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

267 LETTERS longer one. But, given that the laws of elastic bodies are absolutely certain, the shorter one vibrates twice in the same time it takes the longer to vibrate just once. From this, as everybody knows, stems the fact that the proportion of two to one expresses the octave: the two and one expressing the corresponding number of simultaneous vibrations. Geometricians infer from this that, to have the higher octave, one seeks such a change in the struck sounding body as to generate in the air (the means by which sounds pass into the ear) an equal corresponding number of vibrations. The same happens to the sounding bodies and namely to the two strings, if we wish to tune them as a fifth. It will be necessary that one is two thirds of the other; and this will give two vibrations again in the time of the higher sound. Given that, if Your Most Illustrious Lordship enquires of a physicist how the same sound is greater and smaller, which is commonly called small and large, piano and forte , he will promptly reply that the largeness or smallness of the sound depends upon the wideness or narrowness of the waves, which are formed, as by a stone thrown into the calm water, in the same way by the sound of the sounding body in the air. Moreover the height and lowness of the sound, that is to say the varying tone of the sounds will depend entirely upon the certain number of their vibrations; during which the various sounds always remain the very same in pitch. If this doctrine is transferred to our case, and especially to those circular waves which express, according to Your Most Illustrious Lordship, the three known sounds produced by your ingenious experiment and expressed by the straight lines in the circle which, when moved, can produce them [the text breaks off here without any tearing and in the body of the page] 8. Tartini to G.B. Martini I am sending back to Your Most Reverend Father your most learned dissertation in defence of the Animuccia canon. 10 Your Reverence is so right that it is almost shameful to dispute it: I say almost, because I do not want to cause prejudice to the profit that one can obtain therefrom of a thousand other wonderful notions and concepts pertaining to the same matter. I do not place myself in the position of a judge, nor in that of a critic, as I am indeed far from being capable of this; and I only find consolation in having seen, on this occasion, the way in which one should study: glory to Your Reverence and shame on me. I meanwhile thank you with all my heart for the very great favour you have done me in this circumstance, assuring you that my obligations increase alongside 10 On the matters pertaining to the resolution of the canon by Giovanni Animuccia, see Busi, 1891: pp. 433-438 and Parisini, 1896: pp. 55-58.