G Pythgaorean Dorian diminished 4

The G Pythagorean Dorian diminished 4 Scale. I'm always struck by how the Pythagorean diminished fourth (8192/6561) is so close to the 5-limit major third (5/4). The two fall within 2-cents of one another and the ear would probably hear it as the major third in most contexts. In this case it is the interval that breaks up the Dorian symmetry of intervals.