system. His student, Anton Webern, however, is anecdotally claimed to have begun linking dynamics and tone color to the primary row, making rows not only of pitches but of other aspects of music as well. However, actual analysis of Webern's twelve-tone works has so far failed to demonstrate the truth of this assertion. One analyst concluded, following a minute examination of the Piano Variations, op. 27, that
while the texture of this music may superficially resemble that of some serial music ... its structure does not. None of the patterns within separate nonpitch characteristics makes audible (or even numerical) sense ''in itself''. The point is that these characteristics are still playing their traditional role of differentiation.
Twelve-tone technique, combined with the parametrization (separate organization of four aspects of music: pitch, attack character, intensity, and duration) of
Olivier Messiaen Olivier Eugène Prosper Charles Messiaen (, ; ; 10 December 1908 – 27 April 1992) was a French composer, organist, and ornithology, ornithologist. One of the major composers of the 20th-century classical music, 20th century, he was also an ou ...
, would be taken as the inspiration for serialism. Atonality emerged as a pejorative term to condemn music in which chords were organized seemingly with no apparent coherence. In
Nazi Germany Nazi Germany, officially known as the German Reich and later the Greater German Reich, was the German Reich, German state between 1933 and 1945, when Adolf Hitler and the Nazi Party controlled the country, transforming it into a Totalit ...
, atonal music was attacked as "
Bolshevik The Bolsheviks, led by Vladimir Lenin, were a radical Faction (political), faction of the Marxist Russian Social Democratic Labour Party (RSDLP) which split with the Mensheviks at the 2nd Congress of the Russian Social Democratic Labour Party, ...
" and labeled as degenerate (''Entartete Musik'') along with other music produced by enemies of the Nazi regime. Many composers had their works banned by the regime, not to be played until after its collapse at the end of
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
. After Schoenberg's death, Igor Stravinsky used the twelve-tone technique.
Iannis Xenakis Giannis Klearchou Xenakis (also spelled for professional purposes as Yannis or Iannis Xenakis; , ; 29 May 1922 – 4 February 2001) was a Romanian-born Greek-French avant-garde composer, music theorist, architect, performance director and enginee ...
generated pitch sets from mathematical formulae, and also saw the expansion of tonal possibilities as part of a synthesis between the hierarchical principle and the theory of numbers, principles which have dominated music since at least the time of
Parmenides Parmenides of Elea (; ; fl. late sixth or early fifth century BC) was a Pre-Socratic philosophy, pre-Socratic ancient Greece, Greek philosopher from Velia, Elea in Magna Graecia (Southern Italy). Parmenides was born in the Greek colony of Veli ...
.


Free atonality

The twelve-tone technique was preceded by Schoenberg's freely atonal pieces of 1908 to 1923, which, though free, often have as an "integrative element...a minute intervallic
cell Cell most often refers to: * Cell (biology), the functional basic unit of life * Cellphone, a phone connected to a cellular network * Clandestine cell, a penetration-resistant form of a secret or outlawed organization * Electrochemical cell, a de ...
" that in addition to expansion may be transformed as with a tone row, and in which individual notes may "function as pivotal elements, to permit overlapping statements of a basic cell or the linking of two or more basic cells". The decay of the sense of tonality and the subsequent distribution into individual elements brought three concepts into play: 1. Musical elements that had since been secondary to tonal form groups now became autonomous. 2. The absence of tonal coherence prompted the search for a unity that could connect the disjointed musical language in an alternative way. 3. Due to the replacement of diatonic principles, new concepts of form arose. The twelve-tone technique was also preceded by nondodecaphonic serial composition used independently in the works of Alexander Scriabin, Igor Stravinsky,
Béla Bartók Béla Viktor János Bartók (; ; 25 March 1881 – 26 September 1945) was a Hungarian composer, pianist and ethnomusicologist. He is considered one of the most important composers of the 20th century; he and Franz Liszt are regarded as Hunga ...
,
Carl Ruggles Carl Ruggles (born Charles Sprague Ruggles; March 11, 1876 – October 24, 1971) was an American composer, painter and teacher. His pieces employed "dissonant counterpoint", a term coined by fellow composer and musicologist Charles Seeger to ...
, and others. "Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the
ostinato In music, an ostinato (; derived from the Italian word for ''stubborn'', compare English ''obstinate'') is a motif or phrase that persistently repeats in the same musical voice, frequently in the same pitch. Well-known ostinato-based pieces inc ...
."


