Connections between maths and music explored in new book
The links between music and maths have been explored in a fascinating new book from former University of Huddersfield lecturer Dr Julia Winterson.
There are strong links between music and mathematics dating back to Pythagoras and beyond. Maths & Music, published by the University of Huddersfield Press, draws together the two disciplines outlining the key methods and concepts that underpin the subjects, spanning the centuries from early examples of musical cryptography, where maths was used to hide messages within music, through to computer music in the 21st Century. In all, the book covers over 200 pieces of music ranging from classical symphonies to electronic dance music with numerous musical excerpts given.
Clearing places on Music BMus are available - discover more
After studying music at Huddersfield Polytechnic, Dr Winterson attended the Royal Academy of Music as a postgraduate clarinettist before returning to Huddersfield to teach music at the town’s then Technical College.
She has subsequently worked for Edexcel, was Head of New Music for renowned music publishers Peters Edition and lectured on music at the university. She has published over 20 books, with Maths & Music following Railways & Music, based on her love of both music and her family’s connections to the railway industry.
“I’ve always enjoyed maths,” explains Dr Winterson, “I enjoyed it at school but after starting it at A level I decided to veer off and do music. I picked it up again when my daughter was doing her GCSEs and I realised that I was still fascinated by it – and in between times the calculator had been invented which opened up many new avenues.
Pop and jazz also show mathematical connections
“I got around to taking maths GCSE in my 50s, and followed it with a degree and a Masters with the Open University. I loved studying maths again because I found it so challenging, and it made me think about all the connections between the two subjects that I like so much.
Dr Julia Winterson
Author of 'Maths & Music'
“On the other hand, I would not subscribe to the theory that those who are musically talented also have a gift for maths, having taught many talented performers who were unable to pass GCSE maths.”
Dr Winterson’s book covers the expected musical bases of classical music, but also shows how pop and jazz show the links between maths and music, referencing acts as diverse as Metallica and John Coltrane.
“The composer Igor Stravinsky argued that the same kind of thinking is employed in both maths and music, while the American mathematician Joel Cohen said that the processes of creation are similar. In both, the most beautiful combination is selected from an infinitude of possibilities and its logical potentials are developed consistently.
Metallica frequently use polyrhythms, change time signatures and make use of metric modulation
“I can really see that, when writing a musical composition, you are going to have to make lots of decisions all based on others, and how things are going to fit together. The end products in maths and music depend for their meaning upon the relationship of their elements, and the order imposed by their creator.
“Mathematical concepts are encountered in much music. The basis of most western music is basically repetition and contrast, so it is not surprising that symmetrical transformations, for example, are frequently found in music.
Popular composers used mathematical approach
“In the 1940s, composer Joseph Schillinger devised his own system of composition based on mathematical principles, feeling that the mathematical approach was more natural because nature was intrinsically mathematical. His methods influenced people as diverse as George Gershwin, Glen Miller and Quincy Jones.”
Some composers consciously based their music on mathematical principles. Another of the composers discussed in Maths & Music, Iannis Xenakis, has had his music performed at the Huddersfield Contemporary Music Festival on many occasions.
“Xenakis coined the phrase ‘stochastic music’, in which musical steps are governed by the rules of probability. He used stochastic processes to determine musical parameters such as pitches, tempi, durations and timbres
“All other books on this subject have been written by mathematicians, looking at music from a mathematical point of view. Although some of the examples of music are similar I look at them from a different perspective giving further insight into the music.
Next book to assess 70 years of pop music
Dr Winterson’s next book, written in conjunction with pop musicians and performers, songwriters and academics from across the country, analyses a selection of songs.
“The analyses are approached from a musical point of view, whereas most books of song analyses so far come from a sociological or historical perspective. Very few get right down to the music. This book will include detailed analyses of thirty pop songs taken from the last seventy years, covering a wide range of styles and genres.”