music of the spheres 2 - leiden observatory - leiden …pvdwerf/biblio/pdf/sassone09.pdfmusic of the...

Paul van derder Werf

Leiden Observatory

Inside the music of the spheresInside the music of the spheres

SassoneSassone

June 23, 2009June 23, 2009

Music of the spheresMusic of the spheres 2


OverviewOverview

The Galilean revolutionThe Harmony of the SpheresThe Quadrivium: Music, astronomy, mathematics, geometryMusic without sound?A bridge between two worlds: Johannes KeplerHarmony of the spheres after Galileo and Newton

Digressions at various points:problems of tuning an instrumentastronomical aspects of the bicycle

Common approach in music and science


The Galilean revolution (1)The Galilean revolution (1)Copernicus’ heliocentric modelNew accurate measurements by Tycho BraheKepler’s first two lawsInvention 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

Invention of the telescopeInvention of the telescope


The Galilean revolution (2)The Galilean revolution (2)Copernicus’ heliocentric modelNew accurate measurements by Tycho BraheKepler’s first two lawsInvention of the telescopeGalileo’s discoveriesKepler’s third lawGalileo’s trial


Galileo Galileo GalileiGalilei (1564 (1564 –– 1642)1642)

Born in a musical family: his father Born in a musical family: his father VincenzoVincenzo Galileo was a Galileo was a lutenistlutenist, composer, music theorist (author of , composer, music theorist (author of ““DialogusDialogus”” on on two musical systems), and carried out acoustic experimentstwo musical systems), and carried out acoustic experiments

Heard of LippersheyHeard of Lippershey’’s inventions inventionand reconstructed itand reconstructed it

First discoveries in 1609First discoveries in 1609

Principal publication in 1632 (Principal publication in 1632 (““DialogusDialogus””on two world systems), trial inon two world systems), trial in 16331633

RehabilitationRehabilitation in 1980 (!)in 1980 (!)


The Galilean revolution (3)The Galilean revolution (3)Copernicus’ heliocentric modelNew accurate measurements by Tycho BraheKepler’s first two lawsInvention of the telescopeGalileo’s discoveriesKepler’s third lawGalileo’s trialNewton’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.


Foundation of the universeFoundation of the universecentral to antique cosmology was the idea ofharmony 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 untilthe Galilean revolution


Pythagoras (569 Pythagoras (569 –– 475 BC)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


Pythagoras and the science of musicPythagoras and the science of music

ff00 x 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


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


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


Map onto KeysMap onto Keys

C D E F G A B C


Taking the FifthTaking the Fifth



D D 9/8 9/8 Second Second

E E 5/4 5/4 ThirdThird

F F 4/3 4/3 FourthFourth


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 OctaveOctaveCorresponding 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!


Pythagorean tuningPythagorean tuning



D D 9/89/8 Second Second

E E 81/6481/64 ThirdThird

F F 4/34/3 FourthFourth


G G 3/23/2 FifthFifth

A A 27/1627/16 SixthSixth

B B 243/128243/128 SeventhSeventh

C C 2/12/1 OctaveOctaveAll whole step intervals are equal at 9/8

All half step intervals are equal at 256/243Thirds are too wide at 81/64 ≠ 5/4!


Johannes Kepler (1571Johannes Kepler (1571‐‐1630)1630)


Plato (427 Plato (427 –– 347 BC)347 BC)

In his Politeia Plato tells the Myth of Er

First written account ofHarmony of the Spheres

A later version is givenby Cicero in his Somnium Scipionis


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


Boethius (ca. 480 Boethius (ca. 480 ‐‐ 526)526)

Trivium:logicgrammarrhetoric

Quadrivium:mathematicsmusicgeometryastronomy


Music according to BoethiusMusic according to Boethiusmusica mundana

harmony of the spheresharmony of the elementsharmony of the seasons

musica humanaharmony of soul and bodyharmony of the parts of the soulharmony of the parts of the body

musica in instrumentis constitutaharmony of string instrumentsharmony of wind instrumentsharmony 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.


Influence of musical advances and Influence of musical advances and Christian doctrineChristian doctrinefrom the 11th century onwards, there is an enormous development in the composition of music

musical notationadvances 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 creatorthe 9 spheres of heaven became the homes of 9 different kinds of angelstheories of the music of angels developed


The choirs of the angels The choirs of the angels

Hildegard von Bingen (1098 – 1179):O vos angeli


Range more than2.5 octaves!

Unique in musichistory andnot (humanly)singable

Full vocal rangeof angel choirsaccording tocontemporarytheories


KeplerKepler’’ss MysteriumMysterium CosmographicumCosmographicum (1596)(1596)

relating the sizes relating the sizes of the planetary of the planetary orbits via the five orbits via the five Platonic solids.Platonic solids.


