Retrograde (music)
"[3] 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.
[4] 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.
[13] She quotes Daniel Poirion in suggesting that 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.
[14] She concludes that, whatever the reasons, construction of retrogrades and their transmission were part of the medieval composers' world, as they prized symmetry and balance as intellectual feats in addition to the aural experience.
[15]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's compositional techniques.
[16] 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.
[27] 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.
