Serialism

In music, serialism is a technique for composition that uses sets to describe musical elements, and allows the manipulation of those sets.Fact|date=May 2008 Serialism is often, though not universally, held to begin with twelve-tone technique, which uses a set of the 12 notes of the chromatic scale to form a row (a fixed sequence of the 12 tones of the chromatic scale) as the unifying basis for a composition's melody, harmony, structural progressions, and variations. When not used synonymously, serialism differs from twelve-tone technique in that any number of elements from any musical dimension (called "parameters"), such as duration, register, dynamics, or timbre, and/or pitches, may be ordered in sets of fewer or more than twelve elements.Fact|date=May 2008 The term "series" should not be confused with the mathematical definition, which nevertheless comes into conjunction when the scales involved are projected from numerical sequences such as the arithmetic series, harmonic series (including its acoustical manifestation as the overtone series and its inversion, the so-called subharmonic series), geometric series, Fibonacci series, or infinity series.

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 Béla Bartók, Luciano Berio, Benjamin Britten, Aaron Copland, Olivier Messiaen, Arvo Pärt, Walter Piston, Alfred Schnittke, Dmitri Shostakovich, Igor Stravinsky, and even some jazz composers such as Yusef Lateef and Bill Evans, used serialism only for some of their compositions or only for some sections of pieces.

Basic definition

The use of the word "serial" in connection with music was first introduced in French by René Leibowitz (1947), and immediately afterward by Humphrey Searle in English, as an alternative translation of the German "Zwölftontechnik" Twelve-tone technique or "Reihenmusik" (row music); it was 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 Notes related only to one another" (Schoenberg 1975, 218; Anon. [n.d.] ), 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.Fact|date=May 2008 In such usages "post-Webernian serialism" will be used to denote works which extend serial techniques to other elements of music. Other terms used to make the distinction are "12-note serialism" for the former, and "integral serialism" for the latter.

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.

Each row or series is said to have three (or five) other canonical forms (the expression is borrowed from mathematics): retrograde (the basic set backwards), inversion (the basic set "upside down"), and retrograde-inversion (the basic set upside down and backwards), to which is sometimes added the M5 (perfect fourth) and M7 (perfect fifth) transformations.Fact|date=May 2008 The basic set is usually required to have certain properties,Vague|date=May 2008 and may have additional restrictions, such as the requirement that it use each interval only once. The series in itself may be regarded as pre-compositional material: in the process of composition it is manipulated by various means to produce the musical substance.Fact|date=May 2008

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 composition, presenting the original set or sets in a myriad of forms to create a work of music.Fact|date=May 2008 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.Fact|date=May 2008

Composers have oftenweasel-inline|date=May 2008 built their pieces from discrete, atomic units—in most cases oneWho?|date=May 2008 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. To these units attach various quantifiable or at least decidable parameters: pitch, loudness, duration, onset time, articulation, timbre, spatial location, etc.Fact|date=May 2008

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 aims to create musical meaning directly out the variation of parameters.Fact|date=May 2008 This has led many serial composersweasel-inline|date=May 2008 to adopt a style that allows space for each individual unit to assert its identity, to "speak," often using a "punctual" or "pointillist" style modelled in part on the music of Webern as an example.Fact|date=May 2008

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

In the early 20th century composers began to struggle against the ordered system of chords and intervals known as "functional tonality", in an effort to find new forms of expression and underlying structural organizing principles ( [http://www.wsu.edu/~delahoyd/20th/music.intro.html Delahoyd [n.d.] ). Many composersweasel-inline|date=May 2008 used modal organization, and othersweasel-inline|date=May 2008 began to use alternate scales, sometimes within a tonal context provided by jazz.Fact|date=May 2008 There was an increasing movement to avoid any particular chord or pitch as being central,Fact|date=May 2008 which was described as atonal or pantonal.Who?|date=May 2008 Some composersweasel-inline|date=May 2008 seeking to extend this direction in music began to search for ways to compose systematically.

erialism 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.Fact|date=May 2008

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.Fact|date=May 2008 Theyweasel-inline|date=May 2008 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. To differentiate these compositions from twelve-tone works, the terms "multiple serialism" or "total serialism" were used.Vague|date=May 2008 René Leibowitz, as composer, conductor, teacher, and author was also influential in claiming the Second Viennese School as being the foundation for modern music.Fact|date=May 2008

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.Fact|date=May 2008 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.Fact|date=May 2008

In the late 1950s Allen Forte began working on ways to describe atonal harmony, making extensive use of set notation, pitch classes and families and other terms which would later become standard in the description of serial composition.Fact|date=May 2008 For example, in 1964 he published an article entilted "A Theory of Set-Complexes for Music". In 1973 he published the very influential workFact|date=May 2008 "The Structure of Atonal Music".

erialism and high modernism

Serialism, along with John Cage's indeterminate music (music composed with the use of chance operations), and Werner Meyer-Eppler's aleatoricism, 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.

