View source for Retrograde inversion

{{short description|Melodic inversion and reversed ordering of a musical motif's pitches}}
[[Image:P-R-I-RI.png|thumb|300px|
'''P''': [[Prime form (music)|Prime]]<br>
'''R''': [[Retrograde (music)|retrograde]]<br>
'''I''': [[Melodic inversion|inverse]]<br>
'''RI''': retrograde-inverse]]

In [[music theory]], '''retrograde inversion''' is a [[Musical terminology|musical term]] that literally means "backwards and upside down": "The [[Melodic inversion|inverse]] of the series is sounded in reverse order."<ref>Bruce Benward and Marilyn Nadine Saker, ''Music: In Theory and Practice'', seventh edition ({{Full citation needed|date=December 2015}}<!--Place and publisher needed.-->, 2003): Vol. I, p.310. {{ISBN|978-0-07-294262-0}}.</ref> [[Retrograde (music)|Retrograde]] reverses the order of the [[Motif (music)|motif]]'s [[Pitch (music)|pitches]]: what was the first pitch becomes the last, and vice versa.<ref>Steven G. Laitz, ''The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening'', third edition (Oxford and New York: Oxford University Press, 2012): p. 780.</ref> 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."<ref>Benward & Saker (2003): p.&nbsp;359.</ref>

[[File:Stravinsky - Requiem Canticles basic row forms.png|thumb|300px|Basic row forms from Stravinsky's ''Requiem Canticles'':<ref>Arnold Whittall, ''The Cambridge Introduction to Serialism''. Cambridge Introductions to Music (Cambridge and New York: Cambridge University Press, 2008): p.&nbsp;139. {{ISBN|978-0-521-68200-8}} (pbk).</ref> 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.<ref>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.&nbsp;70, and p.&nbsp;88, n.&nbsp;6.</ref>

For example, the forms of the row from ''Requiem Canticles'' are as follows:
  P0: {{Tone row|form=P |0|2|10|11|1|8|6|7|9|4|3|5}}
  R0: {{Tone row|form=R |0|2|10|11|1|8|6|7|9|4|3|5}}
  I0: {{Tone row|form=I |0|2|10|11|1|8|6|7|9|4|3|5}}
 RI0: {{Tone row|form=RI|0|2|10|11|1|8|6|7|9|4|3|5}}
 IR0: {{Tone row|form=IR|0|2|10|11|1|8|6|7|9|4|3|5}}<!--should be: 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.

Other compositions that include retrograde inversions in its rows include works by [[Tadeusz Baird]] and [[Karel Goeyvaerts]]. One work in particular by the latter composer, ''[[Nummer 2]]'', employs retrograde of the recurring twelve-tone row B–F{{Music|sharp}}–F–E–G–A{{Music|flat}}–E{{Music|flat}}–D–A–B{{Music|flat}}–D{{Music|flat}}–C in the piano part.<ref>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.</ref> It is performed in both styles,{{clarify|date=December 2015}}<!--What styles?--> particularly in the outer sections of the piece. The final movement of [[Paul Hindemith]]'s ''[[Ludus Tonalis]]'', the Postludium, is an exact retrograde inversion of the work's opening Praeludium.

==Sources==
{{reflist}}

{{Twelve-tone technique}}

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[[Category:Musical symmetry]]
[[Category:Serialism]]