Maths & Music
- Author: Winterson, Julia
Maths & Music
- Author: Winterson, Julia
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About
There are strong links between music and mathematics dating back to Pythagoras and beyond. This book draws together the two disciplines outlining the key methods and concepts that underpin the subjects from one of the earliest uses of a musical cryptogram to computer music in the twenty-first century.
Maths and Music is divided into sections, each one exploring a different mathematical aspect of music: rhythm; symmetry; scales; form and structure; and finally some musical curiosities. Musical examples are taken from across the world, from ancient and medieval music through to popular music of the twenty-first century. In all, the book covers over 200 pieces of music ranging from classical symphonies to electronic dance music with numerous musical excerpts given. There are clear explanations throughout along with glossaries of musical and mathematical terms.
Contents
- Foreword vii
- Rhythm xi
- 1 Rhythmic devices: time signatures, barlines and polyrhythms 1
- 2 Mathematical approaches to rhythm used
- in the twentieth-century 19
- 3 Rhythm systems in music from across the world 37
- Symmetry 55
- 4 Symmetry in music 57
- 5 Frieze patterns in music 79
- Scales 97
- 6 Diatonic scales and tuning 99
- 7 More scales: whole tone, octatonic, pentatonic,
- and scales that use microtones 113
- 8 Serialism and the 12-note scale 125
- Forms and Structure 139
- 9 Canons and fugues 141
- 10 Proportion: Golden Section and the Fibonacci series 159
- 11 Randomness and chance 177
- 12 Fractals and chaos theory 193
- 13 Musical cryptography 213
- 14 Magic squares and Latin squares 229
- 15 Change ringing 249
- Glossary of musical and mathematical terms 257
- General index 269
- Index of composers and their works 277
- Popular music index 285
