Volume 2: 1771 Edition of the Encyclopedia Britannica!


Harmonical, something belong to harmony.  See Harmony.

Harmonical composition, in a general sense, includes both harmony and melody, i.e. of music or songs, both in a single part, and in several parts.

Harmonical series, a series of many numbers in continual  harmonical proportion.  Thus, if there are four or more numbers, of which every three immediate terms are harmonical, the whole will make an harmonical series: such is 30 : 20 : 15 : 12 : 10.  Or, if every four terms immediately next each other are harmonical, it is also a continual harmonical series, but of another species, as 3, 4, 6, 9, 18, 36, etc.

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, etc. 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, etc. which produced the intervals called octave, fifth, fourth, third, etc.  Mr. Sauveur first considered them in the natural series, 1, 2, 3, 4, 5, etc. 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, etc.

    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.

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