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THE PYTHAGOREAN SOURCEBOOK AND LIBRARY |
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FIGURES FRONTISPIECE. PYTHAGORAS (From Stanley's History of Philosophy, 1687)
FIGURE 1. UNlTY, DUALITY AND HARMONY
FIGURE 2. THE PYTHAGOREAN TABLE OF OPPOSITES
FIGURE 3. SQUARE NUMBER
FIGURE 4. OBLONG NUMBER
FIGURE 5. THE MONOCHORD. String, sounding box and moveable bridge.
FIGURE 6. THE HARMONIC NODAL POINTS AND OVERTONE SERIES ON THE MONOCHORD. The above figure illustrates the reciprocal relation which exists between string length and vibrational frequency. By stopping the string at the geometrical nodal points the harmonic overtones may be individually emphasized.
FIGURE 7. THE HARMONIC PROPORTION
FIGURE 8. THE TETRAKTYS.
FIGURE 9. THE THREE LIVES
FIGURE 10. IAMBLICHUS
FIGURE 11. COIN FROM CROTON
FIGURE 12. THE PYTHAGOREAN Y
FIGURE 13. THE MUSIC OF THE SPHERES
FIGURE 14. THE MUSIC OF THE SPHERES. Shown in this engraving from Renaissance Italy are Apollo, the Muses, the planetary spheres and musical ratios.
FIGURE 15. A TABLE OF TONE NUMBERS. There is evidence that this table of tone numbers is a later addition to the text. The abbreviations I. and ap. represent the two types of semitones, the leimma and the apotome respectively.
FIGURE 16. THE REGULAR SOLIDS. The regular solids, also known as the Platonic solids, were first described by Plato in his Timaeus. Plato identified the dodecahedron with the cosmic sphere (later identified with aither), and the four other solids with the four elements. Each one of the elemental "molecules" is constructed out of the triangular "atoms" shown below. The five regular solids are the only polyhedra that can be constructed out of the same regular polygons. The archetypal ratios and geometries with which they are associated underlie the structure and divisions of three-dimensional space.
DODECAHEDRON: Aither
/ 12 Sides FIGURE 17. THE PLATONIC LAMBDA
FIGURE 18. THE DIVINE MONOCHORD. This particular monochord is tuned in the key of G, while the examples on the right and in the introduction use the key of C. The three top notes on this monochord are incorrectly placed.
FIGURE 19. THE RATIOS OF THE PYTHAGOREAN SCALE
FIGURE 20. MAP OF THE ANCIENT WORLD
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