“Ptolemais of Cyrene wrote about these things briefly in her investigation and Didymos the musician addressed it as well among many other this in his work On the Difference Between Aristoksenians and Pythagoreians… Ptolemais wrote this:
What is the difference in those who are exceptional at music? Some put reason forward as the matter, but others offer sensation, while there are those who posit both. The Pythagoreans offer reason as the issue, those of them who challenge musiciians to abandon perception and instead to accept reason itself as a sufficient criterion. Musicians are refuted when they start by taking up perception in the beginning only to forget it. Instrumentalists tend to emphasize perception because the contemplation of theory is useless to them or in some way weak.
What is the difference of those who believe that both reason and perception are important criteria? Some propose that both perception and reason have similar power, while others position one in front of the other. Aristoxenos of Tarantum thinks that they matter equally. He believes that perception cannot sustain itself apart from reason and that reason is not powerful enough alone to persist without the basic foundations of perception and that it eventually returns the product of introspection back to perception.”
Why does he want to set perception before reasons? It is because of order not power. For, he says, whenever what is sensed in any way takes root then we need to privilege reason in any theory about it. Who else values both principles similarly? Pythagoras and his followers. For they want perception, as a kind of guide, to start by taking the inspirations which they pass on to reason and for reason then to move on from receiving these sensations and to adapt them on its own in moving away from perception. For this reason, if a system of thought founded upon reason seems no longer perfectly fit to perception, they do not undermine it, but instead reproach the sensation for departing from its meaning since reason discovers what is correct through itself and refutes perception.
Who is in opposition to them? Some of the musicians from the school of Aristoxenos, especially those who have assumed a theoretical mindset but have also adding to it from instrumental practice. These people believe that perception is the greater power and that reason is second only because it is useful.”
Περὶ τούτων συντόμως μὲν καὶ ἡ Κυρηναία Πτολεμαῒς ἔγραψεν ἐν τῇ εἰσαγωγῇ, ἐπῆλθε δὲ καὶ Δίδυμος ὁ μουσικὸς διὰ πλειόνων ἐν τῷ Περὶ τῆς διαφορᾶς τῶν ᾿Αριστοξενείων τε καὶ Πυθαγορείων. … γράφει δὴ ἡ μὲν Πτολεμαῒς τάδε· «Τῶν ἐν τῇ μουσικῇ διαπρεψάντων τίς ἡ διαφορά; οἱ μὲν γὰρ τὸν λόγον προέκριναν αὐτόν, οἱ δὲ τὴν αἴσθησιν, οἱ δὲ τὸ συναμφότερον. τὸν μὲν λόγον προέκρινον αὐτὸν τῶν Πυθαγορείων ὅσοι μᾶλλον ἐφιλονείκησαν πρὸς τοὺς μουσικοὺς τελέως τὴν αἴσθησιν ἐκβάλλειν, τὸν δὲ λόγον ὡς αὔταρκες κριτήριον καθ’ ἑαυτὸν εἰσφέρειν. ἐλέγχονται δ’ οὗτοι πάντως τι αἰσθητὸν παραλαμβάνοντες ἐν ἀρχῇ καὶ ἐπιλανθανόμενοι. τὴν δ’ αἴσθησιν προέκριναν οἱ ὀργανικοί, οἷς ἢ οὐδαμῶς ἔννοια θεωρίας ἐγένετο ἢ ἀσθενής. τῶν δὲ τὸ συναμφότερον προκρινάντων τίς ἡ διαφορά; οἱ μὲν ὁμοίως ἀμφότερα ἰσοδυναμοῦντα παρέλαβον τήν τ’ αἴσθησιν καὶ τὸν λόγον, οἱ δὲ τὸ ἕτερον προηγούμενον, τὸ δ’ ἕτερον ἑπόμενον. ὁμοίως μὲν ἀμφότερα ᾿Αριστόξενος ὁ Ταραντῖνος. οὔτε γὰρ αἰσθητὸν δύναται συστῆναι καθ’ αὑτὸ δίχα λόγου, οὔτε λόγος ἰσχυρότερός ἐστι παραστῆσαί τι μὴ τὰς ἀρχὰς λαβὼν παρὰ τῆς αἰσθήσεως, καὶ τὸ τέλος τοῦ θεωρήματος ὁμολογούμενον πάλιν τῇ αἰσθήσει ἀποδιδούς.
τί δὲ μᾶλλον βούλεται προηγεῖσθαι τὴν αἴσθησιν τοῦ λόγου; τῇ τάξει, οὐ τῇ δυνάμει. ὅταν γάρ, φησι, ταύτῃ τὸ αἰσθητὸν συναφθῇ ὁποῖόν ποτέ ἐστι, τότε δεῖν ἡμᾶς καὶ τὸν λόγον προάγειν εἰς τὴν τούτου θεωρίαν. τίνες τὸ συναμφότερον ὁμοίως; Πυθαγόρας καὶ οἱ διαδεξάμενοι. βούλονται γὰρ αὐτοὶ τὴν μὲν αἴσθησιν ὡς ὁδηγὸν τοῦ λόγου ἐν ἀρχῇ παραλαμβάνειν πρὸς τὸ οἱονεὶ ζώπυρά τινα παραδιδόναι αὐτῷ, τὸν δὲ λόγον ἐκ τούτων ὁρμηθέντα καθ’ ἑαυτὸν πραγματεύεσθαι ἀποστάντα τῆς αἰσθήσεως, ὅθεν κἂν τὸ σύστημα τὸ ὑπὸ τοῦ λόγου εὑρηθὲν τῆς πραγματείας μηκέτι συνᾴδῃ τῇ αἰσθήσει, οὐκ ἐπιστρέφονται, ἀλλ’ ἐπεγκαλοῦσι λέγοντες τὴν μὲν αἴσθησιν πλανᾶσθαι, τὸν δὲ λόγον εὑρηκέναι τὸ ὀρθὸν καθ’ ἑαυτὸν καὶ ἀπελέγχειν τὴν αἴσθησιν. τίνες ἐναντίως τούτοις; ἔνιοι τῶν ἀπ’ ᾿Αριστοξένου μουσικῶν, ὅσοι κατὰ μὲν τὴν ἔννοιαν θεωρίαν ἔλαβον, ἀπὸ δ’ ὀργανικῆς ἕξεως προκόψαντες. οὗτοι γὰρ τὴν μὲν αἴσθησιν ὡς κυρίαν ἔθεσαν, τὸν δὲ λόγον ὡς παρεπόμενον πρὸς μόνον τὸ χρειῶδες.