Maths & Music

After many years as a full-time music lecturer, Julia Winterson worked in qualification development for the exam board Edexcel, followed by several years with the music publisher Peters Edition. She now combines part-time lecturing with freelance writing and research, and has had over twenty books on music published. She has a lifelong interest in trains stemming from idyllic childhood holidays spent at Pool-in-Wharfedale station where her grandfather was the station master.

• Foreword viiRhythm xi1 Rhythmic devices: time signatures, barlines and polyrhythms 12 Mathematical approaches to rhythm usedin the twentieth-century 193 Rhythm systems in music from across the world 37Symmetry 554 Symmetry in music 575 Frieze patterns in music 79Scales 976 Diatonic scales and tuning 997 More scales: whole tone, octatonic, pentatonic,and scales that use microtones 1138 Serialism and the 12-note scale 125Forms and Structure 1399 Canons and fugues 14110 Proportion: Golden Section and the Fibonacci series 15911 Randomness and chance 17712 Fractals and chaos theory 19313 Musical cryptography 21314 Magic squares and Latin squares 22915 Change ringing 249Glossary of musical and mathematical terms 257General index 269Index of composers and their works 277Popular music index 285