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

405 LETTERS than evident that when there are such phenomena, we no longer need anything, except to follow and use the physical laws of nature. Whatever methods nature uses to explain itself, it is clear that we have to use the same methods to obtain the same goal that it sets for itself; but it is certain that we must be physically sure of the methods and goal of nature in order to follow and apply its laws correctly. Convinced and led by this solely true principle of our need, I believe I have shown, as far as the evidence leads, the existence of all the physical-sonic phenomena assigned in the first chapter, revealing their common tendency to physical-harmonic unity in different ways. The means and the ways are different, but the purpose is just one, and this is indeed more than sufficient for our needs, so that the first physical foundation of harmony can be established in such a manner that if nature is not missing, the truth of our foundation can never collapse, nor be lacking. Therefore, if on the strength of this foundation, if either I or anybody else is physically compelled to admit this physical-harmonic unity as a first principle (since, being inferred from all the phenomena, it is the true language of nature and the true explanation of itself), the prime necessity of the harmonic proportionality becomes clear; because even if they do not agree in other ways and aspects, all the phenomena hitherto known agree in this aspect of harmonic proportionality as in the only objective of the physical-harmonic unity; and any that will be found in future centuries will also agree. The thing is all too evident in the phenomenon of the third sound for it to be possible to doubt it ever again. If, given any two protracted sounds in any whatsoever relation between each other, except in unison, or in duple, and given either the same or a different category of instruments, that is to say either between two violins, or between two oboes, or between violin and oboe etc., a third sound results, which is unfailingly found either in harmonic proportion, or in a harmonic series with the two given sounds; one that physically and demonstratively is the fundamental harmonic bass of the two given sounds; which shall always result in the same way from any species of sounds, provided that they are protracted. What space, therefore, remains to doubt whether the harmonic proportionality is wanted by nature out of a necessity of principle, and whether nature must, or not, be found uniform in the future? One can indeed doubt the arithmetical, and geometrical proportionality, there not being any phenomenon whatsoever that gives the indication thereof. Actually, if given (for example) the subsesquitertian 3, 4, that for our established sciences is in respect, that is to say in power of arithmetical proportionality, applied to two sounding strings, and producing the two protracted sounds, the resulting third sound destroys the arithmetical regard of our sciences, by physically placing the third term not as 2, which with 3, 4, forms the arithmetical proportion, but either in harmonic proportion as 6 or in harmonic series as 12 (depending on whether this third sound really results in 1 or in 1/2 of the arithmetical series of fractions); it comes as a necessary physical consequence thereof that nature in this phenomenon wants the harmonic, excludes the arithmetical and any other proportionality by first principle; and by corollary we are physically sure of this principle