Plato Republic 7.531

τὰς γὰρ ἀκουομένας κτλ. The intervals reckoned as consonant ( σύμφωνα) were such as the octave, double octave, fifth and fourth: see on IV 430 E. These the Pythagoreans ‘measure by’ (or ‘against’) ‘one another,’ by comparing the lengths of vibrating strings of the same material, thickness and tension. It is thus found that the octave is 2 : 1, the double octave 4 : 1, the fifth 3 : 2, and the fourth 4 : 3. See Dict. of Ant. II p. 193 with Theo Smyrn. pp. 48—51, 56—61 Hiller, and Aristox. Harm. 20 ff. Marquard. Richards proposes <ἐν> ἀλλήλοις, but the dative is strictly accurate: cf. Tim. 39 D τῷ τοῦ ταὐτοῦ καὶ ὁμοίως ἰόντος ἀναμετ ρηθέντα κύκλῳ.

ὥσπερ οἱ ἀστρονόμοι . The parallel is exact: as the astronomers studied visible, so the Pythagoreans investigated audible φοραί (Theo l.c.). To Plato, on the other hand, ἁρμονίη ἀφανὴς φανερῆς κρείσσων (Heracl. Fr. 47 B ywater). ‘Heard harmonies are sweet, but those unheard are sweeter.’ See above on 530 C.

νὴ τοὺς θεοὺς κτλ. There were two rival schools of musical theory in Greece, viz. “(1) the Pythagorean or mathematical, who identified each interval with a ratio, (2) the ‘musical’ ( μουσικοί), who measured all intervals as multiples or fractions of the Tone” (Monro in Dict. Ant. II p. 193). Cf. Modes of Anc. Gk. Mus. p. 124. Plato's criticism was intended to apply to the first school; but Glauco erroneously understands it of the second.

πυκνώματα κτλ . ἄττα ( nescio quae) and ὀνομάζοντες shew that πυκνώματα is a technical term. The word πύκνωμα does not appear to occur elsewhere in this sense, but πυκνόν was a favourite word with writers of the ‘musical’ school, as may be seen from its constant employment by Aristoxenus. πυκνόν is thus defined: τὸ ἐκ δύο διαστημάτων συνεστηκὸς ἃ συντεθέντα ἔλαττον διάστημα περιέξει τοῦ λειπομένου διαστήματος ἐν τῷ διὰ τεσσάρων (Aristox. Harm. 24. 10 ff. Marquard) i.e. any combination of two intervals which are together less than the interval remaining in the Fourth when the πυκνόν is subtracted from the Fourth, e.g. two quarter tone intervals, or even two semitone intervals (but not more): see Aristox. l.c. 50. 15 ff. The definition in Bacchius Isag. 20 von Jan τὸ ἐκ δύο διαστημάτων ἐλαχίστων συγκείμενον ἐν ἑκάστῳ γένει is less exact, but not, so far as it goes, inconsistent with that of Aristoxenus. Plato's πυκνώματα must be “haec ipsa πυκνά vel alia parva et tamen composita intervalla,” so called “propter sonorum in angusto spatio quasi confertorum frequentiam” (Schneider). Cf. πυκνότης in Laws 812 D, καταπυκνοῦσθαι, καταπύκνωσις etc. in Theo 91 and often in Aristoxenus, and see generally Westphal and Rossbach Gr. Harm. etc. pp. 105 ff. It is possible that the musical application of these terms was originally a metaphor borrowed from the art of weaving: for “vestes spatha textae, ob densitatem, quam inde consequebantur, πυκνώματα dictae ap. Aesch. Suppl. 235 πέπλοισι βαρβάροισι, καὶ πυκνώμασι” (Stephanus-Hase s.v. πύκνωμα, where reference is made also to Hesych. s.v. σπάθημα and a Scholiast on Ar. Ach. 180 ). I agree with Schneider in doubting whether Gellius' “frequentamenta” (I 11. 12, V 1. 1) are the same as Plato's πυκνώματα.

οἷον ἐκ γειτόνων κτλ. : ‘as if they were trying to catch a sound in the neighbourhood.’ Cf. Heliod. I 17 πίνει δὲ ἐνταῦθα ἐκ γειτόνων and Blaydes on Ar. Plut. 435 or Stephanus-Hase Thes. s.v. γείτων, where numerous examples of this highly idiomatic phrase are quoted. J. and C.'s translation “from a neighbour's house” is incorrect and pointless: still worse is Westphal's “als ob sie die Intervallgrösse dem Nachbarton ablauschen wollen.” The idiom was understood by Ficinus, who translates it by “viciniore loco.”

