Is there a right way to play G A C Eb

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7th chords can be played with less than 4 notes. A dominant 7, minor 7, major 7 can be be harmonically expressed with root, 3rd and 7th: G7-BFG, Gmin7-BbFG, Gmaj7-BF#G for example. The 3rd and 7th are what defines the chord quality. IMHO
 
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Voicings are a really big topic.

If playing solo, a root is often needed but not always. If playing with a bass player, it can be a bit of an adjustment not having to play a root. Often a 5th is not needed for a chord to sound good. And there are times when a chord note doesn't actually have to be played for it to be "implied", especially with familiar tunes where people will fill in some of those missing tones in their mind, notes you don't even play. And sometimes chords are played more "open", not clustered together but spread out, sometimes using both hands to accomplish the notes intended. Occasionally, just the melody will fill in some of those tones for you.

Jazz is especially well suited (in my opinion) to variations and adaptations, chord substitutions, fun stuff like that. I think most of the more memorable pieces I can think of were somebody's "take" on how to play a particular tune, and not necessarily 100% true to the way somebody wrote it. Classical is much more strict in that regard and taking license like that is usually frowned upon harshly. (I've always thought Bach would be all over jazz if he were alive today. I mean... improv. :) )

It's complicated. And I'm not sure most of us ever even come close to learning it all. Enjoy the journey!
 
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7th chords can be played with less than 4 notes. A dominant 7, minor 7, major 7 can be be harmonically expressed with root, 3rd and 7th: G7-BFG, Gmin7-BbFG, Gmaj7-BF#G for example. The 3rd and 7th are what defines the chord quality. IMHO
Slight correction; you can do dominants by skipping the 5th; like for example G7, will fully trigger with G,B, F (skipping the D).

In this case, as an Am7(b5), since the 5th is flatted, skipping the 5th would change it to an Am7 (A,C,G), so that couldn't be done here... however, since it's also a CM6, you *could* do C, Eb, A (which will give you Adim, which is close enough tonally to a minor 6th or m7 flat 5).

And yes, I've used 1 finger to play 2 adjacent notes.
 

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