From music to mathematics: exploring the connections
"Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and - at times - advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music t...
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Baltimore
Johns Hopkins University Press
[2016]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and - at times - advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deepr study of mathematics." |
| Beschreibung: | xviii, 301 Seiten Illustrationen, Notenbeispiele, Diagramme |
| ISBN: | 9781421419183 1421419181 |
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| 505 | 8 | |a Introduction -- 1. Rhythm. Musical notation and a geometric property -- Time signatures -- Polyrhythmic music -- A connection with Indian Classical Music -- 2. Introduction to music theory. Musical notation -- Scales -- Intervals and chords -- Tonality, key signatures, and the Circle of Fifths -- 3. The science of sound. How we hear -- Attributes of sound -- Sine waves -- Understanding pitch -- The monochord Lab: length versus pitch -- 4. Tuning and temperament. The Pythagorean Scale -- Just intonation -- Equal temperament -- Comparing the three systems -- Strähle's guitar -- Alternative tuning systems -- 5. Musical group theory. Symmetry in music -- The Bartók controversy -- Group theory - -6. Change ringing. Basic theory, practice, and examples -- Group theory revisited -- 7. Twelve-tone music. Schoenberg's Twelve-Tone method of composition -- Schoenberg's Suite für Klavier, Op. 25 -- Tone row invariance -- 8. Mathematical modern music. Sir Peter Maxwell Davies: Magic Squares -- Stever Reich: Phase shifting -- Xenakis: Stochastic music -- Final project: A Mathematical Compositio | |
| 520 | |a "Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and - at times - advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deepr study of mathematics." | ||
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Datensatz im Suchindex
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| adam_text | Titel: From music to mathematics
Autor: Roberts, Gareth E
Jahr: 2016
Contents
Preface xi
Acknowledgments xv
Introduction xvii
1 Rhythm 1
1.1 Musical Notation and a Geometrie Property 1
1.1.1 Duration: Geometrie sequences 2
1.1.2 Dots: Geometrie series 4
1.2 Time Signatures 9
1.2.1 Musical examples 10
1.2.2 Rhythmic repetirion 13
1.3 Polyrhythmic Music 17
1.3.1 The least common multiple 19
1.3.2 Musical examples 22
1.4 A Cortnection with Indian Classical Music 28
References for Chapter 1 31
2 Introduction to Music Theory 33
2.1 Musical Notation 34
2.1.1 The common clefs 34
2.1.2 The piano keyboard 37
2.2 Scales 41
2.2.1 Chrom aric scale 42
2.2.2 Whole-tone scale 44
2.2.3 Major scales 45
2.2.4 Minor scales 49
2.2.5 Why are there 12 major scales? 50
2.3 Intervals and Chords 55
2.3.1 Major and perfect intervals 56
2.3.2 Minor intervals and the tritone 57
2.3.3 Chords 59
2.4 Tonality, Key Signatures, and the Circle of Fifths 64
2.4.1 The critical tonic-dominant relationship 65
2.4.2 Key signatures 67
vii
viii______________________________________________________________Contents
2.4.3 The circle of fifths 69
2.4.4 Transposition 72
2.4.5 The evolution of polyphony 74
References for Chapter 2 79
3 The Science of Sound 81
3.1 How We Hear 81
3.1.1 The magnificent ear-brain system 82
3.2 Attributes of Sound 84
3.2.1 Loudness and decibels 84
3.2.2 Frequency 86
3.3 Sine Waves 88
3.3.1 The sine function 89
3.3.2 Graphing sinusoids 91
3.3.3 The harmonic oscillator 94
3.4 Understanding Pitch 97
3.4.1 Residue pitch 98
3.4.2 A vibrating string 104
3.4.3 The overtone series 105
3.4.4 The starting transient 107
3.4.5 Resonance and beats 108
3.5 The Monochord Lab: Length versus Pitch 115
References for Chapter 3 118
4 Tuning and Temperament 119
4.1 The Pythagorean Scale 119
