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, , &c. which produced the intervals called octave, fifth, fourth, third, &c. Mr Sauveur first considered them in the natural series, , &c. and examined the relations of sounds arising therefrom. The result is, that the first interval, , is an octave; the second, , a twelfth; the third, , a fifteenth, or double octave; the fourth, , a seventeenth; the fifth, , 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.