Message #110047

[Bianca]

                       








Plato, Pliny, Cicero and Ptolemy are amongst the philosophers of the ancient world who contemplated the music of the spheres. The doctrine was transmitted to medieval Europe where it found its most glorious expression in the architecture of great abbeys and cathedrals consciously designed to conform to the proportions of musical and geometric harmony. The English hermeticist Robert Fludd (1574-1637) visualised grand celestial scales spanning three octaves and linking levels of existence from the sub-planetary elemental worlds to exultant choirs of angelic intelligences beyond the stars. The beautiful engravings which illustrate Fludd's encyclopaedic works are amongst the most comprehensive descriptions of pre-Copernican cosmology ever devised. [4]

The ideals of Pythagorean harmony inspired Copernicus himself. Nicholas Copernicus (1473-1543) spent most of his life in the fortified city of Frauenburg in Prussia fulfilling administrative duties as a canon of the cathedral chapter and devoting the rest of his time to contemplation of the cosmic harmonies. The cumbersome mathematics of the Ptolemaic system, with its maze of epicycles grafted on to reconcile various observational discrepancies, offended his Pythagorean sense of proportion. He realised that a Sun-centred planetary system not only gave better predictions of celestial motion but could also he expressed through more elegant geometry — to the greater glory of God the Creator.

Kepler's early enthusiasm for the Copernican system was inspired by the same sense of idealism. He could readily accept the Sun as the centre of the planetary system, but the necessity of rejecting circular orbits came as something of a shock. The circle is an archetypal symbol of harmony and perfection; Kepler recoiled with disgust when an unsightly bulge began to emerge from his analysis of the orbit of Mars. Yet the elliptical orbits eventually revealed a scheme of celestial harmony more subtle and profound than any that had gone before.

Kepler's, First Law states that the planets move in ellipses and that the Sun is not at the exact centre of their orbits. Each planet moves between a 'perihelion' point nearest the Sun and an 'aphelion' point furthest away. The Second Law states that the planets move faster at perihelion than at aphelion. Kepler measured their angular velocities at these extremes (i.e. how far they travel in 24 hours in minutes and seconds of arc as viewed from the Sun) and expressed this ratio as a musical interval. Saturn, for instance, moves at a rate of 106" per day at aphelion and l35" at perihelion. Cancelled down, the ratio 106:135 differs by only two seconds from 4:5 — equivalent to the interval of a major third. Kepler found that the angular velocities of all the planets closely correspond to musical intervals. When he compared the extremes for combined pairs of planets the results were even more marvellous, yielding the intervals of a complete scale. Thus, the ratio between Jupiter's maximum and Mars' minimum speed corresponds, to a minor third; the interval between Earth and Venus to a minor sixth. Rather than the fixed-tone planetary scales of earlier schemes, Kepler's measurements revealed ever-changing polyphonic chords and harmonies as the planets move between perihelion and aphelion. Furthermore, he had shifted the focus of celestial harmony from the Earth to the Sun: "Henceforth it is no longer a harmony made for the benefit of our planet, but the song which the cosmos sings to its lord and centre, the Solar Logos". [5]

Scientific materialists have tended to dismiss the spiritual dimension to Kepler's work as either the remnants of a deeply-ingrained 'medievalism' which he was unable to shake off or, even less charitably, as the fantasies of an over-worked mind. His vision of the music of the spheres, however, is based upon the hard facts of astronomical measurement. The astronomer Fred Hoyle agrees that the correspondence between musical ratios and planetary velocities as described by Kepler is "frighteningly good". [6] The Kepler scholar Francis Warrain extended Kepler's researches and found that the angular velocities of Uranus, Neptune and Pluto, which were unknown during Kepler's lifetime, also correspond to harmonic ratios. The music of the spheres is more than a beautiful poetic intuition. The dynamics of the solar system, first laid bare by Kepler's mathematical genius, are directly analogous to the laws of musical harmony.