How well does this work?How well does this work?actual modelactual model

Saturn aphelionSaturn aphelion 9.727 9.727 ‐‐‐‐> 10.588 => +9%> 10.588 => +9%Jupiter Jupiter 5.492 5.492 ‐‐‐‐> 5.403 => > 5.403 => ‐‐2%2%Mars Mars 1.648 1.648 ‐‐‐‐> 1.639 => > 1.639 => ‐‐1%1%Earth Earth 1.042 1.042 ‐‐‐‐> 1.102 => 0%> 1.102 => 0%Venus Venus 0.721 0.721 ‐‐‐‐> 0.714 => > 0.714 => ‐‐1%1%Mercury Mercury 0.481 0.481 ‐‐‐‐> 0.502 => +4%> 0.502 => +4%


KeplerKepler’’ss Music of the SpheresMusic of the Spheres

In his Harmonices Mundi Libri V Kepler assigns tones to the planets according to their orbital velocitiesSince these are variable, the planets now have melodies which sound together in cosmic counterpoint


Musical example given by KeplerMusical example given by Kepler

Earth has melody mi – fa (meaning miseria et fames)This is the characteristic interval of the Phrygian church modeAs an example he quotes a motet by Roland de Lassus, whom he knew personally: In me transierunt irae tuae


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

semitonesemitone

semitone semitone

semitone

mi fa

ut re mi fa sol la si ut

hexachord


Phrygian mode todayPhrygian mode todayJefferson Airplane: White RabbitBjörk: HunterTheme music from the TV‐series Doctor WhoMegadeth: Symphony of DestructionIron Maiden: Remember TomorrowPink Floyd: Matilda Motherand: Set the Controls for the Heart of the SunRobert Plant: Calling to YouGordon Duncan: The Belly Dancer Theme from the movie PredatorJamiroquai: Deeper Underground The Doors: Not to touch the Earth Britney Spears: If U Seek Amy

http://en.wikipedia.org/wiki/Jefferson_Airplane

http://en.wikipedia.org/wiki/Bj%C3%B6rk

http://en.wikipedia.org/wiki/Doctor_Who

http://en.wikipedia.org/wiki/Megadeth

http://en.wikipedia.org/wiki/Iron_Maiden

http://en.wikipedia.org/wiki/Pink_Floyd

http://en.wikipedia.org/wiki/Robert_Plant

http://en.wikipedia.org/wiki/Gordon_Duncan

http://en.wikipedia.org/wiki/Predator_(film)

http://en.wikipedia.org/wiki/Jamiroquai

http://en.wikipedia.org/wiki/The_Doors

http://en.wikipedia.org/wiki/Britney_Spears


Modal music appears at Modal music appears at unexpected placesunexpected places

The above tune is in the Dorian church modeQuiz question: which Beatles song is this?


KeplerKepler’’ss heavenly motetheavenly motet


After Kepler, Galileo & NewtonAfter Kepler, Galileo & Newton

Universal harmony as underlying principle removedEnd of the Harmony of the SpheresFounding principle of astrology removedHarmony of the Spheres occasionally returnsas a poetic theme or esoteric idea

Examples:Mozart: Il Sogno di ScipioneHaydn: Die SchöpfungMahler: 8th Symphony


Yorkshire Building Society BandYorkshire Building Society Band


Deutsche Deutsche BlBlääserphilharmonieserphilharmonie


““The The ScienceScience of Harmonic Energy and Spiritof Harmonic Energy and Spiritunification of the harmonic languages of color, unification of the harmonic languages of color,

music, numbers and wavesmusic, numbers and waves””, etc. etc, etc. etc……..

““Music of the SpheresMusic of the Spheres””www.spectrummuse.comwww.spectrummuse.com


Cosmological aspects of the bicycleCosmological aspects of the bicycleB

P

L

W


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‐‐55 * ( L / WB )* ( L / WB )1/31/3 = 6.67*10= 6.67*10‐‐88 = Gravitational Constant= Gravitational Constant

PP1/21/2 * B* B1/31/3 / L = 1.496 = Distance to Sun (10/ L = 1.496 = Distance to Sun (1088 km)km)

WWππ * P* P2 2 * L* L1/31/3 * * BB55 = 2.999*10= 2.999*105 5 ~~ Speed of Light (km/s)Speed of Light (km/s)

Mass of Proton Mass of Electron

2.998 measured(so measurements probably wrong)


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

WMAP CMB temperature power spectrum

Modern musical analogiesModern musical analogies


Approach to music and scienceApproach to music and science

modestyplaying someone else’s composition is boldunderstanding the universe is a very ambitious goal

honestyplay only what you think is rightsay only what you think is right

music of the spheres 2 - leiden observatory - leiden …pvdwerf/biblio/pdf/sassone09.pdfmusic of the...

Documents