In Pythagorean tuning, your E would be 81/64 above C, or equal to four fifths minus two octaves. This is slightly higher than E in the article, and the difference (81/80) is called the syntonic comma.

Different tuning systems were invented in order to resolve this discrepancy, and without these advances, jazz would be radically different. One of the things about jazz is that you see distant movements that only really make sense as enharmonics—like how Coltrane’s “Countdown” uses the familiar ii-V-I, but modulates in major thirds, which only makes sense when you allow the final modulation te be the same as the first—something that only works enharmonically.