1911 Encyclopædia Britannica/Tartini, Giuseppe

Tartini is historically important as having contributed to the science of acoustics as well as to musical art by his discovery (independently of Sorge, 1740, to whom the primary credit is now given) of what are still called Tartini's tones " (see Sound and Hearing), or differential tones. The phenomenon is this: — when any two notes are produced steadily and with great intensity, a third note is heard, whose vibration number is the difference of those of the two primary notes. It follows from this that any two consecutive members of a harmonic series have the fundamental of that series for their difference tone—thus,${\displaystyle {\tfrac {E}{C}}}$, the fourth and fifth harmonic, produce C, the prime or generator, at the interval of two octaves under the lower of those two notes; ${\displaystyle {\tfrac {E}{G}}}$ , the third and fifth harmonic, produce C, the second harmonic, at the interval of a 5th under the lower of those two notes. The discoverer was wont to tell his pupils that their double-stopping was not in tune unless they could hear the third note; and Henry Blagrove (1811-1872) gave the same admonition. The phenomenon has other than technical significance; an experiment by Sir F. A. G. Ouseley showed that two pipes, tuned by measurement to so acute a pitch as to render the notes of both inaudible by human ears, when blown together produce the difference of tone of the inaudible primaries, and this verifies the fact of the infinite upward range of sound which transcends the perceptive power of human organs. The obverse of this fact is that of any sound being deepened by an 8th if the length of the string or pipe which