Listening by numbers
Where music and mathematics meet
We’ve long recognized the links between mathematics and music. The Ancient Greeks saw the repetition – and the recognition - of patterns in both disciplines as the same interpretation of the world. Plato said that he “would give children music, physics and philosophy, but the most important is music, for in the patterns of the arts are the keys to all learning.”
And the structural links are clear: counting beats and rests, repeating patterns and sequences are found in both maths and music. So are the expressive similarities: formal systems of description, and symbols to stand in for numbers and sounds. Music notation is a symbolic representation of sound in time.
Rhythm is a form of counting. The mathematician Gottfried Leibniz described music as “the sensation of counting without being aware you were counting." And reading music, like reading mathematical notation, needs counting – of the beat, of the number of notes, of pauses and when to come back in when playing in a group.
Mathematician Marcus du Sautoy says “Music is full of mathematics. Rhythm is about exploring the way different numbers interact. Theme and variation exploit ideas of symmetry.”
So much is clear. But, even on a cognitive level, music and maths have much in common.
Cognitive psychologists see three systems of understanding numbers in a child’s development. The first is spatial sense, or the ability to grasp shape and its place in space. This is the basis of geometric forms, and the arrangement of musical sounds in a sound space. Second is subitizing, which is the ability to identify and differentiate between small amounts. This is the intuitive grasp that three things are more than one thing – whether counters or sounds. And, thirdly, numerical representation, which is the ability to estimate larger quantities. This is the system that leads on to using symbols to represent numbers (and notes).
These three fundamental systems converge in children between the ages of three and six. They are the basis of mathematics – spatial reasoning, quantity recognition and judgement of magnitude. And also of music.
Studies have suggested a connection between music and spatial-temporal reasoning. Since music is sound existing in space and usually moving in time, it seems logical that training in music could facilitate spatial-temporal reasoning. And hence, it seems that music education and learning improve mathematical ability.
Rhythm depends on arithmetic, harmony draws from numerical relationships, and the development of musical themes reflects symmetry and geometry. As Stravinsky said: "The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface."
So, neuroscientists have found that music training increases cognitive function significantly. If maths is the science of pattern, then music and movement are the art of pattern. The exploration of music and dance in the early years, works with the human mind’s need for pattern, and helps develop ordering, classifying, sequencing and predicting - the foundations for understanding maths.
Sources: Law, Jane (2018). Mu sic and Numeracy . Numeracy in Authentic Contexts, University of Newcastle
Smith, D. (2020) ‘How can I support learning across the curriculum through effective use of music? . University of Glasgow
Sanders, E. M. (2018) Music Learning and Mathematics Achievement . University of Cambridge.
Various (2019). Numeracy learning progression and The Arts: Music . Australian Curriculum, Assessment and Reporting Authority
du Sautoy, Marcus (2011). Listen by numbers: Music and maths. The Guardian, 27/6/11
Gowers, Tim (2011). The enduring myth of music and maths . The Independent, 6/7/11