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

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 Jésus. 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.