(Ger. Umkehrvng). The word bears, in musical terminology, five different significations. (1) Intervals are said to be inverted when their lowest notes are raised an octave higher, and thus placed above tho highest ones, or vice versa, thus In order to ascertain the inversion of a given interval, add to it as many units as are necessary to make up the number nine. The sum of these unite will represent the inverted interval. Th u s: 1 2 3 4 5 6 7 8 8 7 G 5 4 3 2 1 The process of inversion not only changes the name of an interval, but, in certain cases, and to a certain extent, influences its nature. Major intervals, for instance, become minor by inversion ; and minor intervals, major. Augmented intervals become diminished, and diminished ones augmented. But the essential character of the interval survives the operation unchanged, and asserts itself, with equal force, in the inversion. I n whatever position they m ay be taken, consonant intervals remain always consonant; 1 dissonant intervals, dissonant; and perfect intervals, perfect. (See I n t e r v a l .) (2) A chord is said to be inverted when any note, other than its root, is taken in tho lowest part. Thus- Common First Chord. Inversion. If the same process be applied to the chord of the seventh we shall, by successively taking the third, fifth and seventh, in the bass, obtain its three inversions, the 6 -5 -3 , the 6 -4 -3 and the 6-4 -2. i Although the Perfect Fo urth-th e Tnver'ion of the Perfect Fif th-is classed, by contrapuntists, among Discords, i t only forms an appa rent exception to the general rule ; since i t is admitted to be a consonance, when i t appears between th e upper p a r ts of a chord. VOL. I I Chord of the First {Seventh. Inversion. -0 - Second Third Inversion. Inversion. =?& = = e ' s= 1 (3) A pedal point (point d'orgue) is described as inverted when the sustained note, instead of being placed in the bass, is transferred to an upper part, as in Mozart's pianoforte fantasia in C minor (op. 11) : etc. -or, to a middle one, as in the following passage from Deh vieni, non tardar (Nozze di Figaro), where the inverted pedal is sustained by the second violins : In these, and similar cases, the characteristic note (whether sustained or reiterated) forms no part of the H a rm o n y (<7.1?.), which remains wholly unaffected, either by its presence or removal. (4) Counterpoint is said to be inverted when the upper part is placed beneath the lower, or vice versa : thus (from Cherubini)- (a) Double Counterpoint for 2 Voices. L - ^ - . - 1-J[ _ ......... . 1 =----H (b) Inversic y L u .a." . n. r r ri -J- #'---f----LI F - ^ - J----- . - 1 We have, here, an example of what is called * Double Counterpoint in the Octave,' in which the inversion is produced by simply transposing tho upper part an octave lower, or the lower part an octave higher. But the inversion may take place in any other interval, thus giving rise to fourteen different species of double counterpoint-those, namely, invertible in the second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth and fifteenth, either above or below. In order to ascertain what intervals are to be avoided in these several methods of inversion, contrapuntists use a table, constructed of two rows of figures, one placed over the other, the upper row beginning with the unit, and the lower on