Connections: Math and Music


Pitches, Scales, Geometry: An old page from Drexel University, but it’s a good one.

More detailed than a beginner needs, but this has good graphics showing the relationships (fractions) of music notes and rests.

A good article about temperament (tuning). A short paragraph about Pythagoras, and some very detailed information.

A really good page (with sound files) about Pythagorean tuning:

A very technical page with short movies which show how strings vibrate.

This starts with a good table showing ratios of intervals, and then it becomes a very technical page about different drums and their acoustical properties.

One of the best pages I’ve seen yet of math/music basics.

Simple music patterns and how you can use them to create your own music.

A good page on the harmonic series

Information about tuning

To learn more about drums and rhythms try this page:

If you want to learn 1200 (really!) rhythmic patterns, this is the place to start:

Flute acoustics: there is a whole series of pages here, with lots of interesting animations and links. Everything you ever wanted to know about how flutes (and other wind instruments) work!

The same website above ( has a good FAQ page for lots of other musical questions:

Pythagoras: a class at Dartmouth put up these pages with interesting illustrations and text that make sense of Pythagoras’ ideas about music and numbers.

Steve Reich’s “clapping music”; an old, small-screen video of two people performing the work

The score for “clapping music” can be found at:

There are several YouTube videos of “clapping music”. One of my favorites shows 6 jugglers---I have no idea how they do it!

A fun interactive game using music.

Make music using the digits of pi

I’ve presented Math and Music to audiences of all ages, from elementary school students to knowledgeable adults at the Smithsonian. The main topics covered include simple arithmetic (counting, fractions); graphs; ratios; patterns; frequencies; harmonics (also called overtones); and tuning. Other topics get thrown in tangentially. 

A few related websites: