The Minds of Children: Experiencing Music and Math

From the lecture series: How Music and Mathematics Relate

By David Kung, Ph.D., St.Mary’s College of Maryland

What do small children and infants know about music and math? It turns out that practically from birth, babies start thinking both mathematically and musically — humans come hardwired for both music and math…

image of child experiencing music and math

You might wonder how we know something like this, after all infants can’t talk. We infer it in part from how long infants look at something. If infants see the same thing over and over again, they tend to look away quicker the more they see it. That is called habituation. If they see something unexpected and something changes, they look longer and that is called fixation.

When babies are just three or four days old they can distinguish three dots from two dots. The way researchers found this out was by showing babies two dots repeatedly until they get habituated and  stop looking for long periods of time. When the researchers switch to three dots, the babies are fixated; they look longer than if they had just been shown two dots. This is evidence of something that mathematics educators have a word for. It’s called subitizing, instantly counting without counting out the individual elements.

This is a transcript from the video series How Music and Mathematics Relate. Watch it now, on The Great Courses.

Subitizing comes from subito; it is Latin and it is actually a musical term. Subito forte means to play suddenly loud. Now, adults subitize three, four, even five items. In my classrooms, I can look at the students and count out groups of five very quickly. If you try to do this with three, four, or five you have virtually no errors and incredibly fast reaction time. But, if you try to do this with more than five, most adults have a lot more errors and a much longer reaction time.

Image of Karen Wynn
Karen Wynn— Professor of Psychology and Cognitive Science at Yale University

Infants are subitizing at three or four days old. They have some innate numerical ability. Okay, they can sort of count in some sense, or subitize, but can they add? Can they combine groups and count them? You would think that would be much harder, but by five months infants can tell that 1 + 1 is 2. They can do basic addition. This is known because of the work by Karen Wynn – a psychologist at the Infant Cognition Center at Yale. The tests she performed involved the violation of expectation. Again, babies will look longer at unexpected images, objects, or outcomes.

Learn more about the harmonic series behind a single note

Her tests seemed deceptively simple. Children were shown dolls behind a screen that could rise and fall.  First, only one doll was shown, then the screen lowered to hide it. Next, a second doll was shown going behind the screen to join the first doll, still hidden. Naturally, when the screen came back up the children would expect to see two dolls. But when only one doll was revealed behind the screen, children as young as five months old spent longer amounts of time looking at the unexpected result.

Learn more about the diverse mathematics of musical scales

Image of baby with toy abacus
By five months old, infants can tell that 1 + 1 is 2 — they can do basic addition.

If you’re skeptical you might ask, how do we know it is really about the numbers and not just some innate counting of dolls. They actually tested to eliminate that possibility. They have switched objects and with five months old if you have 1 doll plus 1 doll and then drop the screen and show the baby two blocks instead of dolls, they do not look very long. There’s a shorter gaze. On the other hand, if you have 1 doll plus 1 doll and then drop the screen and there is 1 block there is a longer gaze. That is unexpected to them. These young babies, they do not know the difference between a doll and a block, but they somehow know that 1 + 1 is 2.

Older babies look longer at both. Older babies by about a year know that a doll and a block are different. And so they know that 1 doll plus 1 doll should not equal 2 blocks. This sort of addition these babies, these infants, are doing that at ve months old. Addition is nearly innate.

What about music? Are there musically innate structures in the brain?  What we know is that there are early preferences about music — babies like fast, loud, and familiar music. In order to understand this, they have developed what is called a conditioned head turning experiment. This work was performed in the early 2000s by Alexander Lamont in the UK.

In the study, a baby’s head controled music that was being played. When the baby looked left, he heard one song. When the baby looked right, he heard a different song. Babies about one year old quickly learn how to control the system, how turning their heads tells them what music they’re going to hear. When they control the music, they prefer upbeat, loud, and  music.

Image of mother playing music for baby in tummy

But what about familiar music? To test for that, they had mothers play music in utero for the last three months of their pregnancies. Then the babies did not hear that music again for a full year after birth. That one year they put these babies in this head turning experiment and the babies preferred the music that they had heard in the womb over similar styled and similar tempoed music. This research showed that infants have musical structures in their brains that can store musical memories. Now, this research got taken way out of control and we heard about the Mozart effect, which was not entirely well-reported in the media.

Learn more about how the table canon from Lecture 8 can be displayed on the single face of a Möbius strip

What’s the big picture take home message from all of this? It points to an obvious connection between math and music. Infant brains are structured in ways that allow them to process fundamentally important aspects of both. Before language, before walking even, infant brains have the ability to process, to remember, and maybe even to understand both math and music.

Common Questions About Music and Math

Q: Can music benefit the study of math?

Music can help with studying math for many reasons: enjoyable music puts one at ease and helps set remembrance points based on the song and additionally, as music is mathematical with repeating rhythms, frequencies, and octaves, the formulas are similar and work together.

Q: Who is thought to be the master of music and mathematics?

Pythagoras from the 6th century B.C.E. is credited with the propagation of a mathematical understanding of music throughout Europe based on his studies with Kemetic scholars.

Q: Who invented math?

Math was understood for millenia in ancient Kemet (Egypt), but the European era of math truly began when Euclid formulated an axiomatic study of math.

Q: Who is credited for inventing the number zero?

While zero was considered a placeholder as far back as the Sumerians, it was in India around A.D. 458 that the concept was derived from the Buddhist Sunyata doctrine.

This article was updated on 9/20/2019

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Karen Wynn: By PeterMacy (Own work) [CC BY 3.0 (], via Wikimedia Commons