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Inside the music of the spheres. Sassone June 23, 2009. Enormous disclaimer. Overview. The Galilean revolution The Harmony of the Spheres The Quadrivium: Music, astronomy, mathematics, geometry Music without sound? A bridge between two worlds: Johannes Kepler

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Inside the music of the spheres l.jpg

Inside the music of the spheres

Sassone

June 23, 2009


Enormous disclaimer l.jpg
Enormous disclaimer

Music of the spheres


Overview l.jpg
Overview

  • 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

Music of the spheres


The galilean revolution 1 l.jpg
The Galilean revolution (1)

  • Copernicus’ heliocentric model

  • New accurate measurements by Tycho Brahe

  • Kepler’s first two laws

  • Invention of the telescope

Music of the spheres


Slide5 l.jpg

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


The galilean revolution 2 l.jpg
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

Music of the spheres


Galileo galilei 1564 1642 l.jpg
Galileo Galilei (1564 – 1642)

  • 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

  • Heard of Lippershey’s invention

    and reconstructed it

  • First discoveries in 1609

  • Principal publication in 1632 (“Dialogus”

    on two world systems), trial in 1633

  • Rehabilitation in 1980 (!)

Music of the spheres


The galilean revolution 3 l.jpg
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 place

    for 2500 years. We can hardly imagine the impact on 17th century man.

Music of the spheres


Foundation of the universe l.jpg
Foundation 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

Music of the spheres


Pythagoras 569 475 bc l.jpg
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

Music of the spheres


Pythagoras and the science of music l.jpg
Pythagoras and the science of music

f0x 1 Prime

f0x9/8 Second e.g., God save the Queen

f0x5/4 Third e.g., Beethoven 5th

f0x4/3 Fourth e.g., Dutch, French anthem

f0x3/2 Fifth e.g., Blackbird (Beatles)

f0x5/3 Sixth

f0x15/8 Seventh

f0x2 Octave

Music of the spheres


Now assign note names l.jpg
Now assign note names

Name Interval

C 1/1 Start

D 9/8 Second

E 5/4 Third

F 4/3 Fourth

Name Interval

G 3/2 Fifth

A 5/3 Sixth

B 15/8 Seventh

C 2/1 Octave

Music of the spheres


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Map onto Keys

C D E F G A B C

Music of the spheres


Taking the fifth l.jpg

This one doesn't work!

Taking the Fifth

Name Interval

C 1/1 Start

D 9/8 Second

E 5/4 Third

F 4/3 Fourth

Name Interval

G 3/2 Fifth

A 5/3 Sixth

B 15/8 Seventh

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

Music of the spheres


Pythagorean tuning l.jpg

All whole step intervals are equal at 9/8

Pythagorean tuning

Name Interval

C 1/1 Start

D 9/8 Second

E 81/64 Third

F 4/3 Fourth

Name Interval

G 3/2 Fifth

A 27/16Sixth

B 243/128Seventh

C 2/1 Octave

All half step intervals are equal at 256/243

Thirds are too wide at 81/64  5/4!

Music of the spheres


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Johannes Kepler (1571-1630)

Music of the spheres


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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

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 – microcosmos correspondence

Music of the spheres


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

Trivium:

  • logic

  • grammar

  • rhetoric

    Quadrivium:

  • mathematics

  • music

  • geometry

  • astronomy

Music of the spheres


Music according to boethius l.jpg
Music 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.

Music of the spheres


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Influence of musical advances and 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

Music of the spheres


The choirs of the angels l.jpg
The choirs of the angels

  • Hildegard von Bingen (1098 – 1179):

    O vos angeli

Music of the spheres


Slide23 l.jpg

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


Kepler s mysterium cosmographicum 1596 l.jpg
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?

actual model

  • Saturn aphelion 9.727 --> 10.588 => +9%

  • Jupiter 5.492 --> 5.403 => -2%

  • Mars 1.648 --> 1.639 => -1%

  • Earth 1.042 --> 1.102 => 0%

  • Venus 0.721 --> 0.714 => -1%

  • Mercury 0.481 --> 0.502 => +4%

Music of the spheres


Kepler s music of the spheres l.jpg
Kepler’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

Music of the spheres


Musical example given by kepler l.jpg
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

Music of the spheres


What is the phrygian mode l.jpg

semitone

semitone

semitone

semitone

semitone

semitone

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 ut

C Major Scale (Ionian Mode)

C Major Scale starting on D (Dorian Mode)

mi fa

C Major Scale starting on E (Phrygian Mode)

hexachord

Music of the spheres


Phrygian mode today l.jpg
Phrygian 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

Music of the spheres


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Modal music appears at unexpected places

  • The above tune is in the Dorian church mode

  • Quiz question: which Beatles song is this?

Music of the spheres


Kepler s heavenly motet l.jpg
Kepler’s heavenly motet

Music of the spheres


After kepler galileo newton l.jpg
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

  • Examples:

    • 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


Cosmological aspects of the bicycle l.jpg

B

Cosmological aspects of the bicycle

L

W

P

Music of the spheres


Amazing results l.jpg
Amazing results!

Mass of Proton Mass of Electron

  • P2 * ( L B )1/2 = 1823 =

  • P4 * W2 = 137.0 = Fine Structure Constant

  • P-5 * ( L / WB )1/3 = 6.67*10-8 = Gravitational Constant

  • P1/2* B1/3/ L = 1.496 = Distance to Sun (108 km)

  • W * P2 * L1/3 * B5 = 2.999*105 ~ Speed of Light (km/s)

2.998 measured(so measurements probably wrong)

Music of the spheres


Slide38 l.jpg

Modern musical analogies

WMAP CMB temperature power spectrum

Musical analogies are still possible, but as results, not as the principle

Music of the spheres


Approach to music and science l.jpg
Approach to music and science

  • 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

Music of the spheres


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