

Suppose that a musical monochord sounds at frequency F. Stopping the string at two places, so dividing it into three segments, causes those segments to sound at frequencies A,B and C satisfying 1/A + 1/B + 1/C = 1/F.

Now if one plucks the stopped monochord at a random place, the lowest of the three frequencies (attached to the longest segment) will sound with the highest probability, and vice versa.

As this piece develops, the stopping of an imaginary such string evolves so that the mathematical entropy of the random process stays approximately constant but gradually increases (until the stopping points divide the string into three equal parts). A graph of this looks like a tight triangular spiral.

Finally the durations of the notes correspond, by design, to the probabilities at any given moment of the three frequencies --- but in a different way in each of the three voices. A high frequency (unlikely note) in the first part grants the next note a short duration; in the second part a high itself gets a short duration; and finally in the third part a high note grants the previous note a short duration (so, from a listener's perspective, a short duration in that part heralds a high frequency coming). This presents the listener with a counterpoint contrasting three different but related music logics.

Another version of the piece (https://soundcloud.com/david-victor-feldman/trio-entropicum-first-version) works almost the same way, except that low frequencies correspond to short durations.

A score for an 12-tone equal temperament approximate version dates back to the late 1970's, but never received a performance. This MIDI realization realizes the pitch relationships quite precisely, and perhaps supersedes the piece originally conceived for human players.


Trio Entropicum (2nd Version)

Composer, mathematician, visual artist. 
Seeks collaboration with performers and choreographers.

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Trio Entropicum (2nd Version)

David Victor Feldman