Harmony of the Spheres:
(The Geometry of Music)
It is now realised
that acoustics have played an important part in our lives for
of thousands of years. Palaeolithic caves have been shown to share a relationship between the
location of their internal cave art and areas which demonstrate high acoustic
We also know that acoustic qualities were deliberately built into
prehistoric constructions around the world.
about Acoustics in Prehistory)
Although there is
little recognition for the relationship between music, mathematics
and physical universe, it seems that such a knowledge has been
understood for thousands of years having been incorporated into
myths and even the dimensions of certain sacred places in order to enhance them. The harmonic
qualities of music can have a profound and beneficial effect on the
human psyche (4),
something that was perhaps realised more than it is today.
It is a simple
fact that music is based on mathematics. Put simply, each note has its own vibration, and it is the frequency of
the vibrations that distinguishes one note from another. The
notes on each scale are seperated from one another by simple
mathematical proportions and our ear is able to recognise that.
1:2, 2:3, 3:4,
What that means
is that when a wrong note is played in a symphony, even the
untrained ear can recognise that there is something wrong,
sounds that conform to these ratios are 'pleasing' to the ear,
whilst those that don't are 'dischordal'. It
seems that our brains are programmed to understand the
mathematical relationships between notes and harmonies.
confirmed discovery of a musical instrument we have comes from
around 35,000 years ago (3), with several flutes having been
found made from mammoth and bird bones. Earlier discoveries have been
claimed from the Neanderthal from 40 - 60,000 years ago, but
these are speculative at present. Significantly these early instruments
have been shown to use the same diatonic scales (based on he
same seven notes that we use today). The same diatonic scales
are also found in early Sumeria, China and Europe,
suggesting an extremely early origin for the preference for
about Bone Flutes)
repetitive music is a well-known method for humans into the
trance, or altered state of consciousness (for example, during
The RigVeda from
Indian prehistory (Veda meaning 'knowledge' or 'wisdom'
in Sanskrit), is believed to be
a mathematical metaphor for a cosmological knowledge base, derived from a musical model.
The Vedas are believed to be the oldest texts in the Indian
subcontinent, handed down by oral tradition alone until c. 100
The metaphors of the Vedas are simultaneously descriptive of
astronomy, mathematics, music, poetry and art. They describe a
dynamic and cyclic universe with the harmonic musical ratios
operating as a physical, figurative and literal medium between
ourselves and the authors.
sources from ancient Sumeria reveal an orderly organized system
of diatonic scales. (8)
How closely connected this was to their astronomical and
mathematical researches is unknown, but we know that the
Sumerian and Vedic cultures were closely connected through the
discoveries of similar clay 'seals' found in both locations and
that they shared a similar understanding of the movements of the
heavens. The immense regard with which later Mesopotamian
sciences showed to astronomy is reflected in the extraordinarily large
number of astronomical records discovered in ruined libraries
such as Nineveh, Nippur and Ur. Apparently the Chaldeans were
the first people to conceive of the heavenly bodies joining in a
cosmic chant as they moved in stately manner across the sky. Job
describes a time "when the stars of the morning sang together,"
Cathedral, and many other medieval buildings, these harmonic
ratios were translated into the architecture of the magnificent
structures. It appears that not only do these ratios define the
sounds we find pleasing but also the physical proportions of
beauty. The architecture of Chartres Cathedral has been
described as 'frozen music' on account of the large number of
musical proportions embodied into the design. It became one of
the most important French pilgrimage sites, and was built at the
same time (11th - 13th centuries) as several other immense
gothic cathedrals in Europe, incorporating sacred geometry and
harmonic proportions in their quest to bring mankind closer to
Harmony of the Spheres:
first confirmed record of a knowledge of the relationship
between astronomy, music and geometry comes (almost predictably) from the Greeks;
In particular, Pythagoras who wrote of the 'Harmony of the
Spheres', and of whom it was said: '...of all men, he alone [Pythagoras]
hear the music of the spheres...'.
