The Topos of Music: Geometric Logic of Concepts, Theory, and Performance

A-addressed abstract address change affine functions algebraic ambient space analysis appendix arrows automorphism bijection canonical cardinality chapter charts chord classification colimit commutative concept construction coordinates corresponding defined definition denotators diagram discussion dodecaphonic dominance elements endomorphisms Euler example fact fiber product figure finite functor geometric germ gestalt given global compositions Grothendieck topology group action harmonic identifier integer interpretation inversion isomorphism classes lemma lexicographic ordering linear mathematical means melody metrical module complex monoid morphism motif motives musicological naive natural transformation navigation nerve notation objective local compositions onset ontology orbit paradigm paradigmatic parameters perspective pitch classes pitch space poeticity precise predicates projection recursive relation rhythms scale semantic semiosis semiotic sequence shape type simplex sound structure subfunctor Summary surjective symmetry symmetry group theorem tonality topology transformation values