Full Description
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
