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

460 4·9, and became the arithmetical between the extremes 4: 8. The value to be carried forward to the mean in a subsesquioctavian relation to 6 will therefore be = 5: 1/3. After the four terms have been transformed to prime numbers and integers, it will be the proportion = 6: 8: 9: 12, of which 8 is the harmonic mean, 9 the arithmetical. This is Plato’s doctrine and law as clearly expressed in the said passage on the formation of the world soul, and from this doctrine and universal law both Pythagoras and Plato inferred the particular musical system, in which the two sesquioctavian tones which certainly form a continuous geometric proportion are found to be contrary to this law and doctrine, and to complete the tetrachord there remains the semitone = 243: 256, which is the particle mentioned by Plato. This is the precise language, as it is not credible that the two philosophers contradicted themselves and opposed law and doctrine to fact; for it is quite clear that if in the universal law they do not admit a continuous geometrical proportion, but want it reduced to the discrete, in the particular fact inferred from the system of the universal law they cannot admit it unless absurdly and with contradiction. For today that is all. May Your Reverence please examine with ease and patience what I have here proposed and expressed, for if I were to decide to crowd everything in all at once, it would be too much both for myself and for Your Reverence, from whom I shall await some response on the printed booklet, and to whom, submitting my most cordial, and most obsequious regards, joined with those of Signor Don Antonio, with ever more deference, I remain Your Reverence’s most humble, devoted and obliged servant Giuseppe Tartini Padua, 28 April 1769 176. Tartini to G.B. Martini During the last week, I had very carefully prepared my letter to accompany the pages which Your Reverence will have received unaccompanied in the last post. I interrupted it, as in that letter I hinted at things which, if they are mentioned, must also be demonstrated; and an informal letter can certainly not become a dissertation. The things which I mentioned there had a bearing on your compendium on the number theory, 107 which I received from our Padre Maestro Vallotti, and for which I thank you a thousand times. Your Reverence, as usual, benefits our profession in 107 Compendio della teoria de’ numeri per uso del musico (Bologna, 1769).