Cool math for hot music: a first introduction to mathematics for music theorists
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2016]
|
| Series: | Computational music science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 323 Seiten Illustrationen, Diagramme (überwiegend farbig) |
| ISBN: | 9783319429359 |
Staff View
MARC
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| 245 | 1 | 0 | |a Cool math for hot music |b a first introduction to mathematics for music theorists |c Guerino Mazzola, Maria Mannone, Yan Pang |
| 264 | 1 | |a Cham |b Springer |c [2016] | |
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| 650 | 4 | |a Mathematics of Computing | |
| 650 | 4 | |a Artificial Intelligence (incl. Robotics) | |
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| 650 | 4 | |a Musik | |
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Record in the Search Index
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Contents
Part I Introduction and Short History
1 The ‘Counterpoint’ of Mathematics and Music . . . . 1
1.1 The Idea of a Contrapuntal Interaction. 1
1.2 Formulas and Gestures. 2
1.3 Mathematics and Technology for Music . 2
1.4 Musical Creativity with Mathematics. 3
2 Short History of the Relationship Between Mathematics
and Music. 5
2.1 Pythagoras. 5
2.2 Artes Liberales. 7
2.3 Zarlino. 8
2.4 Zaiyu Zhu. 8
2.5 Mathematics in Counterpoint. 10
2.5.1 An Example for Music Theorists. 11
2.6 Athanasius Kircher. 14
2.7 Leonhard Euler . 17
2.8 Joseph Fourier. 19
2.9 Hermann von Helmholtz. 20
2.10 Wolfgang Graeser . 21
2.11 Iannis Xenakis. 23
2.12 Pierre Boulez and the IRC AM. 24
2.13 American Set Theory. 25
2.13.1 Genealogy. 25
2.13.2 Comments. 28
2.14 David Lewin. 29
2.15 Guerino Mazzola and the IFM. 30
2.15.1 Preparatory Work:
First Steps in Darmstadt and Zürich (1985-1992). 30
xi
Contents
xii
2.15.2 The IFM Association:
The Period Preceding the General Proliferation of the
Internet (1992-1999). 31
2.15.3 The Virtual Institute:
Pure Virtuality (1999-2003). 31
2.15.4 Dissolution of the IFM Association (2004). 32
2.16 The Society for Mathematics and Computation in Music. 33
Part II Sets and Functions
3 The Architecture of Sets. 37
3.1 Some Preliminaries in Logic . 37
3.2 Pure Sets. 38
3.2.1 Boolean Algebra. 45
3.2.2 Xenakis’ Herma. 46
4 Functions and Relations. 49
4.1 Ordered Pairs and Graphs. 49
4.2 Functions. 52
4.2.1 Equipollence. 56
4.3 Relations. 57
5 Universal Properties. 61
5.1 Final and Initial Sets . 61
5.2 The Cartesian Product. 62
5.3 The Coproduct. 63
5.4 Exponentials. 64
5.5 Subobject Classifier. 64
5.6 Cartesian Product of a Family of Sets. 65
Part III Numbers
6 Natural Numbers. 71
6.1 Ordinal Numbers. 72
6.2 Natural Numbers. 73
6.3 Finite Sets. 75
7 Recursion. 77
8 Natural Arithmetic. 83
9 Euclid and Normal Forms . 85
9.1 The Infinity of Prime Numbers. 86
Contents xiii
10 Integers . 89
10.1 Arithmetic of Integers. 90
11 Rationals . . 93
11.1 Arithmetic of Rationals . 96
12 Real Numbers. 99
13 Roots, Logarithms, and Normal Forms .107
13.1 Roots, and Logarithms. 107
13.2 Adic Representations . Ill
14 Complex Numbers.113
Part IV Graphs and Nerves
15 Directed and Undirected Graphs.121
15.1 Directed Graphs.122
15.2 Undirected Graphs. 124
15.3 Cycles. 126
16 Nerves.129
16.1 A Nervous Sonata Construction.133
16.1.1 Infinity of Nervous Interpretations.136
16.1.2 Nerves and Musical Complexity.137
Part V Monoids and Groups
17 Monoids.143
18 Groups.147
19 Group Actions, Subgroups, Quotients, and Products.151
19.1 Actions. 152
19.2 Subgroups and Quotients.154
19.2.1 Classification of Chords of Pitch Classes.157
19.3 Products.158
20 Permutation Groups.163
20.1 Two Composition Methods Using Permutations.166
20.1.1 Mozart’s Musical Dice Game.166
20.1.2 Mannone’s Cubharmonic.167
xiv Contents
21 The Third Torus and Counterpoint.171
21.1 The Third Torus.171
21.1.1 Geometry on T$X4.173
21.2 Music Theory.174
21.2.1 Chord Classification.174
21.2.2 Key Signatures.175
21.2.3 Counterpoint. 175
22 Coltrane’s Giant Steps.181
22.1 The Analysis.183
22.2 The Composition.186
23 Modulation Theory.191
23.1 The Concept of a Tonal Modulation. 192
23.2 The Modulation Theorem.197
23.3 Nerves for Modulation.198
23.4 Modulations in Beethoven’s op. 106.199
23.5 Quanta and Fundamental Degrees.201
Part VI Rings and Modules
24 Rings and Fields.205
24.1 Monoid Algebras and Polynomials.206
24.2 Fields.211
25 Primes . 213
26 Matrices. 217
26.1 Generalities on Matrices.218
26.2 Determinants.222
26.3 Linear Equations.223
27 Modules.225
27.1 Affine Homomorphisms.230
27.2 Free Modules and Vector Spaces.232
27.3 Bonification and Visualization in Modules .234
27.3.1 Creative Ideas from Math:
A Mapping Between Images and Sounds.235
28 Just Tuning.241
28.1 Major and Minor Scales: Zarlino’s Versus Hindemith’s
Explanation.243
28.2 Comparisons between Pythagorean, Just, and 12-tempered
Tuning. 245
28.3 Chinese Tuning Theory.247
Contents
xv
28.3.1 The Original System.247
