Why in the study of counterpoint by johan fux are minor sixths allowed but not augmented fifth?

Question

If augmented fifths and minor sixths are enharmonically equivalent why does johan fux in his book study of counterpoint allow minor sixths but not augmented fifths if they sound the same? How does one distinguish between the two an augmented fifth and minor sixth when composing?

Answer 1

A much simpler and yet quite accurate answer is that minor sixths (starting on the tonic pitch) will tend to resolve inward (the sixth resolves down by half-step) to a perfect fifth. Whereas an augmented 5th will resolve outward to a major sixth, as that augmented 5th functions as a sort of leading tone to the major 6th. That leading tone relationship suggests a secondary tonic i.e. the major 6th scale degree.

For example - C-Ab (m6) will resolve to C-G (P5) where as C-G# (+5) will resolve to C-A (M6), with A serving as a secondary tonic.

Answer 2

Hi! This depends on the key being used at that point and the harmonic context. All scales have only ONE kind of fifth and ONE kind of sixth... the same for all other intervals), just like most keys can't have "two fifths" or "two sixths". Let's use the C Harmonic Minor scale, for example.

C Natural minor scale: C - D - Eb - F - G - Ab - B ........ C

1.) Chord from the III degree:

Eb+ (Eb aug): Eb - G - B (B is the Augmented 5th of Eb)

2.) Chord from the II degree with a b13 tension (b13 = b6, minor 6th).

Dm7b5/b13: D - F - Ab - Bb (Bb is the b6 / b13 of D).

All depends of the role of the note in the chord and its diatonic relation to the underlying key.