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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

Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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Page 1: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

Paul van derder Werf

Leiden Observatory

Inside the music of the spheresInside the music of the spheres

SassoneSassone

June 23, 2009June 23, 2009

Page 2: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

Music of the spheresMusic of the spheres 2

EnormouEnormous s

disclaimedisclaimerr

Page 3: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

Music of the spheresMusic of the spheres 3

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

Page 4: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 5: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

Music of the spheresMusic of the spheres 5

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

Page 6: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 7: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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 (!)

Page 8: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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.

Page 9: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

Music of the spheresMusic of the spheres 9

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

Page 10: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 11: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 12: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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!

Page 15: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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)

Page 17: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 18: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 19: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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Boethius (ca. 480 - 526)Boethius (ca. 480 - 526)

Trivium: logic grammar rhetoric

Quadrivium: mathematics music geometry astronomy

Page 20: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 22: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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The choirs of the angels The choirs of the angels

Hildegard von Bingen (1098 – 1179):

O vos angeli

Page 23: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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.

Page 25: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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%

Page 26: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 27: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 28: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 29: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 30: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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?

Page 31: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 33: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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Yorkshire Building Society BandYorkshire Building Society Band

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Deutsche BlDeutsche Blääserphilharmonieserphilharmonie

Page 35: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 36: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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Cosmological aspects of the Cosmological aspects of the bicyclebicycle

B

P

L

W

Page 37: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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

Page 39: Der Paul van der Werf Leiden Observatory Inside the music of the spheres Sassone June 23, 2009

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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