Abstract

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 … . 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