Cool Math for Hot Music

Part I: Introduction and Short History.- The 'Counterpoint' of Mathematics and Music.- Short History of the Relationship Between Mathematics and Music.- Part II: Sets and Functions.- The Architecture of Sets.- Functions and Relations.- Universal Properties.- Part III: Numbers.- Natural Numbers.- Recursion.- Natural Arithmetic.- Euclid and Normal Forms.- Integers.- Rationals.- Real Numbers.- Roots, Logarithms, and Normal Forms.- Complex Numbers.- Part IV: Graphs and Nerves.- Directed and Undirected Graphs.- Nerves.- Part V: Monoids and Groups.- Monoids.- Groups.- Group Actions, Subgroups, Quotients, and Products.- Permutation Groups.- The Third Torus and Counterpoint.- Coltrane's Giant Steps.- Modulation Theory.- Part VI: Rings and Modules.- Rings and Fields.- Primes.- Matrices.- Modules.- Just Tuning.- Categories.- Part VII: Continuity and Calculus.- Continuity.- Differentiability.- Performance.- Gestures.- Part VIII: Solutions, References, Index.- Solutions of Exercises.- References.- Index.

Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.

• Inteligência artificial
• Música
• Aplicações de negócios
• Matemática aplicada
• Teoria da música e musicologia
• Matemática para cientistas da computação

Counterpoint;Gestures;Harmony;Melody;Music Theory;Rhythm;Rubato