Nevertheless, there are examples of retrograde motion in the music of J.S. The different relationships set up by reversing the direction of a theme make it completely unrecognizable and when a composer indulges in this device the disclosure of it makes not the slightest difference to our apprehension of the music, which must be listened to as going parallel with the time-processes of our existence.” However, as Edmund Rubbra (1960, p. 35) points out, “This is, of course, a purely mental concept, as music can never do anything but go forwards, even if the given tune is reversed. 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. In contradistinction, Antoine Busnois and Jacob Obrecht, used retrograde and other permutations extensively, suggesting familiarity with one another's compositional techniques. Todd notes that although some composers ( John Dunstaple, Guillaume Dufay and Johannes Ockeghem) used retrograde occasionally, they did not combine it with other permutations. Machaut, the opening and closing bars of 'ma fin est mon commencement' (My end is my beginning.) Listen 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. 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. 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. (The word "Nusmido" is a syllabic retrograde of the word "Dominus.") According to Willi Apel, the earliest example of retrograde in music is the 13th century clausula, Nusmido, in which the tenor has the liturgical melody "Dominus" in retrograde (found in the manuscript Pluteo 29.1, folio 150 verso, located in the Laurentian Library in Florence). In music Nusmido, folio 150 verso of manuscript Pluteo 29.1, located in the Laurentian Library in Florence - the earliest known example of retrograde in musicĭespite not being mentioned in theoretical treatises prior to 1500, compositions written before that date show retrograde. Some writers acknowledge that hearing retrograde in music is a challenge, and consider it a self-referential compositional device. 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. Thomas Morley (1597) described retrograde in the context of canons and mentions a work by Byrd. 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." 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. 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. Nicola Vicentino (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. Retrograde was not mentioned in theoretical treatises prior to 1500. 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. Some composers choose to subject just the pitches of a musical line to retrograde, or just the rhythms. An even more exact retrograde reverses the physical contour of the notes themselves, though this is possible only in electronic music. An exact retrograde includes both the pitches and rhythms in reverse. A melodic line that is the reverse of a previously or simultaneously stated line is said to be its retrograde or cancrizans ( / ˈ k æ ŋ k r ɪ ˌ z æ n z/ "walking backward", medieval Latin, from cancer "crab").
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