152. We must not assume that even the later Pythagoreans made the sun, moon, and planets, including the earth, revolve in the opposite direction to the heaven of the fixed stars. It is true that Alkmaion is said to have agreed with “some of the mathematicians”[834] in holding this view, but it is never ascribed to Pythagoras or even to Philolaos. The old theory was, as we have seen (§ 54), that all the heavenly bodies revolved in the same direction, from east to west, but that the planets revolved more slowly the further they were removed from the heavens, so that those which are nearest the earth are “overtaken” by those that are further away. This view was still maintained by Demokritos, and that it was also Pythagorean, seems to follow from what we are told about the “harmony of the spheres.” We have seen (§ 54) that we cannot attribute this theory in its later form to the Pythagoreans of the fifth century, but we have the express testimony of Aristotle to the fact that those Pythagoreans whose doctrine he knew believed that the heavenly bodies produced musical notes in their courses. Further, the velocities of these bodies depended on the distances between them, and these corresponded to the intervals of the octave. He distinctly implies that the heaven of the fixed stars takes part in the concert; 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 remaining five planets.[835] Further, we are told that the slower bodies give out a deep note and the swifter a high note.[836] Now the prevailing tradition gives the high note of the octave to the heaven of the fixed stars,[837] from which it follows that all the heavenly bodies revolve in the same direction, and that their velocity increases in proportion to their distance from the centre. Footnote 834: The term οἱ μαθηματικοί is that used by Poseidonios for the Chaldæan astrologers (Berossos). Diels, _Elementum_, p. 11, n. 3. As we have seen, the Babylonians knew the planets better than the Greeks. Footnote 835: Arist. _de Caelo_, Β, 9. 290 b 12 sqq. (R. P. 82). Footnote 836: 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. We must not attribute the identification of the seven planets with the seven strings of the heptachord to the Pythagoreans of this date. Mercury and Venus have in the long run the same velocity as the sun, and we must take in the earth and the fixed stars. We can even find room for the _antichthon_ as προσλαμβανόμενος. Footnote 837: