Atonality in its broadest sense describes music Music is an art form whose medium is sound. Common elements of music are pitch , rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike), "(art) of the Muses." that lacks a tonal center Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840 (Reti, 1958; Simms 1975, 119; Judd, 1998; Dahlhaus 1990). Although Fétis used it as a general term for a, or key In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the key of B-flat major, and so. Atonality in this sense usually describes compositions written from about 1908 to the present day where a hierarchy of pitches focusing on a single, central tone is not used and the notes of the chromatic scale function independently of one another (Anon. 1994). More narrowly, the term describes music that does not conform to the system of tonal Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840 (Reti, 1958; Simms 1975, 119; Judd, 1998; Dahlhaus 1990). Although Fétis used it as a general term for a hierarchies that characterized classical Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 9th century to present times. The central norms of this tradition became codified between 1550 and 1900, which is known as the common practice period European music between the seventeenth and nineteenth centuries (Lansky, Perle, and Headlam 2001).

More narrowly still, the term is sometimes used to describe music that is neither tonal nor serial In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of post-tonal thinking (Whittall 2008, 1). Twelve-tone, especially the pre-twelve-tone Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given music of the Second Viennese School The principal members of the school, besides Schoenberg, were Alban Berg and Anton Webern, who were among his first composition pupils. Both of them had already produced copious and talented music in a late-Romantic idiom but felt they gained new direction and discipline from Schoenberg's teaching. Other pupils of this generation included Heinrich, principally Alban Berg Alban Maria Johanne Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique, Arnold Schoenberg Arnold Schoenberg (13 September 1874 – 13 July 1951) was an Austrian and later American composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. He used the spelling Schönberg until after his move to the United States in 1934 (Steinberg 1995, 463), "in deference to American, and Anton Webern Anton Webern was an Austrian composer and conductor. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known exponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of pitch, rhythm and dynamics were formative in the (Lansky, Perle, and Headlam 2001). According to John Rahn, however, "[a]s a categorical label, 'atonal' generally means only that the piece is in the Western tradition and is not 'tonal' " (Rahn 1980, 1); "serialism arose partly as a means of organizing more coherently the relations used in the preserial 'free atonal' music....Thus many useful and crucial insights about even strictly serial music depend only on such basic atonal theory" (Rahn 1980, 2)

Composers such as Alexander Scriabin Alexander Nikolayevich Scriabin (6 January 1872 [O.S. 25 December 1871]–27 April 1915) was a Russian composer and pianist who initially developed a highly lyrical and idiosyncratic tonal language inspired by the music of Chopin. Unlike the later Roslavets and Schönberg, Scriabin developed, via mysticism, an increasingly atonal musical language, Claude Debussy Achille-Claude Debussy (August 22, 1862 – March 25, 1918) was a French composer. Along with Maurice Ravel, he was one of the most prominent figures working within the field of impressionist music, though he himself intensely disliked the term when applied to his compositions. Debussy is not only among the most important of all French composers,, Béla Bartók Béla Viktor János Bartók (pronounced /ˈbɑrtɒk/ , Hungarian pronunciation: [ˈbeːlɒ ˈbɒrtoːk]) (March 25, 1881 – September 26, 1945) was a Hungarian composer and pianist. He is considered to be one of the greatest composers of the 20th century and is regarded, along with Liszt, as his country's greatest composer (Gillies 2001). Through, Paul Hindemith Paul Hindemith was a German composer, violist, violinist, teacher, music theorist and conductor, Sergei Prokofiev Sergei Sergeyevich Prokofiev (27 April [O.S. 15 April] 1891 – 5 March 1953) was a Russian composer, pianist and conductor who mastered numerous musical genres and came to be admired as one of the greatest composers of the 20th century, Igor Stravinsky Igor Fyodorovich Stravinsky (17 June [O.S. 5 June] 1882 – 6 April 1971) was a Russian composer, pianist, and conductor, widely acknowledged as one of the most important and influential composers of 20th century music. He was a quintessentially cosmopolitan Russian who was named by Time magazine as one of the 100 most influential people and of, and Edgard Varèse Edgard Victor Achille Charles Varèse, whose name was also spelled Edgar Varèse , was an innovative French-born composer who spent the greater part of his career in the United States have written music that has been described, in full or in part, as atonal (Baker 1980 & 1986; Bertram 2000; Griffiths 2001; Kohlhase 1983; Lansky and Perle 2001; Obert 2004; Orvis 1974; Parks 1985; Rülke 2000; Teboul 1995–96; Zimmerman 2002).

History

While music without a tonal center had been written previously, for example Franz Liszt Franz Liszt [note 2] (October 22, 1811 – July 31, 1886) was a Hungarian composer, virtuoso pianist and teacher's Bagatelle sans tonalité of 1885, it is with the twentieth century that the term atonality began to be applied to pieces, particularly those written by Arnold Schoenberg Arnold Schoenberg (13 September 1874 – 13 July 1951) was an Austrian and later American composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. He used the spelling Schönberg until after his move to the United States in 1934 (Steinberg 1995, 463), "in deference to American and The Second Viennese School.

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 is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 9th century to present times. The central norms of this tradition became codified between 1550 and 1900, which is known as the common practice period. This situation had come about historically through the increasing use over the course of the nineteenth century of

ambiguous chords, less probable harmonic inflections, and the more unusual melodic and rhythmic inflections possible within the style[s] of tonal music. The distinction between the exceptional and the normal became more and more blurred; and, as a result, there was a concomitant loosening of the syntactical 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. (Meyer 1967, 241)

The first phase, known as "free atonality" or "free chromaticism", involved a conscious attempt to avoid traditional diatonic harmony. Works of this period include the opera Wozzeck Wozzeck is the first opera by the Austrian composer Alban Berg. It was composed between 1914 and 1922 and first performed in 1925. Since then it has established a solid place for itself in the mainstream operatic tradition, and modern productions are consistently sold out. Though its musical style is challenging, the quality of Berg's work amply (1917–1922) by Alban Berg and Pierrot Lunaire (1912) by Schoenberg.

The second phase, begun after World War I World War I was a military conflict that lasted from 1914 to 1918 and involved most of the world's great powers, assembled in two opposing alliances: the Allies and the Central Powers. More than 70 million military personnel, including 60 million Europeans, were mobilized in one of the largest wars in history. More than 15 million people were, 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 Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given. This period included Berg's Lulu and Lyric Suite, Schoenberg's Piano Concerto, his oratorio Die Jakobsleiter and numerous smaller pieces, as well as his last two string quartets. Schoenberg was the major innovator of the system, but his student, Anton Webern Anton Webern was an Austrian composer and conductor. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known exponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of pitch, rhythm and dynamics were formative in the, 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 (Du Noyer 2003, 272). 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. (Westergaard 1963, 109)

Twelve-tone technique, combined with the parametrization Parametrization is the process of deciding and defining the parameters necessary for a complete or relevant specification of a model or geometric object (separate organization of four aspects of music: pitch, attack character, intensity, and duration) of Olivier Messiaen Olivier Messiaen was a French composer, organist and ornithologist, widely regarded as one of the major composers of the 20th century. His music is rhythmically complex (he was interested in rhythms from ancient Greek and from Hindu sources); harmonically and melodically it is based on modes of limited transposition, which he abstracted from his, would be taken as the inspiration for serialism In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of post-tonal thinking (Whittall 2008, 1). Twelve-tone (du Noyer 2003, 272).

Atonality emerged as a pejorative term to condemn music in which chords In music, a chord is any set of harmonically-related notes that is heard as if sounding simultaneously (a "harmonic simultaneity", see Simultaneity ). The most frequently encountered chords in theory and music are triads: major and minor and then the augmented and diminished triads. The descriptions "major", "minor", & were organized seemingly with no apparent coherence. In Nazi Germany Nazi Germany and the Third Reich are the common English names for Germany under the government of Adolf Hitler and the National Socialist German Worker's Party , from 1933 to 1945. Third Reich (German: Drittes Reich) denotes the Nazi state as the historical successor to the mediæval Holy Roman Empire (962–1806) and to the modern German Empire (1, atonal music was attacked as "Bolshevik The Bolsheviks, originally also Bolshevists (Russian: большевики, большевик Russian pronunciation: [bəlʲʂɨˈvʲik], derived from bol'shinstvo, "majority", which comes from bol'she, "more", the comparative form of bol'shoi, "big") were a faction of the Marxist Russian Social Democratic Labour" and labeled as degenerate Degenerate art is the English translation of the German entartete Kunst, a term adopted by the Nazi regime in Germany to describe virtually all modern art. Such art was banned on the grounds that it was un-German or Jewish Bolshevist in nature, and those identified as degenerate artists were subjected to sanctions. These included being dismissed (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 after World War II Albania · Australia · Austria · Azerbaijan · Belarus · Belgium · Brazil · Bulgaria · Burma · Cambodia · Canada · Ceylon (Sri Lanka) · Channel Islands · China · Czechoslovakia · Denmark · Dutch East Indies · Egypt · Estonia · Finland · France · Germany · Gibraltar · Greece · Greenland · Hong Kong · Hungary · Iceland ·.

The Second Viennese School, and particularly 12-tone composition, was taken by avant-garde composers in the 1950s to be the foundation of the New Music, and led to serialism In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of post-tonal thinking (Whittall 2008, 1). Twelve-tone and other forms of musical innovation. Prominent post-World War II composers in this tradition are Pierre Boulez Pierre Boulez (born March 26, 1925) is a French composer of contemporary classical music and a conductor, Karlheinz Stockhausen Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important (Barrett 1988, 45; Harvey 1975b, 705; Hopkins 1972, 33; Klein 1968, 117) but also controversial (Power 1990, 30) composers of the twentieth and early twenty-first centuries. Another critic calls him "one of the great visionaries of 20th-, Luciano Berio, Krzysztof Penderecki Krzysztof Penderecki is a Polish composer and conductor. His 1960 avant-garde Threnody to the Victims of Hiroshima for string orchestra brought him to international attention, and this success was followed by acclaim for his choral St. Luke Passion. Both these works exhibit novel compositional techniques. Since the 1970s Penderecki's style has, and Milton Babbitt Milton Byron Babbitt is an American composer. He is particularly noted for his serial and electronic music. Many composers wrote atonal music after the war, even if before they had pursued other styles, including Elliott Carter Elliott Cook Carter, Jr. is a two-time Pulitzer Prize-winning American composer born and living in New York City. He studied with Nadia Boulanger in Paris in the 1930s, and then returned to the United States. After a neoclassical phase, he went on to write atonal, rhythmically complex music. His compositions, which have been performed all over the and Witold Lutosławski Witold Lutosławski was one of the major European composers of the 20th century, and one of the pre-eminent Polish musicians during his last three decades. During his lifetime, Lutosławski earned many international awards and prizes, including the Order of the White Eagle, Poland's highest honour. After Schoenberg's death, Igor Stravinsky Igor Fyodorovich Stravinsky (17 June [O.S. 5 June] 1882 – 6 April 1971) was a Russian composer, pianist, and conductor, widely acknowledged as one of the most important and influential composers of 20th century music. He was a quintessentially cosmopolitan Russian who was named by Time magazine as one of the 100 most influential people and of began to write music with a mixture of serial and tonal elements (du Noyer 2003, 271). Iannis Xenakis Iannis Xenakis (May 29, 1922 – February 4, 2001) was a Greek composer, music theorist and architect. He is commonly recognized as one of the most important post-war avant-garde composers. Xenakis pioneered the use of mathematical models such as applications of set theory, varied use of stochastic processes, game theory, etc., in music, and was 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 was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy. The single known work of Parmenides is a poem which has survived only in fragmentary form. In this poem, Parmenides describes two views of reality. In The Way of Truth (a part of the (Xenakis 1971, 204).

Free atonality

The twelve tone technique was preceded by Schoenberg's freely atonal pieces of 1908–1923, which, though free, often have as an "integrative element...a minute intervallic cell" 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" (Perle 1977, 2).

The twelve tone technique was also preceded by nondodecaphonic serial composition used independently in the works of Alexander Scriabin Alexander Nikolayevich Scriabin (6 January 1872 [O.S. 25 December 1871]–27 April 1915) was a Russian composer and pianist who initially developed a highly lyrical and idiosyncratic tonal language inspired by the music of Chopin. Unlike the later Roslavets and Schönberg, Scriabin developed, via mysticism, an increasingly atonal musical language, Igor Stravinsky Igor Fyodorovich Stravinsky (17 June [O.S. 5 June] 1882 – 6 April 1971) was a Russian composer, pianist, and conductor, widely acknowledged as one of the most important and influential composers of 20th century music. He was a quintessentially cosmopolitan Russian who was named by Time magazine as one of the 100 most influential people and of, Béla Bartók Béla Viktor János Bartók (pronounced /ˈbɑrtɒk/ , Hungarian pronunciation: [ˈbeːlɒ ˈbɒrtoːk]) (March 25, 1881 – September 26, 1945) was a Hungarian composer and pianist. He is considered to be one of the greatest composers of the 20th century and is regarded, along with Liszt, as his country's greatest composer (Gillies 2001). Through, Carl Ruggles Charles "Carl" Sprague Ruggles was an American composer of the American Five group. He wrote finely-crafted pieces using "dissonant counterpoint", a term coined by Charles Seeger to describe Ruggles' music. His method of atonal counterpoint was based on a non-serial technique of avoiding repeating a pitch class until a, and others (Perle 1977, 37). "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 is a motif or phrase which is persistently repeated in the same musical voice. An ostinato is always a succession of equal sounds. Each note always has the same weight in an ostinato. The repeating idea may be a rhythmic pattern, part of a tune, or a complete melody. Both "ostinatos" and "ostinati" are" (Perle 1977, 37).

Strict atonality

Twelve-tone techniques shares with free atonality premises including the general avoidance of a key or the overemphasis of one note, and some of the rules of twelve-tone technique are designed to ensure this, such as the non-repetition of a pitch before the statement of all other pitches in the row. Twelve-tone practices differ from previous atonal practices in two important ways: all pitches are used and ordered.

Controversy over the term itself

The term "atonality" itself has been controversial. Arnold Schoenberg Arnold Schoenberg (13 September 1874 – 13 July 1951) was an Austrian and later American composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. He used the spelling Schönberg until after his move to the United States in 1934 (Steinberg 1995, 463), "in deference to American, 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. . . . [T]o 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" (Schoenberg 1978, 432). He preferred the term "pantonal."^{[citation needed]} For some, the term continues to carry negative connotations.^{[weasel words]}

"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 progressions. 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.

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 explains that, "the 'free' atonality that preceded dodecaphony precludes by definition the possibility of self-consistent, generally applicable compositional procedures" (Perle 1962, 9). However, he provides one example as a way to compose atonal pieces, a pre-twelve tone technique Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given 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 so that what was not allowed is required and what was required is not allowed. This is what was done by Charles Seeger in his explanation of dissonant counterpoint, which is a way to write atonal counterpoint (Seeger 1930).

Further, Perle agrees with Oster (1960) and Katz (1945) that, "the abandonment of the concept of a root-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" (Perle 1962, 31). 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" (Perle 1962, 1). 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 (DeLone and Wittlich 1975, 362–72).

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" (Perle 1962, 9–10).

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" (Webern 1963, 51). Composer Walter Piston, 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. . . . [T]he 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" (Westergaard 1968, 15).

Criticism of atonal music

Swiss conductor, composer, and musical philosopher Ernest Ansermet, a critic of atonal music, wrote extensively on this in the book Les fondements de la musique dans la conscience humaine (Ansermet 1961), 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 (Mosch 2004, 96). Modern atonal music, incomprehensible to Ansermet, chooses interval relations seemingly at random and cannot achieve such an impact, ethos, or catharsis for an audience.

