Math and Music: Are They Connected?

I wrote a story this week about why advocates say we should fund music education during an economic downturn. I was interested in the connections between music and math, and I stumbled upon some heated debates among researchers about whether academic achievement can be enhanced through music training.

On one side, I talked to Frances Rauscher, a psychologist at the University of Wisconsin at Oshkosh, who helped popularize the term "Mozart effect" by showing that adults performed better on some parts of an IQ test after listening to classical music.

In one of her more recent studies, she found that math test scores for preschool-age students rose for those who received instruction in piano, rhythm or singing. The students who studied rhythm had the biggest gains, and she said she was not surprised. Rhythm is, after all, "the subdivision of a beat," she said. It's about ratios and proportions, the relationship between a part and a whole -- all material from math classes.

One the other side, Wayne D. Parker, director of research and evaluation at Virginia G. Piper Charitable Trust, has researched music instruction and math performance and found a negligible connection. He said he's not compelled by arguments that people should invest in music for the sake of math or reading. "You don't hear math people saying you should study calculus because it will help you be better at the violin," he said.

Since Monday, I have received some heartfelt responses from readers who think, from personal experience or from their own studies, that the connection between music and math is clear.

One Fairfax dad wrote me about his two sons, who are now in their 20's.

They first started taking private violin lessons when they were 6 and 5 years old respectively. I remember my boys starting with cardboard violins before working up to the smallest type. They took private lessons through H.S. and were both members of the Virginia Youth Symphony as well as concert masters in middle school orchestras.... Throughout school both boys excelled in math and in addition to both going to TJ, the older one scored 780 on the math SAT and the younger one got a perfect 800 (back when there were only 2 parts).

My older boy graduated in the top 3% of his class from UVA with a 3.97 GPA majoring in economics in 3 years and the younger one will graduate in May, again in 3 years with a GPA of 3.75.

Violin has given them discipline, confidence and self esteem to perform well under adverse conditions... I’m sure there are many reasons for my boy’s intelligence, but the way I see it the violin has contributed the most.

What do you think about the connections between music and math? How does one help the other? Or is this all overblown?

By Michael Alison Chandler  |  November 18, 2008; 1:26 PM ET  | Category:  Math Resources , Other Math Classrooms
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I took music from elementary through college. In my state university marching band, there were an above-average number of students with engineering majors. My impression from other bands we met with (in competition or while visiting) is the same. However, in the symphony/orchestra, I was one of the only non-music-majors.

It's hard to say though if this is a correlation or a causation -- maybe it's just that parents of students who show an aptitude in math follow the same common wisdom as you mention above and say, "Better get Johnny / Jane into a music class!"

Is there something you can get from music that's directly applicable to math? Well, learning to sight-read in different meters will make you very comfortable with a small set of fractions (1/2, 1/4, 1/8, 1/6, 1/32 .. triplets & such as well). If you start studying how pitch works and what it means, you can get familiar with frequency, period, logarithms (each octave is a doubling, which looks linear in a log scale), and there are some deeper subjects like the "beat frequency" between two mis-tuned instruments (which is a physical manifestation of wave cancellation). My familiarity with pitch and overtones helped a lot when I studied voice encoding in college (digital signal processing).

I'm hard-pressed to think of anything else that music could bring to the math-game, technique- or knowledge-wise. I agree with "Fairfax Dad" about confidence, self-esteem, discipline. Music is definitely not the only way to build those virtues.

Posted by: PseudoNoise | November 18, 2008 3:39 PM | Report abuse

I don't think learning music makes you any better at math. Learning to practice music makes you better at lots of things, including math.
I think that is also true about learning languages.
I read an article about Malcolm Gladwell and his recent book, which seems to be about the constellation of factors necessary for success.
The numbers that stuck in my mind were: 3 hours a day for 10 years! Sounds like a lot, doesn't it? But that's the neighborhood of time you need to devote to a subject to become its master.
I think Americans in particular like to think that you are just born better at something. My encounters with Japanese students (in an exchange program) have shown me that they believe practice is key to mastery - they will give almost anything a try and not give up, thinking it is just not their thing... they will repeat, repeat, repeat. They will then perform whatever they learned - without showmanship.
Malcolm Gladwell doesn't write just about practice - he also takes into account the circumstances surrounding the accomplishment. For instance, he mentions how Bill Gates had access to computers at a time when computers were scarce and new.
Few people mention that Mozart practiced slavishly. We tend to focus on his genius as if he didn't have to do anything but sit at a piano and sound out what was in his head.
Languages are in that never-never land for Americans, that same territory as math. Unless you grow up in a multilingual household, you think it takes a special gift to speak another language. For fluency, it's practice, practice and more practice. Everyone else in the world knows this!

Posted by: KathyWi | November 18, 2008 5:30 PM | Report abuse

Another way that math and music are related is that both of them feature abstract, rules-based, non-phonetic, symbolic notation systems from which the student is supposed to derive meaning. A student who has figured out how to decode bass and treble clef notation may be less intimidated by, say, sigma notation than a student who has never decoded abstract notation of any sort.

Also, both music and mathematics feature patterns and meta-patterns.

Finally, music has an example of a 1-1, invertible functions in transposition. That might help some students understand the idea of functions and inverse functions.

Posted by: BradJolly | November 18, 2008 6:32 PM | Report abuse

My guess is that if it's useful then it's probably only in the very early stages of mathematics. In particular, the concepts and work ethic seem helpful in primary school.

I've never met a mathematician that said they used any form of auditory reasoning to solve problems. It is very common to think about mathematics either symbolicly or geometrically. This is not to say that mathematicians who think based on nontrivial relationships between sounds may not exist .

Posted by: mathlete | November 19, 2008 9:09 AM | Report abuse

While I agree with the premise that math and music are related through the mathematical relationships of scales, beats and harmonics, when it comes to performance in either discipline I think there's a stronger correlation through basic brain functions, such as working memory.

A recent study reported a correlation between the IQ scores of trained musicians as compared to regular college students.

And, from the other direction, my company publishes a brain training product that trains working-memory. I've been fascinated to find that customers report that it helps with musicianship as well as general cognitive ability.

Martin Walker
Mind Sparke

Posted by: martin13 | November 19, 2008 11:57 AM | Report abuse

The study found that the Mozart effect did not result in permanent increase in IQ scores. The test must be taken within a short amount of time after listening. The longer the interval between listening to classical music and testing, the effect fades until there's no difference. The Mozart effect was not found to cause permanent change.

For further information check out

Posted by: wcollins | November 19, 2008 3:20 PM | Report abuse

Would it be too much to ask for people to keep their commercial advertisements out of the comment section? Michael, what is the policy on this?

Mathlete, I agree with you; primary school is where the connection is most beneficial. However, it seems reasonable to assert that something that improves math proficiency early on will have a positive ripple effect for later years.

Posted by: BradJolly | November 20, 2008 8:16 AM | Report abuse

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