Retrograde inversion

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For the English progressive-rock group, see Retrograde Inversion.
Prime, retrograde, inverse, and (bottom-right) retrograde-inverse.

Retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order."[1] 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."[2]

Basic row forms from Stravinsky's Requiem Canticles:[3] P R I IR

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 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.[4]

For example, the forms of the row from Requiem Canticles are as follows:

 P0: 0 2 t e 1 8 6 7 9 4 3 5
 R0: 5 3 4 9 7 6 8 1 e t 2 0
 I0: 0 t 2 1 e 4 6 5 3 8 9 7
RI0: 7 9 8 3 5 6 4 e 1 2 t 0
IR0: 5 7 6 1 3 4 2 9 e 0 8 t

Note that IR is a transposition of RI, the pitch class between the last pitches of P and I above RI.

Sources[edit]

  1. ^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.310. Seventh Edition. ISBN 978-0-07-294262-0.
  2. ^ Benward & Saker (2003), p.359.
  3. ^ Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music, p.139. New York: Cambridge University Press. ISBN 978-0-521-68200-8 (pbk).
  4. ^ Paul Schuyler Phillips, "The Enigma of 'Variations': A Study of Stravinsky's Final Work for Orchestra", Music Analysis 3, no. 1 (March 1984): 69–89. Citation on p. 70, and p. 88, n. 6.