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

Music of the spheres2 Enormous disclaimer

Music of the spheres3 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 spheres4 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 spheres5  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 telescope

Music of the spheres6 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 spheres7 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 and reconstructed it  First discoveries in 1609  Principal publication in 1632 (“Dialogus” on two world systems), trial in 1633 on two world systems), trial in 1633  Rehabilitation in 1980 (!)

Music of the spheres8 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 17 th century man.

Music of the spheres9 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 spheres10 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 spheres11 Pythagoras and the science of music f 0 x 1Prime f 0 x 9/8 Second e.g., God save the Queen f 0 x 5/4 Thirde.g., Beethoven 5th f 0 x 4/3 Fourthe.g., Dutch, French anthem f 0 x 3/2 Fifthe.g., Blackbird (Beatles) f 0 x 5/3 Sixth f 0 x 15/8 Seventh f 0 x 2Octave

Music of the spheres12 Now assign note names NameInterval C 1/1Start D 9/8 Second E 5/4 Third F 4/3 Fourth NameInterval G 3/2 Fifth A 5/3 Sixth B 15/8 Seventh C 2/1Octave

Music of the spheres13 Map onto Keys C D E F G A B C

Music of the spheres14 Taking the Fifth NameInterval C 1/1Start D 9/8 Second E 5/4 Third F 4/3 Fourth NameInterval G 3/2 Fifth A 5/3 Sixth B 15/8 Seventh C 2/1Octave 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!

Music of the spheres15  The Pythagoreans based their tuning on Fourths and Fifths, which were considered harmonically "pure": CFGC  The Fourth was subdivided into two tones (whole step interval), and a half tone (half step interval)  This arrangement of intervals is called a tetrachord  Two tetrachords can be concatenated together (separated by a whole step) to create a diatonic scale Tetrachords Fourth Fifth

Music of the spheres16 Tetrachords C D E F G A B C Tone HalfTone Half Tetrachord Diatonic scale

Music of the spheres17 Pythagorean tuning NameInterval C 1/1 Start D 9/8 Second E 81/64 Third F 4/3 Fourth NameInterval G 3/2 Fifth A 27/16 Sixth B 243/128 Seventh C 2/1Octave 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!

Music of the spheres18 Johannes Kepler ( )

Music of the spheres19 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 spheres20 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 spheres21 Boethius (ca ) Trivium:   logic   grammar   rhetoric Quadrivium:   mathematics   music   geometry   astronomy

Music of the spheres22 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 spheres23 Influence of musical advances and Christian doctrine   from the 11 th 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 spheres24 The choirs of the angels   Hildegard von Bingen (1098 – 1179): O vos angeli

Music of the spheres25 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 spheres26 Kepler’s Mysterium Cosmographicum (1596) relating the sizes of the planetary orbits via the five Platonic solids. relating the sizes of the planetary orbits via the five Platonic solids.

Music of the spheres27 How well does this work? actual model  Saturn aphelion > => +9%  Jupiter > => -2%  Mars > => -1%  Earth > => 0%  Venus > => -1%  Mercury > => +4%

Music of the spheres28 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 spheres29 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 spheres30 What is the Phrygian 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 mi fa ut re mi fa sol la si ut hexachord

Music of the spheres31 Phrygian mode today   Jefferson Airplane: White Rabbit Jefferson Airplane   Björk: Hunter Björk   Theme music from the TV-series Doctor WhoDoctor Who   Megadeth: Symphony of Destruction Megadeth   Iron Maiden: Remember Tomorrow Iron Maiden   Pink Floyd: Matilda Mother Pink Floyd and: Set the Controls for the Heart of the Sun   Robert Plant: Calling to You Robert Plant   Gordon Duncan: The Belly Dancer Gordon Duncan   Theme from the movie PredatorPredator   Jamiroquai: Deeper Underground Jamiroquai   The Doors: Not to touch the Earth The Doors   Britney Spears: If U Seek Amy Britney Spears

Music of the spheres32 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 spheres33 Kepler’s heavenly motet

Music of the spheres34 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: 8 th Symphony

Music of the spheres35 Yorkshire Building Society Band

Music of the spheres36 Deutsche Bläserphilharmonie

Music of the spheres37 “The Science of Harmonic Energy and Spirit unification of the harmonic languages of color, music, numbers and waves”, etc. etc…. “Music of the Spheres”

Music of the spheres38 Cosmological aspects of the bicycle B P L W

Music of the spheres39 Amazing results!  P 2 * ( L B ) 1/2 = 1823 =  P 4 * W 2 = = Fine Structure Constant  P -5 * ( L / WB ) 1/3 = 6.67*10 -8 = Gravitational Constant  P 1/2 * B 1/3 / L = = Distance to Sun (10 8 km)  W  * P 2 * L 1/3 * B 5 = 2.999*10 5 ~ Speed of Light (km/s) Mass of Proton Mass of Electron measured (so measurements probably wrong)

Music of the spheres40 Musical analogies are still possible, but as results, not as the principle WMAP CMB temperature power spectrum Modern musical analogies

Music of the spheres41 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