Composing atonal music

Setting out to compose atonal music may seem complicated because of both the vagueness and generality of the term. Additionally
George Perle George Perle (6 May 1915 – 23 January 2009) was an American composer and music theory, music theorist. As a composer, his music was largely atonality, atonal, using methods similar to the twelve-tone technique of the Second Viennese School. Th ...
explains that, "the 'free' atonality that preceded dodecaphony precludes by definition the possibility of self-consistent, generally applicable compositional procedures". However, he provides one example as a way to compose atonal pieces, a pre-twelve-tone technique piece by Anton Webern, which rigorously avoids anything that suggests tonality, to choose pitches that do not imply tonality. In other words, reverse the rules of the
common practice period In Western classical music, the common practice period (CPP) was the period of about 250 years during which the tonal system was regarded as the only basis for composition. It began when composers' use of the tonal system had clearly supersede ...
so that what was not allowed is required and what was required is not allowed. This is what was done by
Charles Seeger Charles Louis Seeger Jr. (December 14, 1886 – February 7, 1979) was an American musicologist, composer, teacher, and folklorist. He was the husband of the composer Ruth Crawford Seeger, father of the American folk singers Pete Seeger (1919– ...
in his explanation of
dissonant counterpoint In music theory, counterpoint is the relationship of two or more simultaneous Part (music), musical lines (also called voices) that are harmonically dependent on each other, yet independent in rhythm and Pitch contour, melodic contour. The term ...
, which is a way to write atonal counterpoint. Kostka and Payne list four procedures as operational in the atonal music of Schoenberg, all of which may be taken as negative rules. Avoidance of melodic or harmonic octaves, avoidance of traditional pitch collections such as major or minor triads, avoidance of more than three successive pitches from the same diatonic scale, and use of disjunct melodies (avoidance of conjunct melodies). Further, Perle agrees with Oster and Katz that, "the abandonment of the concept of a
root In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...
-generator of the individual chord is a radical development that renders futile any attempt at a systematic formulation of chord structure and progression in atonal music along the lines of traditional harmonic theory". Atonal compositional techniques and results "are not reducible to a set of foundational assumptions in terms of which the compositions that are collectively designated by the expression 'atonal music' can be said to represent 'a system' of composition". Equal-interval chords are often of indeterminate root, mixed-interval chords are often best characterized by their interval content, while both lend themselves to atonal contexts. Perle also points out that structural coherence is most often achieved through operations on intervallic cells. A cell "may operate as a kind of microcosmic set of fixed intervallic content, statable either as a chord or as a melodic figure or as a combination of both. Its components may be fixed with regard to order, in which event it may be employed, like the twelve-tone set, in its literal transformations. … Individual tones may function as pivotal elements, to permit overlapping statements of a basic cell or the linking of two or more basic cells". Regarding the post-tonal music of Perle, one theorist wrote: "While ... montages of discrete-seeming elements tend to accumulate global rhythms other than those of tonal progressions and their rhythms, there is a similarity between the two sorts of accumulates spatial and temporal relationships: a similarity consisting of generalized arching tone-centers linked together by shared background referential materials". Another approach of composition techniques for atonal music is given by Allen Forte who developed the theory behind atonal music. Forte describes two main operations: transposition and inversion. Transposition can be seen as a rotation of ''t'' either clockwise or anti-clockwise on a circle, where each note of the chord is rotated equally. For example, if ''t'' = 2 and the chord is 3 6 transposition (clockwise) will be 5 8 Inversion can be seen as a symmetry with respect to the axis formed by 0 and 6. If we carry on with our example 3 6becomes 9 6 An important characteristic are the invariants, which are the notes which stay identical after a transformation. No difference is made between the octave in which the note is played so that, for example, all Cs are equivalent, no matter the octave in which they actually occur. This is why the 12-note scale is represented by a circle. This leads us to the definition of the similarity between two chords which considers the subsets and the interval content of each chord.


