Perfect, imperfect and dissonant intervals in strict counterpoint (the case of the fourth)

Fux's classification

In strict counterpoint intervals are divided into three families:

Perfect consonances: unison, perfect fifth, perfect octave (and their compounds: twelfth, fifteenth).
Imperfect consonances: major and minor third, major and minor sixth (and the compounds: tenth, thirteenth).
Dissonances: second, perfect fourth, seventh, all augmented and diminished intervals (tritone included), and their compounds (ninth, eleventh).

Perfect consonances are stable but neutral; imperfect ones are stable and full; dissonances must be treated according to the species.

The perfect fourth is the delicate case:

In two voices it is always a dissonance.
In three or more voices it is consonant between two upper voices when a third or a fifth below supports it: in C3 E4 A4 the fourth E4–A4 is accepted because the bass C3 forms a third and a sixth. It remains dissonant if it involves the lowest voice (C3 F3 A3 contains the fourth C–F with the bass).
For the same reason the 6/4 (fourth and sixth over the bass) is excluded from first species.

Beginning and end: perfect consonance (unison, octave; fifth at the beginning only if the counterpoint is above).
Body of the exercise: a clear preference for imperfect consonances, which give variety and allow parallel motion.
Unison: only in the first and last bar.
Dissonances: none.

Species	Where the dissonance may be	How
First	never	—
Second	weak beat	passing, by step between two consonances
Third	second, third and fourth quarter note	passing, neighbor tone, cambiata
Fourth	strong beat	suspension prepared and resolved by descending step
Fifth	combination of the previous ones	under the same conditions

C4–G4 perfect fifth; C4–A4 major sixth, imperfect; C4–F4 fourth: dissonance in two voices.
B3–F4 diminished fifth: dissonance; F3–B3 augmented fourth: dissonance.
E4–C5 minor sixth: imperfect. D4–C5 minor seventh: dissonance.
In C3 E4 A4 (three voices) the fourth E–A is accepted; in C3 F3 A3 the fourth C–F with the bass is not.

Considering the sixth a dissonance: in strict counterpoint the sixth, major or minor, is an imperfect consonance.
Accepting the fourth in two voices because it sounds soft in a high register.
Forgetting that the compound keeps the quality: the ninth (D4–E5) is dissonant like the second; the twelfth is perfect like the fifth.
Miscounting diminished intervals written enharmonically (C#–F is a diminished fourth, dissonant, even though it sounds like a major third).

Pop and rock: the power chord (fifth and octave) is a set of perfect consonances only, which is why it sounds powerful but neutral; adding a third or a sixth in a vocal harmony immediately changes the emotional color.
Film scores: stacked fourths and fifths give space and solemnity; dissonances treated as suspensions (fourth species) create controlled tension in the strings.
Choirs: in three voices the fourth between soprano and alto is very useful for open voicings, as long as the bass supports it with a third or a fifth.

Consonance and dissonance (general theory), intervals and their inversions, the four rules of motion, first species, first species in three voices.