οἱ μὲν Πυθαγόρειοι τὴν μὲν διὰ τεσσάρων συμφωνίαν συλλαβὴν ἐκάλουν, τὴν δὲ διὰ πέντε δι' ὀξειᾶν, τὴν δὲ διὰ πασῶν τῷ συστήματι, ὡς καὶ Θεόφραστος ἔφη, ἔθεντο ἁρμονίαν.Footnote ¹

The overall sense is clear enough: the Pythagoreans called the fourth συλλαβή, the fifth δι' ὀξειᾶν and the octave ἁρμονία.Footnote ² 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.Footnote ³ 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.Footnote ⁴ 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’).Footnote ⁵ 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.

However, I would rather suggest another way of emending the text, which seems to me simpler and even more defensible; it relies on the assumption that τῷ συστήματι is sound and the error lies elsewhere. In our passage the verb τίθεσθαι plainly means ‘to define, to name’; in this sense, it admits the construction with the accusative and the dative, the predicative τὸ ὄνομα being omitted. A good example is Plato, Theaetetus 157b9 ᾧ δὴ ἁθροίσματι ἄνθρωπόν τε τίθενται … (‘and this aggregate they call “man” …’);Footnote ⁶ interestingly enough, this passage, like that in Theophrastus, refers to something that is composite. For our text to fit into this construction, we need only a very little adjustment: οἱ μὲν Πυθαγόρειοι τὴν μὲν διὰ τεσσάρων συμφωνίαν συλλαβὴν ἐκάλουν, τὴν δὲ διὰ πέντε δι' ὀξειᾶν· τῇ δὲ διὰ πασῶν – τῷ συστήματι, ὡς καὶ Θεόφραστος ἔφη – ἔθεντο ἁρμονίαν (‘the Pythagoreans called the concord of fourth συλλαβή and that of fifth δι’ ὀξειᾶν; as for the octave – that is, the σύστημα, as Theophrastus also said – they called it ἁρμονία'). It is quite plausible indeed that τῇ δὲ διὰ πασῶν, occurring after the two accusatives τὴν μὲν διὰ τεσσάρων and τὴν δὲ διὰ πέντε, was erroneously written as an accusative as well.

This emendation also has some bearing on the issue of what exactly Theophrastus should be credited with having said here. If we keep the received text, we are left with the doubt as to whether Porphyry quoted him as the source of the whole sentence or only of the statement about the octave; but with the reading I have suggested we must inescapably conclude that the philosopher's testimony concerned nothing more than the interval of the octave.