HARMONY

, in Music, the agreeable result of an union of several musical sounds, heard at one and the same time; or the mixture of divers sounds, which together have an agreeable effect on the ear.

As a continued succession of musical sounds produces melody, so a continued combination of them produces Harmony.

Among the ancients however, as sometimes also among the moderns, Harmony is used in the strict sense of consonance; and so is equivalent to the symphony.

The words concord and Harmony do really signify the same thing; though custom has made a little difference between them. Concord is the agreeable effect of two sounds in consonance; and Harmony the effect of any greater number of agreeable sounds in consonance.

Again, Harmony always implies consonance; but concord is also applied to sounds in succession; though never but where the terms can stand agreeably in consonance. The effect of an agreeable succession of several sounds, is called melody; as that of an agreeable consonance is called Harmony.

Harmony is well defined, the sum or result of the combination of two or more concords; that is, of three or more simple sounds striking the ear all together; and diffevent compositions of concords make different Harmony.

The ancients seem to have been entirely unacquainted with Harmony, the soul of the modern music. In all their explications of the melopœia, they say not one word of the concert or Harmony of parts. We have instances, indeed, of their joining several voices, or instruments, in consonance; but then these were not so joined, as that each had a distinct and proper melody, so making a succession of various concords; but they were either unisons, or octaves, in every note; and so all performed the same individual melody, and constituted one song.

When the parts differ, not in the tension of the whole, but in the different relations of the successive notes, it is this that constitutes the modern art of Har- mony.

Harmony of the Spheres, or Celestial Harmony, a kind of music much spoken of by many of the ancient philosophers and fathers, supposed to be produced by the sweetly tuned motions of the stars and planets. This Harmony they attributed to the various proportionate impressions of the heavenly bodies upon one another, acting at proper intervals. They think it impossible that such prodigious bodies, moving with such rapidity, should be silent: on the contrary, the atmosphere, continually impelled by them, must yield a set of sounds proportionate to the impression it receives; and that consequently, as they run all in different circuits, and with various degrees of velocity, the different tones arising from the diversity of motions, directed by the hand of the Almighty, must form an agreeable symphony or concert.

They therefore supposed, that the moon, as being the lowest of the planets, corresponded to mi; Mercury, to fa; Venus, to sol; the Sun, to la; Mars, to si; Jupiter, to ut; Saturn, to re; and the orb of the fixed stars, as being the highest of all, to mi, or the octave.

It is though that Pythagoras had a view to the gravitation of celestial bodies, in what he taught concerning the Harmony of the spheres.

A musical chord gives the same note as one double in length, when the tension or force with which the latter is stretched is quadruple; and the gravity of a planet is quadruple of the gravity of a planet at a double distance. In general, that any musical chord may become unison to a lesser chord of the same kind, its tension must be increased in the same proportion as the square of its length is greater; and that the gravity of a planet may become equal to the gravity of another planet nearer the sun, it must be increased in proportion as the square of its distance from the sun is greater. If therefore we should suppose musical chords extended from the sun to each planet, that all these chords might become unison, it would be requisite to increase or diminish their tensions in the same proportions as would be sufficient to render the gravities of the planets equal; and from the similitude of those proportions, the celebrated doctrine of the Harmony of the spheres is supposed to have been derived.

Kepler wrote a large work, in folio, on the Harmonies of the world, and particularly of that of the celestial bodies. He first endeavoured to find out some relation between the dimensions of the five regular solids and the intervals of the planetary spheres; and imagining that a cube, inscribed in the sphere of Saturn, would touch by its six planes the sphere of Jupiter, and that the other four regular solids in like manner fitted the intervals that are between the spheres of the other planets, he became persuaded that this was the true reason why the primary planets were precisely six in number, and that the author of the world had determined their distances from the sun, the centre of the system, from a regard to this analogy. But afterwards finding that the disposition of the five regular solids amongst the planetary spheres, was not agreeable to the intervals between their orbits, he endeavoured to discover other schemes of Harmony. For this purpose he compared the motions of the same planet at its greatest and least distances, and of the different planets in their several orbits, as they would appear viewed|

from the sun; and here he fancied that he found a similitude to the divisions of the octave in music. Lastly, he imagined that if lines were drawn from the earth, to each of the planets, and the planets appended to them, or stretched by weights proportional to the planets, these lines would then sound all the notes in the octave of a musical chord.

See his Harmonics; also Plin. lib. 2, cap. 22; Macrob. in Somn. Scip. lib. 2, cap. 1; Plutarch de Animal. Procreatione, è Timæo; and Maclaurin's View of Newton's Discov. book 1, chap. 2.