Serialism

Serialism is a technique for composing music that uses sets to describe musical elements, and allows the composer manipulations of those sets to create music. Serialism is often, though not universally, held to begin with Twelve-tone technique which uses a set of the 12 notes of the western chromatic scale to form a row (a nonrepeating arrangement of the 12 tones of the chromatic scale) as the unifying basis for a composition's melody, harmony, structural progressions, and variations.

Important serial composers such as Arnold Schoenberg, Anton Webern, Alban Berg, Karlheinz Stockhausen, Pierre Boulez, Luigi Nono, and Jean Barraqué, went through extended periods of time in which they disciplined themselves always to use some variety of serialism in writing their music. Other composers such as Igor Stravinsky, Benjamin Britten, Aaron Copland, Arvo Pärt, Alfred Schnittke, Dmitri Shostakovich, and even jazz composers used serialism only for particular compositions or only for some sections of pieces.

Basic definition

The use of the word serial in connection with music was introduced by René Leibowitz in 1947 in French, and immediately afterward by Humphrey Searle in English, as an alternative translation of the German Zwölftontechnik Twelve-tone technique or Reihenmusik (row music); independently introduced by Herbert Eimert and Karlheinz Stockhausen into German in 1954 as serielle Musik, with a different meaning, translated into English also as "serial music".

Serialism is most specifically defined as the structural principle according to which a recurring series of ordered elements (normally a set – or 'row' – of pitches or 'pitch classes') which are used in order, or manipulated in particular ways, to give a piece unity. Serialism is often broadly applied to all music written in what Arnold Schoenberg called "The Method of Composing with Twelve Tones related only to one another", or dodecaphony, and methods which evolved from his methods. It is sometimes used more specifically to apply only to music where at least one other element other than pitch is subjected to being treated as a row or series. The term Schoenbergian serialism is sometimes used to make the same distinction between use of pitch series only, particularly if there is an adherence to post-Romantic textures, harmonic procedures, voice-leading and other audible elements of 19th century music. In such usages post-Webernian serialism will be used to denote works which extend serial techniques to other elements of music. Another term used to make the distinction is 12 tone serialism.

Serialism has been described by its practitioners as an extension and formalisation of earlier methods of 'cellular' thematic and motivic unification in classical and romantic music. This extension and formalisation is seen as having been motivated by the intensifying drive towards chromatic saturation and the resulting need to unify without using tonality.

Most serial music is deliberately structured as such. A row may be assembled 'pre-compositionally' (perhaps to embody particular intervallic or symmetrical properties), or it may be derived from a spontaneously invented thematic or motivic idea.

This row or series is used in one form as the "basic set", which constitutes the "center" of gravity for the piece. Each row or series is supposed to have three other forms: retrograde, or the basic set backwards, inverted, or the basic set "upside down" and retrograde-inverted, which is the basic set upside down and backwards. The basic set is usually required to have certain properties, and may have additional restrictions, such as the requirement that it use each interval only once. The most common requirement is that first half and second half of the row not be inversions of each other. The series in itself may be regarded as pre-compositional material: in the process of composition it is manipulated by various means to produce musical material.

Serial composition then involves the creation of classes of musical elements; dividing them into equipotential members, such as steps on the chromatic scale; and then using techniques of serial compostion, presenting the original set or sets in a myriad of forms to create a work of music. Very generally the act of composition per se takes the form of fixing, or otherwise constraining, in the case of indeterminate music, a sequence of units with particular parameters. The composer often uses preexisting sets, such as the chromatic scale.

Composers have often built their pieces from discrete, atomic units – in most cases one just calls them "notes" – that enjoy a fixed identity and status within an extended musical practice and beyond the confines of any one particular composition. (Musique concrète, for instance, would fall outside this rubric.) To these units attach various quantifiable or at least decidable parameters: pitch, loudness, duration, onset time, articulation, timbre, spatial location, etc. Specification of all relevant parameters generally does not capture the full sonic reality as composers generally leave important levels of detail to the performer's art.

The first wave of post-war serialism focused on placing more and more of the musical elements in a piece under serial control. The serial composer takes the act of sequencing as itself a central musical concern, for composer, performer and listener. The serial composer aims to create musical meaning directly out the variation of parameters. This has led many serial composers to adopt a style that allows space for each individual unit to assert its identity, to "speak," often using as a model the "pointilist" style of Webern as an example.

