Somehow I missed seeing this when it was posted.

This is an A minor 7th: the A root on the 6th string; the G, which is the flat 7th on the 4th string; and the C, which is the minor 3rd, on the third string. A very handy little chord because it leaves other fingers to play melody notes or other extensions.

When I looked at the chord, I saw the 6th string A root on the 5th fret. The next note is on the same fret as the root and is two strings higher. This is always when you find the flat 7th.

The last note is on the same fret as the flat 7th and is one string higher. If you really know your intervals, you could quickly say that the note a fourth above the flat 7th is the minor 3rd. But I’m not that smart. I just saw the note was on the 5th fret of the 3rd string and I know that’s a C, which is the minor 3rd of A.