Reception and legacy


Controversy over the term itself

The term "atonality" itself has been controversial.
Arnold Schoenberg Arnold Schoenberg or Schönberg (13 September 187413 July 1951) was an Austrian and American composer, music theorist, teacher and writer. He was among the first Modernism (music), modernists who transformed the practice of harmony in 20th-centu ...
, whose music is generally used to define the term, was vehemently opposed to it, arguing that "The word 'atonal' could only signify something entirely inconsistent with the nature of tone... to call any relation of tones atonal is just as farfetched as it would be to designate a relation of colors aspectral or acomplementary. There is no such antithesis". Composer and theorist
Milton Babbitt Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He was a Pulitzer Prize and MacArthur Fellowship recipient, recognized for his serial and electronic music. Biography ...
also disparaged the term, saying "The works that followed, many of them now familiar, include the ''
Five Pieces for Orchestra The ''Five Pieces for Orchestra'' (''Fünf Orchesterstücke''), Op. 16, were composed by Arnold Schoenberg in 1909, and first performed in London in 1912. The titles of the pieces, reluctantly added by the composer after the work's completion up ...
'', ''
Erwartung ' (''Expectation''), Op. 17, is a one-act monodrama in four scenes by Arnold Schoenberg to a libretto by . Composed in 1909, it was not premiered until 6 June 1924 in Prague conducted by Alexander Zemlinsky with Marie Gutheil-Schoder as the sop ...
'', '' Pierrot Lunaire'', and they and a few yet to follow soon were termed 'atonal,' by I know not whom, and I prefer not to know, for in no sense does the term make sense. Not only does the music employ 'tones,' but it employs precisely the same 'tones,' the same physical materials, that music had employed for some two centuries. In all generosity, 'atonal' may have been intended as a mildly analytically derived term to suggest 'atonic' or to signify 'a-triadic tonality', but, even so there were infinitely many things the music was not". "Atonal" developed a certain vagueness in meaning as a result of its use to describe a wide variety of compositional approaches that deviated from traditional chords and
chord progression In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural, or simply changes) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from ...
s. Attempts to solve these problems by using terms such as "pan-tonal", "non-tonal", "multi-tonal", "free-tonal" and "without tonal center" instead of "atonal" have not gained broad acceptance.


Criticism of the concept of atonality

Composer Anton Webern held that "new laws asserted themselves that made it impossible to designate a piece as being in one key or another". Composer
Walter Piston Walter Hamor Piston, Jr. (January 20, 1894 – November 12, 1976), was an American composer of classical music, music theorist, and professor of music at Harvard University. Life Piston was born in Rockland, Maine at 15 Ocean Street to Walter ...
, on the other hand, said that, out of long habit, whenever performers "play any little phrase they will hear it in some key—it may not be the right one, but the point is they will play it with a tonal sense. ... e more I feel I know Schoenberg's music the more I believe he thought that way himself. ... And it isn't only the players; it's also the listeners. They will hear tonality in everything". Donald Jay Grout similarly doubted whether atonality is really possible, because "any combination of sounds can be referred to a fundamental root". He defined it as a fundamentally subjective category: "atonal music is music in which the person who is using the word cannot hear tonal centers". One difficulty is that even an otherwise "atonal" work, tonality "by assertion" is normally heard on the thematic or linear level. That is, centricity may be established through the repetition of a central pitch or from emphasis by means of instrumentation, register, rhythmic elongation, or metric accent.