However, this tendency is generally thought to have peaked around 1954, and composers such as Boulez, Stockhausen and Morton Feldman began to look at serial composition as an approach rather than a specific set of techniques. They began describing it as an attitude towards composition rather than a technique or a style; no sharp line divides serial and nonserial music. Xenakis in his early compositions, for example, combines highly parametric thinking using serial techniques with statistical procedures that generate emergent textures, which are not subjected to serial treatment.

Serial procedures were combined with the use of aleatory techniques, sometimes called indeterminate music. Serial procedures were often applied to computer generated music, and many serial musicians were also in the forefront of developing synthesizers and electronic music.

History of serial music

The serialization of rhythm, dynamics, and other elements of music developed after the Second World War by arguing that the twelve-tone music of Arnold Schoenberg and his followers of the Second Viennese School had serialized pitch, and was partly fostered by the work of Olivier Messiaen and his analysis students, including Karel Goeyvaerts and Boulez, in post-war Paris. Twelve-tone music is regarded by some as a sub-category of serialism, whereas others regard serialism to be an outgrowth of twelve-tone music.

Twelve tone music

In the early 20th century composers in the European classical tradition began searching for other ways to organize works of music other than reliance on the ordered system of chords and intervals known as tonality. Many composers used modal organization, and others began to use alternate scales within a tonal context provided by jazz. There was an increasing movement to avoid any particular chord as being central, which was described as atonal or pantonal. Composers seeking to extend this direction in music began to search for ways to compose systematically.

Just after the First World War, Schoenberg began writing pieces with 12-note motifs and using a procedure to "work with the notes of the motif". He analogized this process to the contrapuntal rules of Bach, arguing that as Bach's rules produced tonality without referencing it, so his rules produced a new basic means of structuring music which was not yet understood. It is for this reason that Schoenberg is often referred to as the "founder" or creator of serialism.

While Schoenberg was concerned with the serial ordering of pitch, his student Anton Webern began to relate other aspects of music to the basic row.

The politics of Nazi Germany intruded into the development of the musical idea. With the rise to power of Adolf Hitler and the implementation of "race laws" with regard to ownership, culture and employment, many of the main composers of 12-note music were placed on a list of Entartete musik ("Degenerate music"), the Nazi term for all music that they disapproved of. There were two reasons, one was simply the nature of the composers as "Jewish", the other was the Nazi ideas of art as part of the propaganda arm of the state. Avant-garde forms of art were thus banned, even if the artist was a political adherent of Nazism. With this regime's rise, Arnold Schoenberg was obliged to emigrate, eventually to America in 1933, and his works and those of his students Alban Berg and Anton Webern were banned.

Serialism invented and described

The period after World War II represents the codification of serialism as a body of theory. Most of the major concepts were named, refined, and a series of notational conventions were developed in order to deal with the particular problems of serial composition.

After the Second World War, students of Olivier Messiaen saw Webern's structure, and Messiaen's techniques of parameterization as the next way forward in composition. They began creating individual sets or series for each element of music. The elements thus serially determined included the duration of notes, their dynamics, their orchestration, and many others. They created the term serialism to describe what they were doing, and argued that the Twelve Tone works of Webern, Schoenberg and others were also "serial" works. To differentiate 12 tone works from those with other forms of parameterization, the term "multiple serialism" was used, and if all parameters were serially controlled total serialism. Because of the Nazi repression, some young composers took serialism to be the advancing the cause of Anti-fascism. These included Stockhausen and Boulez. René Leibowitz, as composer, conductor, teacher and author was also influential in claiming the Second Viennese School as being the foundation for modern music. From these figures emerged two influential schools, the School of Paris around Pierre Boulez and a German school around Stockhausen. banana? Schoenberg's arrival in the US in 1933 helped accelerate the acceptance of both twelve tone music, and serialism more generally in American academia, at that time dominated by neo-classicism, though he himself felt his ideas were being discounted. Even before his death in 1951 two major theorists and composers, Milton Babbitt and George Perle, emerged as prominent figures actively involved with the analysis of serial music as well the creation of new works using sometimes radical extensions and revisions of the method. In many cases older composers were influenced to adopt tone rows or other serial procedures by their students, for example, Roger Sessions began to incorporate them in 1952, influenced by Milton Babbitt, who was his student.

