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

372 the string that is being played the number of oscillations relative to the denominator of the fractions and the sum of the areas of the oscillatory arcs of the fraction itself, because the quantity is the same. May this be said in general so that we can understand each other about the harmonic physical sounding series. But to return to the purpose, the Gsolreut of the given sounding string is physically different indeed from the Gsolreut third sound; as in a comparison with the human voice, the Gsolreut formed in unison with the sound of the Gsolreut string will be musically the same Gsolreut, but physically they will be indeed different. And then my proposition from the beginning to the end of the treatise names the third sound everywhere: a clear sign that I distinguish it physically from the two given sounds; otherwise they would be two sounds alone. If then, the first third sound is the first entirely different physical unit, and in fact resulting in a different way from the sound of Gsolreut sounding string, it is something which is evident per se, and beyond any debate, that from such a unit the series of the third sound must begin. Such a series is not a series in itself, because the third sound is always that one, and it is always one. But it is a relative series, that is to say 1/2 third sound, relative to the physical sounding ratio of 1/2 1/3; 1/2 third sound relative to the physical sonic ratio 1/3 1/4 etc. infinitely. Nor is this third sound comparable to any term of the physical sounding harmonic series, because a single term does not produce and cannot produce any third sound. But one must compare it, that is to say refer it to the series of the physical sounding harmonic ratios, because it proceeds from those, and not from the separated terms of the series. Now you should see that, this being so physically, your paragraph has nothing to do with this case. This is what I can and must tell you in reply. But I repeat again, and then again (I do not know how many times I have hitherto repeated this proposition): if one attempts to separate the physical from the demonstrative in my dissertation, one is wasting time and effort. If I want to keep up with you in dealing with your physical questions, we shall multiply entities infinitely, we shall constantly deviate from the proposition, and we shall never conclude anything. May it please God that it not be so; but I fear this with too good reason. If I have to give my real opinion, the spirit of the system has hitherto not been detected in the examination. It is, in substance, completely different from that which is made to appear when viewing disconnected things. Any one of those which have been hitherto discussed is connected to all the others. And if, in delving into them a little more, one should try to see them all together for comprehension, then one would evidently see that they either are all true, or they are all false, both physically and demonstratively. I mention to you the real need, though I am ready to follow you wherever and however you want to lead me. I submit to both my most reverent respects, and I remain Your Reverence’s most humble, devoted and obliged servant Giuseppe Tartini Padua, 8 September 1752