Fugue in C minor on a theme by Legrenzi, BWV 574 by J.S. Bach

(see also Matrix Video)

The pitch drifting up and down is shown by the tones moving left and right in the matrix above. The extent of the drift is only limited by the requirement that at the start and at the end of the piece the tones should be in the same set of four consecutive columns in the matrix. With almost six minutes, it is quite a long piece. The drifting may be just a bit too capricious in the large middle part, whose pitch is less influenced by the start and end pitch.

Maybe we need more pitch anchors to control the pitch assignment algorithm, not just the start and the end of the piece. As the piece actually consists of three fugues, pitch anchors could be put at the transitions. Or maybe we need to do better than just to minimize the number of syntonic commas: horizontal shifts in the matrix should not come in quick succession in the same direction. Future work.

To put things into perspective, the drift from left to right in the matrix above is 86% of a semitone. The piece has five different C's per octave, syntonic commas apart. So there are four syntonic commas between the extreme C's. A syntonic comma is little over a fifth of a semitone.