§89.10Καὶ γὰρ δή γε εἰ καὶ πορρωτέρω ἐκινεῖτο οὐ διὰ τὸ πλείους κινεῖσθαι ἀριθμοὺς ὁ ὀξύτερος ἀλλὰ διὰ τὸ σχῆμα· ἐπειδὴ ὁ μὲν ὀξὺς ἦχος πρόσω μᾶλλον φέρεται καὶ ἄνω ὁ δὲ βαρὺς πέριξ κατʼ ἴσον μᾶλλον.
For indeed, even if the higher sound were moved to a greater distance, this is not because it moves a greater number of movements, but due to its shape; since the high sound is carried rather forward and upward, while the low sound rather equally around.
Δῆλον δὲ καὶ ἐκ τῶν ὀργάνων· τὸ μὲν γὰρ ὑπόκερας καὶ τὸ σὺν τῷ χαλκώματι περιηχητικώτερα ἅτε τοῦ ἤχου ἴσου περὶ πᾶν γιγνομένου.
This is clear also from instruments; for the lower part of the horn and the one with the bronze fitting are more resonant around, inasmuch as the sound becomes equal all around.
Καὶ γὰρ εἴ τις ὀξὺν φθεγγόμενος φθόγγον ἅπτοιτο τῆς αὑτοῦ πλευρᾶς, ἔπειτα πάλιν βαρὺν, αἰσθάνοιτο ἂν μᾶλλον ἐπὶ τοῦ βαρέος φθόγγου τῇ χειρὶ τῆς περὶ τὴν πλευρὰν κινήσεως.
For indeed, if someone uttering a high note were to touch his own rib, and then again a low note, he would perceive more in the case of the low note the movement around the rib with his hand.
Κἂν τοῦ ὀργάνου ἅπτηται τῆς χέλυος ἢ τοῦ κέρατος ἢ ἀγκῶνος ὁπότε τὴν λεπτὴν τύπτοι καὶ τὴν τοῦ βαρέος προετικὴν, πάλιν ἐπαίσθοιτο ἂν μᾶλλον τῆς περὶ τὸ κύτος κινήσεως ὁπότε τὴν τοῦ βαρυτέρου τύπτοι ἤχου προετικήν.
And if he touches the shell of the instrument or the horn or the arm, whenever he strikes the thin string and the one sending forth the low sound, he would again perceive more the movement around the body of the instrument whenever he strikes the one sending forth the lower sound.
Εἰς πᾶν γὰρ ὁ βαρὺς φθόγγος διικνεῖται πέριξ, ὁ δὲ ὀξὺς πρόσω ἢ εἰς ὁ βιάζεται ὁ φθεγγόμενος.
For the low sound arrives all around, while the high sound goes forward or to wherever the speaker forces it.
§89.11Εἰ οὖν ὅσῳ πρόσω κινεῖται ὁ ὀξὺς τοσόνδε περὶ πᾶν κινοῖτο ὁ βαρὺς οὐκ ἂν ἐλάττους κινοῖτο ἀριθμούς· ὅπερ κἀκ τῶν αὐλητικῶν δῆλον· ὁ γὰρ μακρότερος αὐλὸς βαρύτερος ἐν ᾧ πλεῖον τὸ πνεῦμα περὶ ὃ πᾶν ἡ κίνησις.
If, therefore, by as much as the high sound is moved forward, by so much the low sound were moved all around, it would not move a smaller number of movements; which is clear also from the flute-players' practice; for the longer oboe is lower, in which there is more breath, around the whole of which the movement occurs.
Ἀλλʼ οὐδὲ τάχει ἂν διαφέροι ὁ ὀξύς· προκαυ τελαμβάνετο γὰρ ἂν τὴν ἀκοὴν ὥστε μὴ γίγνεσθαι σύμφωνον· εἰ δὲ γίγνεται ἰστοταχοῦσιν ἄμφω· οὐχὶ οὖν ἀριθμοί τινες ἄνισοι τὸν τῶν διαφορῶν λόγον ποιοῦσιν.
But neither would the high sound differ in speed; for it would have anticipated the hearing so that no consonance would occur; but if consonance occurs, both have equal speed; therefore, it is not unequal numbers that make the ratio of the differences.
