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Inside the music of the spheres
Paul van der Werf
Leiden Observatory
Sassone
June 23, 2009
Enormous
disclaimer
Music of the spheres
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Overview
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The Galilean revolution
The Harmony of the Spheres
The Quadrivium: Music, astronomy, mathematics, geometry
Music without sound?
A bridge between two worlds: Johannes Kepler
Harmony of the spheres after Galileo and Newton
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Digressions at various points:
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problems of tuning an instrument
astronomical aspects of the bicycle
Common approach in music and science
Music of the spheres
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The Galilean revolution (1)
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Copernicus’ heliocentric model
New accurate measurements by Tycho Brahe
Kepler’s first two laws
Invention of the telescope
Music of the spheres
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Invention of the telescope
 September 25, 1608: the lensmaker Hans Lippershey from
Middelburg (the Netherlands) applies for patent for an
instrument “om verre te zien” (to look into the distance).
 October 7, 1608: successful demonstration for the princes of
Orange: Lippershey receives an order for 6 instruments, for 1000
guilders each!.
 within two weeks two other lensmakers (including Lippershey’s
neighbour!) apply for similar patents; as a result, patent is not
granted
 a letter from 1634 mentions an earlier telescope from 1604, based
on an even earlier one from 1590
Music of the spheres
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The Galilean revolution (2)
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Copernicus’ heliocentric model
New accurate measurements by Tycho Brahe
Kepler’s first two laws
Invention of the telescope
Galileo’s discoveries
Kepler’s third law
Galileo’s trial
Music of the spheres
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Galileo Galilei (1564 – 1642)
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Born in a musical family: his father Vincenzo Galileo was a
lutenist, composer, music theorist (author of “Dialogus” on
two musical systems), and carried out acoustic experiments
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Heard of Lippershey’s invention
and reconstructed it
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First discoveries in 1609
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Principal publication in 1632 (“Dialogus”
on two world systems), trial in 1633
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Rehabilitation in 1980 (!)
Music of the spheres
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The Galilean revolution (3)
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Copernicus’ heliocentric model
New accurate measurements by Tycho Brahe
Kepler’s first two laws
Invention of the telescope
Galileo’s discoveries
Kepler’s third law
Galileo’s trial
Newton’s gravitational model of the solar system
This revolution overthrows a system that was in essence in place
for 2500 years. We can hardly imagine the impact on 17th century man.
Music of the spheres
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Foundation of the universe
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central to antique cosmology was the idea of
harmony as a foundation of the universe
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this universal harmony was present everywhere:
in mathematics, astronomy, music…
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therefore, the laws of music, of astronomy and of mathematics
were closely related
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in essence, this principle was the foundation of cosmology until
the Galilean revolution
Music of the spheres
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Pythagoras (569 – 475 BC)
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principle that complex
phenomena must reduce to
simple ones when properly
explained
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relation between frequencies
and musical intervals
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the distances between planets
correspond to musical tones
Music of the spheres
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Pythagoras and the science of music
f0 x 1
Prime
f0 x 9/8
Second
e.g., God save the Queen
f0 x 5/4
Third
e.g., Beethoven 5th
f0 x 4/3
Fourth
e.g., Dutch, French anthem
f0 x 3/2
Fifth
e.g., Blackbird (Beatles)
f0 x 5/3
Sixth
f0 x 15/8 Seventh
f0 x 2
Music of the spheres
Octave
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Now assign note names
Name
C
Interval
1/1 Start
Name
Interval
G 3/2
Fifth
D 9/8 Second
A 5/3 Sixth
E
5/4
Third
B 15/8 Seventh
F
4/3
Fourth
C
Music of the spheres
2/1 Octave
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Map onto Keys
C D
Music of the spheres
E
F G A
B
C
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Taking the Fifth
Name
C
Interval
1/1 Start
Name
Interval
G 3/2
Fifth
D 9/8 Second
A 5/3 Sixth
E
5/4
Third
B 15/8 Seventh
F
4/3
Fourth
C
2/1 Octave
Corresponding notes in each row are perfect Fifths (C-G, D-A,
E-B, F-C), and should be separated by a ratio of 3/2
This one doesn't work!
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Pythagorean tuning
Name
Interval
Name
Interval
C
Start
G
Fifth
1/1
3/2
D 9/8 Second
A 27/16 Sixth
E
81/64 Third
B
243/128
F
4/3
C
2/1 Octave
Fourth
Seventh
All whole step intervals are equal at 9/8
All half step intervals are equal at 256/243
Thirds are too wide at 81/64  5/4!
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Johannes Kepler (1571-1630)
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Plato (427 – 347 BC)
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In his Politeia Plato tells
the Myth of Er
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First written account of
Harmony of the Spheres
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A later version is given
by Cicero in his
Somnium Scipionis
Music of the spheres
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Later development
 many
different systems were used to assign
tones to planetary distances – no standard model
 different
opinions on whether the Music of the
Spheres could actually be heard
 influence
of Christian doctrine
 macrocosmos
Music of the spheres
– microcosmos correspondence
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Boethius (ca. 480 - 526)
Trivium:
 logic
 grammar
 rhetoric
Quadrivium:
 mathematics
 music
 geometry
 astronomy
Music of the spheres
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Music according to Boethius
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musica mundana
harmony of the spheres
 harmony of the elements
 harmony of the seasons
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musica humana
harmony of soul and body
 harmony of the parts of the soul
 harmony of the parts of the body
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musica in instrumentis constituta
harmony of string instruments
 harmony of wind instruments
 harmony of percussion instruments
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The making/performing of music is by far the least important of
these! But this will now begin to gain in importance.
Music of the spheres
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Influence of musical advances and
Christian doctrine
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from the 11th century onwards, there is an enormous
development in the composition of music
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musical notation
advances in music theory (Guido of Arezzo)
early polyphony
Christian doctrine had great influence on the
development of sacred music
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sacred music was in the first place a reflection of the perfection of heaven
and of the creator
the 9 spheres of heaven became the homes of 9 different kinds of angels
theories of the music of angels developed
Music of the spheres
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The choirs of the angels
 Hildegard
von
Bingen (1098 – 1179):
O vos angeli
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Range more than
2.5 octaves!
Unique in music
history and
not (humanly)
singable
Full vocal range
of angel choirs
according to
contemporary
theories
Music of the spheres
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Kepler’s Mysterium Cosmographicum (1596)
relating the sizes
of the planetary
orbits via the five
Platonic solids.
Music of the spheres
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How well does this work?
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Saturn aphelion
Jupiter
Mars
Earth
Venus
Mercury
Music of the spheres
actual
9.727
5.492
1.648
1.042
0.721
0.481
model
--> 10.588
--> 5.403
--> 1.639
--> 1.102
--> 0.714
--> 0.502
=> +9%
=> -2%
=> -1%
=> 0%
=> -1%
=> +4%
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Kepler’s Music of the Spheres
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In his Harmonices Mundi Libri V Kepler assigns tones to the
planets according to their orbital velocities
Since these are variable, the planets now have melodies which
sound together in cosmic counterpoint
Music of the spheres
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Musical example given by Kepler
Earth has melody mi – fa (meaning miseria et fames)
 This is the characteristic interval of the Phrygian church mode
 As an example he quotes a motet by Roland de Lassus, whom he
knew personally: In me transierunt irae tuae
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Music of the spheres
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What is the Phrygian mode?
To create a mode, simply start a major scale on a different pitch.
ut
re
mi
fa
sol
la
si
semitone
ut
semitone
C Major Scale (Ionian Mode)
semitone
semitone
C Major Scale starting on D (Dorian Mode)
mi
fa
semitone
semitone
C Major Scale starting on E (Phrygian Mode)
hexachord
Music of the spheres
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Phrygian mode today
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Jefferson Airplane: White Rabbit
Björk: Hunter
Theme music from the TV-series Doctor Who
Megadeth: Symphony of Destruction
Iron Maiden: Remember Tomorrow
Pink Floyd: Matilda Mother
and:
Set the Controls for the Heart of the Sun
Robert Plant: Calling to You
Gordon Duncan: The Belly Dancer
Theme from the movie Predator
Jamiroquai: Deeper Underground
The Doors: Not to touch the Earth
Britney Spears: If U Seek Amy
Music of the spheres
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Modal music appears at
unexpected places
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The above tune is in the Dorian church mode
Quiz question: which Beatles song is this?
Music of the spheres
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Kepler’s heavenly motet
Music of the spheres
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After Kepler, Galileo & Newton
Universal harmony as underlying principle removed
 End of the Harmony of the Spheres
 Founding principle of astrology removed
 Harmony of the Spheres occasionally returns
as a poetic theme or esoteric idea
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Examples:
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Mozart: Il Sogno di Scipione
Haydn: Die Schöpfung
Mahler: 8th Symphony
Music of the spheres
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Yorkshire Building Society Band
Music of the spheres
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Deutsche Bläserphilharmonie
Music of the spheres
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“Music of the Spheres”
www.spectrummuse.com
“The Science of Harmonic Energy and Spirit
unification of the harmonic languages of color,
music, numbers and waves”, etc. etc….
Music of the spheres
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B
Cosmological aspects of the bicycle
L
W
P
Music of the spheres
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Amazing results!
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P2 * ( L B )1/2 = 1823 = Mass of Proton
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P4 * W2 = 137.0 = Fine Structure Constant
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P-5 * ( L / WB )1/3 = 6.67*10-8 = Gravitational Constant
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P1/2 * B1/3 / L = 1.496 = Distance to Sun (108 km)
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W * P2 * L1/3 * B5 = 2.999*105 ~ Speed of Light (km/s)
Mass of Electron
2.998 measured
(so measurements probably wrong)
Music of the spheres
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Modern musical analogies
WMAP CMB temperature power spectrum
Musical analogies are still possible, but as results, not as the principle
Music of the spheres
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Approach to music and science
 modesty
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playing someone else’s composition is bold
understanding the universe is a very ambitious goal
 honesty
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play only what you think is right
say only what you think is right
Music of the spheres
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