Inversion (music) - Melodies

Melodies

When applied to melodies, the inversion of a given melody is the melody turned upside-down. For instance, if the original melody has a rising major third, the inverted melody has a falling major third (or perhaps more likely, in tonal music, a falling minor third, or even some other falling interval). See m. 24 of Bach's C#m fugue, Well-Tempered Clavier 2, for an example of the subject in its melodic inversion.

Similarly, in twelve-tone technique, the inversion of the tone row is the so-called prime series turned upside-down, and is designated T_nI.

Given a certain prime set, with general element p_i,j; under the inversion operation, p_i,j→I(p_{i, 12 - j}); that is, each element of the prime set is mapped into an element with identical order number but with set number the complement (mod.12) of the original set number. —Babbitt 1992, 16 each element p of P is associated with one and only one inverse element s equals p' in S. —Forte 1964, 144 For each u and v in S (v may possibly equal u), we shall define an operation Iv/u, which we shall call 'u/v inversion.'...
...e conceive any sample s and its inversion I(s) as balanced about the given u and v in a certain intervallic proportion. I(s) bears to v an intervallic relationship which is the inverse of the relation that s bears to u. —Lewin 1987, 50