music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...

, retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." Retrograde reverses the order of the motif's pitches: what was the first pitch becomes the last, and vice versa. This is a technique used in music, specifically in

twelve-tone technique The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale ...

, where the inversion and retrograde techniques are performed on the same

tone row In music, a tone row or note row ( or '), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometime ...

successively, " e inversion of the prime series in reverse order from last pitch to first." Stravinsky - Requiem Canticles basic row forms

Conventionally, inversion is carried out first, and the inverted form is then taken backward to form the retrograde inversion, so that the untransposed retrograde inversion ends with the pitch that began the prime form of the series. In his late twelve-tone works, however,

Igor Stravinsky Igor Fyodorovich Stravinsky ( – 6 April 1971) was a Russian composer and conductor with French citizenship (from 1934) and American citizenship (from 1945). He is widely considered one of the most important and influential 20th-century c ...

preferred the opposite order, so that his row charts use inverse retrograde (IR) forms for his source sets, instead of retrograde inversions (RI), although he sometimes labeled them RI in his sketches. For example, the forms of the row from ''Requiem Canticles'' are as follows: P0: R0: I0: RI0: IR0: Note that IR is a transposition of RI, the pitch class between the last pitches of P and I above RI. Other compositions that include retrograde inversions in its rows include works by

Tadeusz Baird Tadeusz Baird (26 July 19282 September 1981) was a Polish composer. Biography Baird was born in Grodzisk Mazowiecki, in Poland. His father Edward was Polish, while his mother Maria (née Popov) was Russian. In 1944 at the age of 16 he was deport ...

and Karel Goeyvaerts. One work in particular by the latter composer, '' Nummer 2'', employs retrograde of the recurring twelve-tone row B–F–F–E–G–A–E–D–A–B–D–C in the piano part.Herman Sabbe, ''Het muzikale serialisme als techniek en als denkmethode: Een onderzoek naar de logische en historische samenhang van de onderscheiden toepassingen van het seriërend beginsel in de muziek van de periode 1950–1975'' (Ghent: Rijksuniversiteit te Gent, 1977): 55. It is performed in both styles, particularly in the outer sections of the piece. The final movement of

Paul Hindemith Paul Hindemith ( ; ; 16 November 189528 December 1963) was a German and American composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advo ...

's '' Ludus Tonalis'', the Postludium, is an exact retrograde inversion of the work's opening Praeludium.

Sources

{{DEFAULTSORT:Retrograde Inversion Musical symmetry Serialism