The Feldman Project
From Musicomputation
We listened to this 2 minute section of Triadic Memories by Morton Feldman and tried to figure out how it worked.
Our first attempt at analysis led us to believe that if we just said that two successive measures could not have the same number of notes, we would get the right result. We cut up the original score and pasted it back together using this one rule as the basis for our algorithm. The results are here:
What we noticed is that this leaves us with some successive measures where the last note in one measure is the same as the first note in the next measure. Feldman never repeats notes like this, so we know we need a new algorithm.
After this, we wanted to come up with a better algorithm for reconstructing the Feldman. We discovered two methods: reductive reconstruction and constructive reconstruction.
Reductive reconstruction tells the computer where NOT to go next. For example, if measure15 ends with a D and measure10 starts with a D, and we do not want to repeat the D, we would tell the program that measure15 cannot go to measure10, but can go to any other measure that does not start with D.
In constructive reconstruction, we tell the computer where the program CAN go next. For example, measure8 only occurs once in the section of music and only goes to measure16. Therefore, we tell the computer that measure8 can only go to measure16. Constructive reconstruction is essentially a Finite State Machine, which relates to the Phrase Structure Rules that Adam has been talking about.
Here is a breakdown of the Feldman as Finite State Machine:
Below is a program that uses the Finite State Machine to reconstruct the Feldman (please note that this will take a minute to load):
Here is the source code for the finite state feldman machine:
