Paul van der der Werf Leiden Observatory Inside the music of the Inside the music of the spheres spheres Sassone Sassone June 23, 2009 June 23, 2009
Apr 01, 2015
Paul van derder Werf
Leiden Observatory
Inside the music of the spheresInside the music of the spheres
SassoneSassone
June 23, 2009June 23, 2009
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EnormouEnormous s
disclaimedisclaimerr
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OverviewOverview
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
Digressions at various points: problems of tuning an instrument astronomical aspects of the bicycle
Common approach in music and science
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The Galilean revolution (1)The Galilean revolution (1) Copernicus’ heliocentric model New accurate measurements by Tycho Brahe Kepler’s first two laws Invention of the telescope
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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
Invention of the telescopeInvention of the telescope
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The Galilean revolution (2)The Galilean revolution (2) 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
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Galileo Galilei (1564 – 1642)Galileo Galilei (1564 – 1642) Born in a musical family: his father Vincenzo Galileo was a Born in a musical family: his father Vincenzo Galileo was a
lutenist, composer, music theorist (author of “Dialogus” on lutenist, composer, music theorist (author of “Dialogus” on two musical systems), and carried out acoustic experimentstwo musical systems), and carried out acoustic experiments
Heard of Lippershey’s inventionHeard of Lippershey’s invention and reconstructed itand reconstructed it
First discoveries in 1609First discoveries in 1609
Principal publication in 1632 (“Dialogus”Principal publication in 1632 (“Dialogus”
on two world systems), trial inon two world systems), trial in 1633 1633
RehabilitationRehabilitation in 1980 (!) in 1980 (!)
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The Galilean revolution (3)The Galilean revolution (3) 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 placefor 2500 years. We can hardly imagine the impact on 17th century
man.
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Foundation of the universeFoundation of the universe central to antique cosmology was the idea of harmony as a foundation of the universe
this universal harmony was present everywhere: in mathematics, astronomy, music…
therefore, the laws of music, of astronomy and of mathematics were closely related
in essence, this principle was the foundation of cosmology until the Galilean revolution
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Pythagoras (569 – 475 BC)Pythagoras (569 – 475 BC)
principle that complex phenomena must reduce to simple ones when properly explained
relation between frequencies and musical intervals
the distances between planets correspond to musical tones
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Pythagoras and the science of musicPythagoras and the science of musicff00x 1x 1 PrimePrime
ff00 xx 9/8 9/8 Second Second e.g., God save the Queene.g., God save the Queen
ff00 xx 5/4 5/4 ThirdThird e.g., Beethoven 5the.g., Beethoven 5th
ff00 xx 4/3 4/3 FourthFourth e.g., Dutch, French antheme.g., Dutch, French anthem
ff00 xx 3/2 3/2 FifthFifth e.g., Blackbird (Beatles)e.g., Blackbird (Beatles)
ff00 xx 5/3 5/3 SixthSixth
ff00 xx 15/8 15/8 SeventhSeventh
ff00 xx 22 OctaveOctave
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Now assign note namesNow assign note names
NameName IntervalInterval
C C 1/11/1 StartStart
D D 9/8 9/8 Second Second
E E 5/4 5/4 ThirdThird
F F 4/3 4/3 FourthFourth
NameName IntervalInterval
G G 3/2 3/2 FifthFifth
A A 5/3 5/3 SixthSixth
B B 15/8 15/8 SeventhSeventh
C C 2/12/1 OctaveOctave
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Map onto KeysMap onto Keys
C D E F G A B C
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Taking the FifthTaking the Fifth
NameName IntervalInterval
C C 1/11/1 StartStart
D D 9/8 9/8 Second Second
E E 5/4 5/4 ThirdThird
F F 4/3 4/3 FourthFourth
NameName IntervalInterval
G G 3/2 3/2 FifthFifth
A A 5/3 5/3 SixthSixth
B B 15/8 15/8 SeventhSeventh
C C 2/12/1 OctaveOctave
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 tuningPythagorean tuning
NameName IntervalInterval
C C 1/11/1 StartStart
D D 9/89/8 Second Second
E E 81/6481/64 ThirdThird
F F 4/34/3 FourthFourth
NameName IntervalInterval
G G 3/23/2 FifthFifth
A A 27/1627/16 SixthSixth
B B 243/128243/128 SeventhSeventh
C C 2/12/1 OctaveOctave
All whole step intervals are equal at 9/8All 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)Johannes Kepler (1571-1630)
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Plato (427 – 347 BC)Plato (427 – 347 BC)
In his Politeia Plato tells the Myth of Er
First written account of
Harmony of the Spheres
A later version is given by Cicero in his Somnium Scipionis
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Later developmentLater 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 – microcosmos correspondence
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Boethius (ca. 480 - 526)Boethius (ca. 480 - 526)
Trivium: logic grammar rhetoric
Quadrivium: mathematics music geometry astronomy
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Music according to BoethiusMusic according to Boethius musica mundana
harmony of the spheres harmony of the elements harmony of the seasons
musica humana harmony of soul and body harmony of the parts of the soul harmony of the parts of the body
musica in instrumentis constituta harmony of string instruments harmony of wind instruments harmony of percussion instruments
The making/performing of music is by far the least important of these! But this will now begin to gain in importance.
