Mathematical music theory: algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena
Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scho...
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| Format: | Buch |
| Sprache: | English |
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New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2019]
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| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself. The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. (Klappentext) |
| Beschreibung: | xvii, 352 Seiten Illustrationen, Diagramme, Notenbeispiele |
| ISBN: | 9789813235304 |
Internformat
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| 245 | 1 | 0 | |a Mathematical music theory |b algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena |c editors: Mariana Montiel (Georgia State University, USA), Robert W. Peck (Louisiana State University, USA) |
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| 505 | 8 | |a From musical chords to twin primes / Jack Douthett, David Clampitt & Norman Carey -- Hypercubes and the generalized Cohn cycle / Jack Douthett, Peter Steinbach & Rick Hermann -- Associahedra, combinatorial block designs and related structures / Franck Jedrezejewski -- Rythmic and melodic l-canons / Jeremy Kastine -- The Fibonacci sequence es metric suspension in Luigi Nono's Il canto sospeso / Jon Kochavi -- Note samba : navigating notes and their meanings within modes and exo-modes / Thomas Noll -- Difference sets and all-directed-interval chords / Robert W. Peck -- Harmonious opposition / Richard Plotkin -- Orbifold path models for voice leading : dealing with doubling / James R. Hughes -- Remarks on the geometry of chords / Thomas A. Ivey -- Theoretical physics and category theory as tools for analysis of musical performance and composition / Maria Mannone -- Intuitive musical homotopy / Aditya Sivakumar & Dmitri Tymoczko -- Geometric generalizations of the Tonnetz and their relation to Fourier phases space / Jason Yust -- Deterministic geometries : a technique for the systematic generation of musical elements in composition / Brent A. Milam -- Flamenco music and its computational study / Francisco Gómez -- Examining fixed and relative similarity metrics through jazz melodies / David J. Baker & Daniel Shanahan -- In search of arcs of prototypicality / Daniel Shanahan | |
| 520 | |a Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself. The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. (Klappentext) | ||
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Datensatz im Suchindex
| _version_ | 1805066585260425216 |
|---|---|
| adam_text |
Contents
Introduction v
About the Editors xiii
Section I 1
1. From Musical Chords to Twin Primes 3
Jack Douthettj David Clampitt and Norman Carey
2. Hyper cubes and the Generalized
Cohn Cycle 21
Jack Douthett, Peter Steinbach
and Richard Hermann
3. Associahedra, Combinatorial Block Designs
and Related Structures 47
Franck Jedrzejewski
4. Rhythmic and Melodic L-canons 65
Jeremy Kastine
5. The Fibonacci Sequence as Metric
Suspension in Luigi Nono’s
II Canto Sospeso 83
Jon Kochavi
XV
XVI
Contents
6. One Note Samba: Navigating Notes
and Their Meanings Within Modes
and Exo-modes 109
Thomas Noll
7. Difference Sets and All-Directed-Interval
Chords 147
Robert W. Peck
8. Harmonious Opposition 167
Richard Plotkin
Section II 183
9. Orbifold Path Models for Voice Leading:
Dealing with Doubling 185
James R. Hughes
10. Reflections on the Geometry of Chords 195
Thomas A. Ivey
11. Theoretical Physics and Category Theory
as Tools for Analysis of Musical
Performance and Composition 215
Maria Mannone
12. Intuitive Musical Homotopy 233
Aditya Sivakumar and Dmitri Tymoczko
13. Geometric Generalizations of the Tonnetz
and Their Relation to Fourier Phases Spaces 253
Jason Yust
14. Deterministic Geometries: A Technique
for the Systematic Generation of Musical
Elements in Composition 279
Brent A. Milam
Contents xvii
Section III 301
15. Flamenco Music and Its Computational Study 303
Francisco Gomez
16. Examining Fixed and Relative Similarity
Metrics Through Jazz Melodies 319
David J. Baker and Daniel Shanahan
17. In Search of Arcs of Prototypicality 335
Daniel Shanahan
Index
347 |
| any_adam_object | 1 |
| author2 | Montiel, Mariana ca. 20./21. Jh Peck, Robert W. 1963- |
| author2_role | edt edt |
| author2_variant | m m mm r w p rw rwp |
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| author_facet | Montiel, Mariana ca. 20./21. Jh Peck, Robert W. 1963- |
| building | Verbundindex |
| bvnumber | BV045242610 |
| classification_rvk | LR 57780 |
| contents | From musical chords to twin primes / Jack Douthett, David Clampitt & Norman Carey -- Hypercubes and the generalized Cohn cycle / Jack Douthett, Peter Steinbach & Rick Hermann -- Associahedra, combinatorial block designs and related structures / Franck Jedrezejewski -- Rythmic and melodic l-canons / Jeremy Kastine -- The Fibonacci sequence es metric suspension in Luigi Nono's Il canto sospeso / Jon Kochavi -- Note samba : navigating notes and their meanings within modes and exo-modes / Thomas Noll -- Difference sets and all-directed-interval chords / Robert W. Peck -- Harmonious opposition / Richard Plotkin -- Orbifold path models for voice leading : dealing with doubling / James R. Hughes -- Remarks on the geometry of chords / Thomas A. Ivey -- Theoretical physics and category theory as tools for analysis of musical performance and composition / Maria Mannone -- Intuitive musical homotopy / Aditya Sivakumar & Dmitri Tymoczko -- Geometric generalizations of the Tonnetz and their relation to Fourier phases space / Jason Yust -- Deterministic geometries : a technique for the systematic generation of musical elements in composition / Brent A. Milam -- Flamenco music and its computational study / Francisco Gómez -- Examining fixed and relative similarity metrics through jazz melodies / David J. Baker & Daniel Shanahan -- In search of arcs of prototypicality / Daniel Shanahan |
| ctrlnum | (OCoLC)1083294298 (DE-599)HBZHT019728230 |
| discipline | Musikwissenschaft |
| format | Book |
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| isbn | 9789813235304 |
| language | English |
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| spelling | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena editors: Mariana Montiel (Georgia State University, USA), Robert W. Peck (Louisiana State University, USA) New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2019] © 2019 xvii, 352 Seiten Illustrationen, Diagramme, Notenbeispiele txt rdacontent n rdamedia nc rdacarrier From musical chords to twin primes / Jack Douthett, David Clampitt & Norman Carey -- Hypercubes and the generalized Cohn cycle / Jack Douthett, Peter Steinbach & Rick Hermann -- Associahedra, combinatorial block designs and related structures / Franck Jedrezejewski -- Rythmic and melodic l-canons / Jeremy Kastine -- The Fibonacci sequence es metric suspension in Luigi Nono's Il canto sospeso / Jon Kochavi -- Note samba : navigating notes and their meanings within modes and exo-modes / Thomas Noll -- Difference sets and all-directed-interval chords / Robert W. Peck -- Harmonious opposition / Richard Plotkin -- Orbifold path models for voice leading : dealing with doubling / James R. Hughes -- Remarks on the geometry of chords / Thomas A. Ivey -- Theoretical physics and category theory as tools for analysis of musical performance and composition / Maria Mannone -- Intuitive musical homotopy / Aditya Sivakumar & Dmitri Tymoczko -- Geometric generalizations of the Tonnetz and their relation to Fourier phases space / Jason Yust -- Deterministic geometries : a technique for the systematic generation of musical elements in composition / Brent A. Milam -- Flamenco music and its computational study / Francisco Gómez -- Examining fixed and relative similarity metrics through jazz melodies / David J. Baker & Daniel Shanahan -- In search of arcs of prototypicality / Daniel Shanahan Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself. The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. (Klappentext) Musik (DE-588)4040802-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Music / Mathematics Music theory / Mathematics Musical analysis (DE-588)4143413-4 Aufsatzsammlung gnd-content Musik (DE-588)4040802-4 s Mathematik (DE-588)4037944-9 s DE-604 Montiel, Mariana ca. 20./21. Jh. (DE-588)1064779018 edt Peck, Robert W. 1963- (DE-588)1043470131 edt Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030630786&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena From musical chords to twin primes / Jack Douthett, David Clampitt & Norman Carey -- Hypercubes and the generalized Cohn cycle / Jack Douthett, Peter Steinbach & Rick Hermann -- Associahedra, combinatorial block designs and related structures / Franck Jedrezejewski -- Rythmic and melodic l-canons / Jeremy Kastine -- The Fibonacci sequence es metric suspension in Luigi Nono's Il canto sospeso / Jon Kochavi -- Note samba : navigating notes and their meanings within modes and exo-modes / Thomas Noll -- Difference sets and all-directed-interval chords / Robert W. Peck -- Harmonious opposition / Richard Plotkin -- Orbifold path models for voice leading : dealing with doubling / James R. Hughes -- Remarks on the geometry of chords / Thomas A. Ivey -- Theoretical physics and category theory as tools for analysis of musical performance and composition / Maria Mannone -- Intuitive musical homotopy / Aditya Sivakumar & Dmitri Tymoczko -- Geometric generalizations of the Tonnetz and their relation to Fourier phases space / Jason Yust -- Deterministic geometries : a technique for the systematic generation of musical elements in composition / Brent A. Milam -- Flamenco music and its computational study / Francisco Gómez -- Examining fixed and relative similarity metrics through jazz melodies / David J. Baker & Daniel Shanahan -- In search of arcs of prototypicality / Daniel Shanahan Musik (DE-588)4040802-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4040802-4 (DE-588)4037944-9 (DE-588)4143413-4 |
| title | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena |
| title_auth | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena |
| title_exact_search | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena |
| title_full | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena editors: Mariana Montiel (Georgia State University, USA), Robert W. Peck (Louisiana State University, USA) |
| title_fullStr | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena editors: Mariana Montiel (Georgia State University, USA), Robert W. Peck (Louisiana State University, USA) |
| title_full_unstemmed | Mathematical music theory algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena editors: Mariana Montiel (Georgia State University, USA), Robert W. Peck (Louisiana State University, USA) |
| title_short | Mathematical music theory |
| title_sort | mathematical music theory algebraic geometric combinatorial topological and applied approaches to understanding musical phenomena |
| title_sub | algebraic, geometric, combinatorial, topological and applied approaches to understanding musical phenomena |
| topic | Musik (DE-588)4040802-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Musik Mathematik Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030630786&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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