Criticism of atonal music

Swiss conductor, composer, and musical philosopher
Ernest Ansermet Ernest Alexandre Ansermet (; 11 November 1883 – 20 February 1969)"Ansermet, Ernest" in '' The New Encyclopædia Britannica''. Chicago: Encyclopædia Britannica Inc., 15th edn., 1992, Vol. 1, p. 435. was a Swiss conductor. Biography Anserme ...
, a critic of atonal music, wrote extensively on this in the book ''Les fondements de la musique dans la conscience humaine'' (The Foundations of Music in Human Consciousness), where he argued that the classical musical language was a precondition for musical expression with its clear, harmonious structures. Ansermet argued that a tone system can only lead to a uniform perception of music if it is deduced from just a single interval. For Ansermet this interval is the fifth. In France, on December 20, 2012, French pianist Jérôme Ducros gave a conference at the
Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...
entitled ''Atonalism. And after?'' as part of
Karol Beffa Karol Beffa, born on in Paris, is a French and Swiss composer and pianist. Biography Beffa is the son of French-Swiss linguist and ethnologist Marie-Lise Beffa and French linguist , and the nephew of industrialist Jean-Louis Beffa. He studie ...
's chair of artistic creation. He compares the discursive properties of tonal language and non-tonal languages, largely giving the advantage to the former, and considers the return of tonality as inevitable. This conference sparked a heated controversy in the French musical world.


Examples

An example of atonal music would be Arnold Schoenberg's "Pierrot Lunaire", which is a song cycle composed in 1912. The work uses a technique called "Sprechstimme" or spoken singing, and the music is atonal, meaning that there is no clear tonal center or key. Instead, the notes of the chromatic scale function independently of each other, and the harmonies do not follow the traditional tonal hierarchy found in classical music. The result is a dissonant and jarring sound that is quite different from the harmonies found in tonal music.


See also

* Emancipation of the dissonance *
Jazz improvisation Jazz improvisation is the spontaneous invention of melodic solo lines or accompaniment parts in a performance of jazz music. It is one of the defining elements of jazz. Improvisation is composing on the spot, when a singer or instrumentalist inv ...
*
Klangfarbenmelodie ''Klangfarbenmelodie'' (German for "sound-color melody") is a musical concept that treats timbre as a melodic element. Arnold Schoenberg originated the idea. It has become synonymous with the technique of fragmenting a melodic line between differ ...
* Neue Musik *
Noise music Noise music is a genre of music that is characterised by the expressive use of noise. This type of music tends to challenge the distinction that is made in conventional musical practices between musical and non-musical sound. Noise music include ...
* List of atonal compositions


