It is also possible that you are hearing 'too correctly'!!

You may have to find a compromise whereby both chords sound slightly wrong (to you).

The problem dates back a long time, and was even addressed by J.S. Bach in his '48 Preludes and Fugues for the Well-Tempered Clavier'.

Keyboard instruments, you see, are more prone to this problem. It would take a long time to explain the problem satisfactorily, but the short answer is this:

If Middle C and the G a fifth above were tuned exactly to a fifth (by using harmonics), and then the octave C was tuned exactly to a fourth above that G, the two C's would not be in tune! The upper C would be slightly sharp...

When tuning a keyboard instrument, fourths and fifths are always deliberately tuned slightly flat, and that is what 'Well-Tempered' means - the instrument plays acceptably in any key (with the emphasis on acceptably, not strictly in tune!).

Guitars also have this problem, having fixed frets - the violin family do not (and are mostly tuned in fifths, except the Double Bass), because they player can pitch each note individually.

Hope this helps!