I have been thinking about numbers a lot in the past week.  Prime numbers, the Fibonacci sequence, polygons.  Why my Bucky Balls work best in multiples of six.  How our culture might be different if we had evolved thinking in base 8 instead of base 10.  I was introduced to the concept of modular arithmetic on Thursday, quite by accident; while we obviously use it in daily life, it had never previously occurred to me how one would express it mathematically.

Numbers are, of course, inextricably related to music.  Scales (there’s our modular arithmetic again), beat structure, tempo.  Few musicians seem to call this relationship out, but Tool’s “Lateralus” is, among other things, about the Fibonacci sequence, with an apparent nod to the Golden Ratio.  The references are not within the lyrics; rather, it is a part of the music itself.

I am curious to know whether there are other artists who have explicitly explored mathematical concepts in the rhythmic and melodic structure of their music.  I am aware of some that explore math in their lyrical content (Jonathan Coulton and Tom Lehrer come to mind), but I suppose the nature of what I am looking for makes it more difficult to find.

Ivan is very busy

When I was a youngling, I took piano lessons, like many young middle-class children do.  For the most part I kludged through the assigned material, learning it as well as I could to make it through the song mostly without error.  We had a few other books of piano music outside of the assigned material, which I would occasionally stumble through and mostly not bother with.

There was one piece I was once assigned, however, by a composer I’d not heard of otherwise, that made me take notice.  That song was called “Ivan Sings,” composed by Aram Khachaturian.  It was part of a collection of eight compositions for students called Adventures of Ivan.  I found a copy at our local music store* one day, and insisted my mother buy it for me.**  I actually managed to learn all but the last of the compositions with some amount of proficiency.

Things happened. I moved away from home and mostly played bass instead of piano, and largely forgot about Ivan and his Adventures.

This past November, we assembled at my mother’s residence for a holiday celebration, and my sister brought with her a bundle of our old piano books.  In it was Adventures of Ivan.  As I have recently taken an interest in practicing keyboards again, I insisted that I take it home with me, given that it was mine, after all. I promised my sister I would replace her copy (which I did, by the way).***

I can still play most of the way through it relatively well, though I’m a bit rusty.  All but the last song, anyway.

* Not to be confused with “record store”
** To be fair, a $5 book of sheet music is a much easier sell than some random toy or something.
*** By the way, Vriana, was it “A Tale of Strange Lands” that was missing from your copy? I only just now remembered I still haven’t got you a copy of the missing song, while I was writing all this down.