The Connection between Music and Mathematics

Written by Shankar Mahadevan Academy on 02 January 2015

How Learning Music Can Help Your Child Excel In Mathematics

"Music is a secret exercise in arithmetic of the soul, unaware of its act of counting." 
--Gottfried Leibniz, philosopher and mathematician.

The connection between music and mathematics goes back to the days of the ancient Greek philosophers, especially Pluto and Aristotle, who recognized the similarity and greatly researched the bond between the genres. In fact, they were so convinced of music being a genre of mathematics that they included music among the "quadrivium" of other mathematical arts like Geometry, Arithmetic and Astronomy.
Historians also document early Indian and Chinese theorists who sought to show the correlation between the mathematical laws of harmonics and rhythms and its relationship towards human well-being. But of late, both scientists and academicians have been conducting various studies on the inter-relationship between music and mathematics and how this connection can be used for enhancing cognitive development and learning skills (especially math skills) in school children. 

What exactly is the connection between music and mathematics? 

Music, both vocal and instrumental, is primarily made up of beats. Musical beats are pulses in which time is marked. This is then played or sung as a series of notes in accordance to a pattern. Notes can be combined in an endless variety of groupings, but the specific number of notes that exist are finite. Similarly, in mathematics, the result always remains finite despite the various ways in which you can add, multiply, subtract, and divide numbers. It is these patterns and combinations that make music and mathematics very similar, for the art of calculation primarily lies in the understanding of the pattern. And it is this connection that can play an integral role in the cognitive development of children, allowing them to excel in mathematics through the learning of music. 
It is interesting to note that all fields of music including the Western melodic patterns, the Hindu raga, the Japanese pentatonic scale, etc. conform to a mathematically derived code. This is especially true of Indian classical music where the concept of ‘taal’ or metre, is intrinsically linked to numbers. The connection between the two was never doubted in the past, but rather music and mathematics comprised as a single whole concept. Wayne Parker, senior researcher at Hopkins's Institute for the Academic Advancement of Youth, comments upon the divide which has emerged between the two. "Today we think in terms of math/science people or verbal/artistic people. There's that division. In the past, math, music, and reading held the liberal arts together.”

Reiterating this fact is Shankar Mahadevan, famous Indian singer, music director and composer. “I never really connected the dots between music and maths,” says Shankar Mahadevan, who holds an engineering degree in Computer Science from Mumbai University, India. “But maybe learning to play the harmonium and veena before I was five, helped develop my mathematical skills without my realizing it.’

How can this connection help in the learning of mathematics?

With renewed interest being shown in the field of the inter-relationship between music and mathematics, several studies have been conducted on how the learning of one can benefit the other. Here are a few interesting observations.
• Frances Rauscher, a psychologist at the University of Wisconsin at Oshkosh, in one of her recent studies found that the mathematics test scores for preschool-age students increased for those who received instruction in piano, rhythm or singing. Also the students who studied rhythm were found to have the biggest gains. Not surprised at the result, she says, “Rhythm is, after all, ‘the subdivision of a beat’. It's about ratios and proportions, the relationship between a part and a whole - all material from math classes.”
• In a study, published in Neurological Research in February 1997, the authors referred to earlier work that indicated exposure to music might "excite and enhance the cortical firing patterns" used in spatial-temporal reasoning. Such reasoning is required for higher brain functions such as chess, mathematics, and engineering and for composing music.
• Anita Cooper, faculty member at Peabody Prep, says music enhances children's cognitive ability."Composing music is like problem solving-you have to put text and rhythm together,” she says. “Musical rhythms are mathematical equations, like 4/4 or 2/4 time. You use addition and subtraction skills: How many more beats do you need? How many more ways can we divide it? Music also helps children develop language. A musical phrase is like a verbal sentence. It has a beginning, a middle, and an end. And the inflection changes in different parts of the sentence."
• An article published in DNA, spoke of how several schools in Mumbai are using the concept of teaching mathematics through music. For example, IES Vidyamandir School, Bandra, has started using musical beats and rhythms to teach advanced concepts in algebra. This is what Shubhda Vinekar, principal of the school, had to say. “Music has always been intricately linked with maths. Teaching numbers through music helps children grasp concepts more easily. For instance, a mother walks her fussy baby around the house, singing and patting his back as per the rhythm of the lullaby. She might not know it, but her rhythmic patting is her baby’s first experience of patterning, a mathematical concept linked to advanced maths like algebra.”
• The Learning Through The Arts (LTTA) program established by the Royal Conservatory of Music, has teachers and professional artists, working in collaboration together, to bring out innovative on lessons in math, science and other subject areas using art, dance, story and song. 
• In a research study, Peter Jusczyk, professor of psychology and cognitive science, University of Oregon, showed that babies as young as four-and-a-half-months prefer music that's sequential-not broken up by odd, misplaced pauses. This gives rise to the theory that even babies' brains may understand the concept of order, which is the fundamental law of mathematics.
• Music therapist Alicia Barksdale who works with elementary- and middle-school-age children who are developmentally or learning disabled at Hopkins's Kennedy Krieger School in East Baltimore uses rhythm to teach arithmetic. "Somehow a child who is not able to understand the process of a math problem can understand four beats per measure and set rhythm within a measure," Barksdale says. "They understand that the beats have to add up, even if they can't do math.”

What can you, as a parent, do for your child?

All research conducted in this particular field points to one common factor- that music as an activity in itself can contribute to the better understanding of mathematical concepts. Dan Naiman, Hopkins professor of mathematical sciences, a specialist in statistics, and an accomplished saxophone player, is sure about the connection between learning music and math, through his personal experience of having associated with many mathematicians who also turn out to be gifted musicians. “Go to any math department in the country and you'll find some serious musicians,” he says.
As a parent, encouraging your child’s musical abilities may be a way to help her gain better grades at mathematics. If your child is in the elementary school stage you could try teaching them the multiplication tables through song. For older children, you could try enrolling them in an instrumental music class or get them to start their day by chanting shlokas. The Shankar Mahadevan Academy ( offers the benefit of having experts teach online shloka lessons over the Internet. Classical, Hindustani and Bollywood music can also be learnt through self-study OM (online music) books or through expert teachers who conduct online classes that can be scheduled to fit within a customized timeframe. 

Did you know that learning music, vocal or instrumental, can improve a child’s understanding and learning of mathematical concepts?

Magazines: The John Hopkins Magazine Feb 1998
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