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

356 third sound & ? wwww w wwwww wwww w A c d ef c d ef b d gh B A Basso armonico Dimostrazione Serie armonica f 40 h 36 f 40 e 48 g 45 e 48 d 60 d 60 d 60 c 80 b 90 c 80 A 120 B 90 A 120 & wwww wwww wwww A B A 120 90 120 terzo Basso armonico del terzo suono suono terzo suono terzo suono Harmonic bass Demonstration Harmonic series Harmonic bass of the third sound third sound third sound Here then is whether it is true or not to make this third sound depend in a very general way on harmonic nature. It is as true as the foundation. Then, that the third sound results from bowed instruments in particular, and not from wind instruments, from metallic strings etc., is of no relevance, as I have answered other times, and as I usually say. In particular, I say that the deception lies in the universally supposed direct cause of the sounds, that is to say the absolute vibrations; but I repeat that this is not the time, and there is no need to discover it and experience it now. To be more precise, I then say that even if, as a hypothesis, one could have this third sound from any instrument, only string instruments would be useful for my purposes. To prove my main proposition I need a physical line, one that is sounding, and that joined to another of the same nature produces the third sound. All the wind instruments are therefore excluded for my purposes, because they do not have a physical line. All the metallic string instruments and unbowed gut strings are likewise excluded, because despite having the physical line needed, this does not continuously maintain, nor continuously reinforce the sound, and so is incapable of producing a third sound. Only the bowed instruments remain suitable, because with the continuous, sustained and reinforced bowing, the two bodies of air moved by the vibrations of the two strings played are given such an impact that their collision and intersection are sufficient to produce the third sound. But I repeat again, that this is not the matter, and that it can serve for nothing but for wasting time. The third sound is present, and is heard evidently in bowed instruments, and is wanted in very general by harmonic nature, because it is its root. This is my proposition, which I intend to have demonstrated in the present reply, and I furthermore intend it to be demonstrated in my treatise at the fifth proposition, where I start, then (as corollary) given any sine in the circle, and given in comparison to the extended sine, etc. May Signor Dottor Balbi deign to consider that passage, and to delve into it (as the demonstration is restricted to just a few words) and he shall detect it on the evidence. The here included demonstration shall give enlightenment and ease to the understanding of that; but one must then be patient if it is not understood immediately, because in the end these are all systematic demonstrations. One must understand many things at once,