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] 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."[3]
Basic row forms from Stravinsky's Requiem Canticles: 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.[5]
For example, the forms of the row from Requiem Canticles are as follows:
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♯–F–E–G–A♭–E♭–D–A–B♭–D♭–C in the piano part.[6] It is performed in both styles,[clarification needed] 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.
↑ 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.
↑ Arnold Whittall, The Cambridge Introduction to Serialism. Cambridge Introductions to Music (Cambridge and New York: Cambridge University Press, 2008): p.139. ISBN978-0-521-68200-8 (pbk).
↑ 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.
↑ 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.
In music, a tone row or note row, 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 sometimes found.
The chromatic scale is a set of twelve pitches used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the chromatic scale, while other instruments capable of continuously variable pitch, such as the trombone and violin, can also produce microtones, or notes between those available on a piano.
In music theory, a leading-tone is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, the leading tone refers to the seventh scale degree of a major scale, a major seventh above the tonic. In the movable do solfège system, the leading-tone is sung as ti.
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Many important composers who had originally not subscribed to or actively opposed the technique, such as Aaron Copland and Igor Stravinsky, eventually adopted it in their music.
In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. Anton Webern often used derived rows in his pieces. A partition is a segment created from a set through partitioning.
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates. Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."
Chromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. In simple terms, within each octave, diatonic music uses only seven different notes, rather than the twelve available on a standard piano keyboard. Music is chromatic when it uses more than just these seven notes.
In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.
In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation, or multiplicative operations. These may produce reorderings of the members of the set, or may simply map the set onto itself.
A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.
A trope or tropus may refer to a variety of different concepts in medieval, 20th-, and 21st-century music.
Composition for Four Instruments (1948) is an early serial music composition written by American composer Milton Babbitt. It is Babbitt's first published ensemble work, following shortly after his Three Compositions for Piano (1947). In both these pieces, Babbitt expands upon the methods of twelve-tone composition developed by Arnold Schoenberg. He is notably innovative for his application of serial techniques to rhythm. Composition for Four Instruments is considered one of the early examples of “totally serialized” music. It is remarkable for a strong sense of integration and concentration on its particular premises—qualities that caused Elliott Carter, upon first hearing it in 1951, to persuade New Music Edition to publish it.
Elegy for J.F.K. is a piece of vocal music composed by the Russian-born composer Igor Stravinsky in 1964, commemorating the assassination of U.S. President John F. Kennedy.
In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of music. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.
Requiem Canticles is a 15-minute composition by Igor Stravinsky, for contralto and bass soli, chorus, and orchestra. Stravinsky completed the work in 1966, and it received its first performance that same year.
Fritz Heinrich Klein was an Austrian composer.
Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones. As music becomes more complex, dissonance becomes indistinguishable from consonance.
A melodic line that is the reverse of a previously or simultaneously stated line is said to be its retrograde or cancrizans. An exact retrograde includes both the pitches and rhythms in reverse. An even more exact retrograde reverses the physical contour of the notes themselves, though this is possible only in electronic music. Some composers choose to subject just the pitches of a musical line to retrograde, or just the rhythms. In twelve-tone music, reversal of the pitch classes alone—regardless of the melodic contour created by their registral placement—is regarded as a retrograde.
Fanfare for a New Theatre is a 1964 composition for two trumpets by Russian composer Igor Stravinsky. It was premiered on April 19, 1964, and published by Boosey & Hawkes.
A Sermon, a Narrative and a Prayer is a cantata for alto and tenor singers, a narrator, chorus, and orchestra by Igor Stravinsky, composed in 1960–61. It belongs to the composer’s serial period, and lasts a little over a quarter of an hour in performance.
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