Retrograde (music)
Encyclopedia
A musical line which 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 class
es alone—regardless of the melodic contour
created by their registral placement
—is regarded as a retrograde.
(1555) discussed the difficulty in finding canonic imitation: "At times, the fugue or canon cannot be discovered through the systems mentioned above, either because of the impediment of rests, or because one part is going up while another is going down, or because one part starts at the beginning and the other at the end. In such cases a student can begin at the end and work back to the beginning in order to find where and in which voice he should begin the canons." Vicentino derided those who achieved purely intellectual pleasure from retrograde (and similar permutations): "A composer of such fancies must try to make canons and fugues that are pleasant and full of sweetness and harmony. He should not make a canon in the shape of a tower, a mountain, a river, a chessboard, or other objects, for these compositions create a loud noise in many voices, with little harmonic sweetness. To tell the truth, a listening is more likely to be induced to vexation than to delight by these disproportioned fancies, which are devoid of pleasant harmony and contrary to the goal of the imitation of the nature of the words."
Thomas Morley
(1597) described retrograde in the context of canons and mentions a work by Byrd. Friedrich Wilhelm Marpurg
(1754) notes various names for the procedure imitatio retrograda or cancrizans or per motum retrogradum and says it is used primarily in canons and fugues.
Some writers acknowledge that hearing retrograde in music is a challenge, and consider it a self-referential compositional device.
, Nusmido, in which the tenor
has the liturgical melody "Dominus" in retrograde (Ms. Florence Pluteo 29). (The word "Nusmido" is a syllabic retrograde of the word "Dominus.")
Surveying medieval examples of retrograde, Virginia Newes notes that early composers were often also poets, and that musical retrogrades could have been based on similarly constructed poetic texts. She quotes Daniel Poirion in suggesting that a the retrograde canon in Machaut's three-voice rondeau, Ma fin est mon commencement could symbolize a metaphysical view of death as rebirth, or else the ideal circle of the courtly outlook, which encloses all initiatives and all ends. She concludes that, whatever the reasons, construction of retrogrades and their transmission were part of medieval composers' world, as they prized symmetry and balance as intellectual feats in addition to the aural experience.
Todd notes that although some composers (John Dunstaple, Guillaume Dufay
and Johannes Ockeghem
) used retrograde occasionally, they did not combine it with other permutations
. In contradistinction, Antoine Busnois
and Jacob Obrecht
, used retrograde and other permutations extensively, suggesting familiarity with one another. Todd also notes that, by use of retrograde, inversion, and retrograde-inversion, composers of this time viewed music in a way similar to serialists of the 20th century.
expressed the equivalence of melodic and harmonic presentation as a "unity of musical space." Taking the example of a hat, Schoenberg explained that the hat remains the same no matter if it is observed from below or above, from one side or another. Similarly, permutations such as inversion, retrograde, and retrograde inversion are a way to create musical space.
Heinrich Jalowetz discussed Arnold Schoenberg
's frequent use of retrograde (and other permutations) as a compositional device for twelve-tone music: "The technique serves two main functions. One is to provide a substitute for classical tonality, with all its melodic and harmonic consequences...The second function is to provide a means of interrelationship. This is done by presenting the row not only in normal position but in inversion, retrogression, and retrograde inversion. The music derives a strict inner cohesion through the artful treatment of such relationships, even though the listener may often be unable to follow what is happening."
Dorothy Slepian, writing in 1947, observed that "modern American composers write canons that, whether simple or complicated in structure, clearly discernible or subtly concealed, are a natural means of expression growing directly out of the individual needs of the melodic material. Therefore, most of the composers regard cancrizans as an artificial device imposed upon a theme rather than as a consequence germinated by it." Specifically, Douglas Moore, Harold Morris, Paul Creston
, and Bernard Rogers
"flatly refute the expressive powers of the cancrizans" whereas Walter Piston
, Adolph Weiss
, Wallingford Riegger
, and Roger Sessions
use it often. One particularly colorful and effective example is found in the second movement of Piston's Concerto for Orchestra, where continuous rapid string passages with an ostinato bass rhythm and a melody in the English horn returns later in the movement performed backwards as a recapitulation.
In twelve-tone music
, retrograde treatment of pitch is a commonplace, but rhythmic retrogrades are comparatively rare. Examples of rhythmic retrogrades occur in the music of Alban Berg
, for example in the operas Wozzeck
and Lulu
, and in the Chamber Concerto.
Electronic music
Electronic music is music that employs electronic musical instruments and electronic music technology in its production. In general a distinction can be made between sound produced using electromechanical means and that produced using electronic technology. Examples of electromechanical sound...
. Some composers choose to subject just the pitches of a musical line to retrograde, or just the rhythms. In twelve-tone music
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
, reversal of the pitch class
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
es alone—regardless of the melodic contour
Pitch contour
In linguistics, speech synthesis, and music, the pitch contour of a sound is a function or curve that tracks the perceived pitch of the sound over time....
created by their registral placement
Register (music)
In music, a register is the relative "height" or range of a note, set of pitches or pitch classes, melody, part, instrument or group of instruments...
—is regarded as a retrograde.
In treatises
Retrograde was not mentioned in theoretical treatises prior to 1500. Nicola VicentinoNicola Vicentino
Nicola Vicentino was an Italian music theorist and composer of the Renaissance. He was one of the most visionary musicians of the age, inventing, among other things, a microtonal keyboard, and devising a practical system of chromatic writing two hundred years before the rise of equal...
(1555) discussed the difficulty in finding canonic imitation: "At times, the fugue or canon cannot be discovered through the systems mentioned above, either because of the impediment of rests, or because one part is going up while another is going down, or because one part starts at the beginning and the other at the end. In such cases a student can begin at the end and work back to the beginning in order to find where and in which voice he should begin the canons." Vicentino derided those who achieved purely intellectual pleasure from retrograde (and similar permutations): "A composer of such fancies must try to make canons and fugues that are pleasant and full of sweetness and harmony. He should not make a canon in the shape of a tower, a mountain, a river, a chessboard, or other objects, for these compositions create a loud noise in many voices, with little harmonic sweetness. To tell the truth, a listening is more likely to be induced to vexation than to delight by these disproportioned fancies, which are devoid of pleasant harmony and contrary to the goal of the imitation of the nature of the words."
Thomas Morley
Thomas Morley
Thomas Morley was an English composer, theorist, editor and organist of the Renaissance, and the foremost member of the English Madrigal School. He was the most famous composer of secular music in Elizabethan England and an organist at St Paul's Cathedral...
(1597) described retrograde in the context of canons and mentions a work by Byrd. Friedrich Wilhelm Marpurg
Friedrich Wilhelm Marpurg
Friedrich Wilhelm Marpurg was a German music critic, music-theorist and composer. He was friendly and active with many figures of the Enlightenment of the 18th century.-Life:...
(1754) notes various names for the procedure imitatio retrograda or cancrizans or per motum retrogradum and says it is used primarily in canons and fugues.
Some writers acknowledge that hearing retrograde in music is a challenge, and consider it a self-referential compositional device.
In music
Despite not being mentioned in theoretical treatises prior to 1500, compositions written before that date show retrograde. According to Willi Apel, the earliest example of retrograde in music is the 13th century clausulaClausula
In Roman rhetoric, a clausula was a rhythmic figure used to add finesse and finality to the end of a sentence or phrase. There was a large range of popular clausulae...
, Nusmido, in which the tenor
Tenor
The tenor is a type of male singing voice and is the highest male voice within the modal register. The typical tenor voice lies between C3, the C one octave below middle C, to the A above middle C in choral music, and up to high C in solo work. The low extreme for tenors is roughly B2...
has the liturgical melody "Dominus" in retrograde (Ms. Florence Pluteo 29). (The word "Nusmido" is a syllabic retrograde of the word "Dominus.")
Surveying medieval examples of retrograde, Virginia Newes notes that early composers were often also poets, and that musical retrogrades could have been based on similarly constructed poetic texts. She quotes Daniel Poirion in suggesting that a the retrograde canon in Machaut's three-voice rondeau, Ma fin est mon commencement could symbolize a metaphysical view of death as rebirth, or else the ideal circle of the courtly outlook, which encloses all initiatives and all ends. She concludes that, whatever the reasons, construction of retrogrades and their transmission were part of medieval composers' world, as they prized symmetry and balance as intellectual feats in addition to the aural experience.
