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

371 LETTERS Your Reverence, and those who are there, shall hear third sounds, etc. much better in the middle of the room than in the corners involved. Then both Your Reverence and the most esteemed Signor Dottor Balbi will be illuminated of the truth of the fact, of the manner of the phenomenon, and of the physical necessity of the continued protraction of the two given sounds. In certain cases, not only is the experiment necessary in general, but it is necessary in particular, and individually; nor is it sufficient to believe it from others; one must do it oneself and hear it for oneself. It is so easy, that it requires nothing more. Please do it then, and so many useless difficulties will end once and for all, among which I note this one, which emerges from the words of your letter. I furthermore think that this third sound is the constant root of the harmonic series. It is optimal indeed to distinguish between the experiment and the conjecture. I challenge the whole human race to be able to distinguish in this case the experiment from the conjecture. And when the discoveries of Wallis 53 and Mersenne 54 are mentioned to me, I know nothing and understand nothing. I am an entity unto myself and I have no reading nor erudition of any sort; therefore, all the discoveries of such men and of these times are totally unknown to me. This shall infinitely benefit our intent, because truth never contradicts itself. The whole paragraph which deals with my proposition – that the third sound is an infinitely constant root of the harmonic series; and based around the explanation of the series formed with numbers, from which one infers the sole probability (according to your impression) that it might be so, etc., etc. – the whole of that paragraph is falsely supposed. It is supposed (by you, not by me) that given the fifth Gsolreut, Dlasolre the third sound resulting is the exact same Gsolreut; and it is supposed to be so difficult to distinguish that to assert it is almost an arbitrary decision and not a physical truth. I have said full well that it is difficult to distinguish, because it is a unison; but I did not say it is as difficult as you suppose it to be. The difficulty which I talk about pertains to the lesser difficulty there is in distinguishing this third sound, when it ends up being no longer in unison with any of the two given sounds. Moreover, we know that the third sound in unison with Gsolreut (which is the first to be heard in the harmonic series) stands out in such a way that I am willing to give an eye if among a thousand professors there is one alone who does not distinguish it. May this also be said for good. I shall come to the other part of the paragraph about the resulting Gsolreut third sound as the exact same as the Gsolreut given. This is a false supposition, nor have I ever intended it in such a way, and nor can I, because it is physically false. That it is the exact same Gsolreut, as a unison in a musical sense, is perfectly true; that it is the exact same Gsolreut in a physical sense is utterly false. The series of fractions 1/2, 1/3, 1/4, etc. is intrinsically adapted to the sounding physical strings 1/2, 1/3, 1/4, and it is not possible (not even in metaphysical precision) to separate one thing from the other, just as it is not possible to separate from 53 Wallis, John (or Wallisius, 1616-1703). English mathematician. 54 Mersenne, Marin (188-1648). French theologian, philosopher and celebrated mathematician.