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What is the "Music of the Spheres?"
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:
X
XX
XXX
XXXX
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 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 Society
at Merkin Concert Hall in New York, October 2005.)
©Copyright
Stephanie Chase 2005. All Rights Reserved.
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