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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 228 terms in the Gradus musical dictionary, where every definition is written around how composers actually use the word.
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