See also

• Serialism
• Emancipation of the dissonance
• Klangfarbenmelodie

Sources

• Anon. 1994. "Atonal." The Oxford Dictionary of Music, 2nd edition, edited by Michael Kennedy. Oxford & New York: Oxford University Press. ISBN 0198691629
• Ansermet, Ernest. 1961. Les fondements de la musique dans la conscience humaine. 2 v. Neuchâtel: La Baconnière.
• Baker, James M. 1980. "Scriabin's Implicit Tonality". "Music Theory Spectrum" 2:1–18.
• Baker, James M. 1986. The Music of Alexander Scriabin. New Haven: Yale University Press.
• Bertram, Daniel Cole. 2000. "Prokofiev as a Modernist, 1907–1915". PhD diss. New Haven: Yale University.
• DeLone, Peter, and Gary Wittlich (eds.). 1975. Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0-13-049346-5.
• Du Noyer, Paul (ed.). 2003. "Contemporary", in The Illustrated Encyclopedia of Music: From Rock, Jazz, Blues and Hip Hop to Classical, Folk, World and More, pp. 271-272. London: Flame Tree Publishing. ISBN 1-9040-4170-1
• Griffiths, Paul. 2001. "Varèse, Edgard [Edgar] (Victor Achille Charles)". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
• Katz, Adele T. 1945. Challenge to Musical Traditions: A New Concept of Tonality. New York: Alfred A. Knopf, Inc. Reprint edition, New York: Da Capo, 1972.
• Kohlhase, Hans. 1983. "Aussermusikalische Tendenzen im Frühschaffen Paul Hindemiths. Versuch uber die Kammermusik Nr. 1 mit Finale 1921". Hamburger Jahrbuch für Musikwissenschaft 6:183–223.
• Lansky, Paul, and George Perle. 2001. "Atonality §2: Differences between Tonality and Atonality". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
• Lansky, Paul, George Perle, and Dave Headlam. 2001. "Atonality". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
• Meyer, Leonard B. 1967. Music, the Arts, and Ideas: Patterns and Predictions in Twentieth-Century Culture. Chicago and London: University of Chicago Press. (Second edition 1994.)
• Mosch, Ulrich. 2004. Musikalisches Hören serieller Musik: Untersuchungen am Beispiel von Pierre Boulez' «Le Marteau sans maître». Saarbrücken: Pfau-Verag.
• Obert, Simon. 2004. "Zum Begriff Atonalität: Ein Vergleich von Anton Weberns 'Sechs Bagatellen für Streichquartett' op. 9 und Igor Stravinskijs 'Trois pièces pour quatuor à cordes'". In Das Streichquartett in der ersten Hälfte des 20. Jahrhunderts: Bericht über das Dritte Internationale Symposium Othmar Schoeck in Zürich, 19. und 20. Oktober 2001. Schriftenreihe der Othmar Schoeck-Gesellschaft 4, edited by Beat A. Föllmi and Michael Baumgartner. Tutzing: Schneider.
• Orvis, Joan. 1974. "Technical and stylistic features of the piano etudes of Stravinsky, Bartók, and Prokofiev". DMus Piano pedagogy: Indiana University.
• Oster, Ernst. 1960. "Re: A New Concept of Tonality (?)", Journal of Music Theory 4:96.
• Parks, Richard S. 1985. "Tonal Analogues as Atonal Resources and Their Relation to form in Debussy's Chromatic Etude". Journal of Music Theory 29, no. 1 (Spring): 33–60.
• Perle, George. 1962. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern. University of California Press. ISBN 0-520-07430-0.
• Perle, George. 1977. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern. Fourth Edition. Berkeley, Los Angeles, and London: University of California Press. ISBN 0-520-03395-7.
• Rahn, John. 1980. Basic Atonal Theory. New York: Longman, Inc. ISBN 0-582-28117-2.
• Rülke, Volker. 2000. "Bartóks Wende zur Atonalität: Die "Études" op. 18". Archiv für Musikwissenschaft 57, no. 3:240–63.
• Schoenberg, Arnold. 1978. Theory of Harmony, translated by Roy Carter. Berkeley & Los Angeles: University of California Press.
• Seeger, Charles. 1930. "On Dissonant Counterpoint." Modern Music 7, no. 4:25–31.
• Teboul, Jean-Claude. 1995–96. "Comment analyser le neuvième interlude en si♭ du "Ludus tonalis" de Paul Hindemith? (Hindemith ou Schenker?) ". Ostinato Rigore: Revue Internationale d'Études Musicales, nos. 6–7:215–32.
• Webern, Anton. 1963. The Path to the New Music, translated by Leo Black. Bryn Mawr. Pennsylvania: Theodore Presser; London: Universal Edition.
• Westergaard, Peter. 1963. "Webern and 'Total Organization': An Analysis of the Second Movement of Piano Variations, Op. 27." Perspectives of New Music 1, no. 2 (Spring): 107–20.
• Westergaard, Peter. 1968. "Conversation with Walter Piston". Perspectives of New Music 7, no.1 (Fall-Winter) 3-17.
• Xenakis, Iannis. 1971. Formalized Music: Thought and Mathematics in Composition. Bloomington and London: Indiana University Press. Revised edition, 1992. Harmonologia Series No. 6. Stuyvesant, NY: Pendragon Press. ISBN 0-945-19324-6
• Zimmerman, Daniel J. 2002. "Families without Clusters in the Early Works of Sergei Prokofiev". PhD diss. Chicago: University of Chicago.

Further reading

• Beach, David (ed.). 1983. "Schenkerian Analysis and Post-Tonal Music", Aspects of Schenkerian Theory. New Haven: Yale University Press.
• Dahlhaus, Carl. 1966. "Ansermets Polemik gegen Schönberg." Neue Zeitschrift für Musik 127, no. 5:179–83.
• Krausz, Michael. 1984. "The Tonal and the Foundational: Ansermet on Stravinsky". The Journal of Aesthetics and Art Criticism 42:383–86.
• Philippot, Michel. 1964. "Ansermet’s Phenomenological Metamorphoses." Translated by Edward Messinger. Perspectives of New Music 2, no. 2 (Spring-Summer): 129–40. Originally published as "Métamorphoses Phénoménologiques." Critique. Revue Générale des Publications Françaises et Etrangères, no. 186 (November 1962).
• Radano, Ronald M. 1993. New Musical Figurations: Anthony Braxton's Cultural Critique Chicago: University of Chicago Press.

External links

• An Introduction to Atonal Music Analysis by Robert T. Kelly.
• Atonality, Information, and the Politics of Perception by Lee Humphries

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