planets to account for lunar eclipses (§ 29), and Anaxagoras had revived that view (§ 135). Certain Pythagoreans[1] had placed these dark planets between the earth and the central fire in order to account for their invisibility, and the next stage was to reduce them to a single body. Here again we see how the Pythagoreans tried to simplify the hypotheses of their predecessors.
152. 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.[2] 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
- ↑ It is not expressly stated that they were Pythagoreans, but it is natural to suppose so. So, at least, Alexander thought (Simpl. De caelo, p. 515, 25).
- ↑ 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.
