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Serialism 1

In , serialism is a method or technique of composition (Griffiths 2001, 116) that uses a series of values to manipulate different musical elements. Serialism began primarily Six-element row of rhythmic values used in Variazioni canoniche by with 's twelve-tone (Whittall 2008, 165) technique, though his contemporaries were also working to establish serialism as one example of post-tonal thinking (Whittall 2008, 1). Twelve-tone technique orders the 12 notes of the , forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "parameters"), such as duration, dynamics, and timbre. The idea of serialism is also applied in various ways in the visual arts, design, and architecture (Bandur 2001, 5, 12, 74; Gerstner 1964, passim). The musical use of the word "series" should not be confused with the mathematical term "series."

Integral serialism or total serialism is the use of series for aspects such as duration, dynamics, and register as well as pitch (Whittall 2008, 273). Other terms, used especially in Europe to distinguish post–World War II serial music from twelve-tone music and its American extensions, are general serialism and multiple serialism (Grant 2001, 5–6). such as Arnold Schoenberg, , , , , Luigi Nono, and Jean Barraqué, used serial techniques of one sort or another in most of their music. Other composers such as Béla Bartók, , , , , Arvo Pärt, , Alfred Schnittke, , , 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. Richard Yardumian used a unique variation of the 12-tone scale "different from Schoenberg's" in which "series were derived by alternating major and minor thirds" (Schwartz 2001).

Basic definitions Serialism is a method (Griffiths 2001, 116), "highly specialized technique" (Wörner 1973, 196), or "way" (Whittall 2008, 1) of composition. It may also be considered, "a philosophy of life (Weltanschauung), a way of relating the human mind to the world and creating a completeness when dealing with a subject" (Bandur 2001, 5). However, serialism is not by itself a system of composition, nor is it a style. Neither is pitch serialism necessarily incompatible with tonality, though it is most often used as a means of composing atonal music (Griffiths 2001, 116). "Serial music" is a problematic term because it is used differently in different languages and especially because, shortly after its coinage in French, it underwent essential alterations during its transmission to German (Frisius 1998, 1327). The use of the word "serial" in connection with music was first introduced in French by René Leibowitz (1947), and immediately afterward by in English, as an alternative translation of the German Zwölftontechnik Twelve-tone technique or Reihenmusik (row music); it was independently introduced by and Karlheinz Stockhausen into German in 1954 as serielle Musik, with a different meaning, translated into English also as "serial music". Serialism 2

Twelve-tone serialism Serialism of the first type 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 that 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. In such usages post-Webernian serialism will be used to denote works that 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. The basic set may have additional restrictions, such as the requirement that it use each interval only once.

Non-twelve-tone serialism Rules of analysis derived from twelve-tone theory do not apply to serialism of the second type: "in particular the ideas, one, that the series is an intervallic sequence, and two, that the rules are consistent" (Maconie 2005, 119). Stockhausen, for example, in early serial compositions such as and , "advances in unit sections within which a preordained set of pitches is repeatedly reconfigured. . . . The ’s model for the distributive serial process corresponds to a development of the Zwölftonspiel of " (Maconie 2005, 56), and Goeyvaerts, in such a work as Nummer 4, provides a classic illustration of the distributive function of seriality: 4 times an equal number of elements of equal duration within an equal global time is distributed in the most equable way, unequally with regard to one another, over the temporal space: from the greatest possible coïncidence to the greatest possible dispersion. This provides an exemplary demonstration of that logical principle of seriality: every situation must occur once and only once. (Sabbe 1977, 114) For , after an initial period working with twelve-tone technique in works like Sept Versets (1950) and Trois Chants sacrés (1951), serialism evolved away from this bond in Symphonies pour quinze Solistes [1954–55] and in the Quintette [à la mémoire d’Anton Webern, 1955], and from around the time of Impromptu [1955] encounters whole new dimensions of application and new functions. The twelve-tone series loses its imperative function as a prohibiting, regulating, and patterning authority; its working-out is abandoned through its own constant-frequent presence: all 66 intervallic relations among the 12 pitches being virtually present. Prohibited intervals, like the octave, and prohibited successional relations, such as premature note repetitions, frequently occur, although obscured in the dense contexture. The number twelve no longer plays any governing, defining rôle; the pitch constellations no longer hold to the limitation determined by their formation. The dodecaphonic series loses its significance as a concrete model of shape (or a well-defined collection of concrete shapes) is played out. And the chromatic total remains active only, and provisionally, as a general reference. (Sabbe 1977, 264) Serialism 3

History of serial music Serialism first appeared in the 1920s, with antecedents predating that year. Schoenberg was the composer most decisively involved in devising and demonstrating the fundamentals of twelve-tone serialism, though it is clear it is not the work of just one musician (Whittall 2008, 1). 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 had serialized pitch, and was partly fostered by the work of Olivier Messiaen and his analysis students, including and Boulez, in post-war .

