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

259 LETTERS ? w w w mi fa sol 16 ÷ 15 9 ÷ 8 144 120 6 ÷ 5 24: In the systemwhich I propose, the two proportions sesquitenth and sesquieleventh likewise make the proportion of the semiditone, which in practice is almost re mi fa, but the mi is not our one. ? w w w re mi fa 12 ÷ 11 11 ÷ 10 132 110 6 ÷ 5 22: Now, the sum is right in both systems. But I say that both with regard to the order and to the choice of the semitone mi fa in the Greek system, there is a most evident error, and that on the contrary in my system the order is most correct, and the proportion most suited, proper and unique, by continuing the natural order of the number and the necessity of nature, which leads imperceptibly from the more to the less by degrees that are certain and fixed in their quantity, as you can see from the system which you have in your hands. I do not therefore say, nor shall I ever say that the Greeks have erred in the quantity of the proportions. I say rather, and repeat, that in the order or position and choice of the same they erred greatly, as they did in omitting the two known consonances which are born from the division of the sesquithird, or fourth, and the degrees corresponding to the same division in the tone scale, as you can see in the system which you have in your hands. I therefore confirm that they could not, in any way, after the proportion 10/9, jump to the proportion 16/15, and then to 8/9. The order of the number is entirely opposite to these, and with the number, physical nature and the evident proof of the said instruments. Number requires that after 10, 11 follows, and after that 12. And if until 10 we have counted correctly: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, what reason for continuing obliges us to prefer the above order, and instead of counting 10, 11, 12, 13, 14, 15, 16, to decide to count inappropriately 16:15 9:8:10:9:8 16:15 and to do that arbitrarily, for no reason, and, what is worse, repeating those same proportions that nature avoids repeating as the enemy of the superfluous? Physical nature is quite against it. It is sufficient to test my proposition with weights, and you shall see that by adding one equal weight after the other to a string, and examining the sounds which result thereof, you shall find that as you go upwards, the steps become smaller, nature compensating in a most ordered manner to the higher