Playing with Numbers

My theory class right now is all about atonal music. This demands a special kind of analysis since there isn't really a "key" (as in when we say a piece is in the key of E major, for example). There also isn't often any traditional harmony, and it tends to break all the Rules for Good Composition that were set up centuries ago. And it sometimes doesn't sound like it has a definable melody or even melodic fragments. It's a very different school.

So how do you approach something like that?

The secret, scholars have found, is often math. And sometimes, composers seem to write their music deliberately using mathematics - either consciously or intuitively.

In one of the main analytical approaches, you basically divide a piece up into groups of notes. Then, you translate these groups into a numerical code called a "set class".

For example, I can take the notes B, D, and Eb. It doesn't matter what octave they're in. First, place them in ascending order within the octave according to a few rules. (The first and last notes should have the smallest interval possible between them. If there's a tie, break it with the first and second notes, the first and third, etc.)

So that's B, D, Eb.

Then, make the first pitch the number 0. Count the number of half steps between the first pitch and each of the other pitches. Those are the number codes for the other pitches.

So B, D, Eb becomes 034.

034 is its "set class". This enables you to look across a piece and see other similar patterns.
F, Ab, A would also be 034. They are in the same family.

Much of the analysis of these kinds of pieces involves dividing the piece into the right vertical or horizontal groupings and looking for repeated numerical patterns.

Today, we analyzed Webern's Opus 5, Number III, which is a string quartet piece. In measure 6, the two violins and the viola each play a series of three notes that line up in chords. If you look horizontally at the group of notes the first violin plays, they form the set class 034. The notes in the second violin? Also 034. The viola? Also 034.

What's really cool is that, if you look vertically at the chords, each chord (the first note of the two violins and the viola, for instance) also is set class 034.

It's a nifty little acrostic. As we were discussing this in class, I started to think about how very Carollinian this is. Lewis Carol played with numbers and with words so often in his work that he keeps literary and mathematical scholars endlessly entertained. These patterns and pattern-finding games also show up in poetry and other alphabetic delights. Think about palindromes, for instance.

I got to wondering whether any composer had played with both numbers and words in this particular way. My theory prof wasn't sure of anyone, although he mentioned that Luigi Nono used syllables in his work.

It just seems like art song (which is the setting of poetry to music) would be the perfect meeting place for those who love playing with words and with numbers. I'll keep looking for someone who's composed using both. In the meantime, if you know of anyone, please leave a comment and let me know.

~Hope