Musicians, Numbers, and Symmetry

Music, inherently, breeds thinking about numbers. One of the first things you learn as you begin a study of music is numbers. "There are four beats in this measure." "What key are you in when there are three flats in the key signature." "Use fingers 1 and 3 to properly finger that note." And on, and on...

Why such a focus on numbers in music?

Music is abstract. It's not concrete. The notation that we see is mere symbolic representation of what will eventually be turned into music - an art form that exists in time. We need a way to organize and understand the symbols on the page and translate them into something more or less recognizable. Numbers are super helpful in that area.

Composers have often played with the ideas of numbers. In 1974, Randolf Currie published an article for the journal Bach entitled, A Neglected Guide to Bach's Use of Number Symbolism - Part I (yes, Part II came later). Bach was especially fond of the numbers 3 (divine) and 4 (humanity) and the combination of those numbers (3+4=7, 3x4=12, 7x12=84). Tom Service wrote a great blog post for the Guardian listing how different composers - from Bach to Schubert to Schoenberg - used numbers to their advantage. Ever heard of 12-tone music? Yep, numbers. More recently, Estonian composer, Urmas Sisask, used math and observations of the rotation of the planets to create what he called the Planetal Scale - C#, D, F#, G#, A. Pretty far out stuff (Sorry...). And don't get me started on harmonics - Good grief! The numbers of it all!

One of my favorite attributes of numbers are numeric palindromes. There's something immensely satisfying about numbers that are the same either direction you look at them. When I get gas for my car and the pump stops at $35.53, I know it's going to be a good day. When I look at the clock and it's 10:01 PM, I know it's time to get ready for bed.

Several musicians love palindromes as well. Mozart, Bach, and Haydn all have examples in their works of using palindromes in their music. See this post from Miss Jacobson's blog to read more about musical palindromes.

Around 2002, I got interested in the idea of musical palindromes as well and manipulating a piece to still make it sound good. The pieces I wrote weren't exactly palindromes, but more related to the idea of symmetry, or mirror composition. I found five ways to play with the idea of symmetry in short piano works. I posted the first one on my site this morning. The other four will come each day this week.

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