28.3.2 A System that Is Completely Based on Fifths.247
29 Categories.249
29.1 The Yoneda Philosophy.253
Part VII Continuity and Calculus
30 Continuity. 257
30.1 Generators for Topologies .260
30.2 Euler’s Substitution Theory.262
31 Differentiability.263
32 Performance. 267
32.1 Mathematical and Musical Precision.268
32.2 Musical Notation for Performance.268
32.3 Structure Theory of Performance.270
32.4 Expressive Performance.272
33 Gestures .273
33.1 Western Notation and Gestures.273
33.2 Chinese Gestural Music Notation.275
33.3 Some Remarks on Gestural Performance .276
33.4 Philosophy of Gestures.279
33.5 Mathematical Theory of Gestures in Music.281
33.6 Hypergestures. 283
33.7 Hyper gestures in Complex Time.285
Part VIII Solutions, References, Index
34 Solutions of Exercises.289
34.1 Solutions of Mathematical Exercises.289
34.2 Solutions of Musical Exercises.293
References.297
Index
303 |
| any_adam_object | 1 |
| author | Mazzola, Guerino 1947- Mannone, Maria Pang, Yan 1989- |
| author_GND | (DE-588)120861437 (DE-588)1126203343 (DE-588)1142429288 |
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| dewey-full | 004 |
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| dewey-ones | 004 - Computer science |
| dewey-raw | 004 |
| dewey-search | 004 |
| dewey-sort | 14 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik Musikwissenschaft |
| format | Book |
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| publisher | Springer |
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| series2 | Computational music science |
| spelling | Mazzola, Guerino 1947- Verfasser (DE-588)120861437 aut Cool math for hot music a first introduction to mathematics for music theorists Guerino Mazzola, Maria Mannone, Yan Pang Cham Springer [2016] © 2016 xv, 323 Seiten Illustrationen, Diagramme (überwiegend farbig) txt rdacontent n rdamedia nc rdacarrier Computational music science Computer science Music Computer science / Mathematics Artificial intelligence Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing Artificial Intelligence (incl. Robotics) Informatik Künstliche Intelligenz Mathematik Musik Künstliche Intelligenz (DE-588)4033447-8 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Musiktheorie (DE-588)4040876-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Musiktheorie (DE-588)4040876-0 s Mathematik (DE-588)4037944-9 s Informatik (DE-588)4026894-9 s Künstliche Intelligenz (DE-588)4033447-8 s DE-604 Mannone, Maria Verfasser (DE-588)1126203343 aut Pang, Yan 1989- Verfasser (DE-588)1142429288 aut Erscheint auch als Online-Ausgabe 978-3-319-42937-3 Digitalisierung BSB Muenchen - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029269200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazzola, Guerino 1947- Mannone, Maria Pang, Yan 1989- Cool math for hot music a first introduction to mathematics for music theorists Computer science Music Computer science / Mathematics Artificial intelligence Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing Artificial Intelligence (incl. Robotics) Informatik Künstliche Intelligenz Mathematik Musik Künstliche Intelligenz (DE-588)4033447-8 gnd Informatik (DE-588)4026894-9 gnd Musiktheorie (DE-588)4040876-0 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4033447-8 (DE-588)4026894-9 (DE-588)4040876-0 (DE-588)4037944-9 |
| title | Cool math for hot music a first introduction to mathematics for music theorists |
| title_auth | Cool math for hot music a first introduction to mathematics for music theorists |
| title_exact_search | Cool math for hot music a first introduction to mathematics for music theorists |
| title_full | Cool math for hot music a first introduction to mathematics for music theorists Guerino Mazzola, Maria Mannone, Yan Pang |
| title_fullStr | Cool math for hot music a first introduction to mathematics for music theorists Guerino Mazzola, Maria Mannone, Yan Pang |
| title_full_unstemmed | Cool math for hot music a first introduction to mathematics for music theorists Guerino Mazzola, Maria Mannone, Yan Pang |
| title_short | Cool math for hot music |
| title_sort | cool math for hot music a first introduction to mathematics for music theorists |
| title_sub | a first introduction to mathematics for music theorists |
| topic | Computer science Music Computer science / Mathematics Artificial intelligence Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing Artificial Intelligence (incl. Robotics) Informatik Künstliche Intelligenz Mathematik Musik Künstliche Intelligenz (DE-588)4033447-8 gnd Informatik (DE-588)4026894-9 gnd Musiktheorie (DE-588)4040876-0 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Computer science Music Computer science / Mathematics Artificial intelligence Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing Artificial Intelligence (incl. Robotics) Informatik Künstliche Intelligenz Mathematik Musik Musiktheorie |
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