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

349 LETTERS third thing demonstratively inferred is that if the subduple proportion of 1 to 2 is permuted in the duple of 1 to 1/2, the third term will be a third; this third term does not hold either in geometrical progression, or in arithmetical progression, or in harmonic progression according to the minds of mathematicians. 92. G.B. Martini to Tartini The first difficulty we are about to present in this letter is the reason the octave does not produce a third sound; there would need to be a substantial proof. The very same octave, however, is produced by the third sound, and so according to this assertion the octave is produced, but does not produce, a fact that provokes wonder that the mother of consonances and other intervals is itself not capable of producing one. One observes in the third sound a certain inconstancy or disordered conduct that is difficult to grasp, given that nature usually produces things simply, but with a certain order and constancy. That said, one observes from Figure III that the minor third C# and E produces as third sound a tenth below an A, the other minor third of Figure I, D and F (like the minor third B and D of Figure II) produces as minor third a Bb which is a 17th below. One establishes that the third sound of the fifth is the unison, something that entails no small difficulty, in as much as the unison carries no variety of sound, because it contains nothing that is lower or higher and is hence almost, if not completely, imperceptible to the ear, hence the fifth will be universally considered as companion of the octave. It could by many be deemed to be a strange matter that the two main consonances, the octave and the fifth, do not produce a third sound. It would be a very desirable thing, and one satisfying and advantageous to readers, to indicate the reason why the said two sounds produce a third sound, and not any other. That said, one fears that Monsieur Rameau, combined with the Royal Academy of Sciences of Paris, might claim to have demonstrated the reason for this in his Demonstration du principe de l'harmonie , and in other of his treatises, in which it is demonstrated with experiments that given any stable sound, say for example Ut, this [sound] produces two other very high sounds, the one corresponding to a twelfth above the fundamental, the other a major seventeenth above the same fundamental sound, the whole of which, as the gentlemen of the Academy of Sciences state in the extract from the registers dated 10 December 1749, was first observed and known by Father Mersenne and by Wallis. Hence from the experiments the contrary effect is rather found, since that of Signor Rameau produces all the harmonic intervals of the third and fifth upwards, and in that of Signor Tartini downwards. In reply to the