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?
Fux does allow them in counterpoint. As I pointed out in one of my comments, confusion comes from voice-relationships:
A minor-sixth is of course allowable between two voices because it is an imperfect consonant interval.
A minor-sixth is not allowable within the same voice because it is a leap greater than a perfect-fifth and is therefore inexcusable in strict counterpoint.