Another thing that your explanation caused me to realize when focusing on a Major Barre Chord, is that the M3rd is actually a 10th from the Root and a 3rd from the Octave. So it's still a 3rd.
Looking further, I became somewhat confused though..................
Example;
If I play an "A" Major Barre Chord, C# is the M3rd, correct???
What happens if I play an "A7" chord?? Isn't C# still the 3rd even though the Octave is replaced by a b7th note??????????
I'm sure that there is a logical explanation for this, but I can't find it for the life of me.
If someone would be kind enough to shed some light on this grey area for me, I would really appreciate it.