What it is
The Gradus ad Parnassum (1725) by Johann Joseph Fux (c. 1660 – 1741), maestro di cappella at the imperial court in Vienna, is the most studied counterpoint manual in history. Written in Latin and dedicated to the Emperor Charles VI, it was translated into German as early as 1742 by Lorenz Christoph Mizler, a pupil of Bach, and later into Italian, French and English. The standard English edition is the one edited by Alfred Mann: The Study of Counterpoint collects the part on the species in two to four voices, while The Study of Fugue contains the part on fugue together with the treatises of Marpurg, Albrechtsberger and Martini.
The dialogue
The practical part is written as a dialogue between teacher and pupil: the teacher Aloysius represents the style of Palestrina, the pupil Josephus represents Fux himself. The pupil proposes an exercise, the teacher corrects it, explains the mistake and asks for a new version. It is a method of trial and error: the rule emerges from listening to a concrete case, not from an abstract list. For this reason the book still works today as an exercise book.
The path
- Intervals and motions: perfect and imperfect consonances, dissonances, the four motions and the four fundamental rules.
- Five species in two voices on a cantus firmus (a given melody in long notes):
- first species, note against note;
- second species, two notes against one, with the passing dissonance;
- third species, four notes against one, with the cambiata;
- fourth species, syncopations and suspensions (preparation, percussion, resolution);
- fifth species, florid counterpoint that mixes the previous ones.
- The same species in three voices and then in four voices, always on the six modes with finals D, E, F, G, A, C.
- Imitation, fugue and double counterpoint, with examples in the modes.
- Final chapters on the ecclesiastical a cappella style and on the recitative style.
Fux declares that he would have liked to continue beyond four voices, but gives up because of age and illness.
Why the method works
- One variable at a time: in first species only the intervals are studied; in second, rhythm and the passing dissonance are added; in fourth, the suspension. The student does not have to handle everything at once.
- The fixed cantus firmus removes the problem of melodic invention: all the attention goes to the relationship between the voices.
- Every exercise is repeated above and below the melody and in all the modes, so the rules become internalized.
- The stylistic reference is a single one (sixteenth-century vocal polyphony), so every choice is judged by a consistent criterion.
Who used it
Haydn worked through all the exercises on his own and drew from them a compendium for his pupils; Leopold Mozart used it with his son; Beethoven studied it with Haydn and with Albrechtsberger; a copy was in Bach's library. In the twentieth century the tradition continues in the manuals of Jeppesen, Salzer and Schachter, Kennan, and in almost all conservatory courses.
Typical mistakes in study
- Skipping species: those who move straight to florid counterpoint without having internalized first species write lines full of hidden fifths.
- Studying only above the melody: the version with the counterpoint in the bass is harder and teaches the function of the bass.
- Treating the rules as absolute laws: they are rules of style. Fux himself, in the dialogue, admits exceptions when the result sounds better.
- Working without singing: every exercise should be sung or played; the ear is the final judge.
Modern application
- Pop and singer-songwriting: first species is the quickest way to write a second voice or a bass line independent of the melody.
- Film scores: fourth species teaches the chains of suspensions that give tension to the strings in an adagio; fifth species teaches how to write flowing countermelodies.
- Choirs: the species in three and four voices are direct training for arranging a cappella choirs without parallel octaves and fifths.
- Study routine: one cantus firmus a day, one species a week, above and below, in at least two different modes. Recording the exercise in a DAW with choir sounds helps you hear the flaws.
Related topics
Cantus firmus, church modes, the four rules of motion, first to fifth species, species in three and four voices, history of fugue theory.