§89.1Fr. 89
Ἔστι γὰρ τὸ γινόμενον κίνημα μελωδητικὸν περὶ τὴν ψυχὴν σφόδρα ἀκριβὲς ὁπόταν φωνῇ ἐθελήσῃ ἑρμηνεύειν αὐτὸ, τρέπει μὲν τήνδε, τρέπει δὲ ἐφʼ ὅσον οἵα τέ ἐστι τὴν ἄλογον τρέψαι καθὸ ἐθέλει.
For the melodic movement that arises in relation to the soul is extremely precise, and whenever one wishes to express it by means of the voice, it on the one hand alters this, and on the other hand, in so far as it is able, alters the irrational part as it wishes.
Ἧς τὴν ἀκρίβειάν τινες ἐπεβάλοντο εἰς τοὺς ἀριθμοὺς ἀναπέμπειν κατὰ τοὺς ἐν τούτοις λόγους τὴν ἀκρίβειαν τῶν διαστημάτων γίνεσθαι φήσαντες.
Some people attempted to refer its precision to numbers, asserting that the precision of intervals occurs according to the ratios in these.
Ἕνα γὰρ λόγον εἶναι τοῦ διὰ πασῶν ἔφασαν ὡς καὶ τὸν τοῦ διπλασίονος καὶ τὸν τοῦ διὰ πέντε. Ὡς τὸν τοῦ ἡμιολίου καὶ τὸν τοῦ διὰ τεσσάρων ὡς τὸν τοῦ ἐπιτρίτου, καὶ τῶν ἄλλων διαστημάτων ἁπάντων ὁμοίους, ὥσπερ καὶ τῶν ἄλλων ἀριθμῶν ἑκάστου ἴδιον.
For they claimed that there is one ratio of the octave, just as there is that of the double, and that of the fifth, just as that of the sesquialter, and that of the fourth, just as that of the sesquitertian, and similarly for all the other intervals, just as each of the other numbers has its own characteristic ratio.
Οὕτω τε ἐν ποσότητι τὴν μουσικὴν εἶναι, ἐπειδὴ παρὰ τήνδε αἱ διαφοραί.
And so they claimed that music exists in quantity, since differences are due to this.
§89.2Ἃ δὴ λέγοντες συνετώτεροί τισιν ἐφαίνοντο τῶν ἁρμονικῶν καὶ αἰσθήσει κρινόντων, τοῖς τῶν νοητῶν ἀριθμῶν λόγοις ἐπικρίνοντες.
By saying these things, they seemed more intelligent to some than those harmonicians who judge by perception, since they made their judgments by the ratios of intelligible numbers.
Οἳ οὐκ ᾔδεισαν ὅτι, εἰ μέν τι ποσότης ἐστὶν, ἡ διαφορὰ γίγνεται αὕτη παρὰ τὸ ποσότητι διάφορον κἂν μέλος ἢ μέλους μέρος εἴη· ὥστε καὶ ἡ χρόα χρόας ποσότητι διαφέροι, ὅπερ ἀνάγκη κἂν μέλος ἢ μέλους μέρος εἴη, εἴ γε τὸ μέλος καὶ τὸ διάστημα ἀριθμὸς καὶ διὰ τὸν ἀριθμὸν τὸ μέλος καὶ ἡ τοῦδε διαφορά.
They did not know that, if there is indeed some quantity, this difference occurs due to difference in quantity, even if it be a melody or a part of a melody; so that even color would differ from color in quantity, which is necessary even if it be a melody or a part of a melody, if indeed melody and interval are number, and through number melody and its difference exist.
Καὶ γὰρ εἰ πᾶν διάστημα πλῆθός τι, τὸ δὲ μέλος ἐκ διαφόρων φθόγγων, τὸ μέλος ὅτι ἀριθμὸς τοιόνδε ἂν εἴη.
For if every interval is a certain quantity, and melody consists of different notes, then melody, because it is number, would be of such a kind.
§89.3Ἀλλʼ εἰ μηδὲν ἀλλʼ ἢ ἀριθμὸς, πᾶν ἀριθμητὸν μετέχοι ἂν καὶ μέλους ὅσον καὶ ἀριθμοῦ.
But if it is nothing other than number, every countable thing would participate in melody just as much as in number.
Εἰ δ' ὡς τῷ χρώματι συμβέβηκε τὸ πλῆθος ἄλλῳ ὄντι, καὶ τοῖς φθόγγοις, ἔστι τι ἄλλο φθόγγος καὶ ἄλλο τὸ περὶ αὐτὸν πλῆθος.
