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Published online by Cambridge University Press: 16 April 2014
The overall sense is clear enough: the Pythagoreans called the fourth συλλαβή, the fifth δι' ὀξειᾶν and the octave ἁρμονία. We are also told that the octave is a σύστημα, which is a musical structure resulting from an acceptable combination of two or more smaller intervals – in this case, of a fourth and a fifth. But the received text appears problematic: in particular, the double accusative τὴν δὲ διὰ πασῶν … ἁρμονίαν occurring in connection with the dative τῷ συστήματι seems quite difficult to account for. The phrase is perhaps to be taken as meaning that the Pythagoreans ‘posed’ or ‘defined’ the octave as ἁρμονία ‘because of the σύστημα’; nevertheless, the syntax still sounds troubled and, as Andrew Barker has suggested, the text is very likely to be corrupt in some way. An easy emendation would be τὴν δὲ διὰ πασῶν τῷ σύστημα <εἶναι> … (‘they defined the octave as ἁρμονία because of its being a σύστημα, as Theophrastus also said’). The corruption could have taken place in two steps, the accidental loss of εἶναι having caused the correction of the ungrammatical τῷ σύστημα into the dative case.
1 Theophr. fr. 717 FHS&G (ap. Porph. in Ptol. Harm. 1.5, p. 96.21–3 Düring).
2 These expressions seem to date back to an early stage of Greek music, prior to – or independent of – the rise of scientific harmonics; they have no apparent relation to the measurement of intervals in mathematical terms and probably belong to the jargon of practical musicians. See Barker, A., The Science of Harmonics in Classical Greece (Cambridge, 2007), 22CrossRefGoogle Scholar. On συλλαβή, apparently the interval that could be grasped by the hand of a lyre player in its basic position, see Barker, ibid. 264; contra, Hagel, S., Ancient Greek Music: A New Technical History (Cambridge, 2009), 373 n. 22CrossRefGoogle Scholar. As for δι' ὀξειᾶν (the Doric form for δι' ὀξειῶν (sc. χορδῶν), alluding to the fact that the fifth is located in the highest part of the lyre's pitch range, literally ‘through the highest strings’, see Zanoncelli, L., La manualistica musicale greca (Milan, 1990), 196 n. 3Google Scholar. Finally, ἁρμονία is easily explained as hinting at the ‘putting together’ (σύστημα) of a fourth and a fifth.
3 Cf. Aristox. Harm. 6.13, 9.13, 10.2 Da Rios; see also Barker, A., Greek Musical Writings, vol. 2. Harmonic and Acoustic Theory (Cambridge, 1989), 126 n. 3Google Scholar.
4 Barker in Fortenbaugh, W.W., Huby, P.M., Sharples, R.W. and Gutas, D. (edd.), Theophrastus of Eresus. Sources for his Life, Writings, Thought, and Influence, Part Two (Leiden, New York and Cologne, 1992), 573 app. crit. and n. 1Google Scholar.
5 A similar construction is observed in Porphyry's Commentary at 1.7, p. 119.1–2 Düring: καθάπερ ἐπὶ τῶν συμφωνιῶν, καθ' ἣν οἱ ἐμμελέστεροι ῥηθήσονται αὐτῶν τῷ θεωρεῖσθαι ἐν ὑπεροχῇ μείζονι ἢ διαιρέσεσι παρίσοις …
6 Cf. LSJ s.v. τίθημι, IV.