Olivier Messiaen's unordered series for pitch, duration, dynamics, and articulation from the pre-serial Mode de valeurs et d'intensités, upper division only—which Pierre Boulez adapted as an ordered row for his Structures I (Whittall 2008, 178)

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 (Delahoyd [n.d.] [1]).

Serialism and high Serialism, along with '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 codified serial systems, and his 1962 text Serial Composition and became a standard work on the origins of serial composition in the work of Schoenberg, Berg and Webern. Several of the composers associated with , notably Karlheinz Stockhausen, Karel Goeyvaerts, and Henri Pousseur developed a form of serialism that 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). 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, Gerstner 1964, Guderian 1985, Sykora 1983), specifically the paintings of Piet Mondrian, Theo van Doesburg, 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 Serialism 4

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 twelve-tone 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 , uses of inversion, retrograde and 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 and Beethoven (Jalowetz 1944, 387; Keller 1955, passim). 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 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 , , and Witold Lutosławski. Likewise, the mathematical analogues in integral serialism were influential in the development of 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 (1947) is also credited with being the earliest total serial piece. On the other hand, is credited with extending serial controls to parameters other than pitch and to formal planning as early as 1930–33 (Tick 2001).

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 Serialism 5

called "serial" but does not employ note-rows at all, let alone twelve-tone technique (e.g., Stockhausen's , Pousseur's ).

Theory of twelve-tone serial music The vocabulary of serialism eventually became rooted in set theory, and uses a seemingly quasi-mathematical vocabulary 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 that 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 that 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 is to be serialized, then 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 or 6 notes of a basic tone row. A that is self-complementing for a particular permutation is referred to as prime combinatorial. A hexachord that 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. Serialism 6

Notable composers Further information: List of pieces that use serialism and twelve-tone

• • - middle and late periods • - early period • • Lucien Goethals • • • Karel Goeyvaerts • Michel Philippot • Denis ApIvor • • Walter Piston • • Pelle Gudmundsen-Holmgreen • Henri Pousseur • • Cesar Guerra-Peixe • Roger Reynolds • Milton Babbitt • Lou Harrison • • • Jonathan Harvey • - middle period • • • Claudio Santoro • Jean Barraqué • • • Jürg Baur • York Höller • • Alban Berg • • Arnold Schoenberg - considered the founder of serialism • • Bill Hopkins • Humphrey Searle • • • Ruth Crawford Seeger • Luciano Berio • • • • • • André Boucourechliev • • • Pierre Boulez • • • • Rudolf Kelterborn • Ann Southam • • • Leopold Spinner • • Józef Koffler • Karlheinz Stockhausen • Niccolò Castiglioni • • Igor Stravinsky - late period • • René Leibowitz • Robert Suderburg – early period • Aaron Copland • Ingvar Lidholm • • • John McGuire • • • • Gilles Tremblay • • Ursula Mamlok • • Karlheinz Essl • Philippe Manoury • • Franco Evangelisti • • Anton Webern • • Paul Méfano • Hugo Weisgall • Irving Fine • Jacques-Louis Monod • Peter Westergaard • • Robert Morris • • Roberto Gerhard • Luigi Nono • • Frans Geysen • Per Nørgård •

