in music, is derived from the Latin preposition in, and vertere, "to turn any thing a contrary way." The analogy of this term, and its use in music, will appear more obvious from the sequel.

It signifies a change in the order of the notes which form a chord, or in the parts which compose harmony; which happens by substituting in the bass, those sounds which ought to have been in the upper part: an operation not only rendered practicable, but greatly facilitated, by the resemblance which one note has to another in different octaves; whence we derive the power of exchanging one octave for another with so much propriety and success, or by substituting in the extremes those which ought to have occupied the middle station; and vice versa.

It is certain, that in every chord there must be a fundamental and natural order, which is the same with that of its generation: but the circumstances of succession, taste, expression, the beauty of melody, and variety, the approximation of harmony, frequently oblige the composer to change that order by inverting the chords, and of consequence the disposition of the parts.

As three thing may be arranged in six different orders, and four things in twenty-four; it would seem at first, that a perfect chord should be susceptible of six inversions, and a dissonant chord of twenty-four; since one is composed of four and the other of three sounds, and since inversion consists only in a transposition of octaves. But it must be observed, that in harmony all the different dispositions of acuter sounds are not reckoned as inversions, whilst the same sounds remain in the lower parts. Thus, the two orders of the perfect chord ut mi sol, or C E G, and ut sol mi, or C G E, are only taken for the same inversion, and only bear the same name; this reduces the whole of inversions of which a perfect chord is susceptible to three; that is to say, to as many inversions as the chord contains different sounds: for the replications of the same sound are here reckoned as nothing.

Every time, therefore, when the fundamental bass is heard in the lowest parts, or if the fundamental bass be retrenched, every time when the natural order is preferred in the chords, the harmony is direct. As soon as that order is changed, or as soon as the fundamental sounds, without being in the lower parts, are heard in some of the others, the harmony is inverted. It is an inversion of the chord, when the fundamental sound Inverted found is transposed; it is likewise an inversion of the harmony, when the treble or any other part moves as the bass ought to have done.

Every where, where a direct chord can be well placed, its inversions will likewise be so with respect to the harmony; for it is still the same fundamental succession. Thus, at every note of the fundamental bass, it is in the power of the composer to arrange the chord at his pleasure, and of consequence every moment to produce different inversions; provided that he does not change the regular and fundamental succession; provided also, that the dissonances may always be prepared and resolved in the same parts where they are first heard, that the sensible note may always ascend, and that such false relations may be avoided as would be too harsh upon the ear in the same part. This is the key of these mysterious distinctions which composers have made between those chords where the treble is syncopated, and those in which the bass ought to be syncopated; as, for instance, between the ninth and the second: it is thus that in the first the chord is direct, and the dissonance in the treble; in the others, the chord is reversed, and the dissonance in the bass.

With respect to chords by supposition, greater precaution is necessary in inverting them. As the sound which they add to the bass is absolutely foreign to the harmony; it is often only tolerably there, on account of its vast distance from the other sounds, which renders the dissonance less harsh. But if these added sounds should happen to be transposed in the higher parts, as it sometimes does; if this transposition be not performed with much art, it may produce a very bad effect; and never can this be happily practised without taking away some other sound from the chord. See, at the article Accord in the Musical Dictionary, the cases when inversion may be practised, and the choice of such as are proper.

The perfect knowledge of inversion depends on art and study alone: the choice is a different matter; to this an ear and a taste are necessary; experience of the different effects are likewise indispensable; and though the choice of inversions be indifferent with respect to the foundation of the harmony, it is by no means such in regard of the effect and expression. It is certain, that the fundamental bass is formed to support the harmony, and to prevail beneath. Every time therefore when the order is changed and the harmony inverted, there ought to be good reasons for it: without which, the composer will fall into the vice of our more recent music, where the melody of the treble is often like what the bass should be, and the bass always like that of the treble, where every thing is confounded, reversed, disordered, without any other reason than to subvert the established order, and to spoil the harmony.