Cool Math for Hot Music A First Introduction to Mathematics for Music Theorists /
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:...
| Main Authors: | , , |
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| Corporate Author: | |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edition: | 1st ed. 2016. |
| Series: | Computational Music Science,
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| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-319-42937-3 |
Table of Contents:
- 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.