οἱ μέν φασιν κτλ. Some will have it that they overhear a note between (let us say) B and C, and that this is the smallest interval, and should be the unit of measurement: others say ‘No! it is not different from B.’ Plato (who is all for simplicity in music Laws 812 C) here satirises the μουσικοί, who made the quartertone or δίεσις their unit: see Theo 55 δίεσιν δὲ καλοῦσιν ἐλαχίστην οἱ περὶ Ἀριστόξενον τὸ τεταρτημόριον τοῦ τόνου, ἥμισυ δὲ ἡμιτονίου, ὡς ἐλάχιστον μελῳδητὸν διάστημα, and on the ἐναρμόνιον γένος generally, which Plato strongly disliked (Theo 56; cf. also Procl. in Tim. 191 E), and in which the δίεσις played a large part, Dict. of Ant. l.c. and Westphal and Rossbach l.c.

ἀμφισβητοῦντες . We should expect ἀμφισβητοῦσιν (so Theo 6) or else φάσκοντες instead of φασιν above. Cobet would emend, but the anacoluthon is not difficult in a writer like Plato: see on VI 488 C, D and supra 519 A note

φθεγγομένων : sc. τῶν χορδῶν, omitted as in ἡ διὰ πασῶν.

ὦτα κτλ. This bitter epigram was applied by Adrastus to Aristoxenus (Procl. in Tim. 192 B). The cap fits admirably; for Aristoxenus was afterwards the leader of the μουσικοί whose principle is here ridiculed. With the expression itself cf. Pliny Epp. VII 27, 8 sed offirmare animum auribusque praetendere.

σὺ μὲν κτλ. Socrates now corrects Glauco's error: see on νὴ τοὺς θεοὺς κτλ. 531 A. τοὺς χρηστούς is of course contemptuous. Plato has no sympathy with the ‘ μουσικοί.’

τοὺς ταῖς χορδαῖς κτλ. : ‘who persecute and torture the strings, racking them upon the pegs. But lest my figure become somewhat tedious if I dwell upon the blows delivered with the plectrum, and the accusations brought against the strings, as well as their denials and braggadocio behaviour’ etc. The figure ( εἰκών) is from torturing and beating slaves, as βασανίζοντας, στρεβλοῦντας and πληγῶν shew: even πράγματα παρέχοντας suggests a court of law (cf. Crit. 44 E ). The strings are the victims, while the pegs are the pulleys by which they were racked upon the τροχός (see Dict. Ant. s. v. eculeus). For ἐπί Herwerden proposes ὑπό: but the strings are racked by the musicians upon the pegs.

πλήκτρῳ τε πληγῶν κτλ. The etymological meaning of πλῆκτρον adds point to this part of the comparison.

πέρι from its position divides πληγῶν and κατηγορίας, which refer to the behaviour of the musicians, from ἐξαρνήσεως καὶ ἀλαζονείας, in which the behaviour of the strings is described. For the anastrophe of πέρι see Lina de praeposit. usu Plat. pp. 26—30. The angry musician is like the prosecutor, and blames the strings, which in their turn repudiate the charge and swagger away like a stubborn slave however savagely the screw is turned. For a further discussion of this passage see App. XI.

ἐκείνους : i.e. the Pythagoreans, and not the μουσικοί, as Glauco supposed.

τοὺς γὰρ κτλ. It is strange that in spite of οὓς ἔφαμεν νῦν δὴ κτλ. this should have been so frequently understood as referring to the school satirised by Glauco: see for example Susemihl Gen. Entw. II p. 210. Plato is of course, as Schneider pointed out, speaking about the Pythagoreans who investigated the numbers or ratios of audible consonances: see 531 A note and RP.^{7} § 56 C.

ἀλλ’ οὐκ κτλ. Cf. 530 B. ἀνίασιν is undoubtedly present, and not future, here: see on V 473 C.

