Tartini and Combination Tones

Abstract

The first part of the article describes the contemporary standpoint in explaining the occurence of combination tones. They are caused by a nonlinear process in the human hearing organ. To the original tone, according to the Fourier theorem, higher harmonics are added. Similarly, if two tones with two different frequencies strike the human ear, higher harmonics together with their combinations are produced. Regarding the mathematical sign in individual combinations, these tones are divided in summation and difference tones respectively. As a rule, they appear in a series of orders with the loudest being the lower ones. The second part deals with the actual discovery of combination tones. The first communications about a third tone, audible during simultaneous sounding of two tones, were given by Sorge (1744), Romieu (1751), and the violinist and composer G. Tartini (1754). But as Jones (1935) has shown, it is likely, that, with respect to the date of discovery, the order of these names should be reversed, so that not unjustly the third tone is sometimes named after Tartini. The third part explains some pratical uses of difference tones. First, in tuning two violin strings in a perfect fifth, a phenomenon known already to Tartini. The second case explains the frequently wrong descriptions of "bells' subharmonics", being in fact difference tones produced in the human ear. Eventually, the importance of difference tones in organ construction is described. Extremely long organ pipes can be substituted by two shorter ones tuned in a perfect fifth thus using their difference tone as the fundamental one (acoustic bass), as well as combinations of different pipes in popular organ stops.