Ausmultiplikation (literally, "multiplying-out" [a]) is a German term used by the composer, Karlheinz Stockhausen to describe a technique in which a long note is replaced by shorter " melodic configurations, internally animated around central tones", resembling the ornamental technique of divisions (also called " diminutions") in Renaissance music. Stockhausen first described this technique in connection with his "opus 1", Kontra-Punkte, composed in 1952–53, [1] but in his later formula composition there is a related method of substituting a complete or partial formula for a single tone that is very long in a much slower, "more background" projection of the formula. [2] When this is done at more than one level, the result is reminiscent of a fractal. [3]
Notes and references
Notes
- ^ In German, the term is used to describe a distributive property in elementary algebra.
References
- ^ Stockhausen 1989, pp. 323–224.
- ^ Kohl 1990, p. 281.
- ^ Hartwell 2012, p. 394.
Sources
- Hartwell, Robin. 2012. "Threats and Promises: Lucifer, Hell, and Stockhausen's Sunday from Light". Perspectives of New Music 50, nos. 1 & 2 (Winter–Summer): 393–424. doi: 10.7757/persnewmusi.50.1-2.0393 JSTOR 10.7757/persnewmusi.50.1-2.0393
- Kohl, Jerome. 1990. "Into the Middleground: Formula Syntax in Stockhausen's Licht". Perspectives of New Music 28, no. 2 (Summer): 262–291.
- Stockhausen, Karlheinz. 1989. "Wille zur Form und Wille zum Abenteuer". In his Texte zur Musik 6, edited by Christoph von Blumröder, 320–346. DuMont Dokumente. Cologne: DuMont Buchverlag. ISBN 3-7701-2249-6.
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