Early Greek Philosophy by John Burnet, with Burnet's notes
151. The Antichthon 153. Things Likenesses of Numbers

From Chapter VII., The Pythagoreans

152. The Harmony of the Spheres
We have seen (§ 54) that the doctrine commonly, but incorrectly, known as the "harmony of the spheres" may have originated with Pythagoras, but its elaboration must belong to a later generation, and the extraordinary variations in our accounts of it must be due to the conflicting theories of the planetary motions which were rife at the end of the fifth and the beginning of the fourth centuries B.C. We have the express testimony of Aristotle that the Pythagoreans whose doctrine he knew believed that the heavenly bodies produced musical notes in their courses. Further, the pitch of the notes was determined by the velocities of these bodies, and these in turn by their distances, which were in the same ratios as the consonant intervals of the octave. Aristotle distinctly implies that the heaven of the fixed stars takes part in the celestial symphony; for he mentions "the sun, the moon, and the stars, so great in magnitude and in number as they are," a phrase which cannot refer solely or chiefly to the five planets.114 We are also told that the slower bodies give out a deep note and the swifter a high note, and the prevailing tradition gives the high note of the octave to the heaven of the fixed stars, which revolves in twenty-four hours. Saturn, of course, comes next; for, though it has a slow motion of its own in a contrary direction, that is "mastered" (κρατεῖται) by the diurnal revolution. The other view, which gives the highest note to the Moon and the lowest to the fixed stars, is probably due to the theory which substituted an axial rotation of the earth for the diurnal revolution of the heavens.115

Burnet's Notes

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114. Arist. De caelo, B, 9. 290 b, 12 sqq. (R. P. 82). Cf. Alexander, In met. p. 39, 24 (from Aristotle's work on the Pythagoreans) τῶν γὰρ σωμάτων τῶν περὶ τὸ μέσον φερομένων ἐν ἀναλογίᾳ τὰς ἀποστάσεις ἐχόντων . . . ποιούντων δὲ καὶ ψόφον ἐν τῷ κινεῖσθαι τῶν μὲν βραδυτέρων βαρύν, τῶν δὲ ταχυτέρων ὀξύν. There are all sorts of difficulties in detail. We can hardly attribute the identification of the seven planets (including sun and moon) with the strings of the heptachord to the Pythagoreans of this date; for Mercury and Venus have the same mean angular velocity as the Sun, and we must take in the heaven of the fixed stars.

115. For the various systems, see Boeckh, Kleine Schriften, vol. iii. pp. 169 sqq., and Carl v. Jan, " Die Harmonie der Sphären " (Philol. 1893. pp. 13 sqq.). There is a sufficient account of them in Heath's Aristarchus, pp. 107 sqq., where the distinction between absolute and relative velocity is clearly stated, a distinction which is not appreciated in Adam's note on Rep. 617 b (vol. ii. p. 452), with the result that, while the heaven of the fixed stars is rightly regarded as the νήτη (the highest note), the Moon comes next instead of Saturn—an impossible arrangement. The later view is represented by the "bass of Heaven's deep Organ" in the "ninefold harmony" of Milton's Hymn on the Nativity (xiii.). At the beginning of the Fifth Act of the Merchant of Venice, Shakespeare makes Lorenzo expound the doctrine in a truly Pythagorean fashion. According to him, the "harmony" in the soul ought to correspond with that of the heavenly bodies ("such harmony is in immortal souls"), but the "muddy vesture of decay" prevents their complete correspondence. The Timaeus states a similar view, and in the Book of Homage to Shakespeare (pp. 58 sqq.) I have tried to show how the theories of the Timaeus may have reached Shakespeare. There is no force in Martin's observation that the sounding of all the notes of an octave at once would not produce a harmony. There is no question of harmony in the modern sense, but only of attunement (ἁρμονία) to a perfect scale.






















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