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I don't have a clear understanding of the notation used in the following sentence from the article on Augmented major seventh chord from Wikipedia:

As with dominant seventh chords, non-dominant seventh chords including the augmented major seventh usually progress according to the circle, thus III+_M^7 resolves to vi or VI.

If we are referring to the C maj7(♯5) does the III in III+_M^7 represents C, or does it represent E? Knowing that will allow me to know whether C maj7(♯5) usually resolves to D (when III is C) or F (when III is E).

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If your Cmaj7(#5) is interpreted as a III+_M^7, the third degree in A minor, then it should resolve to F which is the sixth degree in A minor.

  • Is there any reason the Cmaj7(#5) shouldn't resolve to C, or a Cmaj7(#5)/G# shouldn't resolve to a C/G? While it's not typical for a chord to resolve to another with the same root, the contrary motion of the augmented fifth and leading tone work to create a satisfying release of tension. – supercat Jul 2 '18 at 22:35
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The article is poorly written. But if you look a little further down, it clearly states "C maj7(♯5) usually resolves to F."

  • It can. However, sounding rather similar to E+, it resolves nicely to Am. The F sounds like an interrupted cadence. – Tim Jul 2 '18 at 7:45
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The wikipedia article is probably incorrect. In the key of C major, the III augmented major 7th chord is E Augmented major seventh. You would be much more likely to find a III augmented chord as a dominant chord if it is going to resolve to VI, a minor VI chord in this case.

Something else to consider, a I augmented major seventh would lead nicely to a VI minor chord (C aug maj 7 to A minor.)

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