Cantus firmus
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In music, a cantus firmus is a pre-existing melody forming the basis of a polyphonic composition, often set apart by being played in long notes.
Composition using a cantus firmus was a common technique in Medieval music, forming the basis of organum as well as 13th- and 14th-century motets. In these works the cantus firmus was originally always taken from Gregorian Chant and was the fixed melodic material, moving in long notes, around which other more florid lines, instrumental and/or vocal, were composed. (This line was usually allocated to the tenor, from the Latin verb 'tenere', to hold).
In the early Renaissance composers experimented with other ways of using the cantus firmus, such as introducing it into each voice as a contrapuntal subject (theme), or using it with a variety of rhythms, or using secular tunes for canti firmi, even in sacred compositions.
Probably the most widely set of the secular cantus firmus melodies was L'homme armé. Over 30 settings are known. Most early Renaissance masters each set at least one mass on this melody, and the practice lasted into the seventeenth century, with a late setting by Carissimi. Some have suggested that the 'armed man' represents St Michael the Archangel, whilst others have suggested it merely represents the name of a popular tavern (Maison L'Homme Arme) near Dufay's rooms in Cambrai. Other secular examples include 'Fortuna Desperata', 'Mille regretz' and 'The western wynde'.
Setting the cantus firmus was the essential pedagogical tool in Gradus ad Parnassum by Johann Joseph Fux and formed the basis of teaching his species counterpoint.
German composers in the Baroque period in Germany, notably Bach, used chorale melodies as canti firmi. In the opening movement of Bach's St. Matthew Passion, the chorale "O Lamm Gottes, unschuldig" appears in long notes, sung by a separate choir of boys "in ripieno". Many of his chorale preludes include a chorale tune in the pedal part.
Reference
Sparks, E. H. 'Cantus firmus in Mass and Motet', Berkeley, (1963)