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Regards on two regards by Messiaen: Post-tonal music segmentation using pitch context distances in the spiral array 

Author: Elaine Chew a
Affiliation:   a University of Southern California Viterbi School of Engineering, Los Angeles, California, USA
DOI: 10.1080/09298210600578147
Publication Frequency: 4 issues per year
Published in: journal Journal of New Music Research, Volume 34, Issue 4 December 2005 , pages 341 - 354
Formats available: HTML (English) : PDF (English)
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Abstract

This paper describes an O(n) algorithm for segmenting music automatically by pitch context using the Spiral Array, a mathematical model for tonality, and applies it to the segmentation of post-tonal music, namely, Olivier Messiaen's Regards IV and XVI from his Vingt Regards sur l'Enfant Jeacutesus. Using the idea of the centre of effect (c.e.), a summary point in the interior of the Spiral Array, segmentation boundaries map to peaks in the distances between the c.e.'s of adjacent segments of music. The best-case computed boundaries are, on average, within 0.94% (for Regard IV) and 0.11% (for Regard XVI) of their targets.
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