Cool Math for Hot Music: A First Introduction to Mathematics for Music Theorists

by Guerino Mazzola

Part Introduction and Short History.- The 'Counterpoint' of Mathematics and Music.- Short History of the Relationship Between Mathematics and Music.- Part Sets and Functions.- The Architecture of Sets.- Functions and Relations.- Universal Properties.- Part Numbers.- Natural Numbers.- Recursion.- Natural Arithmetic.- Euclid and Normal Forms.- Integers.- Rationals.- Real Numbers.- Roots, Logarithms, and Normal Forms.- Complex Numbers.- Part Graphs and Nerves.- Directed and Undirected Graphs.- Nerves.- Part 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 Rings and Modules.- Rings and Fields.- Primes.- Matrices.- Modules.- Just Tuning.- Categories.- Part Continuity and Calculus.- Continuity.- Differentiability.- Performance.- Gestures.- Part Solutions, References, Index.- Solutions of Exercises.- References.- Index.

Genres: Music, Mathematics

344 pages, Paperback

Published October 31, 2016

Reviews

[Tom Schulte · Rating 4 out of 5]

...Among the many highlights of this both compact and encompassing work is a detailed analysis of the jazz composition “Giant Steps” of John Coltrane through symmetric groups of chords. Also fascinating is an exploration of “gestures” from the evolution of musical notation to a “mathematical theory of gestures in music” covering the movement of a pianist’s hands in a topological space. It feels like a missed opportunity in this fascinating work to not include here something on the Theremin, controlled without physical contact by two metal antennas allowing the performer to control frequency with one hand’s gestures and amplitude (volume) with the other.

[Look for my entire review up at MAA Reviews.]

[Alan · Rating 4 out of 5]

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