Counterpoint is what makes the chord progression in my opinion. To me there is two things going on, the melody which is the finger picking of the e, b, and g strings. The other is the bass line. The sound to me is clearly going minor to major to major. The first chord is an A minor chord, but saying it's C6 shows how the melody moves. It's an ascending harmony on a C major chord from C6 (a, e, c) to Cmaj7 (b, e, c) to Cmaj (c, e, c). The bass is minor, starts with the relative minor and descends. Together, you can call the first chord Am or C6/A (C6/A is there to show the contrast between the bass and the melody), the second is Cmaj7/G# (i don't see how you could call that anything else. Am/maj7 ??? I see where the thought comes from, but what do you make of the B? It would have to be Am/maj7add9/G#. ;) I wouldn't think of it as such, it's clearly Cmaj7/G#. The third chord can't be minor either, it sounds major and it's doesn't even have A in it. Analytically that's a bad call, together the chord makes up g, c, e, c. How could you not call that Cmaj/G?? The next chord as A minor sounds like calling the second chord A m/maj7. The tones in that chord are (f#, a, d, f#), and as an A minor the spelling is Am6sus4/F#. Hmm. No, it's D/F#.
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