Is this a Major 6th chord or a minor 7th?

Question

--------------5---
--------------5---
--------------5---
x-------------------
x-------------------
------3-----------

Answer 1

This chord can be viewed in several ways, but let's examine the notes first. the first three strings are playing A, E, and C. the Bass is playing a G. the most obvious way to name this chord would be A Minor with a G in the Bass Amin/G

It could also be viewed as an A minor seventh with the seventh in the bass, (somewhat unusual, but not unheard of)

The third interpretation would be a C6 chord with a G in the Bass. the best interpretation would be within the context of how it is used, and what chords precede and follow it.

For instance, if you started with 6/5, 5X, 4X, 3/5, 2/5, 1/5 (the first number designates the string and the second number designates the fret) that would be a simple A Minor chord. If you move the bass down to 6/3, then you are playing the chord you asked about. The proper way to label it would be Amin7/G (or A Minor seven with a G in the Bass)

If you started with a 6/X, 5/3, 4/X, 3/5, 2/5, 1/5 and moved from a 5/3 to a 6/3 (6/3, 5/X, 4/X, 3/5, 2/5, 1/5) then the chord would be labeled C6/G (or a C Major with an added sixth and a G < the fifth > in the bass)

So you can see how it depends on how the chord moves within the framework of the song, and what your perception of it is. I hope this helps.

Answer 2

Putting aside the deep analysis of what it could be, and going on what you've shown, it's an incomplete C6 chord. To complete the chord, finger it as follows: 335555