Abstract
Frequently minimal music, particularly the sub-species referred to as “repetitive music,” turns around in loops. I never really wrote repetitive music, but I’ve written an awful lot of musical loops, and there are a great many ways of doing this. Most of the loops we’ll be discussing here might better be called “rhythmic canons”, a term introduced in Perspectives of New Music in 1991-1992 in an article by the Rumanian mathematician and music theorist Dan Tudor Vuza. Basically this article has to do with rhythms that repeat canonically in such a way that every point in time is touched exactly once by one of the voices.
“Rational Melody No. 15” from Tom Johnson: Rational Melodies. New World Records #80705-2 (P) 2008 © 2008 Anthology of Recorded Music. Inc. Used by permission
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References
Amiot, E. 2009. Autosimilar melodies. Journal of Mathematics and Music 3(1): 1–26.
Vuza, D.T. 1991–1993. Supplementary sets and regular complementary unending canons. Perspectives of New Music Part 1, 29(2), Part 2, 30(1), Part 3, 30(2), Part 4, 31(1) .
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Amiot, E. 2011. Algorithms and algebraic tools for rhythmic canons structures. Perspectives of New Music 40(2): 93–142.
Davalan, J.P. 2011. Perfect rhythmic tilings. Perspectives of New Music 40(2): 144–197.
Further Reading
Coven, E., and A. Meyerowitz. 1999. Tiling the integers with translate of one finite set. Journal of Algebra 212: 161–174.
Feldman, D. 1996. Review of self-similar melodies by Tom Johnson. Leonardo Music Journal 8: 80–84.
F. Jedrzejewski. 2006. Mathematical theory of music. Paris: Ircam Delatour.
Szabó, S. 1985. A type of factorization of finite abelian groups. Discrete Mathematics 54: 121–124.
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Johnson, T., Jedrzejewski, F. (2014). Loops. In: Looking at Numbers. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0554-4_9
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DOI: https://doi.org/10.1007/978-3-0348-0554-4_9
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