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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


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    1. Inside the music of the spheres Sassone June 23, 2009

    2. Enormous disclaimer Music of the spheres

    3. 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

    4. 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

    5. 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

    6. 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

    7. 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

    8. 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

    9. 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

    10. 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

    11. 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

    12. 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

    13. Map onto Keys C D E F G A B C Music of the spheres

    14. 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

    15. 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

    16. Johannes Kepler (1571-1630) Music of the spheres

    17. 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

    18. 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

    19. Boethius (ca. 480 - 526) Trivium: • logic • grammar • rhetoric Quadrivium: • mathematics • music • geometry • astronomy Music of the spheres

    20. 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

    21. 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

    22. The choirs of the angels • Hildegard von Bingen (1098 – 1179): O vos angeli Music of the spheres

    23. 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

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

    25. 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

    26. 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

    27. 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

    28. 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

    29. 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

    30. 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

    31. Kepler’s heavenly motet Music of the spheres

    32. 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

    33. Yorkshire Building Society Band Music of the spheres

    34. Deutsche Bläserphilharmonie Music of the spheres

    35. “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

    36. B Cosmological aspects of the bicycle L W P Music of the spheres

    37. 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

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

    39. 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