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Influence of musical advances Influence of musical advances and Christian doctrineand Christian doctrine
from the 11th century onwards, there is an enormous development in the composition of music musical notation advances in music theory (Guido of Arezzo) early polyphony
Christian doctrine had great influence on the development of sacred music 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
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The choirs of the angels The choirs of the angels
Hildegard von Bingen (1098 – 1179):
O vos angeli
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Range more than2.5 octaves!
Unique in musichistory andnot (humanly)singable
Full vocal rangeof angel choirsaccording tocontemporarytheories
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Kepler’s Mysterium Cosmographicum (1596)Kepler’s Mysterium Cosmographicum (1596)
relating the relating the sizes of the sizes of the planetary orbits planetary orbits via the five via the five Platonic solids.Platonic solids.
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How well does this work?How well does this work?
actual modelactual model Saturn aphelionSaturn aphelion 9.727 --> 10.588 => +9%9.727 --> 10.588 => +9% Jupiter Jupiter 5.492 --> 5.403 => -2%5.492 --> 5.403 => -2% Mars Mars 1.648 --> 1.639 => -1%1.648 --> 1.639 => -1% Earth Earth 1.042 --> 1.102 => 0%1.042 --> 1.102 => 0% Venus Venus 0.721 --> 0.714 => -1%0.721 --> 0.714 => -1% Mercury Mercury 0.481 --> 0.502 => +4%0.481 --> 0.502 => +4%
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Kepler’s Music of the SpheresKepler’s Music of the Spheres
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
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Musical example given by Musical example given by KeplerKepler
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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What is the What is the Phrygian Phrygian mode?mode?
To create a mode, simply start a major scale on a different pitch.
C Major Scale (Ionian Mode)
C Major Scale starting on D (Dorian Mode)
C Major Scale starting on E (Phrygian Mode)
semitone
semitone
semitone
semitone
semitone
semitone
mi fa
ut re mi fa sol la si ut
hexachord
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Phrygian mode todayPhrygian mode today 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
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Modal music appears at Modal music appears at unexpected placesunexpected places
The above tune is in the Dorian church mode Quiz question: which Beatles song is this?
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Kepler’s heavenly Kepler’s heavenly motetmotet
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After Kepler, Galileo & After Kepler, Galileo & NewtonNewton
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
Examples: Mozart: Il Sogno di Scipione Haydn: Die Schöpfung Mahler: 8th Symphony
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Yorkshire Building Society BandYorkshire Building Society Band
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Deutsche BlDeutsche Blääserphilharmonieserphilharmonie
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““The The ScienceScience of Harmonic Energy and Spirit of Harmonic Energy and Spiritunification of the harmonic languages of color, unification of the harmonic languages of color,
music, numbers and waves”, etc. etc….music, numbers and waves”, etc. etc….
““Music of the Spheres” Music of the Spheres” www.spectrummuse.comwww.spectrummuse.com
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Cosmological aspects of the Cosmological aspects of the bicyclebicycle
B
P
L
W
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Amazing results!Amazing results! PP22 * ( L B ) * ( L B )1/21/2 = 1823 = = 1823 =
PP44 * W * W22 = 137.0 = Fine Structure Constant = 137.0 = Fine Structure Constant
PP-5-5 * ( L / WB ) * ( L / WB )1/31/3 = 6.67*10 = 6.67*10-8-8 = Gravitational = Gravitational ConstantConstant
PP1/21/2 * B* B1/31/3 / L = 1.496 = Distance to Sun (10/ L = 1.496 = Distance to Sun (1088 km) km)
WW * P * P2 2 * L* L1/31/3 * * BB55 = 2.999*10 = 2.999*105 5 ~~ Speed of Light Speed of Light (km/s)(km/s)
Mass of Proton Mass of Electron
2.998 measured(so measurements probably wrong)
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Musical analogies are still possible, but as results, not as the principle
WMAP CMB temperature power spectrum
Modern musical Modern musical analogiesanalogies
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Approach to music and Approach to music and sciencescience
modesty playing someone else’s composition is bold understanding the universe is a very ambitious goal
honesty play only what you think is right say only what you think is right