27 September 2007

Fun with fugues

At Science after Sunclipse, Blake Stacey links to some videos from Stephen Malinowski's Music Animation Machine. The Music Animation Machine animates music; the basic idea is that notes are represented by rectangles, the length of which corresponds to the length of the note. What I found particularly interesting was that the videos use color to represent either:
  • the "voices" in the score, as in the first video below (Bach), and
  • harmonic information, as in the second video below (Chopin)
Here are the videos I'm referring to: (Many others are available from Malinowski's site.)
Johann Sebastian Bach, Toccata and Fugue in D Minor:

Frederic Chopin, Etude, opus 10 #7:

The harmonic coloration is based on the circle of fifths, which is an interesting solution to the problem that notes which are close together in pitch are not close together in some sort of "harmonic space".

I find myself wondering if the coloring based on voice could be automated. This would be trivial for things written entirely in, say, standard four-part voice leading as taught in an introductory music theory class, because there are always exactly four notes at any given time and the voices don't cross; it would be very nontrivial for actual music. (This isn't just a musical problem, believe it or not. A related problem is as follows: a baseball team has five starting pitchers, which it uses in a pitching rotation: ideally pitcher n pitches on days n, n+5, n+10, ... But there are off days, people get hurt, and so on. How do you decide when one pitcher has "replaced" another in the rotation? The people at Baseball Prospectus have thought about this -- sorry I can't find the link -- but their solutions basically involve just staring at a list of who pitched what day and writing numbers next to them kind of arbitrarily. It's not quite the same thing, though, because there's only one starting pitcher per game (relief pitchers are used in a much more ad hoc manner) but notes are played simultaneously. I suspect there are other problems of this sort where there are logical ways to sort some sequence of things into bins -- musical voices, rotation slots, and so on -- but none come to mind.)

The sort of notation they're using here seems like a logical historical antecedent of present-day musical notation (though I don't know enough about the history to know if it is); the main differences are that in modern notation we decide that seven of the notes in each octave are more important than the other five (and enshrine this in the notation) and we don't write a whole note as being, say, sixteen times as long as a sixteenth note. This is probably a good thing from the point of view of readability. It also resembles a player piano roll (modulo coloring) which I doubt is a coincidence.

Oh, and you have to watch the "Oops, I Did It Again" fugue, which I found from Good Math, Bad Math:


Dan said...

You might be interested in David Temperley's The Cognition of Basic Musical Structures, which addresses the automation of perception of voice separation, in addition to other musical elements (key signatures, which accidental to use, harmonic analysis, etc.).

Isabel said...


thanks for the tip. I'm not seriously interested in the question, but our library has the book, so I think I'll check it out.