Ptolemy Harmonics 2.14

Ἔκθεσις τῶν ποιούντων ἀριθμῶν τὴν τοῦ διὰ πασῶν κατατομὴν ἐπί τε τοῦ ἀμεταβόλου τόνου καὶ τῶν καθ’ ἕκαστον γενῶν.

Παρεγράψαμεν δὴ κανόνια γʹ, στίχων μὲν ἕκαστον ηʹ, σελιδίων δὲ τὸ μὲν πρῶτον εʹ, τὸ δὲ δεύτερον ηʹ, τὸ δὲ τρίτον ιʹ, τοῖς προτεταγμένοις πάντων σελιδίοις παρατιθεμένης τῆς τάξεως τῶν φθόγγων. Τὸ μὲν οὖν πρῶτον κανόνιον περιέχει τὰ ἐναρμόνια γένη: ἐπὶ μὲν τοῦ πρώτου σελιδίου τὸ κατὰ Ἀρχύταν ἐν λόγοις ἐπὶ δʹ καὶ ἐπὶ λεʹ καὶ ἐπὶ κζʹ, ἐπὶ δὲ τοῦ δευτέρου τὸ κατὰ Ἀριστόξενον ἐν διαστάσει μοιρῶν κδʹ καὶ γʹ καὶ γʹ, ἐπὶ δὲ τοῦ τρίτου τὸ κατὰ Ἐρατοσθένην ἐν λόγοις τῷ τῶν ιεʹ πρὸς ιθʹ καὶ ἐπὶ ληʹ καὶ ἐπὶ λθʹ, ἐπὶ δὲ τοῦ τετάρτου τὸ κατὰ Δίδυμον ἐν λόγοις ἐπὶ δʹ καὶ ἐπὶ λʹ καὶ ἐπὶ λαʹ, ἐπὶ δὲ τοῦ πέμπτου τὸ καθ’ ἡμᾶς ἐν λόγοις ἐπὶ δʹ καὶ ἐπὶ κγʹ καὶ ἐπὶ μεʹ. Τὸ δὲ δεύτερον κανόνιον περιέχει [τὰ χρωματικὰ γένη: ἐπὶ μὲν τοῦ πρώτου σελιδίου τὸ κατὰ Ἀρχύταν ἐν λόγοις τῷ τῶν λβʹ πρὸς κζʹ καὶ τῷ τῶν σμγʹ πρὸς σκδʹ καὶ ἐπὶ κζʹ, ἐπὶ δὲ τοῦ δευτέρου τὸ κατὰ Ἀριστόξενον χρῶμα μαλακὸν ἐν διαστάσει μοιρῶν κβʹ καὶ δʹ καὶ δʹ ἐπὶ δὲ τοῦ τρίτου τὸ κατὰ Ἀριστόξενον χρῶμα ἡμιόλιον ἐν διαστάσει μοιρῶν καʹ καὶ δʹ καὶ ἡμίσεος καὶ δʹ καὶ ἡμίσεος, ἐπὶ δὲ τοῦ τετάρτου τὸ κατὰ Ἀριστόξενον χρῶμα τονιαῖον ἐν διαστάσει μοιρῶν ιηʹ καὶ Ϛʹ καὶ Ϛʹ, ἐπὶ δὲ τοῦ πέμπτου τὸ κατὰ Ἐρατοσθένην ἐν λόγοις ἐπὶ εʹ καὶ ἐπὶ ιηʹ καὶ ἐπὶ ιθʹ, ἐπὶ δὲ τοῦ ἕκτου τὸ κατὰ Δίδυμον ἐν λόγοις ἐπὶ εʹ καὶ ἐπὶ κδʹ καὶ ἐπὶ ιεʹ, ἐπὶ δὲ τοῦ ἑβδόμου τὸ καθ’ ἡμᾶς χρῶμα μαλακὸν ἐν λόγοις ἐπὶ εʹ καὶ ἐπὶ ιδʹ καὶ ἐπὶ κϚʹ, ἐπὶ δὲ τοῦ ὀγδόου τὸ καθ’ ἡμᾶς χρῶμα σύντονον ἐν λόγοις ἐπὶ Ϛʹ καὶ ἐπὶ ιαʹ καὶ ἐπὶ καʹ. Τὸ δὲ τρίτον κανόνιον περιέχει τὰ διατονικὰ γένη: ἐπὶ μὲν τοῦ πρώτου σελιδίου τὸ κατὰ Ἀρχύταν ἐν λόγοις ἐπὶ ηʹ καὶ ἐπὶ ζʹ καὶ ἐπὶ κζʹ, ἐπὶ δὲ τοῦ δευτέρου τὸ κατὰ Ἀριστόξενον διατονικὸν μαλακὸν ἐν διαστάσει μοιρῶν ιεʹ καὶ θʹ καὶ Ϛʹ, ἐπὶ δὲ τοῦ τρίτου τὸ κατὰ Ἀριστόξενον διατονικὸν σύντονον ἐν διαστάσει μοιρῶν ιβʹ καὶ ιβʹ καὶ Ϛʹ, ἐπὶ δὲ τοῦ τετάρτου τὸ κατὰ Ἐρατοσθένην ἐν λόγοις ἐπὶ ηʹ καὶ ἐπὶ ηʹ καὶ τῷ τοῦ λείμματος, ἐπὶ δὲ τοῦ πέμπτου τὸ κατὰ Δίδυμον ἐν λόγοις ἐπὶ ηʹ καὶ ἐπὶ θʹ καὶ ἐπὶ ιεʹ, ἐπὶ δὲ τοῦ ἕκτου τὸ καθ’ ἡμᾶς διατονικὸν μαλακὸν ἐν λόγοις ἐπὶ ζʹ καὶ ἐπὶ θʹ καὶ ἐπὶ κʹ, ἐπὶ δὲ τοῦ ἑβδόμου τὸ καθ’ ἡμᾶς διατονικὸν τονιαῖον ἐν λόγοις ἐπὶ ηʹ καὶ ἐπὶ ζʹ καὶ ἐπὶ κζʹ, ἐπὶ δὲ τοῦ ὀγδόου τὸ καθ’ ἡμᾶς διατονικὸν διτονιαῖον ἐν λόγοις ἐπὶ ηʹ καὶ ἐπὶ ηʹ καὶ τῷ τοῦ λείμματος, ἐπὶ δὲ τοῦ ἐνάτου τὸ καθ’ ἡμᾶς διατονικὸν σύντονον ἐν λόγοις ἐπὶ θʹ καὶ ἐπὶ ηʹ καὶ ἐπὶ ιεʹ, ἐπὶ δὲ τοῦ δεκάτου τὸ καθ’ ἡμᾶς διατονικὸν ὁμαλὸν ἐν λόγοις ἐπὶ θʹ καὶ ἐπὶ ιʹ καὶ ἐπὶ ιαʹ.]

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