Mathematics and Music

In this article, Christopher Jeneker explores just a few of the ways in which mathematics and music are intricately linked. Read more about how the structure and precision of mathematics and the beauty and emotion of music have more in common than you may imagine.

Illustration by Sara Eskandari

I enjoyed the fact that it combined three separate aspects of the Math / Music relationship into one short but informative piece – Lesley Scott

Theories. Frequency. Notation.

What do all these words have in common? Mathematics and Music.

For many centuries it has been shown that math and music share significant relation (, 2017). In this article, we are about to explore some of the ways for us to recognise the relationship between these two fields and how they align.

Cognitive Development

When teaching mathematics in the classroom, it is important to explore way in which we can enhance teaching method by connecting mathematical concepts to practical applications, such as music, to make the subject more relatable to everyday life.

While the study of mathematics can be rather abstract, it can be extended to many real-life applications, such as music. Listening to music and playing instruments enhances many of our youths’ mathematical abilities, such as:

Pattern Recognition

Consider the repetition in refrains and choruses of today’s music and even classical music. We can see that patterns and changes in rhythm and tempo play an essential role in music. The variable changes in the music can also be translated mathematically since pattern recognition plays an important role in maths. Many valuable theories and formulae have derived from pattern recognition and music allows some development thereof, like division and even some nontrivial topological features that even further strengthen the relationship between mathematics and music (Sethares, 2011).

Spatial Awareness

Spatial proprioception is also developed in our youth when incorporating movement with music where distance, form, direction, and location play vital roles in dance. The development of this awareness also improves spatial reasoning abilities such as studying geometric shapes, where these cognitive skills are exercised.

We cannot have a conversation about mathematics without including Pythagoras. In this case, we can appreciate his foundational work in relation to the topic of mathematics and music.

Rather than referring to the four blacksmiths’ hammers, we can look at how Pythagoras has introduced harmonics from a mathematical perspective. The Greek philosopher is attributed to the discovery of how harmonics are determined by string length when playing music. He discovered that when plucking a string of exactly half the length of the first string, it would result in a sound of an octave difference between the two. As the string is shortened, the pitch becomes higher.

To this day, we still use the Pythagorean method of tuning to tune our instruments, but division is not only used in tuning and harmonics. Time signatures in music theory notation also continue to make use of division to keep track of the tempo throughout a piece, where the numerator shows the number of beats and the denominator denoting the type of beat for each bar in a musical piece.

Auditory Processing

Aside from how mathematics applies to music theory, it has also afforded us many advances in the Biology and Physics of sound, especially in audiometry.

Sound waves, vibrations, and frequencies, also known as sinusoidal waves, can mathematically be denoted as a sine function. With the sine function, we can show the natural oscillations of wavelengths and audible sound.

The ear translates these wavelengths into electric signals for our brains to interpret emotion, pitch, rhythm, and tone. These interpretations exercise the brain’s cortexes, in turn strengthening our prefrontal cortex and left fusiform gyrus which are used for performing mathematical operations (Canmore & Tunks, 2015).

Christopher Jeneker


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Canmore, J., & Tunks, J. (2015). Brain Research on the Study of Music: A Meta-Synthesis . Journal of Mathematics Education , 149-151.

CFI Team. (2022). Sine Wave. Retrieved from CFI:

Kindermusik. (n.d.). spatial awarness Archives . Retrieved from Kindermusik: (2017). Mathematics and Music. Retrieved from Math Tutor DVD:

OSMD. (2016). 4 Ways That Music And Mathematics Are Related. Retrieved from Omaha School of Music and Dance:

Sethares, W. A. (2011, January 6). Topology of Musical Data. Retrieved from Joint Mathematics Meetings Program by AMS Special Session:

Sheela Edwards, S. E. (2020). Aurora Early Education. Retrieved from How Learing Music is linked to Learing Mathematics:

Stewart, J. (2015). Timeline 002: Pythagoras And The Connection Between Music And Math. Retrieved from Vermont Public:

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