- As well as being a profound philosopher and mathematician, Pythagoras
is accredited for discovering the simple fact that the pitch of a musical note depends
upon the length of the string which produces it. This allowed
him to correlate the intervals of the musical scale with simple
numerical ratios. His
discoveries in the fields of music and astronomy led him to his
most profound realisation, namely, 'The Harmony of the Spheres',
he proposed that the planets and stars moved according to
mathematical equations, which corresponded to musical ratios,
therefore producing a symphony.
the Pythagoreans thought that the heavenly bodies were separated
from one another by intervals corresponding to the harmonic
lengths of strings, they held that the movement of the spheres
gives rise to a musical sound called the "harmony of the
Encarta Encyclopaedia 2000)
The names given
by the Pythagoreans to the various notes of the diatonic scale
were, according to Macrobius, derived from an estimation of the
velocity and magnitude of the planetary bodies. Each of these
gigantic spheres as it rushed through space was believed to
sound a certain tone caused by its continuous displacement of
the �thereal diffusion. As these tones were a manifestation of
divine order and motion, it must necessarily follow that they
partook of the harmony of their own source. "The assertion that
the planets in their revolutions round the earth uttered certain
sounds differing according to their respective 'magnitude,
celerity and local distance,' was commonly made by the Greeks.
Thus Saturn, the farthest planet, was said to give the gravest
note, while the Moon, which is the nearest, gave the sharpest.
'These sounds of the seven planets, and the sphere of the fixed
stars, together with that above us [Antichthon], are the nine
Muses, and their joint symphony is called Mnemosyne.'"
Quote from Aristotle: ...
"[the Pythagoreans] saw that
the ... ratios of musical scales were expressible in numbers
[and that] .. all things seemed to be modelled on numbers,
and numbers seemed to be the first things in the whole of
nature, they supposed the elements of number to be the
elements of all things, and the whole heaven to be a musical
scale and a number." (10)
Pythagoreans also used music to heal the body and to elevate the
soul, believing that earthly music was '...a
faint echo of the universal harmony of the spheres...'
Johannes Kepler - 'Harmonice Mundi'
(The Harmony of the World), published in 1619.
who was influenced by arguments in Ptolemy�s Optics and
Harmonica, compiled his Harmonices Mundi ('Harmony
of the World'), which presented his own analysis of optical
perceptions, geometrical shapes, musical consonances and
planetary harmonies. According to Kepler, the connection between
geometry (sacred geometry), cosmology, astrology, harmonics and
music is through musica universalis.
physical harmonies in planetary motion. He found that the difference
between the maximum and minimum angular speeds of a planet in its
orbit approximates a harmonic proportion. For instance, the maximum
angular speed of the Earth as measured from the Sun varies by a
semitone (a ratio of 16:15), from mi to fa, between
aphelion and perihelion. Venus only varies by a tiny 25:24 interval
(called a diesis in musical terms).
also discovers that all but one of the ratios of the
maximum and minimum speeds of planets on neighbouring
orbits approximate musical harmonies within a margin of
error of less than a diesis (a 25:24 interval). The
orbits of Mars and Jupiter produce the one exception to
this rule, creating the un-harmonic ratio of 18:19.
In fact, the cause of Kepler's dissonance might be
explained by the fact that the asteroid belt separates
those two planetary orbits, as discovered in 1801, 150
years after Kepler's death.
perhaps interesting to note that all the platonic solids
also realised by Kepler are represented in the several hundred
small, carved Scottish prehistoric petrospheres.
on the Stone Balls of Scotland)
Recent Articles on the
'Harmony of the Spheres'.
Article: The Telegraph.
works of Plato, the ancient classical Greek philosopher,
appear to contain a hidden musical code, a British
academic has claimed':
Dr Jay Kennedy,
an historian and philosopher of
science at the University of
Manchester, found Plato
used a regular pattern of
symbols to give his writing a
"musical" structure. In his five
year study, Dr Kennedy found
Plato, who died around 347BC,
used the symbols inherited from
the ancient followers of
Pythagoras. His findings,
published in the American
classics journal Apeiron,
suggested Plato was not only a
secret follower of Pythagoras
but also shared his belief that
the universe�s secrets lay maths
and its numbers. Dr
Kennedy said the key to
unlocking the code came from the
12 notes of the Greek musical
scale, which he said was popular
among followers of Pythagoras.
Using computer technology, he
restored contemporary versions
of Plato's manuscripts to their
original form, which he said
consisted of lines of 35
characters, with no spaces or
punctuation. Dr Kennedy
discovered that some key
phrases, themes and words
occurred during regular
intervals throughout, which
matched the spacing in the 12
note scale. He argued that
Plato did not use the code for
pleasure, but instead for his
own safety after his teacher was
executed for heresy.
(Link to Full Article:
'Distant stars make music'.
'Music of the stars' now louder.
and Technology Homepage)