What connects Music with Mathematics?

Town Hall Symphony Hall invited Finance and Accounting student and current Digital Content Intern Hanzala Khan to explore the connection between Maths and Music.

The relationship between music and maths has actually been considered for thousands of years now. Pythagoras, an ancient philosopher and mathematician famously stated there is geometry in the humming of the strings, there is music in the spacing of the spheres.” Although some may interpret this statement as poetry, Pythagoras was actually making a direct comment on the relationship between music and mathematics.

Elements of music including form, rhythm and meter can be closely associated with the measurement of time where we often use symbols and numbers in both music and maths to relay information. For example, the fraction symbol used to define quantities in maths can also indicate the length of a note within the music world.  

Music has a lot in common with mathematics. But in music, two and two need not make four, they add up to whatever you wish.

Jascha Heifetz

The Fibonacci Sequence

Just as notes and rhythms are not all there is to music, arithmetic and counting are not all there is to mathematics. Mathematics is about structure and pattern. You could draw countless links between a composer and mathematician– both drawn to the intricate structure of a composition.


The Fibonacci sequence refers to a number sequence where the next number is created by adding the two previous numbers before it for example 0 + 1 = 1 , then 1 + 1 = 2. YouTuber David MacDonald used this mathematical sequence to influence his own piano piece by assigning numbers to the E major scale.

Mozart’s piano sonata #1 in C major K279 uses the Fibonacci sequence through what is referred to as the Golden ratio. The Golden ratio is the ratio (1.6) between numbers in the Fibonacci sequence and Mozart used this to influence his piano concerto so that the movement from the Exposition to the Development and Recapitulation equalled exactly the golden ratio.

When he was doing sums, the table, the chair, the walls and even the floor would be covered with chalked numbers.

Johan A. Schachtner, a friend of the Mozart family

The Mozart Effect

The Mozart Effect suggests that listening to Mozart’s music can increase Spatial-temporal reasoningthe ability to manipulate figures, use problem-solving skills and the improvement of other short-term mental tasks often associated to maths.

The term was first coined by Alfred A. Tomatis and suggests that Mozart’s music could promote healing and the development of the brain. In a 1992 study at the University of California it was also discovered that college students performed better on a maths test while listening to Mozart than those who hadn't.

Bach's Goldberg Variations depend on games of symmetry to create the progression from theme to variation. Messiaen is drawn to prime numbers to create a sense of unease and timelessness in his famous Quartet for the End of Time.

The Guardian

Personally, I’ve always seen a link between music and maths – it is a beautiful symphony of patterns, trends and formulae that relates to mathematics. Where we might find examples of maths influencing music, I’d like to see how music could be used to influence maths. 

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