Arbitrary Extractions (2020)

Scored for Alto Flute and String Trio; challenging. These three short movements each derive their pitch content from relationships extracted – somewhat arbitrarily – from the 10 points (rows of 1, 2, 3, and 4 points, arranged as an equilateral triangle) of the ancient Pythagorean tetractys.   The pitch sets/scales are each produced by manipulations of a sequence of intervals, and the resulting pitches assigned – in a consistent order – to the points on the tetractys.  To promote variety, each movement utilizes two differently-generated pitch sets.  This approach seems more or less appropriate, as Pythagoras may well have used the ratios suggested by the tetractys – 2:1 (P8), 3:2 (P5) and 4:3 (P4) – to formulate the Pythagorean scales.  The object is simply to empower the geometry of the tetractys to influence the pitch content, while leaving abundant freedom of choice in the compositional process – i.e., letting each pitch hierarchy flavor the melody & harmony of each movement.  These no deep quasi-mystical intent here, just an attempt to produce audible harmonic/melodic effects that the music would not have had otherwise.  Details of the structure are here. Publication by Tetractys Publishing, London, is anticipated.