The four motions and Fux's four fundamental rules

The four motions

When two voices pass from one interval to the next, they move in one of these ways:

• Direct motion (or similar): the voices go in the same direction with different intervals. Example: C4–E4 rises to D4–A4.
• Parallel motion: same direction and same interval. Example: thirds C4/E4 → D4/F4.
• Contrary motion: opposite directions. Example: C4/G4 → B3/A4.
• Oblique motion: one voice stays still, the other moves. Example: C4/E4 → C4/F4.

Contrary motion gives the greatest independence; oblique gives stability; parallel fuses the voices; direct is the most dangerous when it arrives on a perfect consonance.

The four fundamental rules

Fux reduces all voice leading to four rules, based on the type of starting and arrival consonance:

1. From perfect consonance to perfect consonance: only contrary or oblique motion.
2. From perfect consonance to imperfect consonance: any motion.
3. From imperfect consonance to perfect consonance: only contrary or oblique motion.
4. From imperfect consonance to imperfect consonance: any motion.

In short: a perfect consonance is reached only by contrary or oblique motion. This sentence alone eliminates parallel and hidden fifths and octaves in two-voice writing.

Why

Perfect consonances (unison, fifth, octave) fuse the voices: two voices arriving together on a fifth by direct motion sound like a single doubled voice. Contrary motion keeps the identity of the two lines even when the interval is perfect.

Examples in C

• Correct (rule 1): C4/G4 (fifth) → B3/B4 (octave) by contrary motion.
• Wrong (rule 1): C4/G4 → D4/A4, parallel fifths.
• Wrong (rule 3): E4/C5 (sixth) → G4/D5 (fifth) by direct motion: hidden fifth.
• Correct (rule 3): E4/C5 → D4/D5, a sixth that opens out onto the octave by contrary motion.
• Correct (rule 4): E4/C5 → F4/D5, parallel sixths.
• Correct (rule 2): C4/C5 → D4/B4 (sixth) by contrary motion, or C4/C5 → E4/C5 by oblique motion.

Complete example in D Dorian

Cantus firmus D4 F4 E4 D4 G4 F4 A4 G4 F4 E4 D4; counterpoint A4 D5 C5 D5 B4 A4 C5 E5 D5 C#5 D5. The octaves in bar 4 and at the end are reached by contrary motion (C5→D5 against E4→D4; C#5→D5 against E4→D4); the passages between imperfect consonances use parallel motion (thirds B4/G4 → A4/F4 → C5/A4) or direct motion freely.

How to check an exercise

1. Write the interval under each bar (3, 5, 6, 8…).
2. Circle every perfect consonance.
3. For each circle look at the previous interval and the direction of the two voices: if both rise or both fall, there is an error.
4. Count the motions: in a good exercise contrary motion is in the majority.

Typical mistakes

• Thinking that oblique motion is always safe: it is fine, but too many repeated notes in the counterpoint make the line static.
• Overusing parallel motion in thirds and sixths: correct, but with more than three or four in a row the voices lose independence.
• Applying the rules only between neighboring notes: in second species you must also look from one strong beat to the next.

Modern application

• Bass and melody in pop: checking the relationship between the bass line and the lead vocal with the four rules eliminates the hollow sound of parallel fifths.
• Choirs: in two-voice harmonies in thirds and sixths, rules 2 and 4 leave freedom; the problem arises at the cadence, where contrary motion is needed.
• Film orchestration: two string lines arriving on an octave by contrary motion sound full and open; by direct motion they sound like an unintentional doubling.

Related topics

Rules of voice leading, consonances in strict counterpoint, parallel and hidden fifths and octaves, first species.