Notating Augmented Chords

Question

When writing an Augmented chord, which inversion of the chord should I use?

The problem came up while I was composing (piano). I came to an augmented chord and couldn't think of which version to use due to the accidentals.

The key I was writing for here is C# Minor. 'n' reperesents a natural:

1. G#+ Root: G - #B - nxD
2. C+ 2nd Inv: G - nC - E
3. E+ 1st Inv: G - B# - E

I remember from my music theory that an inverted augmented chord creates another augmented chord. But I have no clue how I should write it. If I had to guess, I would say that you chose based off the key that you're writing in.

Answer 1

Really you're talking about augmented triads, specifically, and yes, all augmented triad inversions create another augmented triad.

You already know which augmented triad you want, so this is more a question of accidental notation--this can come up in many other circumstances as well, especially if you're working in a neotonal context or are very far away from your key center.

If you're writing traditional harmony, the answer is probably going to be whichever notes fit your key signature the best. #2 and b1 (xD and nC in your key of C# minor) are rare, so the notation you're looking for is probably G# - B# - E. This is also really the same as finding one of the chords diatonic to your key signature. In C# harmonic minor, the only diatonic augmented triad is indeed rooted on b3 (E - G# - B#).

If this is not the case, then in order to answer the question properly, we'd have to know how you got to that chord and where you're going. i.e. how does the augmented triad function in the chord progression you've written. You would then choose an inversion that most clearly describes the root movement of the bass, or how you're planing something, or a weird deceptive cadence, or any number of other compositional techniques.

One last thing worth noting is that the first method I mentioned (look in the key signature when writing traditional harmony) is really exactly the same as the last one (do what makes logical sense): when you're writing traditional harmony, the logical progressions generally all fall on the diatonic notes, or not far from them in the case of secondary dominants.

Answer 2

I assume here that you are looking for the way to name the chord, rather than to spell it in notes.

You seem to know that you want the G# at the bass. I would probably write the chord that does not call for an inversion, for the sake of simplicity. G#+ is much easier to read than B#+/G# or E+/G#.

In the general case, if one of the tones forming the augmented chord is not in the current tonality, you could put that as the augmented 5th. For example in C major, I would use G+ rather than other inversions because D# is the accidental. However in your example, all tones of G#+ are in C# minor harmonic (B# is really in the scale although it does look like an accidental. That's an annoying shortcoming of our notation system).

One way to decide which of the inversions to use could also be to test the associated aug7 chord. Test G#+7, B#+7, and E+7, see which one fits best. That could give you your answer.