τίνες ξύμφωνοι κτλ. As the true astronomer should study intelligible stars with the mathematical intelligence, using the visible stars only as imperfect παραδείγματα (529 C, D note), so the true ἁρμονικός must investigate intelligible, and not audible, consonances. In the words of a modern writer, he must “look, not into the tone-world here, but into the world of harmony beyond.” Plato holds that certain mathematical numbers are in themselves ξύμφωνοι, and others not: see Theo 72—75, where examples of both varieties are given. The numbers or ratios of audible consonances are only particular and imperfect embodiments or expressions of these numbers: they may serve as παραδείγματα, but nothing more. In the Timaeus Plato represents the World-soul as the grandest expression of certain ξύμφωνοι ἀριθμοί, so that it is natural enough for him to crown his προπαιδεία with the study of mathematical ξυμφωνία, and say that it is ‘useful in seeking out the beautiful and good.’ It must nevertheless be admitted that Plato's conception of Harmonics as well as of Astronomy is fundamentally different from that of modern science, in spite of the attempts which Bosanquet and others have made to prove their essential harmony. See on 530 C and App. II.

ᾗ ‐‐ οἰκεῖα κτλ. Cf. [ Epin.] 991 E ff. πᾶν διάγραμμα ἀριθμοῦ τε σύστημα καὶ ἁρμονίας σύστασιν ἅπασαν τῆς τε τῶν ἄστρων περιφορᾶς τὴν ὁμολογίαν οὖσαν μίαν ἁπάντων ἀναφανῆναι δεῖ τῷ κατὰ τρόπον μανθάνοντι, ἀναφανήσεται δὲ ἂν— ὀρθῶς τις εἰς ἒν βλέπων μανθάνῃ· δεσμὸς γὰρ πεφυκὼς πάντων τούτων εἷς ἀναφανήσεται διανοουμένοις· εἰ δ’ ἄλλως πως ταῦτα μεταχειριεῖταί τις, τύχην δεῖ καλεῖν. The apprehension of the ‘one in the many’ in these preliminary studies prepares us for the dialectical conception of the universe of Thought as an organic and correlated whole (VI 511 B—D notes); but the mere specialist in mathematics for example, or astronomy, can never become a dialectician. Cf. 537 C and Euthyd. 290 B ff.

νόμου : ‘song’ or ‘strain.’ There is no pun on νόμος ‘law,’ as Bosanquet supposes. Dialectic is not a ‘law’ in the Greek sense of the word.

οὐ γάρ που κτλ. Theodorus in the Theaetetus (146 B) is a good example, and everyone who knows men who are distinguished mathematicians and nothing more will heartily echo Glauco's emphatic οὐ μὰ τὸν Δία. Taught on the Platonic method, not as an end, but as a means, by teachers who have themselves penetrated into regions beyond and above the sphere of pure mathematics, and who are constantly on the alert to direct their pupils thither, the study of mathematics may prove one of the most valuable of all instruments of education. See App. II.

ὧν . For the attraction see VI 510 B note

ἀλλ’ ἤδη κτλ. ‘Well, did it ever seem to you that persons who are unable’ etc. The subject is μὴ δυνατοί τινες ὄντες— λόγον, and after ἤδη “supplendum est ἔδοξαν, quod ipsum Glauconis verbis magis accommodatum est quam δοκοῦσι” (Schneider). The form of Socrates' question is in fact affected by Glauco's reference to the past in ὧν ἐγὼ ἐντετύχηκα. I formerly, with v and three other MSS, including Vind. F, read ἀλλὰ δή, understanding δοκοῦσι: but ἀλλὰ δή is scarcely appropriate here (see on II 365 C), and Schneider's explanation gives a satisfactory meaning to ἤδη. J. and C. take ἤδη with μὴ δυνατοί τινες ὄντες (‘persons who are as yet unable’ etc.); but the hyperbaton is too difficult, and the meaning (which Plato would rather have expressed by μήπω δυνατοὶ κτλ.) unsuitable. Few will approve of Badham's ἀλλ’ οἱ δὴ κτλ. or even of Burnet's ἀλλὰ δή, εἶπον, μὴ δυνατοὶ οἵτινες δοῦναί τε κτλ. For the sentiment, which is a commonplace of the Socratic school, cf. Xen. Mem. IV 6. 1 , Prot. 336 C , Phaed. 76 B , Crat. 390 C ff. al.

οὐδ’ αὖ κτλ. ‘My answer to this question is also no.’