References Serialism 7

[2] • Anon. [n.d.]. "Arnold Schoenberg ". Milken Archive of American • Maconie, Robin. 2005. Other Planets: The Music of Karlheinz Jewish Music. (Accessed 22 July 2008) Stockhausen. Lanham, Maryland, Toronto, Oxford: The Scarecrow Press, Inc. ISBN 0-8108-5356-6 • Bandur, Markus. 2001. Aesthetics of Total Serialism: Contemporary • Meyer, Leonard B. 1967. Music, the Arts, and Ideas: Patterns Research from Music to Architecture. Basel, Boston and : and Predictions in Twentieth-Century Culture. Chicago and Birkhäuser. : University of Chicago Press. (Second edition 1994.) [3] • Bochner, Mel. 1967. "The Serial Attitude". Artforum 6, no. 4 (December): • Morgan, Robert. 1975. "Stockhausen's Writings on Music" . 28–33. (Subscription access) The Musical Quarterly 61, no. 1 (January): 1–16. Reprinted in the Musical Quarterly 75, no. 4 (Winter 1991): 194–206. • Cott, Jonathan. 1973. Stockhausen; Conversations with the Composer, New • Mosch, Ulrich. 2004. Musikalisches Hören serieller Musik: York: Simon & Schuster. Untersuchungen am Beispiel von Pierre Boulez’ «Le Marteau sans maître». Saarbrücken: Pfau-Verlag. [1] • Delahoyd, Michael. [n. d.]. "20th-Century Music ". Author's website, • Newlin, Dika. 1974. "Secret Tonality in Schoenberg's Piano Washington State University. ." Perspectives of New Music 13, no. 1 (Fall-Winter):137-39. • Felder, David. 1977. “An Interview with Karlheinz Stockhausen.” • Perle, George. 1962. Serial Composition and Atonality: An Perspectives of New Music 16, no. 1 (Fall-Winter): 85–101. Introduction to the Music of Schoenberg, Berg, and Webern. Berkeley: University of California Press. • Forte, Allen. 1964. "A Theory of Set-Complexes for Music." Journal of • Perle, George. 1977. Twelve-tone Tonality. Berkeley: 8, no. 2 (Winter): 136-84. University of California Press. • Forte, Allen. 1973. The Structure of Atonal Music. New Haven and • Pousseur, Henri. 1959. “Forme et pratique musicales.” Revue London: Press. Belge de Musicologie 13:98–116. Slightly revised and expanded version, . into English as “Music, Form and Practice (An Attempt to Reconcile Some Contradictions) ”, 6 (1964): 77–93. • Forte, Allen. 1998. The Atonal Music of Anton Webern. New Haven: Yale • Ruwet, Nicolas. 1959. “Contradictions du langage sériel.” University Press. Revue Belge de Musicologie 13 (1959), 83–97. English trans., as “Contradictions within the Serial Language”, Die Reihe 6 (1964): 65–76. [4] • Frisius, Rudolf. 1998. Serielle Musik. In: Die Musik in Geschichte und • Sabbe, Herman. 1977. Het muzikale serialisme als techniek en Gegenwart: allgemeine Enzyklopädie der Musik. Second, newly compiled als denkmethode: Een onderzoek naar de logische en edition, edited by Ludwig Finscher, part 1 (Sachteil), vol. 8 (Quer–Swi): historische samenhang van de onderscheiden toepassingen van 1327–54. Kassel & New York: Bärenreiter; Stuttgart: Metzler. ISBN het seriërend beginsel in de muziek van de periode 1950–1975. 978-3-7618-1109-2 (Bärenreiter) ISBN 978-3-476-41008-5 (Metzler) Ghent: Rijksuniversiteit te Gent. • Gerstner, Karl. 1964. Designing Programmes: Four Essays and an • Schoenberg, Arnold. 1975. Style and Idea: Selected Writings Introduction, with an introduction to the introduction by Paul Gredinger. of Arnold Schoenberg. Edited by Leonard Stein, translated by English version by D. Q. Stephenson. Teufen, Switzerland: Arthur Niggli. Leo Black. Berkeley and Los Angeles: University of California Enlarged, new edition 1968. Press. ISBN 0-520-05294-3.

• Grant, Morag Josephine. 2001. Serial Music Serial Aesthetics: • Schwartz, Steve. 2001. "Richard Yardumian: Orchestral [5] Compositional Theory in Post-War Europe. Music in the Twentieth Works ". Classical Net (Accessed 10 May 2011). Century, Arnold Whitall, general editor. Cambridge: Cambridge University Press. ISBN 0-521-80458-2 • Griffiths, Paul. 2001. "Serialism". The New Grove Dictionary of Music and • Shatzkin, Merton. 1977. "A Pre- Serialism in Musicians, edited by and John Tyrrell, 23:116–23. London: Stravinsky". Perspectives of New Music 16, no. 1 Macmillan; New York: Grove's Dictionaries. (Fall-Winter): 139–43. • Guderian, Dietmar. 1985. “Serielle Strukturen und harmonikale Systeme.” • Smith-Brindle, Reginald. 1966. Serial Composition. London, In Vom der Bilder: die Musik in der Kunst des 20. Jahrhunderts, New York: Oxford University Press. edited by Karin von Maur, 434–37. Munich: Prestel-Verlag. • Heinemann, Stephen. 1998. "Pitch-Class Set Multiplication in Theory and • Steinberg, Michael. 1998. The Symphony: A Listener's Guide. Practice." Music Theory Spectrum 20, no. 1:72-96. Oxford: Oxford University Press. [6] • Jalowetz, Heinrich. 1944. "On the Spontaneity of Schoenberg's Music". • Stockhausen, Karlheinz, and Rudolf Frisius. 1998. "Es geht (Subscription access) The Musical Quarterly 30, no. 4 (October): 385–408. aufwärts". In: Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 391–512. Kürten: Stockhausen-Verlag. Serialism 8

