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A fixed melody against which other voices are written in counterpoint exercises. Literally "fixed song."
The cantus firmus provides the foundation for species counterpoint exercises. A good cantus firmus moves primarily by step, has a single climax, begins and ends on the tonic, and stays within an octave. Writing counterpoint against a cantus firmus trains your ear to hear vertical and horizontal simultaneously.
Fux's cantus firmi from "Gradus ad Parnassum" are still used in counterpoint classes worldwide — simple melodies designed to support multiple contrapuntal voices.
Cantus firmus is one of 1760 terms in the Gradus musical dictionary: the words, abbreviations and instrument names that appear in printed scores, plus the vocabulary composers use to talk about them.
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