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

258 B w w wb w 25:24 25· 24 50·49·48 Doni’s example B w w wb wn w 14:13 Example of my system if between a and b you search for the dividing term, it is this one below B w w wb 28 · 27 · 26 Notice that in the ancient common system, the ditone being divided into two tones, one a sesquioctave, the other a sesquininth, of the former there is no division whatsoever in our music, and yet order required that the division of the former be looked for, not of the latter. The reason is clear. The duple is divided into a sesquialter, and into a sesquithird. The greater proportion, which is the sesquialter, is divided into the ditone and semiditone, and the smaller, which is the sesquithird, is omitted. One takes the higher proportion, which is the ditone, and the semiditone. One takes the greater proportion, which is the ditone, and one divides it into the sesquioctave and sesquininth tone, and the lower, which is the semiditone, if it is not omitted, is patched up with a disorder. Reason then would want one to take (when continuing to divide) the greater proportion of the ditone, which is the sesquioctave tone, not the lower, which is the sesquininth. Nonetheless, even our good elders omitted the sesquioctave and took the sesquininth. This and another thousand disorders we shall see in the course of our examination. With regard to what the bachelor father of the convent, Padre Maestro Benvenuti, says, namely that the Greeks may have neglected some notes, but they never mistook the proportions, I tell you that if we mean mistake the proportion with regard to quantity, the Greeks never erred, nor could they err, as it is sufficient to add up the numbers to know the correctness of the proportion. But with regard to the order of the proportions and their choice, they clearly erred, and this is what I am saying. For example, in the Greek System the major tone, added to the major semitone, make the proportion of the semiditone, which in practice is mi, fa, sol.