§89.5Οὕτως οὐδὲ ἡ ὀξεῖα φωνὴ ἐκ πλειόνων συνέστηκεν ἢ πλείους ἀριθμοὺς κινεῖται οὐδὲ ἡ βαρεῖα· οἷόν τε γὰρ ἢ ταύτην λέγειν ἢ κἀκείνην, ἐπειδὴ ἴδιόν τι μέγεθος βαρείας ἐστὶ φωνῆς.
Similarly, neither does the high voice consist of more parts nor is it moved in a greater number of movements, nor does the low; for it is possible to say this of either the former or the latter, since there is a certain characteristic magnitude of the low voice.
Δῆλον δὲ ἐκ τῆς βίας τῆς γεονομένης περὶ τοὺς μελῳδοῦντας· ὡς γάρ τινος δέονται δυνάμεως εἰς τὸ τὴν ὀξεῖαν ἐκφωνῆσαι οὕτω εἰς τὸ τὴν βαρεῖαν φλέγξασθαι.
This is clear from the effort that occurs in those who sing; for just as they need a certain effort to utter the high voice, so too to sound the low.
Ἔνθα μὲν γὰρ συνάγουσι τὰ πλεῦρα καὶ τὴν ἀρτηρίαν ἐκτείνουσι βίᾳ ἀποστενοῦντες. Ἔνθα δὲ διευρύνουσι τὴν ἀρτηο ρίαν, διὸ βραχύτερον τὸν τράχηλον ποιοῦσι τὸ μῆκος τῆς εὐρύτητος συναγούσης.
For in the one case they contract the ribs and stretch the windpipe, narrowing it by force, while in the other they expand the windpipe, for which reason they make the neck shorter, the width contracting the length.
§89.6Τοιαύτης ἔοικεν ἔν τε τοῖς αὐλοῖς εἰς τὸ ἐμπνεῦσαι βίᾳ τῷ στενωτέρῳ δυνάμεως δεῖν καὶ εἰς τὸ τῷ εὐρυτέρῳ ἵνα πληρωθῇ·
A similar thing seems to occur also in the case of oboes, where effort is needed to blow with force into the narrower part, and also into the wider part so that it may be filled.
καὶ γὰρ δὴ καὶ μᾶλλον ἐν τοῖς αὐλοῖς· ἀπονώτερον γὰρ τὸ ὀξὺ τῷ διὰ τῶν ἄνω γίγνεσθαι τρημάτων· βίας δὲ δεόμενον τὸ βαρὺ καὶ μείζονος εἰ διʼ ὅλου τὸ πνεῦμα πέμποιτο, ὥστε ὅσον μήκους προστίθεται τοσόνδε καὶ πνεύματος ἰσχύος προστίθεται.
Indeed, this is even more the case with oboes; for the high sound is less laborious because it occurs through the upper holes, but the low sound needs effort, and even greater effort if the breath is to be sent through the whole, so that as much as is added to the length, so much is also added to the strength of the breath.
§89.7Ἐν δὲ ταῖς χορδαῖς τὸ ἴσον κατὰ θάτερον δῆλον· ὅσῳ γὰρ εὐτονωτέρα ἡ τῆς λεπτοτέρας τάσις τοσῷδε ἡ ἀνεῖσθαι δοκοῦσα παχυτέρα, οὕτω τε ὅσῳ ἰσχυρότερος ὁ ἦχος ἐκ τῆς λεπτοτέρας τοσῷδε βαρύτερος ὁ ἕτερος·
In strings, the equality in the other way is clear: for by as much as the tension of the thinner string is more intense, by so much is the thicker string, which seems to be relaxed, tense in its own way; and thus, by as much as the sound from the thinner string is stronger, by so much is the other lower.
ἐκ γὰρ μείζονος ὁ πλείων καὶ τοῦ πέριξ ἦχος.
For the greater sound, including that of the surrounding air, comes from the larger.
Πῶς γὰρ ἂν σύμφωνοι ἐγίγνοντό τινες φθόγγοι εἰ μὴ ἰσότης ἦν;
For how would some notes become consonant if there were no equality?
ἀσύγκριτον γὰρ τὸ πλεονάζον, τὸ γὰρ ὑπέρμετρον ὑπὲρ τὴν μῖξιν διάδηλον γίγνεται.
For that which exceeds is incomparable, for that which is excessive becomes clearly visible beyond the mixture.
