circular logic

Warning:  this is a geeky process post about how I wrote my piece for the UVic orchestra readings this past year.  It’s is called Circular Logic, and you can hear it here.  Many thanks to Christopher Butterfield for conducting, and to the orchestra for playing a pretty tough thing.

I wanted to write something based on the digits of Pi…because I’m a huge geek, and thought it wuold be an interesting challenge.  The obvious thing to do with a string of digits is to serialize them – either as pitches or as chords.  So I ignored that, and thought about meter.

Pi, as you no doubt know, used to be approximated as 22 / 7.   As I’m a huge fan of compound meters like 7/4, I wanted to somehow invert that fraction, and do 7/22…which is nonsense in typical time signature notation.  However, 7/8 + 7/4 + 7/8 + 7/2 is not.  It’s just very hard to play.

The next order of business was pitch.  For no reason other than mental simplicity, I set 1 to C, 2 to D, etc.  8 became B-flat, 9 became E-flat, and 0 became F-sharp, giving me roughly a C-Major scale.  The opening notes, in particular, are almost traditional harmony:  3.1415 becomes E-C-F-C-G.

Then, after a lot of false starts, I got rhythm figured out.  I decided that I was only going to use the first 22 digits of Pi, for pitches:  3.141592653589793238462.  In keeping with the 22 / 7 idea, then, I decided to use the first 7 digits for rhythms:  3.141592.  By ‘rhythms’, by the way, I mean a single bar of rhythm, somehow related to the number.  A rhythm for ‘2’ might have two notes per bar, or have a note every second beat, or every half beat.
To put it all together, I added an extra layer of serialization.  In addition to having a list of pitches and rhythms to work through, I serialzed the rate of change.  In the first bar, 3 things change.  Then 1 thing.  Then 4, then 1, then 5, 9, 2, 6, 5, 3, 5, and so on, based on the digits of Pi.  A “thing” here is defined by a change to the next pitch, a change to the next rhythm, or a change in volume.  This gave me some measure of control, as opposed to just copying down pitches based on a string of numbers.  I ended up working through all the pitches once and the rhythms twice – moving from a C to a D.  The piece could, of course, then be played again, only in D Major rather than C Major….

The most interesting part about the piece, for me, is the chance to turn this sort of thing into a live exercise of sorts, with a conductor point to sections and instructing them to change as the piece plays.  I certainly lack the chops to run such a thing, although it would be easy enough to do in software.  A future project, maybe.