Todd notes that although some composers (John Dunstaple, Guillaume Dufay
Guillaume Dufay
Guillaume Dufay was a Franco-Flemish composer of the early Renaissance. As the central figure in the Burgundian School, he was the most famous and influential composer in Europe in the mid-15th century.-Early life:From the evidence of his will, he was probably born in Beersel, in the vicinity of...
and Johannes Ockeghem
Johannes Ockeghem
Johannes Ockeghem was the most famous composer of the Franco-Flemish School in the last half of the 15th century, and is often considered the most...
) used retrograde occasionally, they did not combine it with other permutations
Permutation (music)
In music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...
. In contradistinction, Antoine Busnois
Antoine Busnois
Antoine Busnois was a French composer and poet of the early Renaissance Burgundian School. While also noted as a composer of sacred music, such as motets, he was one of the most renowned 15th-century composers of secular chansons...
and Jacob Obrecht
Jacob Obrecht
Jacob Obrecht was a Flemish composer of the Renaissance. He was the most famous composer of masses in Europe in the late 15th century, being eclipsed by only Josquin des Prez after his death.-Life:...
, used retrograde and other permutations extensively, suggesting familiarity with one another. Todd also notes that, by use of retrograde, inversion, and retrograde-inversion, composers of this time viewed music in a way similar to serialists of the 20th century.
Examples in modal and tonal music
- Guillaume de MachautGuillaume de MachautGuillaume de Machaut was a Medieval French poet and composer. He is one of the earliest composers on whom significant biographical information is available....
, Ma fin est mon commencement (rondeauRondeau (music)The rondeau was a Medieval and early Renaissance musical form, based on the contemporary popular poetic rondeau form. It is distinct from the 18th century rondo, though the terms are likely related...
14) - William ByrdWilliam ByrdWilliam Byrd was an English composer of the Renaissance. He wrote in many of the forms current in England at the time, including various types of sacred and secular polyphony, keyboard and consort music.-Provenance:Knowledge of Byrd's biography expanded in the late 20th century, thanks largely...
, "Diliges Dominum", no. 25 from Cantiones Sacrae - Jacob ObrechtJacob ObrechtJacob Obrecht was a Flemish composer of the Renaissance. He was the most famous composer of masses in Europe in the late 15th century, being eclipsed by only Josquin des Prez after his death.-Life:...
, Missa Grecorum, Agnus Dei - Leonhard PämingerLeonhard PämingerLeonhard Päminger was an Upper-Austrian born Lutheran theologian, poet and composer in Catholic Bavaria....
, Vexilla regis prodeunt, from the Secundus tomus ecclesiasticarum cantionum (Nuremberg, 1573). - Gregorius Joseph Werner, Der curiose musikalische Instrumentalkalende, Die Sonne im Krebs (Menuetto cancrizante)
- Joseph HaydnJoseph HaydnFranz Joseph Haydn , known as Joseph Haydn , was an Austrian composer, one of the most prolific and prominent composers of the Classical period. He is often called the "Father of the Symphony" and "Father of the String Quartet" because of his important contributions to these forms...
canon, "Thy Voice, O Harmony" - Joseph Haydn, Symphony no. 47, 3rd movement, "Minuetto al Roverso"
- Joseph Haydn, piano sonata, XVI/26, minuet (a transcription of the 3rd movement from Symphony no. 47)
- Joseph Haydn, Violin Sonata no. 4
- Carl Philipp Emanuel BachCarl Philipp Emanuel Bachright|250pxCarl Philipp Emanuel Bach was a German Classical period musician and composer, the fifth child and second son of Johann Sebastian Bach and Maria Barbara Bach...
