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Hit a high note exploring the math behind music

Posted 11/01/2018 by Ellen Fishpaw

Sure, math probably isn’t the first thing that comes to mind when you think of music. But, surprisingly, the creative art of music is intimately tied to the structure and logic of math. Some of these concepts are easy to explain, while others are probably better suited for someone professionally trained in music (or math for that matter). So let’s just cover a few of the basics of music by the numbers.

It was Greek philosopher and mathematician Pythagoras who discovered that you can make different sounds with different weights and vibrations. Ultimately, this led to his discovery that the pitch of a vibrating string is proportional to and can be controlled by the length of the string. Strings that are halved in length are one octave higher than the original (the shorter the string, the higher the pitch). That’s why a guitar players hands get really close together when the pitch is really high.

Pythagoras also discovered that notes of certain frequencies sound better in combination with frequencies that are proportional to that note. For example, notes that are of a ratio of 2:3 such as a note of 440Hz and a note of 660Hz, sound good together. In music theory, that ratio is a “fifth.” Music theory relies on relationships like this to make music sound good to our ears.

As you know, in math, we look for patterns in numbers to explain how things relate to one another. Music is much the same. When writing music, musicians use structures, like proportional relationships, to guide the way they plan and play note sequences. Relationships are fundamental to math and create a compelling link between music and math that will help you hit a high note in class.

Try these lessons below to help explore the math and science behind music:

Characteristics of Exponential Functions (Algebra 1): In this activity for TI-Nspire, students explore the properties and characteristics of exponential curves. Students will compare and contrast the characteristics of exponential functions of the form f(x)=bx where b>1 with functions of the form f(x)=bx where 0 <b<1.

Exponential vs. Power (Algebra 2): In this activity students will compare and contrast functions of the form f(x)=bx with functions of the form f(x)=xb. They will explore and determine for what values of x and b, are those functions equivalent. They will also explore intervals where the power function has greater value than the corresponding exponential.

Sound Waves and Beats (Physics): In this data collection activity, students use a Vernier microphone attached to the TI-Nspire Lab Cradle to collect wave data from tuning forks or an electronic keyboard. Students compare the amplitude and wavelength for different tuning forks, and then observe the beat frequencies between the sounds of two tuning forks or two keys on the keyboard.

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