• Keller, Hans. 1955. "Strict Serial Technique in ." Tempo • Straus, Joseph N. 1999. "The Myth of Serial 'Tyranny' in the [7] (new series) no. 37 (Autumn): 12-16, 21-24. 1950s and 1960s " (Subscription access). The Musical Quarterly 83:301–43. • Leibowitz, René. 1947. Schoenberg et son école: l'étape contemporaine du • Sykora, Katharina. 1983. Das Phänomen des Seriellen in der langage musical. [Paris]: J.B. Janin. (English edition, as Schoenberg and Kunst: Aspekte einer künstlerischen Methode von Monet bis His School: The Contemporary Stage in the Language of Music. Translated zur amerikanischen . Würzburg: Könighausen + by Dika Newlin. New York: Philosophocal Library, 1949). Neumann. • Lerdahl, Fred. 1988. "Cognitive Constraints on Compositional Systems." In • Tick, Judith. 2001. "Crawford (Seeger), Ruth (Porter)". The Generative Processes in Music, ed. John Sloboda. Oxford: Oxford New Grove Dictionary of Music and Musicians, second University Press. Reprinted in Contemporary Music Review 6, no. 2 edition, edited by Stanley Sadie and John Tyrrell. London: (1992):97-121. Macmillan Publishers. • Lerdahl, Fred, and Ray Jackendoff. 1983. A Generative Theory of Tonal • Whittall, Arnold. 2008. The Cambridge Introduction to Music. Cambridge, Mass.: MIT Press. Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN 978-0-521-86341-4 (hardback) ISBN 978-0-521-68200-8 (pbk). • Wörner, Karl H. 1973. Stockhausen: Life and Work, introduced, translated, and edited by Bill Hopkins. London: Faber and Faber; Berkeley and Los Angeles: University of California Press. ISBN 0-520-02143-6

Further reading • 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. • Gredinger, Paul. 1955. "Das Serielle". Die Reihe 1 ("Elektronische Musik"): 34–41. English as "Serial Technique", translated by Alexander Goehr. Die Reihe 1 ("Electronic Music"), (English edition 1958): 38–44. • Rahn, John. 1980. Basic Atonal Theory. New York: Schirmer Books. • Savage, Roger W. H. 1989. Structure and Sorcery: The Aesthetetics of Post-War Serial Composition and Indeterminancy. Outstanding Dissertations in Music from British Universities. New York: Garland Publications. ISBN 0-8240-2041-3. • Schoffman, Nathan. 1981. "Serialism in the Works of ". Tempo, new series, no. 138 (September): 21–32. • Scruton, Roger. 1997. . 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. • 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 [8] serial and/or twelve-note works by American composers. • The tone row in the last movement of Mozart's Symphony No. 40 [9]. Beginning at Bar 128 on page 54, the tone row might be the following: B, C, D, E♭, F♯, B♭, 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. [10] Serialism 9

References

[1] http:/ / www. wsu. edu/ ~delahoyd/ 20th/ music. intro. html

[2] http:/ / www. milkenarchive. org/ artists/ artists. taf?artistid=191

[3] http:/ / mq. oxfordjournals. org/ content/ 75/ 4/ 194. full. pdf+ html

[4] http:/ / www. frisius. de/ rudolf/ texte/ tx317. htm

[5] http:/ / www. classical. net/ music/ recs/ reviews/ p/ phx00112a. php

[6] http:/ / mq. oxfordjournals. org/ content/ XXX/ 4/ 385. full. pdf+ html

[7] http:/ / mq. oxfordjournals. org/ content/ 83/ 3/ 301. full. pdf+ html

[8] http:/ / artofthestates. org/ cgi-bin/ genresearch. pl?genre=serial%2Ftwelve-note

[9] http:/ / www. dlib. indiana. edu/ variations/ scores/ bgn8245/ large/ sco40045. html#54

[10] http:/ / www. dlib. indiana. edu/ variations/ scores/ bgn8245/ large/ index. html Article Sources and Contributors 10 Article Sources and Contributors

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