Pitch Drift

Pitch drift is the phenomenon that the general pitch of a piece of music gradually drops - or rises - as the piece is played/sung. It is most prominent in amateur choirs singing a capella. In ordinary keyboard music, there is no pitch drift, because the pitch associated with a note name is fixed: if middle A is tuned to 440 Hz, it will usually remain at 440 Hz longer than the piece lasts. In just intonation, however, a note name may have several different pitches associated with it, separated by steps of a syntonic comma (pitch ratio 81/80, or 21.50628 cents, which is about a fifth of a semitone). A typical piece of music could use the following tones, as in the matrix introduced here:

F♯♯
F♯C♯G♯D♯A♯E♯
DAEBF♯C♯G♯D♯
GDAEBF♯C♯
A

Say this piece contains several occasions of the F♯ minor chord. They could have either of the three highlighted shapes. Two consecutive shapes differ by four matrix columns and also by one syntonic comma. So, if we want a pitch drift metric, we could say that a shift of one column represents a pitch drift of 1/4 syntonic comma, or 5.37657 cents. In the example pitch drift graph below, the horizontal axis is elapsed time from left to right. The vertical axis indicates the drift in cents. Each harmonic chord in the piece has one or more tones and the column numbers of those tones are averaged and converted to cents - a distance of one column is a quarter of a syntonic comma.

Pitch Drift Graph

We can see that there is quite a bit of pitch drift up and down. The piece ends at roughly the same pitch it started at, but that is because the optimization algorithm has been configured to achieve this. Music theorists discuss pitch drifts of one syntonic comma or more. Choir directors usually start to worry when a piece drops by as much as a semitone (100 cents, or about 5 syntonic commas).

Obviously, one cannot play this music together with a fixed pitch instrument such as a guitar or a clarinet. On the other hand, singing with this music should not cause any tuning problem. But how about playing a violin with this music? If you are a violinist, I would be interested in hearing from you: is it easy to adapt to the drift that occurs in the music on this website?

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