an appellation given, by Mr Sauveur, to such sounds as always make a determinate number of vibrations, in the time that one of the fundamentals, to which they are referred, makes one vibration.

Harmonical sounds are produced by the parts of chords, &c. which vibrate a certain number of times, while the whole chord vibrates once.

The relations of sounds had only been considered in the series of numbers, $1 : 2, 2 : 3, 3 : 4, 4 : 5$, &c., which produced the intervals called octave, fifth, fourth, third, &c. Mr Sauveur first considered them in the natural series, $1, 2, 3, 4, 5$, &c. and examined the relations of sounds arising therefrom. The result is, that the first interval, $1 : 2$, is an octave; the second, $1 : 3$, a twelfth; the third, $1 : 4$, a fifteenth, or double octave; the fourth, $1 : 5$, a seventeenth; the fifth, $1 : 6$, a nineteenth, &c.

This new consideration of the relations of sounds is more natural than the old one; and is, in effect, all the music that nature makes without the assistance of art.