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.
Sigh.
ReplyDeleteWhen 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..."