TY  - BOOK
AU  - Mazzola,Guerino
AU  - Mannone,Maria
AU  - Pang,Yan
ED  - SpringerLink (Online service)
TI  - Cool Math for Hot Music: A First Introduction to Mathematics for Music Theorists 
T2  - Computational Music Science,
SN  - 9783319429373
AV  - NX260 
U1  - 004 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Computer science
KW  - Music
KW  - Mathematics
KW  - Artificial intelligence
KW  - Application software
KW  - Computer Science
KW  - Computer Appl. in Arts and Humanities
KW  - Mathematics in Music
KW  - Mathematics of Computing
KW  - Artificial Intelligence (incl. Robotics)
N1  - 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
N2  - This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions
UR  - http://148.231.10.114:2048/login?url=http://dx.doi.org/10.1007/978-3-319-42937-3
ER  -