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

400 Reverence shall be immediately notified. I submit to you my most cordial regards as I do to the Most Illustrious Balbi, and I remain Your Reverence’s most humble, devoted and obliged servant Giuseppe Tartini Padua, 2 January 1756 120. Leonhard Euler to Tartini Although I have little knowledge of the Italian language, I have tried to understand the ideas of the famous virtuoso Signor Tartini upon the theory of harmony, which must be all the more important as they are the work of the greatest composer of these times. Now, I do not believe that it is necessary to judge the merits of this work from the principles of harmony, which being sufficiently established, appear to belong rather to geometricians and physicists than to great musicians. But, seeing that these same principles have been hitherto too far from the harmony of modern compositions, the greatest merit in Signor Tartini’s toils must be sought in the passage that leads from first principles to the practice of these times, which has remained until the present almost entirely uncultivated, being on the one hand too superior for the reach of geometricians, and on the other, too superior for that of musicians. I believe I have established well enough, in my essay on a theory of music, 75 that the first principles of harmony consist neither in that proportion called harmonic, nor in the arithmetic proportion, nor in the geometric one, but solely in the actual perception of the ratios which there are between sounds. With the result that every sound strikes our hearing organ with a certain number of vibrations in a certain period of time, and the nature of every sound consists in the number of vibrations by which the ear is struck in that time. Exempli gratia in the time of a second. A smaller number of vibrations produces a lower sound, and a greater number a higher sound. Sounds can therefore be represented by means of numbers, which denote the vibrations made in the same time, so that high sounds are expressed by means of larger numbers, lower sounds by smaller numbers. That having been established, harmony consists in the perception of the ratio of the numbers which represent the simultaneous and consecutive sounds. Therefore, it is clear that after the unison, the easiest perception is of the sounds represented by the numbers 1 to 2, and 75 Leonhard Euler, known in Italy as Eulero (1707-1783), was a Swiss mathematician and physicist. He published the Tentamen novae theoriae musicae (Petersburg, 1739) in which he attempts the formulation of a theory of music upon an entirely mathematical basis.