What key is a piece in if an augmented chord is used as a dominant?

Question

I personally think that augmented chords can be just as consonant as major if used in a certain way. For example, in the first octave of a piano, if I play an augmented chord, yes it will want to resolve but not as much as say if I played that same chord an octave lower in the small octave. But in a way, augmented is ambiguous. You don't have 1 single root, you have 3 roots, 3 mediants, and 3 dominants. But at the same time these can be viewed as inversions of a single chord. Here are the resolutions I get for C augmented in order of most natural to least: C aug -> A minor 1st inversion(Harmonic minor scale has this augmented chord in it) C aug -> C major C aug 1st inversion -> E major C aug 1st inversion -> A minor 2nd inversion C aug 1st inversion -> C major 1st inversion C aug 1st inversion -> C# minor 1st inversion C aug 2nd inversion -> Ab major C aug 2nd inversion -> A minor C aug 2nd inversion -> C major 2nd inversion C aug 2nd inversion -> F minor 1st inversion That's all from 1 chord but that is 3 separate major/minor key pairs. At the same time E major can be viewed as the resolution of E aug and same for the Ab major and Ab aug. In turn C major can be viewed from any of those 3 keys as a resolution so what key are you playing something in if you are using the augmented chord as a dominant function chord? The major with the same lower note as the chord? The relative minor of that? Something else entirely? It sounds like it is not sure where it wants to resolve, just where it naturally would land out of 6 chords(namely the relative minor of the lower note). But all 6 chords are resolutions that sound equally as good. With diminished you have a similar thing going on but only between 2 chords which are not equidistant on the circle of 5ths(for example B major and C minor both from C diminished). I mean to go from B major to C minor would take 8 or 4 steps through the majors and then 1 more step to relative minor depending on whether you go in the flat direction or in the sharp direction. With augmented, it is 4 steps in either direction through the majors that both resolve so what key are you in? C major? E major? Ab major? So how can you tell the key a piece is in just from an augmented chord in the harmony? Is that even possible?

Answer 1

The appeal of augmented chords, like that of diminished 7th chords, is their ambiguity. Each of the resolutions you mention works precisely because the chord divides the octave into equal parts—tonality, remember, depends on the asymmetry of the major and minor scales.

As far as telling the key of a piece—if the composer has been punctilious about spelling, you might be able to conclude something from how an augmented chord is spelled. It's still two stacked thirds; so it's either C-E-G#, or E-G#-B#, or Ab-C-E. Which one is the root should tell you something about how it's being used.