, Minuet, C major - Beethoven, Piano Sonata no. 29, op. 106, "Hammerklavier", fugal fourth movement includes an episode with the subject in retrograde
- Franz SchubertFranz SchubertFranz Peter Schubert was an Austrian composer.Although he died at an early age, Schubert was tremendously prolific. He wrote some 600 Lieder, nine symphonies , liturgical music, operas, some incidental music, and a large body of chamber and solo piano music...
, Die Zauberharfe, No. 3, Melodram ("Der Finke fing") - John StainerJohn StainerSir John Stainer was an English composer and organist whose music, though not generally much performed today , was very popular during his lifetime...
, "Per Recte et Retro"
In post-tonal music
As early as 1923, Arnold SchoenbergArnold Schoenberg
Arnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
expressed the equivalence of melodic and harmonic presentation as a "unity of musical space." Taking the example of a hat, Schoenberg explained that the hat remains the same no matter if it is observed from below or above, from one side or another. Similarly, permutations such as inversion, retrograde, and retrograde inversion are a way to create musical space.
Heinrich Jalowetz discussed Arnold Schoenberg
Arnold Schoenberg
Arnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
's frequent use of retrograde (and other permutations) as a compositional device for twelve-tone music: "The technique serves two main functions. One is to provide a substitute for classical tonality, with all its melodic and harmonic consequences...The second function is to provide a means of interrelationship. This is done by presenting the row not only in normal position but in inversion, retrogression, and retrograde inversion. The music derives a strict inner cohesion through the artful treatment of such relationships, even though the listener may often be unable to follow what is happening."
Dorothy Slepian, writing in 1947, observed that "modern American composers write canons that, whether simple or complicated in structure, clearly discernible or subtly concealed, are a natural means of expression growing directly out of the individual needs of the melodic material. Therefore, most of the composers regard cancrizans as an artificial device imposed upon a theme rather than as a consequence germinated by it." Specifically, Douglas Moore, Harold Morris, Paul Creston
Paul Creston
Paul Creston was an Italian American composer of classical music.Born in New York City to Sicilian immigrants, Creston was self‐taught as a composer. He was an honorary member of Phi Mu Alpha Sinfonia music fraternity, initiated into the national honorary Alpha Alpha chapter...
, and Bernard Rogers
Bernard Rogers
Bernard Rogers was an American composer.Rogers was born in New York City. He studied with Arthur Farwell, Ernest Bloch, Percy Goetschius, and Nadia Boulanger. He taught at the Cleveland Institute of Music, The Hartt School, and the Eastman School of Music...
"flatly refute the expressive powers of the cancrizans" whereas Walter Piston
Walter Piston
Walter Hamor Piston Jr., , was an American composer of classical music, music theorist and professor of music at Harvard University whose students included Leroy Anderson, Leonard Bernstein, and Elliott Carter....
, Adolph Weiss
Adolph Weiss
Adolph Weiss was an American composer. A modernist, he was a pupil of Arnold Schoenberg in Vienna; his father was a pupil of Ferruccio Busoni...
, Wallingford Riegger
Wallingford Riegger
Wallingford Constantine Riegger was a prolific American music composer, well known for orchestral and modern dance music, and film scores...
, and Roger Sessions
Roger Sessions
Roger Huntington Sessions was an American composer, critic, and teacher of music.-Life:Sessions was born in Brooklyn, New York, to a family that could trace its roots back to the American revolution. His mother, Ruth Huntington Sessions, was a direct descendent of Samuel Huntington, a signer of...
use it often. One particularly colorful and effective example is found in the second movement of Piston's Concerto for Orchestra, where continuous rapid string passages with an ostinato bass rhythm and a melody in the English horn returns later in the movement performed backwards as a recapitulation.
In twelve-tone music
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
, retrograde treatment of pitch is a commonplace, but rhythmic retrogrades are comparatively rare. Examples of rhythmic retrogrades occur in the music of Alban Berg
Alban Berg
Alban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique.-Early life:Berg was born in...
, for example in the operas Wozzeck
Wozzeck
Wozzeck is the first opera by the Austrian composer Alban Berg. It was composed between 1914 and 1922 and first performed in 1925. The opera is based on the drama Woyzeck left incomplete by the German playwright Georg Büchner at his death. Berg attended the first production in Vienna of Büchner's...
and Lulu
Lulu (opera)
Lulu is an opera by the composer Alban Berg. The libretto was adapted by Berg himself from Frank Wedekind's plays Erdgeist and Die Büchse der Pandora .-Composition history:...
