Designing a cantus firmus

The fixed voice every species exercise is built against is itself composed to rules: it moves in equal whole notes, begins and ends on the final of its mode, rises to a single climax it touches once, proceeds mostly by step with any leap modest and answered, stays within about a tenth, and approaches its last note by step. The plainness is deliberate — a cantus firmus is scaffolding, and everything worth studying happens in the relationship built over it.

Every species exercise begins by choosing or writing one, and the habits it trains — a single climax, stepwise recovery from leaps, a stepwise close — are the same habits that make any melody sound inevitable. A poor cantus firmus poisons everything above it: a line with two peaks or a dead tessitura gives the counterpoint nothing to answer. Writing them is composition at its smallest scale, which is why the tradition began there.

• Touching the climax twice, which flattens the arc into a plateau and leaves the line without a single point of greatest tension.
• Leaping without answer — a large leap that continues in the same direction instead of turning back by step.
• Ending by leap, when the final must be approached by step for the close to sound like a close.
• Outlining a tritone across a few notes, which the ear catches even when no single leap is forbidden.
• Wandering past about a tenth of range, which turns a singable scaffold into an instrumental line.

• Johann Joseph Fux, Gradus ad Parnassum (1725), Liber secundus, on the cantus firmus — The plain given voice, one per mode, against which all five species are taught.
• Johann Georg Albrechtsberger, Gründliche Anweisung zur Composition (1790), The counterpoint chapters, on the cantus firmus — The Classical-era course keeps the same scaffolding and the same design norms.