In the late 1950s Allen Forte began working on ways to describe atonal harmony, and to combine the methods of Heinrich Schenker, who was an ardent opponent of such music, with the developments in what was then contemporary music. He made extensive use of set notation, pitch classes and families and other terms which would later become standard in the description of serial composition. For example in 1964 he published an article entilted "A Theory of Set-Complexes for Music". In 1973 he published the very influential work The Structure of Atonal Music.

Serialism and high modernism

Serialism, along with John Cage's aleatoric music, was enormously influential in post-war music. Theorists such as George Perle codified serial systems, and his 1962 text Serial Composition and Atonality became a standard work on the origins of serial composition in the work of Schoenberg, Berg and Webern. Declaring itself "revolutionary" and "a new tonality", serialism created an environment where experimentation with sound, in a manner similar to the exploration of pure painting in Abstract Expressionism was at the forefront of composition, which led to increased use of electronics and other applications of mathematical notation to composition, developed by theorists such as the composer and mathematician Milton Babbitt.

Other composers to use serialism include Luigi Nono, who developed similar ideas separately, Roger Reynolds, and Charles Wuorinen, the later works of Igor Stravinsky and the early works of George Rochberg. Major centers for serialism were the Darmstadt School and the "School of Paris" centered around Pierre Boulez.

Several of the composers associated with Darmstadt, notably Karlheinz Stockhausen, Karel Goeyvaerts, and Henri Pousseur developed a form of serialism which initially rejected the recurring rows characteristic of twelve-tone technique, in order to eradicate any lingering traces of thematicism. Schoenberg wrote [citation needed] that the eradication of overt elements of traditional musical unity had been part of the avant-garde project in music since the first decade of the 20th century, and saw these developments as a fulfillment of a broader movement in modern art.

Integral serialism had demanded that all parameters in a work be treated as scaled sets (not necessarily in fixed successions) with an equal right to participate in the compositional process, but beginning in the mid-1950s, Stockhausen and others began to focus on "serial principles" as well as methods. Pieces were structured by closed sets of proportions, a method closely related to one type of art serialism (Bochner 1967, Sykora 1983, Guderian 1985), represented by artists and architects such as Piet Mondrian, Theo van Doesberg, Bart van Leck, Georg van Tongerloo, Richard Paul Lohse, and Burgoyne Diller, who had been seeking to “avoid repetition and symmetry on all structural levels and working with a limited number of elements” (Bandur 2001, 54).

Stockhausen described the final synthesis, where proportions and intervals had replaced harmony (Cott 1973, ^{[verification needed]}) and thematic manipulation in this manner:

So serial thinking is something that's come into our consciousness and will be there forever: it's relativity and nothing else. It just says: Use all the components of any given number of elements, don't leave out individual elements, use them all with equal importance and try to find an equidistant scale so that certain steps are no larger than others. It's a spiritual and democratic attitude toward the world. The stars are organized in a serial way. Whenever you look at a certain star sign you find a limited number of elements with different intervals. If we more thoroughly studied the distances and proportions of the stars we'd probably find certain relationships of multiples based on some logarithmic scale or whatever the scale may be. (Cott 1973, 101)

Igor Stravinsky's adoption of serial techniques offers an example of the level of influence that serialism had after the Second World War. Previously Stravinsky had used series of notes without rhythmic or harmonic implications (Shatzkin: "A Pre-Canticle Serialism in Stravinsky" 1977). Because many of the basic techniques of serial compositon have analogs in traditional counterpoint, uses of inversion, retrograde and retrograde inversion from before the war are not necessarily indicative of Stravinsky adopting Schoenbergian techniques. However with his meeting Robert Craft and acquaintance with younger composers, Stravinsky began to consciously study Schoenberg's music, as well as the music of Webern and later composers, and began to use the techniques in his own work, using, for example, serial techniques applied to fewer than 12 notes. Over the course of the 1950's he used procedures related to Messiaen, Webern and Berg. While it is difficult to label each and every work as "serial" in the strict definition, every major work of the period has clear uses and references to its ideas.

During this period, the concept of serialism influenced not only new compositions but also the scholarly analysis of the classical masters. Adding to their professional tools of sonata form and tonality, scholars began to analyze previous works in the light of serial techniques; for example they found uses of tone rows in previous composers going back to Mozart. In particular, using the analytical tools of serialism, scholars noted that the orchestral outburst that introduces the development section half-way through the last movement of Mozart's next-to-last symphony is a tone row that Mozart punctuates in a very modern and violent episode that Michael Steinberg called "rude octaves and frozen silences" (Steinberg 1998:400).

Furthermore, the organizing principles of serialism inspired mathematical analogues, such as uses of set theory, group theory, operators, and parametrization, for example in the post-war works of Elliott Carter, Iannis Xenakis, and Witold Lutosławski. Likewise, the mathematical analogues in integral serialism were influential in the development of electronic music and synthesized music. The first piece in total serialism may have been Nummer 2 (1951) for 13 instruments by Karel Goeyvaerts, although Milton Babbitt's Three Compositions for Piano (1947) is also credited with being the earliest total serial piece.

Serialism in the present

Reactions to and against serialism

Serialism never found wide favour with classical-music audiences, even though many composers adopted it in various forms. It is no exaggeration to say that it became, in theory at least, the favored means of expression for high modernism beginning around 1950, and for the next two or three decades it continued to be regarded, predominantly in the musical academia of the USA and Germany, as the most important principle of musical construction. Some theorized that it would provide the basis for integration of electronic music and aleatoric music; though in fact the latter, making recourse to chance procedures, evolved partly as a reaction against the over-controlled nature of Total Serialism. The various reactions against Serialism became matters of controversy in musical circles, helping to produce such movements as Minimalism and Neo-Romanticism.

Part of the reason for the centrality of serialism in the debate over the meaning and direction of concert music is that it was far from alone in an attempt to systematize music, and root music theory in the modern age. At the same time that Schoenberg was working on his pantonal ideas, other experimental composers were attempting to define harmony in terms of fundamental and measurable qualities, such as rhythm. This attempt to found music on a more axiomic and rigorous basis formed the background for the introduction of the theories of the late 1940s and early 1950s. In Europe, the style of some serial as well as non-serial music of that time emphasized the determination of all parameters for each note independently, often resulting in widely spaced, isolated "points" of sound, an effect called first in German "punktuelle Musik" ("pointist" or "punctual music"), then in French "musique ponctuelle", but quickly confused with pointillistic (German "pointillistische", French "pointilliste") the familiar term associated with the densely packed dots in paintings of Seurat, despite the fact that the conception was at the opposite extreme (Stockhausen and Frisius 1998, 451).

The debate was often decidedly uncollegial: serial and other forms of avant garde music were condemned as being "not music", while proponents such as Pierre Boulez argued that "music exists in the avant garde or not at all". In the words of Roger Scruton (1997), "the order that exists in [serial compositions] is not an order that can be heard, when we hear the sounds as music." Academic departments often became battlegrounds, with professors trying to tilt the balance one direction or another. Ideologies formed around what constituted progress in music, and the history of music was retold, from different viewpoints, either to support the inevitability of serialism, or conversely to ground tonality in immutable realities.

Some music theorists have criticized serialism on the basis that the compositional strategies employed are often incompatible with the way information is extracted by the human mind from a piece of music. Nicolas Ruwet (1959) was one of the first to criticise serialism through a comparison with linguistic structures. Henri Pousseur (1959) questioned the equivalence made by Ruwet between phoneme and the single note, and suggested that analyses of serial compositions that Ruwet names as exceptions to his criticisms might "register the realities of perception more accurately." Later writers have continued Ruwet's line of reasoning. Fred Lerdahl, for example, outlines this subject further in his essay "Cognitive Constraints on Compositional Systems" (Lerdahl 1988). Lehrdahl has in turn been criticized for excluding "the possibility of other, non-hierarchical methods of achieving musical coherence," and for concentrating on the audibility of tone rows (Grant 2001, 219), and the portion of his essay focussing on Boulez's "multiplication" technique (exemplified in three movements of Le Marteau sans maître) has been challenged on perceptual grounds by Stephen Heinemann (1998). Serialism also spawned a host of other attempts to incorporate process into music, including aleatory, or chance, music, and graphical notations which provided for wide ranging improvisation on the part of musicians. This might seem counter-intuitive given the assertion by many serial composers that serialism was about control over more and more of the score, but, in fact, it arose out of the desires for greater variety and texture to music, as expressed in the arguments in the 1950's over Total Serialism.