4.1.1 Consonance and integer ratios 120
4.1.2 The spiral of fifths 122
4.1.3 The overtone series revisited 124
4.2 Just Intonation 127
4.2.1 Problems with just Intonation: The syntonic comma 129
4.2.2 Major versus minor 131
4.3 Equal Temperament 133
4.3.1 A conundrum and a compromise 133
4.3.2 Rational and irrational numbers 135
4.3.3 Cents 138
4.4 Comparing the Three Systems 141
4.5 Strähle s Guitar 144
4.5.1 An ingenious construction 145
4.5.2 Continued fractions 149
4.5.3 On the accuracy of Strähle s method 155
4.6 Alternative Tuning Systems 158
4.6.1 The significance of log2(3/2) 158
4.6.2 Meantone scales 159
4.6.3 Other equally tempered scales 161
References for Chapter 4 163
Contents ix
5 Musical Group Theory 165
5.1 Symmetry in Music 165
5.1.1 Symmetrie transformations 166
5.1.2 Inversions 169
5.1.3 Other examples 173
5.2 The Bartok Controversy 182
5.2.1 The Fibonacci numbers and nature 183
5.2.2 The golden ratio 184
5.2.3 Music for Strings, Percussion and Celesta 185
5.3 Group Theory 191
5.3.1 Some examples of groups 192
5.3.2 Multiplication tables 193
5.3.3 Symmetries of the square 195
5.3.4 The musical subgroup of D 197
References for Chapter 5 201
6 Change Ringing 203
6.1 Basic Theory, Practice, and Examples 203
6.1.1 Nomenclature 204
6.1.2 Rules of an extent 205
6.1.3 Three bells 208
6.1.4 The number of permissible moves 210
6.1.5 Example: Piain Bob Minimus 211
6.1.6 Example: Canterbury Minimus 213
6.2 Group Theory Revisited 216
6.2.1 The Symmetrie group S 216
6.2.2 The dihedral group revisited 218
6.2.3 Ringing the cosets 221
6.2.4 Example: Piain Bob Doubles 223
References for Chapter 6 227
7 Twelve-Tone Music 229
7.1 Schoenberg s Twelve-Tone Method of Composition 229
7.1.1 Notation and terminology 230
7.1.2 The tone row matrix 233
7.2 Schoenberg s Suite für Klavier, Op. 25 235
7.3 Tone Row Invariance 238
7.3.1 Using numbers instead of pitches 241
7.3.2 Further analysis: The Symmetrie interval property 242
7.3.3 Tritone symmetry 245
7.3.4 The number of distinet tone rows 248
7.3.5 Twelve-tone music and group theory 249
References for Chapter 7 252
x___________________________________________________________Contents
8 Mathematical Modern Music 253
8.1 Sir Peter Maxwell Davies: Magic Squares 253
8.1.1 Magic Squares 255
8.1.2 Some examples 256
8.1.3 The magic constant 258
8.1.4 AMirrorofWhitening Light 260
8.2 Steve Reich: Phase Shifting 268
8.2.1 Clapping Music 271
8.2.2 Phase shifts 276
8.3 Xenakis: Stochastic Music 278
8.3.1 A Greek architect 278
8.3.2 Metastasis and the Philips Pavilion 279
8.3.3 Pithoprakta: Continuity versus discontinuity 280
8.4 Final Project: A Mathematical Composition 283
References for Chapter 8 287
Credits 289
Index 293
|
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| spelling | Roberts, Gareth E. Verfasser (DE-588)1139448447 aut From music to mathematics exploring the connections Gareth E. Roberts (College of the Holy Cross, Worcester, Massachesetts) Baltimore Johns Hopkins University Press [2016] © 2016 xviii, 301 Seiten Illustrationen, Notenbeispiele, Diagramme txt rdacontent n rdamedia nc rdacarrier Introduction -- 1. Rhythm. Musical notation and a geometric property -- Time signatures -- Polyrhythmic music -- A connection with Indian Classical Music -- 2. Introduction to music theory. Musical notation -- Scales -- Intervals and chords -- Tonality, key signatures, and the Circle of Fifths -- 3. The science of sound. How we hear -- Attributes of sound -- Sine waves -- Understanding pitch -- The monochord Lab: length versus pitch -- 4. Tuning and temperament. The Pythagorean Scale -- Just intonation -- Equal temperament -- Comparing the three systems -- Strähle's guitar -- Alternative tuning systems -- 5. Musical group theory. Symmetry in music -- The Bartók controversy -- Group theory - -6. Change ringing. Basic