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What Is the Math and Music Connection?

If you love music but are convinced that you hate math, you may not believe there’s a math and music connection.

But there is. And it’s pretty substantial.

In fact, if you pause to consider it for a moment, numbers and math are essential to describing and teaching music. This is one of the reasons that an arts academy high school uses music to teach math.

Mathematics involves seeking patterns that can explain and predict the unknown. Music uses similar strategies.

Numbers Say a Lot About Musical Pieces

Reading music is like reading a math problem. Not one of those two- or three-step story problems. But you read musical pieces in the same way you read math symbols.

The symbols are a representation of some piece of information.

Also, music is divided into sections known as measures or bars. Each measure is divided into equal portions called beats and each embodies equal amounts of time. They’re actually mathematical divisions of time.

Musicians must also be able to read the time signature to determine the rhythm of a piece. It’s written as two integers; one on the bottom, one on the top. The bottom number indicates which note gets a count, and the top number indicates how many times this note appears in each measure.

Music and Fractions

In music, fractions indicate the length of a note. A whole note has one note per measure, a half note has two notes per measure, a quarter note has four notes per measure, and so on. Musicians must have an understanding of fractions so that they know how long to hold a note in a musical piece.

In a nutshell, musicians have to continually incorporate fractions, decimals, and percentages in order to understand rhythm in much the same way mathematicians do to solve any part-whole problem. It’s just in a different context.

Interesting Research on the Math and Music Connection

The above is a basic breakdown. But a fascination with the math and music connection has been the source of research in many areas of mathematics.

In fact, research shows that certain pieces of music are popular most likely because of their mathematical structure.

For example, there’s a crazy opening chord to A Hard Day’s Night by the Beatles. If you’ve heard it, you know exactly what we’re talking about. It’s unforgettable.

Anyhow, people have, for DECADES, been trying to figure out which instruments and notes make up that chord. One professor utilized a mathematical tool called a “Fourier Transform” to solve the mystery. As much as you may want to credit George Harrison’s 12-string guitar, that wasn’t it alone.

And Pachelbel’s Canon in D has a repetitive structure that appeals to the masses. That’s why you hear it at every other wedding. The popularity of hip-hop can also be at least partially ascribed to the rhythmic beats and looping breaks that connect with our intrinsic mathematical need for patterns and rhythm.

Pythagoras and Fibonacci

The Beatles and Pachelbel are relatively modern examples. But go way back to the days of Pythagoras (born ca. 570 BCE) and Fibonacci (born 1170) and there are further examples of the math and music connection.

It was Pythagoras – ancient Greek philosopher and namesake for the Pythagorean Theorem we all learn in math –  who recognized that different sounds are created by varying weights and vibrations. From this, he concluded that a vibrating string is proportional to and can be controlled by its length. A string that is cut in half will play an octave higher.

In other words, the shorter the string, the higher the pitch.

He went on to discover that notes of certain frequencies are best complemented by notes that are multiples of that frequency. For instance, a note of 250Hz sounds best with notes of 500Hz, 750Hz, and so on. (You do the math.)

Nearly 1,800 years later, Fibonacci developed his famous sequence that goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. The pattern is created by adding each term to the one before it to calculate the following term.

So 1 + 1 = 2, 2 + 1 = 3, 3 + 2 = 5, 5 + 3 = 8, ad infinitum. This same sequence can be found in piano scales.

Take the C scale, for example. There are a total of 13 keys from C to C. There are eight white keys and five black keys. The black keys are arranged in groups of two and three.  on the piano consists of 13 keys from C to C; eight white keys and five black keys, with black keys arranged in groups of three and two.

This Is Your Brain on Mozart

There’s even interest in the cognitive research field on this connection. The “Mozart effect” was first popularized in the 1990s when several studies showed that students performed better on spatial-temporal tasks right after listening to a Mozart sonata.

In other words, they were better able to visualize a machine and then build it with Legos immediately after kicking back with, let’s say, Piano Sonata No. 16.

Researchers theorize that this is because the parts of the brain required for spatial-temporal reasoning are the same ones that are active when listening to Mozart.

The connection appears even more substantial for those who do more than listen to music but actually play a musical instrument. Studies show that when young children are provided with instrumental instruction, they score significantly higher on tasks measuring arithmetic, spatial-temporal cognition, and hand-eye coordination.

Further research shows that students who learn math and other academics through music and dance retain the information better than children who learn by purely verbal instruction. So there is clearly an overlap between music skills and math skills.

All of this is good news for students who are musically inclined but feel that they don’t understand math. In fact, they do. They just need a way to reframe it.

This is where arts-integrated education is so helpful. By teaching math through music, students are able to grasp the concepts and problems so much more clearly. And they no longer believe they’re “bad at math.”

Could Your Child Benefit from the Math and Music Connection?

If your child believes that being creative means he or she will never understand math, then it’s time to look into an arts-integrated education.

Arts Academy in the Woods not only takes advantage of the math and music connection, but the entire curriculum focuses on teaching academics through all of the arts.

So contact us today to set up a tour of our school. And give your artistic child the opportunity to explore academics in a whole new way.   


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