, and in the Chamber Concerto.
Examples in post-tonal music
- Alban BergAlban BergAlban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique.-Early life:Berg was born in...
, Der Wein (1929), "Der Wein der Liebenden" (measures 112–40 are then heard in retrograde as measures 140–70) - Ruth Crawford-Seeger, Diaphonic Suite No. 3 for two clarinets (1930), third movement, the first clarinet in bars 45–56 present an exact retrograde of the same part, bars 2–13,
- Karel GoeyvaertsKarel GoeyvaertsKarel Goeyvaerts was a Belgian composer.-Life:After studies at the Royal Flemish Music Conservatory in Antwerp, Goeyvaerts studied composition in Paris with Darius Milhaud and analysis with Olivier Messiaen...
, Nummer 5Nummer 5Nummer 5 met zuivere tonen is a musical work by the Belgian composer Karel Goeyvaerts, realized in 1953 and one of the earliest pieces of electronic music.-History:...
met zuivere tonen (Number 5 with Pure Tones, 1953) superimposes an exact retrograde of its materials on the "forwards" version. As a result, not only does each event in the second half occur according to an axis of symmetry at the centre of the work, but each event itself is reversed, so that the note attacks in the first half become note decays in the second, and vice-versa. - Charles IvesCharles IvesCharles Edward Ives was an American modernist composer. He is one of the first American composers of international renown, though Ives' music was largely ignored during his life, and many of his works went unperformed for many years. Over time, Ives came to be regarded as an "American Original"...
, Scherzo: All the Way Around and Back (1907–08) is palindromic. - Olivier MessiaenOlivier MessiaenOlivier Messiaen was a French composer, organist and ornithologist, one of the major composers of the 20th century. His music is rhythmically complex ; harmonically and melodically it is based on modes of limited transposition, which he abstracted from his early compositions and improvisations...
, "Abîme des oiseaux", from the Quatuor pour la fin du tempsQuatuor pour la fin du tempsQuatuor pour la fin du temps, also known by its English title Quartet for the End of Time, is a piece of chamber music by the French composer Olivier Messiaen. It was premiered in 1941...
(1941) exhibits many retrograde relationships among its elements, as well as one rhythm that is "a retrograde version of rāgavardhana, No. 93 in SharngadevaSarangadevaSarangadeva was the author of the Sangita Ratnakara, which is considered by many to be the most important work on music, after Bharata's Natya Shastra...
's collection," the Sangita Ratnakara. - Luigi NonoLuigi NonoLuigi Nono was an Italian avant-garde composer of classical music and remains one of the most prominent composers of the 20th century.- Early years :Born in Venice, he was a member of a wealthy artistic family, and his grandfather was a notable painter...
, Incontri (1955). - Charles RugglesCharles RugglesCharles Sherman “Charlie” Ruggles was a comic American actor. In a career spanning six decades, Ruggles appeared in close to 100 feature films. He was also the brother of director, producer, and silent actor Wesley Ruggles .-Background:Charlie Ruggles was born in Los Angeles, California in 1886...
, Sun-Treader (1926–31) has a rhythmically free pitch palindrome in b. 68–118, and a retrograde canon in b. 124–33. - Igor StravinskyIgor StravinskyIgor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....
, Canticum SacrumCanticum SacrumCanticum Sacrum ad Honorem Sancti Marci Nominis is a 17-minute choral-orchestral piece composed in 1955 by Igor Stravinsky in tribute "To the City of Venice, in praise of its Patron Saint, the Blessed Mark, Apostle." The piece is compact and stylistically varied, ranging from established...
(1956). The fifth movement is an almost exact retrograde of the first. - Iannis XenakisIannis XenakisIannis Xenakis was a Romanian-born Greek ethnic, naturalized French composer, music theorist, and architect-engineer. He is commonly recognized as one of the most important post-war avant-garde composers...
, Metastasis (1953–54) contains many instances of retrograde relationships.