## Mathematical Monday 11/15/10: Overtones

Did you know that there’s math in music? Lots of really interesting math actually about what frequency the various tones are and why some sound good together and some don’t. So, for today’s quick Math Monday, I want to talk about my favorite mathematical musical phenomenon: overtones.

This is a reunion of the Allegheny College Choirs led by the man who taught me overtones. I’m in there somewhere!

An overtune is a higher frequency than the lowest frequency of the sound being produced. Every time I hit a key on the piano, you near a main sound called the fundamental frequency, and then above that there are numerous other sounds at higher frequencies and lower volumes. Different instruments make different overtones based on physical aspects of how they are made. Overtones are the reason that a Steinway and a Yamaha piano can play the same note and sound completely different. I tend to hate Yamaha pianos, by the way.

Now that you know what an overtone is, you can manipulate it. When I sing, I can make minute changes in the shape of my throat to change the overtones, but this is not easy. My favorite overtone game was some I used to do in choir, and it was adding notes (see, more math!). When two different fundamental frequencies are produced at the same time, they can produce the effect of an audible higher note somewhere else in the room. Ghost notes! This is very common in barbershop quartets.

The one I always used to do was to have an octave: the same note being sung high by the women and low by the men. The notes add together to make a 5th above the women’s note ring in the room. If both parts were singing F’s, then a C could be heard.

Here’s a youtube video where the choirs do some of the same things I used to do!

There you go: Math in music! Two things I love. Well, I was a music theory minor back in the day, so I would hope I loved it. There is more math in music, so expect other posts like this in the future.