Major centers for serialism were the Darmstadt School and the "School of Paris" centered around Pierre Boulez.Fact|date=May 2008

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 (Felder 1977, 92). Instead of a recurring, referential row, "each musical component is subjected to control by a series of numerical proportions" (Morgan 1975, 3). In Europe, the style of some serial as well as non-serial music of the early 1950s 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).

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,Fact|date=May 2008 but beginning in the mid-1950s, Stockhausen and others began to focus on "serial principles" as well as methods.Fact|date=May 2008 Pieces were structured by closed sets of proportions, a method closely related to certain works from the de Stijl and Bauhaus movements in design and architecture called "serial art" by some writers (Bochner 1967, Sykora 1983, Guderian 1985), specifically the paintings of 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 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 1977). Because many of the basic techniques of serial composition 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 1950s 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 the use of row technique in previous composers going back to Mozart (Keller 1955). 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 European piece using total serialism may have been "Nummer 2" (1951) for 13 instruments by Karel Goeyvaerts, although in America Milton Babbitt's "Three Compositions for Piano" (1947) is also credited with being the earliest total serial piece.

Reactions to and against serialism

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) and Ulrich Mosch (2004).

Within the community of modern music, exactly what constituted serialism was also a matter of debate. The conventional English usage is that the word "serial" 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. Nevertheless, a large body of music exists that is called "serial" but does not employ note-rows at all, let alone twelve-tone technique (e.g., Stockhausen's "Stimmung", Pousseur's "Scambi").

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 and nonserial atonal music.

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 by reordering its elements. 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 pitch rows with very strong tonal implications, and even to write tonal music using 12-tone technique. Most tone rows contain subsets that can imply a pitch center; a composer can create music centered on one or more of the row's constituent pitches by emphasizing or avoiding these subsets, respectively, as well as through other, more complex compositional devices (Newlin 1974; Perle 1977).

To serialize other elements of music, a system quantifying an identifiable element must be created or defined (this is called "parametrization", after the term in mathematics). For example, if duration is to be serialized, then a set of durations must be specified. If tone colour, then the a set of separate tone colours must be identified, and so on.

The selected set or sets, their permutations and derived sets form the basic material with which the composer works.

Composition using 12-tone serial methods focuses on each appearance of the collection of twelve chromatic notes, called an aggregate. (Sets of more or fewer pitches, or of elements other than pitch may be treated analogously.) 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".

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 of the canonic operations – Inversion, Retrograde and Retrograde Inversion – is referred to as "all-combinatorial".

The composer then presents the aggregate. 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 may be achieved through the use of combinatorial devices, for example, subjecting a subset of the basic set to a series of combinatorial devices.

Notable composers

*Gilbert Amy
*Louis Andriessen
*Hans Erich Apostel
*Kees van Baaren
*Milton Babbitt
*Don Banks
*Jean Barraqué
*Alban Berg
*Arthur Berger
*Erik Bergman
*Luciano Berio
*André Boucourechliev
*Pierre Boulez
*Martin Boykan
*Jacques Calonne
*Niccolò Castiglioni
*Aldo Clementi
*Aaron Copland
*Luigi Dallapiccola
*Franco Donatoni
*Hanns Eisler
*Karlheinz Essl
*Franco Evangelisti
*Brian Ferneyhough
*Irving Fine
*Wolfgang Fortner
*Roberto Gerhard
*Frans Geysen
*Alberto Ginastera - middle and late periods
*Lucien Goethals
*Karel Goeyvaerts
*Glenn Gould
*Lou Harrison
*Jonathan Harvey
*Hermann Heiss
*Hans Werner Henze
*York Höller
*Heinz Holliger
*Bill Hopkins
*Klaus Huber
*Hanns Jelinek
*Ben Johnston
*Rudolf Kelterborn
*Gottfried Michael Koenig
*Józef Koffler
*Ernst Krenek
*René Leibowitz
*Ingvar Lidholm
*Bruno Maderna
*Ursula Mamlok
*Philippe Manoury
*Donald Martino
*Paul Méfano
*Jacques-Louis Monod
*Robert Morris
*Luigi Nono
*Per Nørgård
*Krzysztof Penderecki - early period
*Barbara Pentland
*Goffredo Petrassi
*Michel Philippot
*Walter Piston
*Henri Pousseur
*Roger Reynolds
*Terry Riley
*George Rochberg - middle period
*Peter Schat
*Dieter Schnebel
*Arnold Schoenberg - middle/late period
*Humphrey Searle
*Mátyás Seiber
*Roger Sessions
*Nikos Skalkottas
*Roger Smalley
*Ann Southam
*Leopold Spinner
*Karlheinz Stockhausen
*Igor Stravinsky - late period
*Richard Swift
*Camillo Togni
*Gilles Tremblay
*Wladimir Vogel
*Anton Webern
*Hugo Weisgall
*Peter Westergaard
*Stefan Wolpe
*Charles Wuorinen
*La Monte Young

References

*Anon. [n.d.] . " [http://www.milkenarchive.org/artists/artists.taf?artistid=191 Arnold Schoenberg] ". Milken Archive: American Jewish Music. (Accessed 22 July 2008)
*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.
*Delahoyd, Michael. [n. d.] . "http://www.wsu.edu/~delahoyd/20th/music.intro.html 20th-Century Music] ". Author's website, Washington State University.
*Felder, David. 1977. “An Interview with Karlheinz Stockhausen.” "Perspectives of New Music" 16, no. 1 (Fall-Winter): 85–101.
*Forte, Allen. 1964. "A Theory of Set-Complexes for Music." "Journal of Music Theory" 8, no. 2 (Winter): 136-84.
*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.
*Gollin, Edward. 2007. "Multi-Aggregate Cycles and Multi-Aggregate Serial Techniques in the Music of Béla Bartók." "Music Theory Spectrum" 29, no. 2 (Fall): 143–76.
*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. ISBN 0521804582
*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.
*Heinemann, Stephen. 1998. "Pitch-Class Set Multiplication in Theory and Practice." "Music Theory Spectrum" 20, no. 1:72-96.
*Keller, Hans. 1955. "Strict Serial Technique in Classical Music." "Tempo" (new series) no. 37 (Autumn): 12-16, 21-24.
*Leibowitz, René. 1947. "Schoenberg et son école: l'étape contemporaine du langage musical". [Paris] : J.B. Janin. (English edition, as "Schoenberg and His School: The Contemporary Stage in the Language of Music". Translated by Dika Newlin. New York: Philosophocal Library, 1949).
*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.
*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.)
* Morgan, Robert. 1975. "Stockhausen's Writings on Music". "Musical Quarterly 61, no. 1 (January): 1–16. Reprinted in the "Musical Quarterly" 75, no. 4 (Winter 1991): 194–206.
*Mosch, Ulrich. 2004. "Musikalisches Hören serieller Musik: Untersuchungen am Beispiel von Pierre Boulez’ «Le Marteau sans maître»". Saarbrücken: Pfau-Verlag.
*Newlin, Dika. 1974. "Secret Tonality in Schoenberg's Piano Concerto." "Perspectives of New Music" 13, no. 1 (Fall-Winter):137-39.
*Perle, George. 1962. "Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern". Berkeley: Univerity of California Press.
*Perle, George. 1977. "Twelve-tone Tonality". Berkeley: University of California Press.
*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. 1975. "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.
*Shatzkin, Merton. 1977. "A Pre-Cantata Serialism in Stravinsky". "Perspectives of New Music" 16, no. 1 (Fall-Winter): 139–43.
*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.
*Straus, Joseph N. 1999. "The Myth of Serial 'Tyranny' in the 1950s and 1960s." "Musical Quarterly" 83:301–43.
*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

* [http://artofthestates.org/cgi-bin/genresearch.pl?genre=serial%2Ftwelve-note Art of the States: serial/twelve-note] serial and/or twelve-note works by American composers.
* The tone row in the [http://www.dlib.indiana.edu/variations/scores/bgn8245/large/sco40045.html#54 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 [http://www.dlib.indiana.edu/variations/scores/bgn8245/large/index.html this link.]