| Music of the spheres Pythagoras’ belief in the power of number extended far beyond explaining the harmony of stringed musical instruments: he believed that the planets in their orbits emitted a heavenly harmony determined by the intervals between them, ‘the music of the spheres’. The doctrine persisted until the time of Kepler, who thought that each planet sounded particular musical notes. The earth’s notes were mi, fa, mi, which stood for misery, famine, misery! A page of Kepler’s is shown right. |
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| Exercise 2 In a well-tuned piano, the frequency of each note is  times the frequency of the note below it. In many orchestras, the note A below middle C is set at 440 vibrations per second. (C is two whole notes above A.)(a) What is the frequency of middle C? (b) If the frequency of A is set at 435 vibrations per second, how much difference would this make to middle C? |
(a) 494
(b) 488
(approximeately)