音楽の数学理論 Exploring Musical Spaces : A Synthesis of Mathematical Approaches

著者名：Hook, Julian

Oxford University Press（2021/12/01発売）

• 言語：ENG
• ISBN：9780190246013
• eISBN：9780197577257

Description

Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric modelsthe first examples of the musical spaces of the book's titledepicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.

Table of Contents

PrefaceAcknowledgmentsPart I Foundations of Mathematical Music Theory: Spaces, Sets, Graphs, and GroupsChapter 1: Spaces I: Pitch and Pitch-Class SpacesChapter 2: Sets, Functions, and RelationsChapter 3: GraphsChapter 4: Spaces II: Chordal, Tonal, and Serial SpacesChapter 5: Groups I: Interval Groups and Transformation GroupsPart II Transformation Theory: Intervals and Transformations, including Neo-Riemannian TheoryChapter 6: Groups II: Permutations, Isomorphisms, and Other Topics in Group TheoryChapter 7: IntervalsChapter 8: Transformations I: Triadic TransformationsChapter 9: Transformations II: Transformation Graphs and Networks; Serial TransformationsPart III Geometric Music Theory: The OPTIC Voice-Leading SpacesChapter 10: Spaces III: Introduction to Voice-Leading SpacesChapter 11: Spaces IV: The Geometry of OPTIC SpacesChapter 12: DistancesPart IV Theory of Scales: Diatonic and BeyondChapter 13: Scales I: Diatonic SpacesChapter 14: Scales II: Beyond the DiatonicAppendix 1: List of Musical SpacesAppendix 2: List of Sets and GroupsReferences