Giuseppe Tartini - Lettere e documenti / Pisma in dokumenti / Letters and Documents - Volume / Knjiga / Volume II

406 in a harmonic respect, but not so in any other respect; and we are equally convinced that no other principle of harmony outside this one is possible. But precisely here my wonder is born, and it grows infinitely, as the veneration of others towards you must grow, who, knowing nothing of this phenomenon of the third sound, when you deigned to give your considerations on our music, nonetheless proposed an excellent criterion; in getting closest to the truth you have surpassed everyone, and in the inferred and demonstrated particular proposition of yours, you have grasped the physical nature of the third sound so well, which, when it is understood as it should be, and the issues will have been clarified, which I here present, is that the third sound is demonstratively the same as it is physically. First of all, not only do I agree with you on the difference of octave that there is between your rule and the third sound, when the latter is in 1/2, and not in the unit, but that does not invalidate your rule, because the difference is not substantial; but I grant you a lot more, and it is that for the quite different quality of this third sound, which results from two given sounds, it not having been hitherto possible to determine with physical certainty if it really results either in the unit, or in 1/2, although through physical evidence its intonation is detected, I who have been hitherto persuaded, with the majority, that this was constituted in 1/2, want to be the first to grant to you that it is really constituted in the unit. So we shall be able more exactly and with more precision to compare your rule to the phenomenon of the third sound, which must finally be decisive in the hitherto turbulent search for the true principle of harmony. This proposition of mine is evident per se , because if given on the one hand a certain Euler, who, expounding on such research, assigns the demonstrative rule of this principle; and given on the other hand an expert, who in the course of his physical research discovers a phenomenon so precise and significant as the third sound; given the comparison of the demonstrative rule with the phenomenon in any precision, and having found it to be identical to the phenomenon, the true principle of harmony is certain of physical and demonstrative certainty; and, as a consequence, it shall be certain that from the connection of two extremes, that is to say one infinitely great (and that is Euler), and one infinitely small (Tartini), the matter will be finally determined after centuries, at last bringing the endless research to a close. Advancing then with a cheerful and secure spirit to the comparison, be it your formula and rule, that given (for example) what you call (and I agree) exponent 6 of the consonance, the relative consonant ratios are its divisors 1, 2, 3; given the exponent 12, let the consonant ratios be its divisors 1, 2, 3, 4, 6, etc. Let there be on the other side two sounding strings in sesquialter quantity of line, that is to say in a ratio of three parts to two. Playing these two strings equitemporaneously, the third unison sound will result, that is to say equal to the sound of a sounding line of six parts. Hence equal in the number of the parts to the exponent 6. But from the multiplication of 2 by 3 one has 6 as a product. Therefore from the multiplication of the numbers indicating the parts of the two played lines one shall have demonstratively the number indicating the intonation of the third sound which shall have to result from two