Διὸ τοῖς κατὰ τὴν κρᾶσιν ἰσχυροτέροις τὸ ἀνειμένον πλεῖον ἐπιμίγνυται εἰς τὸ ἰσοδυναμῆσαι·
Therefore, to those elements that are stronger in the mixture, more of the relaxed element is mixed in so that they may be of equal power.
§89.8ὥστε ἐστί τις συμφωνία καὶ ἰσότης τῶν ἐξ ὧν γίνεται.
So that there is a certain consonance and equality of the things from which it arises.
Εἰ γὰρ ὁ ὀξὺς πλείους κινοῖτο ἀριθμοὺς, πῶς ἂν συνήχησις γένοιτο;
For if the high sound moved a greater number of movements, how would sounding-together occur?
καὶ γὰρ, ὥς φασι, καὶ πορρωτέρω ἀκούεται ὁ ὀξύτερος φθόγγος τῷ πορρωτέρω διὰ τὴν τῆς κινήσεως ὀξύτητα διικνεῖσθαι.
For indeed, as they say, the higher note is heard also at a greater distance because it arrives further due to the sharpness of its movement.
Εἰ διὰ τὸ πλῆθος γίγνεται, οὐκ ἄν ποτε γένοιτο σύμφωνος οὗτος πρὸς τὸν βαρὺν, οὔθʼ ὅτε ἀκούεται, εἴ γε ἐν ἀμφοτέροις ἡ συμφωνία, οὔθʼ ὅτε ἐκλείπει ὁ βαρύτερος, ἀνάγκη γὰρ κατὰ τὴν λεληθυῖαν ἔκλειψιν μηκέτʼ ἀκούεσθαι· οὔτε μάλιστα ἄμφω ἀκούονται·
If this occurs because of the quantity, it would never become consonant with the low note, neither when it is heard (if indeed consonance is in both), nor when the lower ceases—for it is necessary that, according to the unnoticed cessation, it is no longer heard—nor, most of all, when both are heard; for even then the high note is more intense, inasmuch as it is capable of arriving also at a distance.
καὶ τότε γὰρ ὁ ὀξὺς σφοδρότερός ἐστιν ἅτε οἷός τε ὢν καὶ πόρρω διικνεῖσθαι· φθάνει τε οὖν τὸν βαρὺν καὶ κατισχύει ὥστε σφετερίζεσθαι τὴν αἴσθησιν ἀεὶ μειονεκτοῦντος τοῦ βαρυτέρου.
Therefore, it outruns the low note and overpowers it, so that it monopolizes the perception, while the lower is always at a disadvantage.
§89.9Ἀλλʼ ἐπεί ἐστί τι σύμφωνον ἰσότητα δηλοῦν ἀμφοῖν τοῖν φθόγγοιν, ἰσότης ἐστὶ τῶν δυνάμεων διαφέρουσα τῇ ἰδιότητι ἑκατέρα.
But since there is a certain consonance that reveals the equality of both notes, there is an equality of their powers, each differing in its specificity.
Τὸ γὰρ ὀξύτερον φύσει ὂν ἐκδηλότερον οὐκ ἰσχυρότερον πορὁ ρωτέρω ἀντιληπτόν ἐστι τοῦ βαρυτέρου, ὥσπερ τὸ λευκὸν ἄλλου του χρώματος, ἤ τι ἕτερον ὃ οὐχὶ τῷ θάτερον ἧττον εἶναι ὁ πέφυκε μᾶλλον ἀντιληπτόν ἐστιν, ἢ τῷ μὴ διὰ τοὺς ἴσους ἀριθμοὺς κινεῖσθαι, ἀλλὰ τῷ μᾶλλον τῷδε ἢ τῶδε ἐπιβάλλειν τὴν αἴσθησιν διὰ τὴν πρὸς τὰ πέριξ ἀνομοιότητα.
For the higher, being by nature more manifest, is perceived at a greater distance than the lower, not because it is stronger, just like white in comparison to some other color, or any other thing which is more perceptible by nature, not because the other is less, nor because it is moved through unequal numbers, but because the perception strikes this one rather than that one due to its dissimilarity to the surroundings.
Οὕτως διικνεῖται μὲν καὶ ὁ βαρύς, ἡ δʼ ἀκοὴ θᾶττον ἀντιλαμβάνεται διὰ τὴν ἰδιότητα τοῦ ὀξέος, οὐ διὰ τὸ ἐν αὐτῷ πλῆθος.
Thus, the low note also arrives, but the hearing perceives the high note more quickly due to its specificity, not due to the quantity in it.