Naming convention for augmented 6th chords?

Question

There are three types of Augmented 6th chord the German, the Italian, and the French. Most chords are named for the intervals they contain or their function, but these seem like just arbitrary names for chords. Why are the augmented chords named this and is there an alternative name for each that better captures how they are constructed?

Answer 1

The reason why they don't have names based on the intervals is because they all have the same function, and the intervals that they each have are not different enough to warrant new names. All of them are derived from the basic flat 6, tonic, and sharp 4 (and between the flat 6 and sharp 4 create the augmented 6 interval), with the French having scale degree 2 in addition, and German having scale degree 3 (creating a spelling of a dominant 7). They all resolve the same way, and they are not named any differently according to the inversion either. (i.e. French aug. 6 in second inversion in stil Fr+6). The Neapolitan chord also serves a predominant function and although can technically be named flat II, is not, according to its function. I hope this helps