Fred Lerdahl

The Music and Writings of Composer Fred Lerdahl

Program note for Three Diatonic Studies 


Three Diatonic Studies originated in a commission from the Irving S. Gilmore International Keyboard Festival to write a variation based on the “Aria” of Bach’s Goldberg Variations. The result was the diatonic and canonic Chasing Goldberg, composed in 2004. After hearing a number of performances, I decided that this unusual little piece needed companions. It felt presumptuous to compose more variations on Bach’s masterpiece, so instead, in 2009, I added two pieces that continue to explore the diatonic collection, Cyclic Descent and Scalar Rhythms. The three pieces together last about nine minutes.

1. Each measure of Chasing Goldberg employs pitch classes from the equivalent measure in the “Aria” of Bach’s Goldberg Variations. Pitches played staccato are dislocated registrally in pointillistic fashion, creating intricate cross-rhythms out of the constant 16th-note texture. Instead of straight binary repeats, each repeat is a canon (unison at the distance of a quarter note) on the original statement. Chasing Goldberg is dedicated to Gilbert Kalish.

2. The pensive Cyclic Descent juxtaposes the diatonic set with its pentatonic complement and follows partial and nested sequences, successively transposed down a scale step. Contrasting ideas gradually merge, and by a circuitous route the music ends up where it began.

3. Scalar Rhythms is built on a strict parallel between scales and rhythms. Counting up the major diatonic scale in semitones, the pattern is 2-2-1-2-2-2-1. Similarly, the pattern for the pentatonic scale is 2-2-3-2-3; for the major triad it is 4-3-5. West African drumming often employs these asymmetrical patterns as durational proportions. Scalar Rhythms is constructed entirely, and in canonic fashion, from these isomorphisms between scales and rhythms.

Fred Lerdahl


all materials copyright Fred Lerdahl 2009