theory, practice, and examples -- Group theory revisited -- 7. Twelve-tone music. Schoenberg's Twelve-Tone method of composition -- Schoenberg's Suite für Klavier, Op. 25 -- Tone row invariance -- 8. Mathematical modern music. Sir Peter Maxwell Davies: Magic Squares -- Stever Reich: Phase shifting -- Xenakis: Stochastic music -- Final project: A Mathematical Compositio "Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and - at times - advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deepr study of mathematics." Music / Mathematics Music and geometry Music / Acoustics and physics Music theory Music / Acoustics and physics fast Music and geometry fast Music / Mathematics fast Music theory fast Mathematik Musik Mathematik (DE-588)4037944-9 gnd rswk-swf Musik (DE-588)4040802-4 gnd rswk-swf Musik (DE-588)4040802-4 s Mathematik (DE-588)4037944-9 s DE-604 Erscheint auch als Online-Ausgabe, ebook 978-1-4214-1919-0 Erscheint auch als Online-Ausgabe, ebook 1-4214-1919-X HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028918190&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roberts, Gareth E. From music to mathematics exploring the connections Introduction -- 1. Rhythm. Musical notation and a geometric property -- Time signatures -- Polyrhythmic music -- A connection with Indian Classical Music -- 2. Introduction to music theory. Musical notation -- Scales -- Intervals and chords -- Tonality, key signatures, and the Circle of Fifths -- 3. The science of sound. How we hear -- Attributes of sound -- Sine waves -- Understanding pitch -- The monochord Lab: length versus pitch -- 4. Tuning and temperament. The Pythagorean Scale -- Just intonation -- Equal temperament -- Comparing the three systems -- Strähle's guitar -- Alternative tuning systems -- 5. Musical group theory. Symmetry in music -- The Bartók controversy -- Group theory - -6. Change ringing. Basic theory, practice, and examples -- Group theory revisited -- 7. Twelve-tone music. Schoenberg's Twelve-Tone method of composition -- Schoenberg's Suite für Klavier, Op. 25 -- Tone row invariance -- 8. Mathematical modern music. Sir Peter Maxwell Davies: Magic Squares -- Stever Reich: Phase shifting -- Xenakis: Stochastic music -- Final project: A Mathematical Compositio Music / Mathematics Music and geometry Music / Acoustics and physics Music theory Music / Acoustics and physics fast Music and geometry fast Music / Mathematics fast Music theory fast Mathematik Musik Mathematik (DE-588)4037944-9 gnd Musik (DE-588)4040802-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4040802-4 |
| title | From music to mathematics exploring the connections |
| title_auth | From music to mathematics exploring the connections |
| title_exact_search | From music to mathematics exploring the connections |
| title_full | From music to mathematics exploring the connections Gareth E. Roberts (College of the Holy Cross, Worcester, Massachesetts) |
| title_fullStr | From music to mathematics exploring the connections Gareth E. Roberts (College of the Holy Cross, Worcester, Massachesetts) |
| title_full_unstemmed | From music to mathematics exploring the connections Gareth E. Roberts (College of the Holy Cross, Worcester, Massachesetts) |
| title_short | From music to mathematics |
| title_sort | from music to mathematics exploring the connections |
| title_sub | exploring the connections |
| topic | Music / Mathematics Music and geometry Music / Acoustics and physics Music theory Music / Acoustics and physics fast Music and geometry fast Music / Mathematics fast Music theory fast Mathematik Musik Mathematik (DE-588)4037944-9 gnd Musik (DE-588)4040802-4 gnd |
| topic_facet | Music / Mathematics Music and geometry Music / Acoustics and physics Music theory Mathematik Musik |
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