Exploring musical spaces : a synthesis of mathematical approaches / Julian Hook.

Format:

Book

Author/Creator:

Hook, Julian, author.

Series:

Oxford studies in music theory

Language:

English

Subjects (All):

Music theory--Mathematics.

Music theory.

Physical Description:

xviii, 662 pages : illustrations, music ; 26 cm.

Place of Publication:

New York, NY : Oxford University Press, [2023]

Contents:

Machine generated contents note: pt. ONE FOUNDATIONS OF MATHEMATICAL MUSIC THEORY: SPACES, SETS, GRAPHS, AND GROUPS

1. Spaces I: Pitch and Pitch-Class Spaces

1.1. Pitch spaces

1.2. Pitch-class spaces

1.3. Spaces generated by fifths and thirds

1.4. Tonnetz spaces

Notes

Suggested Reading

2. Sets, Functions, and Relations

2.1. Sets

2.2. Ordered sets and multisets

2.3. Functions

2.4. Relations

2.5. Modular arithmetic

2.6. Relationships among modular spaces

3. Graphs

3.1. Graphs

3.2. Isomorphism of graphs

3.3. Loops, multiple edges, and infinite graphs

3.4. Directed graphs

3.5. Transformation graphs and networks

4. Spaces II: Chordal, Tonal, and Serial Spaces

4.1. Double-circle spaces and related constructions

4.2. Tonnetz-related chordal and tonal spaces

4.3. Generic and diatonic chordal spaces

4.4. Some additional models

4.5. Analytical examples

5. Groups I: Interval Groups and Transformation Groups

5.1. The interval and transposition groups of pitch space

5.2. Definition of a group; additive, modular, and multiplicative groups

5.3. Abstract groups; further properties of groups

5.4. Interval groups and interval spaces

5.5. Transformation groups and group actions

5.6. The relation between intervals and transformations

pt. TWO TRANSFORMATION THEORY: INTERVALS AND TRANSFORMATIONS, INCLUDING NEO-RIEMANNIAN THEORY

6. Groups II: Permutations, Isomorphisms, and Other Topics in Group Theory

6.1. Permutation groups

6.2. Group tables and Cayley diagrams

6.3. Isomorphism of groups

6.4. Direct-product groups

6.5. Groups, equivalence relations, and symmetry

6.6. Quotient groups; considerations with non-commutative groups

7. Intervals

7.1. Label functions for interval spaces

7.2. Homomorphisms and isomorphisms of interval spaces

7.3. Direct products of interval spaces

7.4. Quotients of interval spaces

7.5. Transposition operators and interval-preserving mappings

7.6. Inversion operators and interval-reversing mappings

8. Transformations I: Triadic Transformations

8.1. Uniform triadic transformations

8.2. Riemannian UTTs and neo-Riemannian analysis

8.3. Other topics in triadic transformation theory

9. Transformations II: Transformation Graphs and Networks; Serial Transformations

9.1. Transformation graphs and networks: basic properties

9.2. Consistency properties

9.3. Isomorphism and isography

9.4. Klumpenhouwer networks

9.5. Serial transformations and UTTs

9.6. Transformations of pitch dasses and order numbers

pt. THREE GEOMETRIC MUSIC THEORY: THE OPTIC VOICE-LEADING SPACES

10. Spaces III: Introduction to Voice-Leading Spaces

10.1. The hexatonic triad graph as a continuous voice-leading space

10.2. A larger space of three-voice chords

10.3. The OPT/C relations

10.4. Normal forms in OPTIC spaces

11. Spaces IV: The Geometry of OPTIC Spaces

11.1. Manifolds and orbifolds; one-voice spaces

11.2. Two-voice spaces

11.3. Three-voice OP-space

11.4. Three-voice T-, PT-, PTI-, OPT-, and OPTI-space

11.5. Four-voice OP-space

11.6. Four-voice T-, OPT-, and OPT/-space

12. Distances

12.1. Interval functions and measures of distance

12.2. Distance functions; real and modular interval spaces as distance spaces

12.3. Distance functions denned by graphs or groups

12.4. Distance functions on product spaces

12.5. Distance functions on quotient spaces; OPTIC spaces as distance spaces

pt. FOUR THEORY OF SCALES: DIATONIC AND BEYOND

13. Scales I: Diatonic Spaces

13.1. Diatonic and generic scales as musical spaces

13.2. Diatonic scales in chromatic space

13.3. Signature transformations

13.4. Genus and species

Suggested reading

14. Scales II: Beyond the Diatonic

14.1. Seven-note scales and spelled heptachords

14.2. Maximal evenness and the geometry of scales

14.3. Beyond the chromatic: other specific cardinalities

Suggested reading.

Notes:

Includes bibliographical references (pages 631-642) and index.

ISBN:

0190246014

9780190246013

OCLC:

1273075672

Publisher Number:

99992505491