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R: retrograde I: inverse RI: retrograde-inverse. In music theory, retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." [1] Retrograde reverses the order of the motif's pitches: what was the first pitch becomes the last, and vice versa. [2]
In contradistinction, Antoine Busnois and Jacob Obrecht, used retrograde and other permutations extensively, suggesting familiarity with one another's compositional techniques. [16] Todd also notes that, by use of retrograde, inversion, and retrograde-inversion, composers of this time viewed music in a way similar to serialists of the 20th century.
turning each interval direction to its opposite, giving the inversion (I). The various transformations can be combined. These give rise to a set-complex of forty-eight forms of the set, 12 transpositions of the four basic forms: P, R, I, RI. The combination of the retrograde and inversion transformations is known as the retrograde inversion (RI).
An interval is inverted by raising or lowering either of the notes by one or more octaves so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved.
The permutations resulting from applying the inversion or retrograde operations are categorized as the prime form's inversions and retrogrades, respectively. Applying both inversion and retrograde to a prime form produces its retrograde-inversions, considered a distinct type of permutation. Permutation may be applied to smaller sets as well.
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Inversion: The notes D–F–E–B can be reversed to B–E–F–D; this form of inversion is called retrograde. The upward intervals can become downward intervals and vice versa; this is the form that is properly called inversion. These two can be combined and the result can be transposed: these are inclusive rather than exclusive processes.
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