James Adam, The Republic of Plato

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ἅμα ἀλλήλοις . Πλάτων καὶ οἱ μαθηματικοὶ ἰσοδρόμους εἶναι τὸν ἥλιον, τὸν ἑωσφόρον (Venus), Στίλβωνα (Mercury): see Diels Dox. Gr. 346 and cf. Tim. 36 D, [Epin.] 986 E and Proclus l.c. 226. 21. Plato's language certainly means that these three bodies travel at the same pace, and if their speed is the same, obviously they cannot complete their orbits in the same period. But it is doubtful whether the contradiction was present to Plato's mind, and Proclus may be right in holding that Plato was really thinking of the periods of the planets (l.c. and in Tim. 259 C). See also on 617 B below.

τρίτον δὲ κτλ. See cr. n. The article, which was first rejected by Schleiermacher, is probably a dittographical mistake. Schneider, Hermann and Baiter retain it, despite the ambiguity.

ἐπανακυκλούμενον. The revolution, relatively to that of the whole, is retrograde: hence ἐπανακυκλούμενον.

Ἀνάγκης γόνασιν. Plato means us to imagine Necessity as seated in the centre of the Universe. The notion is probably Pythagorean; for Parmenides, who attaches himself to the Pythagoreans in this part of his system (Zeller^{5} I p. 572), speaks of a central Ἀνάγκη as the cause of all movement and birth: see Diels Dox. Gr. 335. 12 ff. τῶν δὲ συμμιγῶν (sc. στεφανῶν) τὴν μεσαιτάτην ἁπάσαις τοκέα πάσης κινήσεως καὶ γενέσεως ὑπάρχειν, ἥντινα καὶ δαίμονα κυβερνῆτιν καὶ κλῃδοῦχον ἐπονομάζει δίκην τε καὶ ἀνάγκην, and Zeller l.c. p. 577 note 3. (Zeller identifies this Ἀνάγκη with the central fire of the Pythagoreans.) The same school seem also to have held that Ἀνάγκη surrounds and holds the world together (Diels l. c. 321), and Zeller thinks it is this external Ἀνάγκη of which Plato here avails himself (l.c. p. 434 note 3). But it is quite clear that Plato's Ἀνάγκη is in the middle: see on 616 B and 621 A, B. The interpretation of Plato's symbolism of course is that Necessity and Law spin the threads of life—the life of the Universe as well as that of man. ἐν τοῖς τῆς Ἀνάγκης γόνασιν is an echo of θεῶν ἐν γούνασι κεῖται and the like: cf. Proclus l.c. 227. 12.

ἐπὶ δὲ τῶν κύκλων κτλ. βεβηκέναι means ‘is perched.’ Proclus more suo assures us that the Sirens are ψυχαί τινες νοερῶς ζῶσαι (l.c. 238. 6), but they are of course only a poetic fiction to express the ‘music of the spheres.’ Cf. Merchant of Venice V I “There's not the smallest orb which thou behold'st, But in his motion like an angel sings.” Plato goes beyond Shakespeare, setting the angels on the orbs and making them sing. Cf. Milton Arcades 63 ff. “the celestial Sirens' harmony That sit upon the nine”—in Plato there are only eight— “infolded Spheres.” The seven planets by their movements were supposed by the Pythagoreans to give forth sounds corresponding to the notes of the Heptachord. This was probably the original form of the ‘Music of the Spheres.’ Later, it was held that the circle of the fixed stars had also a note of its own, and a ‘harmony’ or mode (see on III 398 E ff.) resulted like that of the Octachord. The underlying idea of the doctrine of the ‘Music of the Spheres’ was well expressed by Dorylaus when he said the Universe was the ‘organum Dei’ (Censor. de die natali 13: cf. also Milton Ode on the Nativity “And bid the bass of heaven's deep organ blow”). See also next note.

φωνὴν μίαν, ἕνα τόνον: ‘a single sound, a single musical note.’ “Additum ἕνα τόνον per epexegesin est” (Stallbaum). Cf. Proclus l.c. 236. 27 ff. ἡ μὲν γὰρ μία φωνὴ δηλοῖ τὴν ἀμετάβολον τοῦ τῆς ἐνεργείας εἴδους εἰς ἄλλο καὶ ἄλλο μέλος ὕπαρξιν, ὡς ἑκάστης Σειρῆνος ἀεὶ τὴν αὐτὴν ἱείσης φωνήν: ὁ δὲ εἷς τόνος τὴν ποιὰν φωνὴν ἐδήλωσεν εἰς ἑνὸς ἀπήχησιν φθόγγου τελοῦσαν: παρὰ γὰρ τὴν τάσιν καὶ ὁ φθόγγος καλεῖται τόνος. There is also perhaps a slight rhetorical effect, though less than in τὸ δεινόν, τὸ μέγα IX 590 A. The reading ἕνα τόνον is confirmed by Plut. de anim. procr. 1029 C and Proclus in Tim. 259 C and in remp. l.c. et al. It is difficult to understand ἀνὰ τόνον, which Hermann and Baiter read, following q and a few inferior MSS. ἀνὰ τόνον could hardly mean ‘one note each,’ as Hermann supposes. With regard to the ἁρμονία itself, the pitch of the several notes will of course be determined by the speed of the different whorls (cf. VII 530 D note), so that if we express the notes by the names of the circles which produce them, the ἁρμονία will be:—

It is clear that Plato is thinking of a sort of mode (ἐκ πασῶν δὲ ὀκτὼ οὐσῶν μίαν ἁρμονίαν ξυμφωνεῖν), but if we understand ἅμα ἀλλήλοις strictly, there will only be six notes, because Mercury, Venus and the Sun will each have the same note. Difficulties of this sort might have troubled the later Pythagoreans, but scarcely Plato, least of all in an imaginative picture of this kind. We note however that according to Plato the speed of the planets—except in the case of the Sun, Venus and Mercury—diminishes in proportion to their distance from the Earth. Now we may reasonably suppose that Plato thought the more distant planets took longer to complete their orbit than those which are nearer, so that it is by no means improbable that in speaking of the speed of the planetary movements, Plato really had in his mind the time occupied by the orbital periods and not the rate of progression of the planets themselves. See also above on ἅμα ἀλλήλοις. In that case the octave will be complete, because in order to complete their orbits in the same time, the Sun, Venus and Mercury will have to travel at different rates of speed. Later writers knew all about the Music of the Spheres, and a choir of eight Neo-Pythagoreans would have had no difficulty in rendering it on a small scale: see for example von Jan's Mus. Scr. Gr. pp. 241 ff., 271 ff., 418 f. Cf. also Zeller^{5} I pp. 429—434.