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The structure of RI-invariant tweleve-tone rows

Published online by Cambridge University Press:  17 February 2009

James A. Fill  and
Alan J. Izenman
James A. Fill
Affiliation:
Department of Statistics, University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637 United States of America
Alan J. Izenman
Affiliation:
Department of Applied Statistics, School of Statistics, University of Minnesota, Saint Paul, Minnesota 55108, United States of America.
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Abstract

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This paper presents an efficient method for generating the class of all twelve-tone rows which are transpositions of their own retrograde-inversions. It is shown here that the members of this class can be obtained from a subclass of those rows whose first six notes are ascending and whose first note is C. The number of twelve-tone rows in this subclass is 192, and a complete listing is given in an appendix to this paper. The theory as developed here can be applied to tone rows having any even number of notes.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 4 , April 1980 , pp. 402 - 417
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Babbitt, Milton, “Twelve-tone invariants as compositional determinants”, The Musical Quart. 46 (1960), 246–259.Google Scholar
[2]Fill, James A. and Izenman, Alan J., “Invariance properties of Schoenberg's tone row system”, J. Austral. Math. Soc. B 21 (1979), 268–282.CrossRefGoogle Scholar
[3]Perle, George, Serial composition and atonality (University of California Press, second edition, 1968).Google Scholar