We may observe, however, that the above is not an exact account of the first, or early Greek scale; for that scale was founded on a primary division of the interval of two octaves (the extreme range which it admitted) into five _tetrachords_, each tetrachord including the interval of a fourth. All the notes of this series had different names borrowed from this division[26\4]; thus _mese_ was the middle or key-note; the note below it was _lichanos mesôn_, the next below was _parypate mesôn_, the next lower, _hypate mesôn_. The fifth above _mese_ was _nete diazeugmenôn_, the octave was _nete hyperbolæôn_. [Note 26\4: Burney's _History of Music_, vol. i. p. 28.] 4. But supposing a complete system of such denominations established, how could it be with certainty and rigour applied? The human ear is fallible, the organs of voice imperfectly obedient; if this were not so, there would be no such thing as a _good_ ear or a _good_ voice. What means can be devised of finding at will a _perfect_ concord, a fifth or a fourth? Or supposing such concords fixed by an acknowledged authority, how can they be referred to, and the authority adduced? How can we enact a Standard of sounds? A Standard was discovered in the _Monochord_. A musical string properly stretched, may be made to produce different notes, in proportion as we intercept a longer or shorter portion, and make this portion {339} vibrate. The relation of the length of the strings which thus sound the two notes G and C is fixed and constant, and the same is true of all other notes. Hence the musical interval of any notes of which we know the places in the musical scale, may be reproduced by measuring the lengths of string which are known to give them. If C be of the length 180, D is 160, E is 144, F is 135, G is 120; and thus the musical relations are reduced to numerical relations, and the monochord is a complete and perfect _Tonometer_. We have here taken the length of the string as the measure of the tone: but we may observe that there is in us a necessary tendency to assume that the ground of this measure is to be sought in some ulterior cause; and when we consider the matter further, we find this cause in the frequency of these vibrations of the string. The truth that the same note must result from the same frequency of vibration is readily assented to on a slight suggestion of experience. Thus Mersenne[27\4], when he undertakes to determine the frequency of vibrations of a given sound, says 'Supponendum est quoscunque nervos et quaslibet chordas unisonum facientes eundem efficere numerum recursuum eodem vel equali tempore, quod perpetuâ constat experientiâ.' And he proceeds to apply it to cases where experience could not verify this assertion, or at least had not verified it, as to that of pipes. [Note 27\4: _Harmonia_, lib. ii. prop. 19.]