Two-Voice Counterpoint

Introduction: Lines Before Chords

So far we've mostly thought of music as a series of chords. But for most of Western music history, composers thought first in lines: independent melodies that sound good together. The art of combining melodies is called counterpoint (from Latin punctus contra punctum, "note against note").

In 1725, the Austrian composer Johann Joseph Fux published Gradus ad Parnassum, a step-by-step course in counterpoint that Haydn, Mozart, and Beethoven all studied. Fux's method, called species counterpoint, starts with a fixed melody called the cantus firmus ("fixed song," CF) and adds a second line against it in five increasingly free species. It's still the best training there is for writing lines that are independent but cooperate.

Click any example to hear it. Numbers between the staves are the intervals between the voices.

The Cantus Firmus

A cantus firmus is a short, plain melody in whole notes. A good one:

• begins and ends on the tonic, and approaches the final tonic by step (usually 2̂–1̂);
• moves mostly by step, with a few leaps (no larger than an octave, and never augmented or diminished);
• follows each larger leap with a step in the opposite direction;
• has one clear high point (climax) and stays within about a tenth.

Consonance and Dissonance in Two Voices

With only two voices, every vertical interval is heard very clearly, so the rules for consonance are strict:

Motion Between Two Voices

Recall the four types of motion from Chapter 8. In counterpoint they matter even more:

• Contrary (voices move in opposite directions): the most independent; use it often.
• Oblique (one voice holds while the other moves): useful, but rare in first species, where both voices move every bar.
• Similar (same direction, different intervals): fine into imperfect consonances.
• Parallel (same direction, same interval): fine in 3rds and 6ths, but not more than three in a row; never in perfect 5ths, octaves, or unisons.

First Species: Note Against Note

In first species, the counterpoint has one whole note for each note of the cantus firmus. The rules:

1. Every interval is a consonance. Use mostly imperfect consonances (3rds, 6ths, 10ths).
2. Begin on a perfect consonance: unison or octave (or a 5th if the counterpoint is above). End on a unison or octave.
3. Approach the final note by step in contrary motion: in the counterpoint, 7̂–1̂ (when the CF has 2̂–1̂) or 2̂–1̂. In minor and the modes, raise 7̂ to make a leading tone.
4. No parallel 5ths, octaves, or unisons, and no 5ths or octaves approached by contrary motion either ("consecutives").
5. Approach perfect intervals only by contrary or oblique motion (no direct, or hidden, 5ths and octaves).
6. Use the unison only at the beginning and end. Don't cross the voices.
7. No more than three parallel 3rds or 6ths in a row.
8. Make the counterpoint a good melody too: mostly steps, leaps recovered, a single climax that doesn't coincide with the CF's.

Second Species: Two Against One

Now the counterpoint moves in half notes, two for each whole note of the cantus (the last note is a whole note). The new freedom is the weak beat:

• The downbeat must be consonant, as in first species.
• The weak beat may be consonant (by step or leap) or dissonant, but only as a passing tone: approached and left by step in the same direction.
• Check for parallel 5ths and octaves from downbeat to downbeat, and from a weak beat to the next downbeat.
• Don't repeat a note; keep the line moving.

Third, Fourth, and Fifth Species

Third species puts four quarter notes against each whole note. Downbeats stay consonant; the other beats can carry passing and neighbor tones, and figures like the cambiata (a decoration that leaps away from a dissonance).

Fourth species is the most expressive: the counterpoint is syncopated, with each note tied across the barline. Every tie produces either a consonance or a suspension (Chapter 12): the note is prepared as a consonance on the weak beat, held over as a dissonance on the downbeat, and resolved down by step. Above the cantus, the standard suspensions are 7–6 and 4–3 (and 9–8); below it, 2–3.

Fifth species (florid counterpoint) mixes all the others into a free, natural-sounding line, the closest thing to real music. From here it's a short step to Bach's two-part inventions, where both voices are florid and they trade motives back and forth.

Try It: First-Species Checker

Summary

• Species counterpoint adds a line to a cantus firmus in five stages of increasing rhythmic freedom.
• In two voices, 3rds and 6ths are the backbone; perfect intervals are used sparingly; the 4th counts as a dissonance.
• Never write parallel (or contrary) perfect 5ths and octaves, and approach perfect intervals by contrary or oblique motion.
• Second species allows weak-beat passing dissonances; fourth species builds expressive suspensions from tied notes.
• A good counterpoint is a good melody: mostly stepwise, leaps recovered, one climax.

Check Your Understanding