Formula composition

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Formula composition is a serially-derived technique encountered in the music of Karlheinz Stockhausen, involving the projection, expansion, and Ausmultiplikation of either a single melody-formula, or a two- or three-voice contrapuntal construction (sometimes stated at the outset). Though foreshadowed in the once-withdrawn Formel of 1951, the technique made its first appearance in Mantra in 1970, and became the central focus of Stockhausen's music up to 2003. Stockhausen's mammoth opera cycle Licht is based on a three-strand "super-formula".

Hermann Conen (1991, 57) identifies two kinds of formula composition in Stockhausen’s works prior to Licht:

formula compositions in which the form results from projection of the formula, . . . [and] works in which melodies in themselves possess many internal characteristics of formulas, but where the formal idea itself does not originate from the formula(s) used in their realisation

Works of the first type include Mantra (1970), Inori (1973–74), Jubiläum (1977), and In Freundschaft (1977); works of the second type comprise Alphabet für Liège (1972), the “Laub und Regen” duet from Herbstmusik (1974), Musik im Bauch (1975), Harlekin (1975), Der kleine Harlekin (1975), and Sirius (1974–75). Other works from the 1970s, such as Sternklang (1971), Trans (1971), Ylem (1972), Atmen gibt das Leben (1974/77), Tierkreis (1974–75), and Amour (1976) do not employ formula technique.

York Höller, who studied with Stockhausen in 1971–72, uses a similar method, which he names Klanggestalt, though at least one writer has used the expression "formula composition" to describe it (Stenzl 1991, 12–15). Finbar O'Súilleabháin points out parallels between the techniques in Höller's opera The Master and Margarita (1984–85) and Stockhausen's Licht cycle (1977–2003), but concludes that, despite the close similarity, Höller's conception is "perfectly distinct" (O'Súilleabháin 1992).

[edit] Sources

Blumröder, Christoph von. 1976. "Karlheinz Stockhausens Mantra für 2 Pianisten. Ein Beispiel für eine symbiotische Kompositionsform." Melos 43, no. 2/Neue Zeitschrift für Musik 137 (March-April): 94–104.
Blumröder, Christoph von. 1982. "Formel-Komposition—Minimal Music—Neue Einfachheit: Musikalische Konzeptionen der siebzigr Jahre." In Neuland Jahrbuch 2 (1981/82), edited by Herbert Henck, 160–78. Bergisch Gladbach: Neuland Verlag.
Conen, Hermann. 1991, Formel-Komposition: Zu Karlheinz Stockhausens Musik der siebziger Jahre. Kölner Schriften zur Neuen Musik 1, ed. Johannes Fritsch and Dietrich Kämper. Mainz: Schott's Söhne.
Hufschmidt, Wolfgang. 1981. "Musik aus Zahlen: Prinzipien der musikalischen Formgestaltung in der seriellen Kompositionspraxis." In Reflexionen über Musik heute, edited by Wilfried Gruhn, 24–57. Mainz: B. Schott’s Söhne.
Kohl, Jerome. 1983–84."The Evolution of Macro- and Micro-Time Relations in Stockhausen's Recent Music." Perspectives of New Music 22:147–85.
Kohl, Jerome. 1990. "Into the Middleground: Formula Syntax in Stockhausen’s Licht." Perspectives of New Music 28, no. 2 (Summer): 262–91.
Kohl, Jerome. 1993. "Time and Light." Contemporary Music Review 7, no. 2:203–19.
Kohl, Jerome. 1994. "Der Aspekt der Harmonik in Licht." In Internationales Stockhausen-Symposion 2000: LICHT. Musikwissenschaftliches Institut der Universität zu Köln, 19. bis 22. Oktober 2000. Tagungsbericht. Edited by Imke Misch and Christoph von Blumröder, 116–32. Münster, Berlin, London: LIT-Verlag.
O'Súilleabháin, Finbar. 1992. [Letter to the Editor]. Tempo New Series, no. 181 (June): 68.
Stenzl, Jürg. 1991. "York Höller's The Master and Margarita: A German Opera." Translated by Sue Rose. Tempo New Series, no. 179 (December): 8–15.