In music theory, the word inversion has a number of meanings.
When applied to melodies, the inversion of a given melody is the melody turned upside-down - so if the original melody has a rising major third (see interval), the inverted melody has a falling major third. Similarly, in the twelve-tone technique, the inversion of the tone row is the so-called prime series turned upside-down.
When applied to counterpoint, a contrapuntal inversion of two melodies simultaneously being played by two voices is the switching of the melodies between voices, so that the upper-voice melody is now played in the lower voice, and vice versa.
An inverted interval is an interval whose top note has been transposed down an octave, or whose bottom note has been transposed up an octave. When perfect intervals are inverted they remain perfect. When major intervals are inverted they become minor and minor becomes major. Augmented intervals become diminished, and diminished become augmented. Thus the interval of a perfect fifth becomes a perfect fourth, minor second a major seventh.
An inverted chord is a chord which has a note other than its root in the bass. For example, the root position of a triad of C major has the C in the bass:
A triad in root position, therefore, is made up of the root note and a third and a fifth above it.
The first inversion of the same triad has the E, the third of the triad, in the bass:
This means that a triad in first inversion is made up of the root plus a third and a sixth above it. In figured bass, a first inversion is indicated by the number 6.
The second inversion has the fifth, the G, in the bass:
A triad in second inversion, therefore, is made up of the root plus a fourth and a sixth above it. The figured bass notation for this is 64.
The third inversion of a triad cannot be constructed, since a triad has only three notes. Chords of four notes or more, however, can be in their third inversion: the third inversion of a dominant seventh in C major, for example (made up of the notes G, B, D and F) has the seventh, F, in the bass. This gives a chord made up of the root plus a second, fourth and sixth above it. The figured bass notation is accordingly 642.
The terms "root", "first inversion", and "second inversion" may also be applied to chords in which the notes are not closely spaced. For instance, C-G-E, where the E is a major sixth above G, is also considered to be in root position, and more generally, any C major chord in which C is the lowest note is considered to be in root position. Similarly, any C major chord with E on the bottom counts as a first inversion, any C major chord with G on the bottom counts as a second inversion; and analogously for all other chords.
For other meanings of the word inversion, see inversion.