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6th chords along with diminished scales are the foundation of Gypsy jazz - think Django Reinhardt.

Consider this quarter note chord progression: | Am Am Am Am | Am Am Am Am | Dm Dm Dm Dm | E E E E|

Now substitute with: | Am6 Am6 Am6 Am6 | Am6 Am6 Am6 Am6 | Bdim7 Bdim7 Bdim7 Bdim7 | E7b5 E7b5 E7b5 E7b5 |

In jazz and gypsy jazz, major 6th chords are often used as a substitute in the I and IV chords (so in the key of C, instead of Cmaj7 and Fmaj7, sub for C6 and F6).

Oh and one very obvious use of the major 6th chord is in the boogie woogie and blues bass riff used by Chuck Berry, Little Richard, Jerry Lee Lewis and so many bar bands playing blues rock since then (example: the left hand shuffle in Johnny B Goode, Tutti Frutti, etc).

I wrote a piece that goes from D to Ami 6 (which a C bass) to Bmi to D (with a passing A bass). I thought the transition sounds interesting. Gives a more poignant effect that simply going to D7 on the second chord.

Also didn't the Beatles and a lot of other 60s groups used to end their songs with a major sixth chord - with a full vocal harmony. It's a rather "open" way of closing something down...seems to suggest the song is going on somewhere else!

When writing that chord progession I meant to put Bmi7

OOO don't forget that also invert chord too for ease and effect! only just came to me!

You need to check out Barry Harris and his dim6th scale approach to jazz harmonization - You will see and hear how important a 6th chord can be.

I recently started looking at Blue In Green, the version in Fake Book 6th. It starts with a G-6. In this case that chord with it's Bb-E tritone creates a mood that I don't think the normal G-7 would do.