Fux – Basic Rules of Counterpoint

Voice leading

Voice leading is concerned with melody, or the succession of notes in time (the horizontal direction on the staff).

  • No “devil in music”: never skip by a tritone or other augmented/diminished interval (Hindemith’s imperfect dissonances)
  • Compensate skips: the motion after a skip should be stepwise in the opposite direction
    • If a skip cannot be compensated, stepwise motion in the same direction is preferred
    • If skips have to occur successively, they should be in opposite directions
    • If two skips must absolutely happen in the same direction, the second skip should be smaller than the first.
    • If even this isn’t possible, rethink your voice leading
  • Prefer steps over skips

Counterpoint

Counterpoint is concerned with harmony, or the combination of several pitches at the same time (the vertical direction on the staff).

  • No parallels: never move by parallel motion from a perfect consonance
    • Parallel imperfect consonances are okay, but don’t overdo them (maximum 3 in a row)
  • No hidden parallels: never approach a perfect consonance by direct motion
    • Prefer contrary and oblique motion over direct motion
    • Do not approach (1) unison or (8) octave by skip.
  • Keep adjacent voices reasonably close, within the interval of a (10) tenth
  • For theory purposes, treat (P4) perfect fourth as dissonant

First species counterpoint

The simplest method of writing counterpoint, this outlines the harmonic “skeleton” for a phrase.

  • Note against note: for every note in the cantus firmus (c.f.), or the voice that is given, write a corresponding note
  • Consonance only: every interval between the counterpoint and cantus firmus must be a perfect or imperfect consonance
  • No voice crossing: the written counterpoint should be entirely above or below the cantus firmus (c.f.)
    • Voice crossing is allowed only for “exceptionally pleasing lines”
  • Start and end in the right mode (key): if writing above the c.f., the last note should be the tonic, meaning the last interval should be (1) unison or (8) octave. If writing below the c.f., both the first and last intervals should be tonic (1 or 8).
    • Perfect consonances are preferred for openings and cadences, imperfect consonances for the middle of phrases
    • Avoid unisons in the middle of phrases
    • The last interval (cadence) should be approached stepwise in contrary motion.
  • Avoid skips greater than a (5) fifth

Second species counterpoint

The next method of writing counterpoint, this introduces the possibility of dissonance (non-harmonic tones).

  • Two notes against one: for every note in the cantus firmus write two notes of half the value
  • Consonance only (on the strong beat): strong beats (where the cantus firmus moves) should use a consonant interval
  • Dissonance on weak beat by passing tone: a dissonance is allowed only on a weak beat (where the cantus firmus is stationary), and the counterpoint must approach and leave by step in the same direction
  • No parallels (across strong beats): the same interval on two adjacent strong beats is considered parallel even if the interval changes on the weak beat in between.
    • In other words, remove the weak beats from second species counterpoint and it should look just like first species
    • First species can be converted into second species simply by adding a note on every weak beat

Reference and worksheet

Johann Joseph Fux wrote Gradus Ad Parnassum in the time of Bach, but his treatise describes the counterpoint of Renaissance music, and especially that of Palestrina. While the musical style contained in Gradus Ad Parnassum was out of date even while it was written, it remains one of the best introductions to theory ever written, explaining how to write counterpoint in a short, simple, and entertaining manner.

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