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Inside the music of the spheres Paul van der Werf Leiden Observatory Sassone June 23, 2009 Enormous disclaimer Music of the spheres 2 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 Pythagoras and the science of music f0 x 1 Prime f0 x 9/8 Second e.g., God save the Queen f0 x 5/4 Third e.g., Beethoven 5th f0 x 4/3 Fourth e.g., Dutch, French anthem f0 x 3/2 Fifth e.g., Blackbird (Beatles) f0 x 5/3 Sixth f0 x 15/8 Seventh f0 x 2 Music of the spheres Octave 11 Now assign note names Name C Interval 1/1 Start Name Interval G 3/2 Fifth D 9/8 Second A 5/3 Sixth E 5/4 Third B 15/8 Seventh F 4/3 Fourth C Music of the spheres 2/1 Octave 12 Map onto Keys C D Music of the spheres E F G A B C 13 Taking the Fifth Name C Interval 1/1 Start Name Interval G 3/2 Fifth D 9/8 Second A 5/3 Sixth E 5/4 Third B 15/8 Seventh F 4/3 Fourth 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 This one doesn't work! Music of the spheres 14 Pythagorean tuning Name Interval Name Interval C Start G Fifth 1/1 3/2 D 9/8 Second A 27/16 Sixth E 81/64 Third B 243/128 F 4/3 C 2/1 Octave Fourth Seventh 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 spheres 17 Johannes Kepler (1571-1630) Music of the spheres 18 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 19 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 Music of the spheres – microcosmos correspondence 20 Boethius (ca. 480 - 526) Trivium: logic grammar rhetoric Quadrivium: mathematics music geometry astronomy Music of the spheres 21 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 22 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 23 The choirs of the angels Hildegard von Bingen (1098 – 1179): O vos angeli Music of the spheres 24 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 25 Kepler’s Mysterium Cosmographicum (1596) relating the sizes of the planetary orbits via the five Platonic solids. Music of the spheres 26 How well does this work? Saturn aphelion Jupiter Mars Earth Venus Mercury Music of the spheres actual 9.727 5.492 1.648 1.042 0.721 0.481 model --> 10.588 --> 5.403 --> 1.639 --> 1.102 --> 0.714 --> 0.502 => +9% => -2% => -1% => 0% => -1% => +4% 27 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 28 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 29 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 semitone ut semitone C Major Scale (Ionian Mode) semitone semitone C Major Scale starting on D (Dorian Mode) mi fa semitone semitone C Major Scale starting on E (Phrygian Mode) hexachord Music of the spheres 30 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 31 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 32 Kepler’s heavenly motet Music of the spheres 33 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 34 Yorkshire Building Society Band Music of the spheres 35 Deutsche Bläserphilharmonie Music of the spheres 36 “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 37 B Cosmological aspects of the bicycle L W P Music of the spheres 38 Amazing results! P2 * ( L B )1/2 = 1823 = Mass of Proton 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) Mass of Electron 2.998 measured (so measurements probably wrong) Music of the spheres 39 Modern musical analogies WMAP CMB temperature power spectrum Musical analogies are still possible, but as results, not as the principle Music of the spheres 40 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 41