The phrase “music of the spheres” refers to the intertwined relationship between the structures of music and those of the physical world, and a conscious awareness of mystical or spiritual qualities being transmitted through composed sound.
All music consists of a form of dualism, an aural yin and yang in which consonance is inextricably linked with its complementary force of dissonance; one does not meaningfully exist without the other. Dissonance provokes a form of tension – an unsettled relation in the notes of music – and is relieved by the consonance of resolution. We hear this whether we are listening to Bach, Mozart, Bartók or Applebaum, although the balance is often shifted towards dissonance in post-20th century music, perhaps in reflection of societal conflicts.
Pythagoras is credited with having discovered the physical relationship, expressible as ratios, between mass and sound. He is also credited with having invented the monochord, essentially a stretched gut string on a soundboard with moveable bridges, for testing harmonic properties and their rapport with numerical ratios. (We will hear a monochord in Edward Applebaum’s Dirt Music, which may be the first instance ever of its use in composed music; more recent instruments with basic similarities to the monochord would include the Japanese koto and the Chinese ch’in.)
The octave ratio of 1:2 means that a mass, such as a string of any material, will produce a frequency an octave above the pitch of its full length when it is reduced by one half. For example, the open ‘A’ string of the violin sounds that pitch at about 440 vibrations per second. When the string is “stopped” by the violinist’s finger so that only half of its original length is vibrating, it sounds an ‘A’ that is an octave higher and vibrating twice as quickly. Simply stated, to play this musical interval, one part of the string length out of two parts total (the ratio 1:2) is set into vibration. The ratio for the fifth is 2:3 (two parts out of three are vibrating) and that of the fourth is 3:4.
Pythagoras and his followers believed that a universal philosophy could be founded in numbers. They differentiated three types of music: the music of instruments, the music of the human body and soul, and the music of the spheres, which was the music of the cosmos. Geometric shapes and even orbiting motions could be linked to this philosophy – indeed, Pythagoras could arguably be the first proponent of “string theory” as a tool to understanding the universe – and the important symbol of the tetractys contains the numbers of the perfect musical intervals of an octave, a fifth and a fourth:
According to Pliny, Pythagoras devised a literal “music of the spheres” by using musical intervals to describe the distances between the moon and the known planets. In his Timaeus, Plato took up the idea of a universal philosophy thorough numbers and their musical associations and devised a series that he termed the World Soul: 1, 2, 3, 9, 8, and 27. By using these as musical ratios (1:2, 2:3, 3:9, etc.) he created a series of musical notes that gave a default mathematical ratio for the half-step. By mathematical derivation, one can arrive at theoretical proportions for the non-Pythagorean intervals of seconds, thirds, sixths and sevenths. These intervals are inherently subjective and context-sensitive, however, and have led to epic battles over “desirable” tuning temperaments, in part due to the fact that fixed-pitch instruments like pianos have one pitch to represent at least two distinct notes.
One of these battles was between the lutenist and pedagogue Vincenzo Galilei and his teacher, Gioseffo Zarlino. A member of a neo-Platonic academy, where the ancient associations of music, science and philosophy were again united, Galilei’s use of practical experimentation in his scientific studies of tuning temperaments and their physical properties was influential on his son Galileo, whose own didactic techniques and observations from nature led to revolutionary discoveries in physics.
The great Johannes Kepler followed these leads in developing his laws of planetary motion, describing the relationships of planets and their orbits through numbers and ratios and using them to create geometric figures of two and three dimensions. He also employed musical references and even desired to create a “symphony of the cosmos,” stating that “the movements of the heavens are nothing except a certain everlasting polyphony.” Sir Isaac Newton was likewise inspired by the cosmic music of the ancients, as set forth in Proposition VIII of his Principia.
The notion of the “music of the spheres” continues today through studies of cosmic background radiation and “string theory,” among many other applications, and composers have often been directly or indirectly inspired by its concepts: Density 21.5 by Varèse combines an ancient instrument type with a radical view of the ratios of music and an inspiration from the earth itself: the gravitational weight of platinum, the metal used to build the flute that first played this work. Mozart’s frequent musical allusions to Masonic symbolism continue this notion, and Lou Harrison used the sounds of our world’s music – through time and space – to create memorably beautiful and compelling sounds in new combinations. Beethoven’s “music of the spheres” derives from a Romantic appreciation of the oneness of nature with the interior music of the soul, and Edward Applebaum’s Dirt Music was inspired by a love story (by Tim Winton) and the jazz idiom, with a nod to the architectural proportions of a Stradivarius violin transformed into music. Josef Strauss was also moved to write the “Music of the Spheres” Waltz, which links many lovely dances after a celestial introduction.
(Notes by Stephanie Chase from a chamber music program presented by the Music of the Spheres Society at Merkin Concert Hall in New York, October 2005.)