Within the community of modern music, exactly what constituted serialism was also a matter of debate. The wide conventional usage, is that the world "serial" music applies to all 12 tone music, which is a "subset" of serial music, and it is this usage that is generally intended in reference works. However, many practitioners, including Roger Sessions and Allen Forte argued that serialism was an historic outgrowth of a search for a new tonality, and that both were subsets of this wider search. Other practitioners of serial music argued that individual elements should not be under serial control, but instead under some form of stochastic patterning, or that the large scale of the composition should be under serial control, but individual events at the selection of the composer, or the performer.

Serialism, because of its focus on process, would give birth to process musics, for example of John Cage and the early Steve Reich works such as Drumming. Some process music would retain the concern for the "liberation of dissonance" that Schoenberg declared to be essential, while other composers would select largely consonant, or non-functionally dissonant materials.

Jazz artists in the middle of the 20th century began to work with serial and 12 tone techniques to expand the palette of jazz music. Most of these attempts were of the compositional nature such as composer-pianist Bill Evans who wrote tunes like "12 Tone Tune". More recently you have the works of American guitarist Bruce Arnold who composes and improvises with 12 tone and serial techniques.

Even 75 years after its creation (or 55, depending on which version of history one subscribes to), serial music maintains its aura of being "difficult" and archetypically "modern". Critics routinely fall into stances which praise or condemn it as a category, and works composed using serial techniques are considered "daring" programming choices. However, for every assertion of uniqueness, there are also critics that argue that fundamentally the much of the music is "very late Romanticism" raised to a very high level, and that it should be played with the same eye to harmonic richness and musical aesthetic.

Theory of serial music

The vocabulary of serialism is rooted in set theory, and uses a quasi-mathematical language to describe how the basic sets are manipulated to produce the final result. Musical set theory is often used to analyze and compose serial music, but may also be used to study tonal music. According to Boulez, "Classical tonal thought is based on a world defined by gravitation and attraction, serial thought on a world which is perpetually expanding." The latter types of metaphors – which seek to closely associate contemporary art with contemporary science – are typical of mid-twentieth century Modern composers.

The basis for serial composition is Schoenberg's twelve-tone technique, where the 12 notes of the basic chromatic scale are organized into a row. This "basic" row is then used to create permutations, that is rows derived from the basic set. The row may be used to produce a set of intervals, or a composer may have wanted to use a particular succession of intervals, from which the original row was created. A row which uses all of the intervals in their ascending form once is an all-interval row. In addition to permutations, the basic row may have some set of notes derived from it which is used to create a new row, these are derived sets.

Because there are tonal chord progressions which use all 12 notes, it is possible to create rows with very strong tonal implications, and even to write tonal music using 12 tone technique, but this is not the norm. Most tone rows contain tonal cells which imply a root pitch, a composer can therefore emphasize or avoid emphasizing the tonal cell.

To serialize other elements of music, a system of quantifying an identifiable element must be created or defined. For example, if duration is to be serialized, then durations are to be specified. If tone colour, then the separate tone colours must be identified, and so on.

The selected set or sets, their permutations and derived sets form the basic material from which the composer works. Some serial works specify as little as possible, to give the composer the maximum amount of freedom when working, other works attempt to pre-compose as much as possible, which, taken to its limit is referred to as automatism.

Composition using pitch-serial methods focuses on each appearance of the collection of twelve chromatic notes, called an aggregate. The principle is that in a row, no element of the aggregate should be reused until all of the other members have been used, and each member must appear only in its place in the series. This rule is violated in numerous works still termed "serial". A work is said to be "aggregate complete" if only one aggregate is sounding at the same time.

An aggregate may be divided into subsets, and all the members of the aggregate not part of any one subset are said to be its complement. A subset is self-complementing if it contains half of the set and its complement is also a permutation of the original subset. This is most commonly seen with hexachords or 6 notes of a basic tone row. A hexachord which is self-complementing for a particular permutatition is referred to as prime combinatorial. A hexachord which is self complementing for all basic permutations – Inversion, Retrograde and Retrograde Inversion – is referred to as all-combinatorial. The concepts of combinatoriality were explored by Schoenberg and Webern, but were rigorously defined and explored in the work of Milton Babbitt.

The composer then presents the aggregate. If only the basic row is serialized, while duration, tone colour and other parameters form free variables in the presentation. If there are multiple serial sets, or if several parameters are associated with the same set, then a presentation will have these values calculated. Large scale design is achieved through the use of combinatorial devices, for example, treating of a subset of the basic set to a series of combinatorial devices. The presentation of an aggregate corresponds to units of music in common practice harmony, in that when the listener has heard all of the materials of the aggregate, they know that new presentation of the aggregate should be expected to begin, with its own combinatorial presentation. The sequence of presentations of aggregates corresponds to the cadential structure of tonal harmony, in that it forms units which are complete unto themselves.

