Among our forefathers there were three ways of devising a new part for an existing piece: Descant, Counterpoint, and Divisions. The first and last of these are ways of improvising music super librum (without a written part). Counterpoint refers specifically to the technique of adding a new written part to an existing body of music, although Tinctoris specifically states that his text on counterpoint should also be useful for musicians improvising super librum. Of these three techniques, Counterpoint is the most important theoretically, and the others bear a strong relation to it.
The techniques of descant date back to the time of the Ars Antiqua. They are rules by which a singer can while reading one part (the cantus) improvise another (the descant) above it, so that the descant will sound harmoniously with the cantus. This was especially popular in England, where they were fond of using the third ( ditone and semiditone) and the sixth ( diapente plus tone and diapente plus semitone). Riemann summarizes these rules. He also claims that descant is the forerunner of true counterpoint. The rules of descant do, however, bear a strong relation to the rules of counterpoint, especially the rules for the placement of dissonant and perfect intervals.
Counterpoint is the orderly setting of note against note in such a way that the intervals made by the two voices are divided among consonances and dissonances in an orderly fashion. Although Gafurius and other theorists of the day cite the authority of Boethius and the Pythagoreans (they did certainly classify intervals as consonant and dissonant), this orderly approach to music probably originated with Phillipe de Vitry and the Ars Nova.
Gafurius and Tinctoris, both writing at the end to the Fifteenth Century, give rules for Counterpoint as it must have been used at the time of the basse dance. Zarlino, writing in the middle of the Sixteenth Century, provides a much more lucid account of counterpoint which differs mainly in the level of detail it provides about various contrapuntal rules. As Zarlino's his primary purpose was to codify the rules used by earlier famous composers (such as Josquin and Isaac), much of what he says is relevant the problem of reconstructing the basse dances. Many contemporary authors have also written about counterpoint, in particular, Jeppesen and Gauldin. Reimann summarizes the work of many of the early theorists on the subject. Because of the importance of this art in the reconstruction of the basse dance, the following chapters review the rules of counterpoint.
Tinctoris describes the relationship between counterpoint and the improvising super librum. He regards them as one and the same, only in improvisation musicians are permitted more license to make dissonances between multiple improvised voices (as these are difficult to avoid).
Ortiz, writing at the same time as Zarlino, describes by example both the rules for divisions (ornamenting a given line) and for improvising above a cantus firmus. A contrapuntal analysis of his technique shows that he is following the rules of counterpoint as expressed by his contemporary Zarlino.
Given the central role of counterpoint in both composition and improvisation; it must form a central part of the reconstruction of the basse dance. The following chapters describe it in detail.
Onward to: Chapter 7: The Genera and Species of Intervals used in Counterpoint.
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