Enumerating indeterminacy

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Bruce Allan Moser (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
John Salmon

Abstract: In much of the indeterminate music composed in the 1950s and 60s, the roles of the composer and performer are blurred, the performer having been given control over musical elements previously dictated solely by the composer. Often, decisions must be made by the performer that impact a work’s form and content, the composer’s quiet voice heard only in the directives influencing these decisions. In many cases, these directives lack specificity, allowing for an infinite number of performance possibilities; in some cases, however, composer directives severely restrict that number, permitting it to be discretely counted. To these latter cases we turn our attention, mathematically modeling the composer’s directives to enumerate all possible realizations of certain indeterminate scores. Taking Morton Feldman’s Durations 2 and Karlheinz Stockhausen’s Klavierstück XI as primary examples, we calculate the total number of possible realizations, generalizing each case in order to enumerate the realizations of other works with similar characteristics.

Additional Information

Language: English
Date: 2009
John Cage, Combinatorics, Morton Feldman, Indeterminacy, Piano, Karlheinz Stockhausen
Piano music $x Analysis, appreciation.
Combinatorial analysis.
Feldman, Morton, $d 1926-1987.
Stockhausen, Karlheinz, $d 1928-2007.

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