Αἱ δὲ φύσει τοιαίδε φωναὶ φύσει συνηρμοσμέναι οὖσαι· οὐδὲ γὰρ τὰ διαστήματα, ὥς τινές φᾶ σιν, αἴτια τῶν διαφορῶν, διὸ καὶ ἀρχαί· §89.12ἐπειδὴ καὶ τούτων παραλειπομένων γίγνεται τάδε αἴτια τοῦ εἶναι οὐχ ὡς ποιοῦντα ἀλλὰ ὡς μὴ κωλύοντα.
But voices of this kind are by nature harmonized by nature; for neither are intervals, as some say, the causes of differences, for which reason they are also principles; since even when these are set aside, the following become the causes of existence, not as active causes but as not hindering.
Οὐδὲ γὰρ ἡ ἐκμέλεια τῆς ἐμμελείας αἰτία· ἐπειδὴ οὐκ ἂν γένοιτο ἐμμέλεια εἰ μὴ ἡ ἐκμέλεια παραπέμποιτο.
For neither is discord the cause of concord; since concord would not occur unless discord were set aside.
Οὐδʼ ἄν τι ἄλλο ἐπιστημονικὸν γένοιτο εἰ μὴ τοὐναντίον ἀνεπίστημον τοῦ ἐπιστήμονος, ἀλλὰ παραπεμπόμενον, τοῦ μὴ κωλύειν.
Nor would any other scientific thing occur unless the opposite, the unscientific, were set aside in relation to the scientific, so as not to hinder.
§89.13Ὥστʼ οὐδὲ τὰ ὁιαστήματα τοῦ μέλους αἴτια ὡς ποιοῦντα ἀλλʼ ὡς μὴ κωλύοντα.
So that neither are intervals the causes of melody as active causes but as not hindering.
Εἰ γάρ τις ἅμα φθέγγοιτο κατὰ τὸ συνεχὲς καὶ τοὺς μεταξὺ τόπους, ἆρʼ οὖν ἐκμελῆ ποιοῖτο φωνήν;
For if someone were to utter simultaneously along the continuous scale and the intermediate spaces, would he not make a discordant voice?
ὧν οὖν μὴ παραπεμπομένων ἐκμέλεια γίγνοιτο ἂν οὐχὶ λειφθεῖεν κωλυσόντων.
Therefore, when these are not set aside, discord would occur, but they would not be left behind as things that will hinder.
Μέγα οὖν ὄφελος τὸ περιίστασθαι ταύταις τὴν μελῳδίαν, ὥστε ἀνευρίσκειν τοὺς συνηρμοσμένους πρὸς ἀλλήλους φθόγγους· ἀλλʼ οὗτοι μὲν αἴτιοι τοῦ μέλους ὄντες, τὰ δὲ διαστήματα παραπεμπόμενα ἐπιδηλούμενα ἐκμελείας αἴτιά ἐστιν· ἧς καὶ ἀρχαὶ λέγοιντʼ ἂν οὐχὶ τῆς ἐμμελοῦς φωνῆς.
It is therefore of great benefit for melody to avoid these, so as to discover the notes harmonized with one another; but while these notes are the causes of melody, intervals, being set aside and yet indicated, are the causes of discord, of which they might also be called the principles, and not of the concordant voice.
§89.14Οὔτʼ οὖν τὰ διαστήματα αἴτια τῆς ἐμμελείας ἀλλὰ βλαπτικὰ αὐτῆς φαινόμενά γε· οὔτε οἱ ἀριθμοὶ αἴτιοι τῇ ποσότητι διαφέρειν ἀλλήλων τοὺς φθόγγους· κατʼ ἄλλο γὰρ ἴσοι εὑρίσκονται οἱ βαρεῖς τοῖς ὀξέσι καθὸ καὶ ὁ πόνος ἴσος κατὰ τοὐναντίον· οὐ γὰρ ἧττον τῶν τοὺς ὀξεῖς φθόγγους φθεγγομένων οἱ τοὺς βαρεῖς πονοῦσι βιαζόμενοι εἰς τοὐναντίον πάλιν.
Therefore, neither are intervals the causes of concord, but they are clearly harmful to it; nor are numbers the causes of notes differing from one another in quantity; for in another respect the low notes are found to be equal to the high notes, insofar as the effort is equal in the opposite direction; for those who utter low notes do not labor less, forcing themselves back in the opposite direction.
Μία δὲ φύσις τῆς μουσικῆς, κίνησις τῆς ψυχῆς ἡ κατὰ ἀπόλυσιν γιγνομένη τῶν διὰ τὰ πάθη κακῶν.
And the single nature of music is a movement of the soul that occurs in accordance with the release from the evils caused by the passions.