# 1911 Encyclopædia Britannica/Tartini, Giuseppe

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 produces it be doubled. The law is without exception throughout the compass in which our ears can distinguish pitch, and so, of necessity, a string of twice the length of that whose vibrations induce the deepest perceivable sound must stir the air at such a rate as to cause a tone at an 8th below that lowest audible note. It is hence manifest that, however limited our sense of the range of musical sound, this range extends upward and downward to infinity. Tartini made his observations the basis of a theoretical system which he set forth in his Trattato di Musica, secondo la vera scienzia dell’ Armonia (Padua, 1754) and Dei Principij dell' Armonia Musicale (Padua, 1767). He also wrote a Trattato delle Appogiature, posthumously printed in French, and an unpublished work, Delle Ragioni e delle Proporzioni, the MS. of which has been lost.