Ptolemy’s Dilemma

Ptolemy’s Observation was written for Mira Benjamin as a set of studies for teaching basic just intonation performance on stringed instruments.

The name of these studies refers to the Greco-Egyptian mathematician and philosopher from the second century, Ptolemy, who extended the Pythagorean conception of musical harmony from a 5-limit to a 7-limit just intonation in his influential treatise on music entitled Harmonics.

The score may be played by any number of string players beyond four, and in any combination of, cellos, violas, and violins. Each study uses a drone with two or three soloists playing on top. In performance, the musicians may take turns playing the solo parts while the remainder create the drone. The movements often repeat at different tempi, allowing for roles to be passed around and switched between players as they like.