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

403 LETTERS correspond to the consonances. Now, since in those the two numbers 3 and 5 are only each found once, one can say that exponents of dissonances will be all those in which one of these numbers 3 and 5 is found more than once; which is fully in line with the rule given by the Author on page 74; because the repetition of the same number 3 or 5 produces in the chord two similar intervals. Moreover, there would indeed be another important question: whether musicians are right in treating all these chords as dissonant. The illustrious author declares himself for the negative on page 157 where he has found the means to use with such good success the chord composed of a major third and an augmented fifth, as a perfect consonance; and why could one not use, with as much success, the chords contained in the exponent 3 · 3? And all the more so as Signor Tartini himself treats as a consonance the augmented sixth contained in this chord, B www# 16 20 25 the three sounds of which cannot have between them a simpler ratio than that indicated by the numbers 18, 45, 64, of which the exponent is 2880 = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5, which, because of its great complication B ww# 45 64 should be deemed the strongest dissonance. But I would like to entreat Signor Tartini to examine well, if the ear, or rather some misplaced principle, causes him to see such a chord as a consonance; and I am quite sure that an unprepared ear will always reject this chord as an insufferable dissonance. I greatly fear that some prejudices may have a part in adopting some chords which are used nowadays, given that my theory of exponents is not only based in the nature of sounds and in the perception of the same, but is still perfectly in accordance with most of the consonances and the dissonances that musicians make use of. It furthermore seems to me that musicians limit themselves too much to the denomination of the intervals and that sometimes they forget that it is not the denomination of the intervals but the ratio of the numbers which express the sounds that produces harmony. What confirms me more in this opinion is that the fine composition by Signor Tartini which is found after page 160 of his work, and which seems quite distant from the principles received in the composition, is wonderfully in accordance with my principles: because in it he does not use other sounds than those in which the numbers are divisors of the exponent 3 · 3 · 5 · 5 multiplied by any power of 2, thus 3 · 3 · 5 · 5 can be regarded as the exponent of the whole work: I nonetheless believe that Signor Tartini could make it much more harmonious if he freed it from the above-mentioned chord of the augmented sixth, which is repeated so frequently. I dare to claim, with the permission of Signor Tartini, that the true principles of harmony are very firmly established, and I flatter myself to have set them out in their whole