Opus number: op. 82

Title: Harmony of the Spheres

I. Jupiter

II. Mars

III. Saturn

IV. Earth

V. Uranus

VI. Venus

VII. Neptune

VIII. Mercury

IX. Pluto

Date written: 2006

Length: 25 minutes

Premiere performance: October 16, 2006, Jordan Hall at New England Conservatory, Larry Bell, pianist

Program Notes: The sculptural mobiles of Alexander Calder, which I saw at the San Francisco Museum of Modern Art in March 2006, inspired this work for solo piano. Calder’s preoccupation with the planetary orbits and his unique sense of motion and balance gave me the idea of doing something similar in a musical medium.

While this work has no direct connection to Holst’s “Planets,” indirect references to the characters of the Greco-Roman gods can be heard. Jupiter, for instance, begins with a lightening bolt, Mars has a certain militaristic rhythm, and Mercury is quite rapid and fanciful.

Unlike Pythagoras, who was preoccupied by the relationship between harmonic intervals and the proportional distance of the other planets to the earth, my main interest was to derive the rhythmic proportions of the music from the planets’ relative distance to the sun. One underlying macro-speed connects all the movements with their respective proportions. That fundamental speed is expressed in time as dotted half note equals 33: In both Mars and Earth the quarter note equals 99, which means the dotted half equals 33. Uranus is scored at dotted quarter equals 66 (so the dotted half equals 33). In Neptune the dotted quarter note equals 44, in Pluto the quarter equals 44 (both two-thirds of 66; a 2:3 ratio); and in Jupiter that quarter is doubled to equal 88. Saturn’s quarter equals 66 (twice 33), while for Venus and Mercury it equals 132 (twice as fast as 66, or four times 33).

Earth here is considered to have a 1:1 relationship to the sun. The uniqueness of the Earth is characterized by unison and octave textures. Mercury, the shortest distance, has a relationship of about .4 of that of the Earth, its relative distance closer to the sun. Its relationship in the music is expressed as the polyrhythm 5:2–another way of expressing .4, that is, two-fifths of a beat, or five sounds against two beats. Pluto is approximately 39.5 times further from the sun than the earth, and this is expressed musically in chords whose durations are 39.5 sixteenth notes. In Venus the proportion 5:4, which expresses its .8 of the distance of the Earth to the sun.

Uranus is nineteen times the distance from the Earth to the sun, therefore the chords in its movement occur every nineteen sixteenth notes. Similarly, Pluto has a chord every 39 sixteenth notes. Jupiter, which is 5.2 times the Earth’s distance from the sun, is first rounded down to five and written as groups of phrases with five beats. Mars, at 1.5 the distance to the sun, lends itself nicely to 2:3, two beats sound against three beats. Neptune, on the other hand, is thirty times our distance from the sun, and therefore is broken into 5 times 6, or six five-beat phrases = 30. The swirling, circular figures of Saturn represent its rings. Saturn is 9.5 times the Earth’s distance from the sun, which I rounded down to 9:2 to represent nine and a half eighths.

In order to present nine separate pieces in a dramatic sequence, I arranged them so that the increasingly further away orbits alternate with the increasingly closer: Jupiter, Saturn, Uranus, Neptune, and Pluto become slower and alternate with Mars, Earth, Venus, and Mercury, which become faster. Thus the work ends with fastest piece, Mercury, followed by the slowest, Pluto. In addition, the first piece, Jupiter, functions somewhat as an overture that foreshadows each of the other movements. Just after I had written and learned these pieces did astronomers decide to renumber the planets and eliminate Pluto!

Recording: Larry Bell, on Casa Rustica Recordings 001