HARMONICAL SOUNDS, 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.