Important composers

References

Bandur, Markus. 2001. Aesthetics of Total Serialism: Contemporary Research from Music to Architecture. Basel, Boston and Berlin: Birkhäuser.
Bochner, Mel. 1967. "The Serial Attitude". Artforum 6, no. 4 (December): 28–33.
Cott, Jonathan. 1973. Stockhausen; Conversations with the Composer, New York: Simon & Schuster.
Forte, Allen. 1973. The Structure of Atonal Music. New Haven and London: Yale University Press.
Forte, Allen. 1998. The Atonal Music of Anton Webern. New Haven: Yale University Press.
Guderian, Dietmar. 1985. “Serielle Strukturen und harmonikale Systeme.” In Vom Klang der Bilder: die Musik in der Kunst des 20. Jahrhunderts, edited by Karin von Maur, 434–37. Munich: Prestel-Verlag.
Grant, Morag Josephine. 2001, Serial Music Serial Aesthetics: Compositional Theory in Post-War Europe. Music in the Twentieth Century, Arnold Whitall, general editor. Cambridge: Cambridge University Press.
Heinemann, Stephen. 1998. "Pitch-Class Set Multiplication in Theory and Practice." Music Theory Spectrum 20, no. 1:72-96.
Lerdahl, Fred. 1988. "Cognitive Constraints on Compositional Systems." In Generative Processes in Music, ed. John Sloboda. Oxford: Oxford University Press. Reprinted in Contemporary Music Review 6, no. 2 (1992):97-121.
Lerdahl, Fred, and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. Cambridge, Mass.: MIT Press.
Perle, George. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg and Webern
Pousseur, Henri. 1959. “Forme et pratique musicales.” Revue Belge de Musicologie 13:98–116. Slightly revised and expanded version, trans. into English as “Music, Form and Practice (An Attempt to Reconcile Some Contradictions)”, Die Reihe 6 (1964): 77–93.
Rahn, John. 1980. Basic Atonal Theory. New York: Schirmer Books.
Ruwet, Nicolas. 1959. “Contradictions du langage sériel.” Revue Belge de Musicologie 13 (1959), 83–97. English trans., as “Contradictions within the Serial Language”, Die Reihe 6 (1964): 65–76.
Savage, Roger, and John Caldell (eds.). 1989. Structure and Sorcery: The Aesthetetics of Post-War Serial Composition and Indeterminancy. [Place]: Garland. ISBN 0-8240-2041-3.
Schoenberg, Arnold. Style and Idea: Selected Writings of Arnold Schoenberg. Edited by Leonard Stein, translated by Leo Black. Berkeley and Los Angeles: University of California Press. ISBN 0-520-05294-3.
Scruton, Roger. 1997. Aesthetics of Music. Oxford: Clarendon Press. ISBN 0-19-816638-9. Quoted in Arved Ashbey, The Pleasure of Modernist Music (University of Rochester Press, 2004) p.122. ISBN 1-58046-143-3.
Smith-Brindle, Reginald. 1966. Serial Composition. London, New York: Oxford University Press.
Steinberg, Michael. 1998. The Symphony: A Listener's Guide. Oxford: Oxford University Press.
Stockhausen, Karlheinz, and Rudolf Frisius. 1998. "Es geht aufwärts". In: Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 391–512. Kürten: Stockhausen-Verlag.
Sykora, Katharina. 1983. Das Phänomen des Seriellen in der Kunst: Aspekte einer künstlerischen Methode von Monet bis zur amerikanischen Pop Art. Würzburg: Könighausen + Neumann.
White, Eric Walter, and Jeremy Noble. 1984. "Stravinsky". In The New Grove Modern Masters. London: Macmillan.

External links

Art of the States: serial/twelve-note serial and/or twelve-note works by American composers.
The tone row in the last movement of Mozart's Symphony No. 40. Beginning at Bar 128 on page 54, the tone row might be the following: B, C, D, Eb, F#, Bb, C#, F, G#, A, E, G -- where the exposition of the last three notes of the tone row trails into the sounding of the A major dominant chord for the d minor development section that follows. The first page of Mozart's Symphony No. 40 can be found at this link.