The 6th chord (major) can probably be best described as whimsical. It’s the kind of chord you’d think a harp would play. The structure of the chord is the same as the major or minor plus an added 6th note. The 6th is not flatted, this would make the chord a C 6 flat or C minor 6 flat.
It is a four note chord, with the notes construction of 1-3-5-6. So for example a C6 will have the notes C-E-G-A. A think of it as typical of Western Swing. Here is a little chart to help you with your practice.
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