Retrograde inversion is the practice of flipping and reversing a musical passage. Used throughout music history, the technique gained prominence in the 20th century through the work of the Second Viennese School.
Definition Retrograde inversion is the process of playing a melody upside down and backwards."Retrograde inversion", The New Harvard Dictionary of Music. Edited by Don Randel. Belknap Press of Harvard University Press, 1986. 697. It combines two closely related horizontal and vertical mirror techniques: inversion and retrogression.Wuorinen, Charles. Simple Composition. Edition Peters, 1979. 90ff.
Inversion turns every interval in the melody upside down. Where a chromatic scale proceeds upwards by semitones, its inversion moves downwards by semitones.Drabkin, William. "Inversion", Grove Music Online. Oxford University Press, 2001. Retrogression reverses all of the pitches in a melody.Laitz, Steven Geoffrey. The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening. Oxford University Press, 2003. 780. The retrograde inversion of a melody is its inverted form played in reverse.
History The Italian marking Al rovescio could refer to either an inverted or a reversed passage of music."Al rovescio." Grove Music Online. Oxford University Press, 2001. Reversed and inverted passages are extensively found in Ars Nova. The techniques were closely related, but they were not often combined into retrograde inversion. Some composers did write in retrograde inversion such as Jacob Obrecht and Antoine Busnois.Todd, R. Larry. "Retrograde, Inversion, Retrograde-Inversion, and Related Techniques in the Masses of Jacobus Obrecht", The Musical Quarterly, vol. 64, no. 1, 1978. 50–78.
Retrograde inversion could be found in highly specialized mirror canons where the comes is the dux upside down and in reverse. These works were known as canon al contrario riverso."Canon", The New Harvard Dictionary of Music. Edited by Don Randel. Belknap Press of Harvard University Press, 1986. 128. Johann Sebastian Bach composed a notable example in The Musical Offering. The canon begins with an alto clef and an upside down bass clef to indicate the way it should be performed.J.S. Bach. Edited by Malcolm Boyd. Oxford University Press, 1999. 296.
As Arnold Schoenberg developed twelve-tone technique, retrograde inversion became a crucial compositional strategy. Along with transposition, a tone row could be transformed through inversion (I), retrograde (R), and retrograde inversion (RI) in ways that would generate enough harmony and counterpoint to sustain prolonged compositions.Slonimsky, Nicolas. Volume III: Music of the Modern Era. Routledge, 2004. 106f. These three transformations and the original tone row, which is sometimes called its "prime", are the four basic forms of any set.
During his doctoral studies in musicology, Anton Webern focused on early counterpoint, particularly the Franco-Flemish School.Moldenhauer, Hans, and Rosaleen Moldenhauer. Anton von Webern: A Chronicle of His Life and Work. London: Victor Gollancz Ltd., 1978. He repeatedly cited such work as an inspiration for his own. Webern eventually began germinating twelve-tone rows by applying the three primary operations (I, R, RI) to three-note cells. In Concerto for Nine Instruments, the first operation Webern applies to the original trichord of the tone row is retrograde inversion.Taruskin, Richard. "Music in the Early Twentieth Century", in Oxford History of Western Music. Oxford University Press, 2010. 724.
The technique was not limited to serial composers in the 20th century. The Postludium of Paul Hindemith's Ludus Tonalis is an exact retrograde inversion of the work's opening Praeludium.Roberts, Gareth E. From Music to Mathematics: Exploring the Connections. Johns Hopkins University Press, 2016. 178.
A common alternative to retrograde inversion is inverted retrograde (IR), where the reversed melody is inverted. In later works like Requiem Canticles (1966), Igor Stravinsky preferred to use inverted retrograde, although he often conflated it with retrograde inversion in his sketches.Phillips, Paul Schuyler. "The Enigma of 'Variations': A Study of Stravinsky's Final Work for Orchestra", Music Analysis 3, no. 1 (March 1984): 70, 88 n. 6.
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