Boulez’s creative analysis: An arcane compositional strategy in the light of mathematical music theory

We investigate part I of the famous composition Structures pour deux pianos by Pierre Boulez with regard to their mathematical construction principles and interpret the analytical results in order to obtain computational schemes for generalized compositions following Boulez’s approach and also in the lines of Boulez’s principle of creative analysis. These generalized schemes are then implemented in rubettes of the software Rubato and yield corresponding compositions. Our analysis confirms the visionary force of Boulez’s innovation in that his matrix methods for part I turn out to be in complete congruence with the category-theoretical situation created by generally addressed points in the spirit of the Yoneda lemma and then systematically used by Alexander Grothendieck.