References


Cited sources

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


Further reading

* Beach, David (ed.). 1983. "
Schenkerian Analysis Schenkerian analysis is a method of musical analysis, analyzing tonal music based on the theories of Heinrich Schenker (1868–1935). The goal is to demonstrate the organic coherence of the work by showing how the "foreground" (all notes in the sco ...
and Post-Tonal Music", ''Aspects of Schenkerian Theory''. New Haven: Yale University Press. * Dahlhaus, Carl. 1966. "Ansermets Polemik gegen Schönberg." ''
Neue Zeitschrift für Musik The New Journal of Music (, and abbreviated to NZM) is a music magazine, co-founded in Leipzig by Robert Schumann, his teacher and future father-in law Friedrich Wieck, Julius Knorr and his close friend Ludwig Schuncke. Its first issue appe ...
'' 127, no. 5:179–183. * Forte, Allen. 1963. "Context and Continuity in an Atonal Work: A Set-Theoretic Approach". ''
Perspectives of New Music ''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Musi ...
'' 1, no. 2 (Spring): 72–82. * Forte, Allen. 1964. "A Theory of Set-Complexes for Music". ''
Journal of Music Theory The ''Journal of Music Theory'' is a peer-reviewed academic journal specializing in music theory and analysis. It was established by David Kraehenbuehl (Yale University) in 1957. According to its website, " e ''Journal of Music Theory'' fosters co ...
'' 8, no. 2 (Winter): 136–183. * Forte, Allen. 1965. "The Domain and Relations of Set-Complex Theory". ''Journal of Music Theory'' 9, no. 1 (Spring): 173–180. * Forte, Allen. 1972. Sets and Nonsets in Schoenberg's Atonal Music. ''Perspectives of New Music'' 11, no. 1 (Fall–Winter): 43–64. * Forte, Allen. 1978a. ''The Harmonic Organization of The Rite of Spring''. New Haven : Yale University Press. . * Forte, Allen. 1978b. "Schoenberg's Creative Evolution: The Path to Atonality". ''
The Musical Quarterly ''The Musical Quarterly'' is the oldest academic journal on music in America. Originally established in 1915 by Oscar Sonneck, the journal was edited by Sonneck until his death in 1928. Sonneck was succeeded by a number of editors, including C ...
'' 64, no. 2 (April): 133–176. * Forte, Allen. 1980. "Aspects of Rhythm in Webern's Atonal Music". ''
Music Theory Spectrum ''Music Theory Spectrum'' () is a peer-reviewed, academic journal specializing in music theory and analysis. It is the official journal of the Society for Music Theory, and is published by Oxford University Press. The journal was first published ...
'' 2:90–109. * Forte, Allen. 1998. ''The Atonal Music of Anton Webern''. New Haven and London: Yale University Press. . * Forte, Allen, and Roy Travis. 1974. "Analysis Symposium: Webern, Orchestral Pieces (1913): Movement I ('Bewegt')". ''
Journal of Music Theory The ''Journal of Music Theory'' is a peer-reviewed academic journal specializing in music theory and analysis. It was established by David Kraehenbuehl (Yale University) in 1957. According to its website, " e ''Journal of Music Theory'' fosters co ...
'' 18, no. 1 (Spring, pp. 2–43. * Krausz, Michael. 1984. "The Tonal and the Foundational: Ansermet on Stravinsky". ''
The Journal of Aesthetics and Art Criticism ''The Journal of Aesthetics and Art Criticism'' is a quarterly peer-reviewed academic journal covering the study of aesthetics and art criticism. It was published by Wiley-Blackwell Wiley-Blackwell is an international scientific, technical, med ...
'' 42:383–386. * Krenek, Ernst. 1953. "Is the Twelve-Tone Technique on the Decline?" ''
The Musical Quarterly ''The Musical Quarterly'' is the oldest academic journal on music in America. Originally established in 1915 by Oscar Sonneck, the journal was edited by Sonneck until his death in 1928. Sonneck was succeeded by a number of editors, including C ...
'' 39, no. 4 (October): 513–527. * Philippot, Michel. 1964. "Ansermet's Phenomenological Metamorphoses." Translated by Edward Messinger. ''
Perspectives of New Music ''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Musi ...
'' 2, no. 2 (Spring–Summer): 129–140. Originally published a
"Métamorphoses Phénoménologiques."
''Critique. Revue Générale des Publications Françaises et Etrangères'', no. 186 (November 1962). * Radano, Ronald M. 1993. ''New Musical Figurations:
Anthony Braxton Anthony Braxton (born June 4, 1945) is an American experimental composer, educator, music theorist, improviser and multi-instrumentalist who is best known for playing saxophones, particularly the alto. Braxton grew up on the South Side of Chi ...
's Cultural Critique'' Chicago: University of Chicago Press. * Stegemann, Benedikt. 2013. ''Theory of Tonality''. Theoretical Studies. Wilhelmshaven: Noetzel. .


External links


An Introduction to Atonal Music Analysis
by Robert T. Kelly.

by Lee Humphries *
Atonal, Music Dictionary
' {{Authority control 19th century in music 20th century in music 21st century in music Post-tonal music theory