But if, just as quantity is accidental to color which is something else, so it is also with notes, then a note is one thing and the quantity concerning it is another.
Ἀλλʼ εἰ ἄλλο τι φθόγγος ὁ ἀκουστὸς καὶ ὁ βαρύτερος καὶ ὁ ὀξύτερος, διαφέρουσιν ἀλλήλων ἢ ὡς φθόγγοι ἢ ὡς τὸ πλήθει.
But if the audible note, both the lower and the higher, is something else, do they differ from one another either as notes or in quantity?
Εἰ μὲν ὡς τὸ πλήθει, καί ἐστιν ὁ ὀξύτερος τοιοῦτος τῷ πλείονας ἀριθμοὺς κεκινῆσθαι καὶ ὁ βαρύτερος τῷ ἐλάττους, τί ἄλλο τὸ ἴδιον τῆς φωνῆς ἂν εἴη;
If indeed in quantity, and the higher note is such by being moved in a greater number of movements and the lower by being moved in fewer, what other characteristic of the voice would there be?
πᾶσα γὰρ ἀντιληπτικὴ ἢ κατὰ τὸ ὀξὺ ἢ κατὰ τὸ βαρύ ἐστι· πᾶσα γὰρ φωνή ἐστιν ἧς μὲν ὀξυτέρα ἧς δὲ βαρυτέρα, ὥστε ἧς μὲν ἔλαττον τὸ πλῆθος ἧς δὲ πλεῖον, ὥστε ἀριθμός·
For every perceptible voice is according to either highness or lowness; for every voice is higher than one and lower than another, so that for one its quantity is less and for another greater, and so it is number.
οὗ αἰρομένου τί τὸ ἀπολειπόμενον εἴη ἄλλο τι καθὸ φωνή;
If this is removed, what would be the remaining other thing in so far as it is a voice?
ἡ φωνὴ δὲ ὀξυτέρα τινὸς ἢ βαρυτέρα ἐστίν· ἔχει τὸ ποσὸν ἡ φωνή· εἰ δὲ ἄλλο τι οὐκ ἔτι ἔσται φωνή τις.
A voice is higher or lower than something; a voice has quantity; but if it is something else, it will no longer be any voice at all.
§89.4Εἰ δὲ ᾗ φθόγγοι διοίσουσιν οἱ ὀξεῖς καὶ βαρεῖς, οὐκέτι τοῦ πλήθους δεησόμεθα· ἡ γὰρ αὐτῶν φύσει διαφορὰ αὐτάρκης ἔσται εἰς τὴν τῶν μελῶν γένεσιν.
But if high and low notes differ in so far as they are notes, we shall no longer need quantity; for their natural difference will be sufficient for the generation of melodies.
Καὶ εἴδησις ἔσται τῶν διαφορῶν.
And there will be knowledge of the differences.
Οὐκέτι γὰρ ἔσονται διαφοραὶ παρὰ τὰ πλήθη ἀλλὰ παρὰ τὴν ἰδιότητα τῶν φωνῶν ὥσπερ ἐν τοῖς χρώμασιν.
For differences will no longer be due to quantities but due to the specificity of the voices, just as in colors.
Οὐδὲ γὰρ χρῶμα ἁπλοῦν ἁπλοῦ χρώματος ποσότητι διαφέρει· ἴσαι γὰρ ἂν εἶεν αἱ ποσότητες· ὥσπερ εἰ συμμιγείη ἢ μέλαν λευκῷ ἴσον ἴσῳ, οὐκ ἂν οἱ τοῦ λευκοῦ ἀριθμοὶ τῶν τοῦ μέλανος πλείους λέγοιντο οὐδʼ ἂν οἱ τοῦ μέλανος τῶν τοῦ λευκοῦ.
For a simple color does not differ from another simple color in quantity; for the quantities would be equal; just as if black were mixed with white, equal with equal, the numbers of white would not be said to be more than those of black, nor those of black more than those of white.
Οὕτως οὐδὲ τὸ γλυκύπικρον· ἕκαστον γὰρ καθὸ ἐπιτέτακται ἴσον· ἀλλʼ ἔστι τὸ πλῆθος ἐπʼ ἴσον ἐπιτεταγμένον κατὰ τὸ ἴδιον.
So too with the bittersweet; for each, in so far as it has been intensified, is equal; rather, the quantity has been intensified equally according to its own specificity.