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This is a technique used in music, specifically in twelve-tone technique, where the inversion and retrograde techniques are performed on the same tone row successively, "[t]he inversion of the prime series in reverse order from last pitch to first." [3] Basic row forms from Stravinsky's Requiem Canticles: [4] P R I IR
Inversional combinatoriality is a relationship between two rows, a principal row and its inversion. The principal row's first half, or six notes, are the inversion's last six notes, though not necessarily in the same order. Thus, the first half of each row is the other's complement. The same conclusion applies to each row's second half as well.
Here is an example of non-permutation of trichords, using retrogradation, inversion, and retrograde-inversion, combined in each case with transposition, as found within the tone row (or twelve-tone series) from Anton Webern's Concerto: [4]
In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of music. [2] In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.
Rows may be derived from a sub-set of any number of pitch classes that is a divisor of 12, the most common being the first three pitches or a trichord.This segment may then undergo transposition, inversion, retrograde, or any combination to produce the other parts of the row (in this case, the other three segments).
In this tone row, if the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion, the next three are retrograde, and the last three are its inversion. A row created in this manner, through variants of a trichord or tetrachord called the generator, is called a derived row.
The inverted row is an exercise in calisthenics. It primarily works the muscles of the upper back—the trapezius and latissimus dorsi —as well as the biceps as a secondary muscle group. The supine row is normally carried out in three to five sets, but repetitions depend on the type of training a lifter is using to make their required gains.
The melody may vary through transposition, inversion, or otherwise, but retain its original character. The intervals and rhythms of an imitation may be exact or modified; imitation occurs at varying distances relative to the first occurrence, and phrases may begin with voices in imitation before they freely go their own ways.