A General Method for Composing a Canon Against a Cantus Firmus Using Sergei Taneev's Double-Shifting Counterpoint.

This article applies Sergei Taneev's theory of double-shifting counterpoint to the problem of composing two voices in canonic imitation against a pre-composed cantus firmus. This approach sheds light on previous historical approaches to the same problem, in particular the improvised canons that were the subject of studies during the sixteenth and seventeenth centuries, and it may be used for the analysis of such canons as they occasionally occur in written repertoire, such as in the canonic chorale preludes and ground-bass compositions of J. S. Bach. When presented as a contrapuntal exercise, this method can be used to compose all manner of canons against a cantus firmus, including advanced canons written in contrary motion, augmentation and diminution, retrograde motion, and inverted retrograde motion. [ABSTRACT FROM AUTHOR]