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

264 and with all reason and evidence, because since the second duple divided first into a low fifth, and then into a high fourth, one would immediately come to change and turn nature itself upside down when one puts the fourth before the fifth, precisely as happens in our scale, in which, given that there is between the first and the fourth element the sesquithird proportion, that is to say a perfect fourth, this allows (but against reason and nature) that there again one can modulate the tone. Another observation is taken from said natural scale to know the fundamental ratio of the handling of a seventh, which is used loosely, that is to say without being tied or prepared in advance as is done with every dissonance. The seventh which is used in this way has always, after its fundamen- tal, a major third above it; above the major third the minor third, and above the minor third another minor third which makes the seventh. Therefore, not only is it possible, but indeed one must operate this way, it not being otherwise a dissonance, but a ful- ly-fledged consonance, its root being in the third duple, that is 4 fundamental, 5 major third, with 4 6 minor third, with the 5 and 7 another minor 3rd of the minor with 6. If the harpsichord or organ does not have the right intonation of the 7, as a fault of the same, not of nature, which all too often has put everything in its place, but we, or rather the first founders, did not use it or did not understand it. 5) One must examine the monochord in this manner, and not in another. 1 the whole string, 1/2 half, 1/3 one third, 1/4 one fourth, 1/5 one fifth, etc. And so on, descending degree by degree to the smaller quantity without ever mistaking the order of the num- ber, and this because we have been taught, and are taught, by nature itself in the said instruments and the unshakeable reason of the number, which proceeds thus. c ottava quinta quarta terza maggiore terza minore sesquisesta sesquisettima c c g A b B e g c c i 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 + + + sesquiseventh sesquisixth minor third major third fourth fifth octave