Thursday, December 10, 2009

How do Mozart and Chopin use their notes?

Mozart's minuets don't sound much like Chopin's mazurkas. There are many reasons for this -- the rhythms, the tone of their pianos, changes in repetition, and so on. But one of the ways that music21 let us discover is that they articulate their pitch space differently. For instance, here is the pitch distribution in the soprano register of one minuet by Mozart:

The x (left<->right) axis shows shorter and longer notes -- this excerpt [like the Chopin] uses almost entirely quarter notes (1.0) and eighth notes (0.5 quarterLength). The y (front<->back) axis shows lower to higher notes (middle C = 60). The z (top<->bottom) axis shows the number of times each pitch/rhythm combination appears. Looking along the y axis, we see something like a bell-shaped curve. Mozart uses notes in the middle of the register the most often, followed by a smooth trailing off towards higher and lower notes.

Contrast the Mozart graph with the pitch distribution of the right hand of a Chopin mazurka:

Chopin emphasizes certain notes quite a bit more than other notes. There is no smooth distribution; instead some pitch-classes (C# and G# especially) recur much more often in certain registers of the piano. We will be returning to these examples (probably refining the graphs slightly to deal better with grace-notes, etc.) as music21 moves toward its initial beta release.

1 comment:

  1. Sigh.
    When I was in high school I tried doing a science project about the Mathematics of Music. I loved playing Bach's Inventions and really felt there were some mathematical patterns that made Bach's music sound like Bach. But I had neither the music-theory training nor the computer programming ability to make the music visually accessible.

    I spent a lot of time charting notes and intervals into Excel and writing a very simple program in BASIC that attempted to generate Bach-style music, but I didn't have any tools like this, and none of the science fair judges really understood my project at all. Eventually, I gave up the idea.

    A year later the 3DO (a now-defunct videogame console) came out with a program called CPU Bach, a program that generated Bach-like music on the fly. It proved that my hypothesis was correct, but I just didn't have access to the right technology.

    I see stuff like this and think, "If only..."