Article only looks at the 4th and 5th, but I think the more interesting observation is that if you pick any small number ratio between 1:1 and 2:1 (i.e. using numbers from 1..10 and lying within a single octave), they almost all have a reasonable 12-EDO approximation.
1:1 is the unison. Not terribly interesting.
2:1 is the octave, which is exact.
3:2 is the perfect fifth. About 2 cents of error.
4:3 is the perfect fourth. Also about 2 cents of error.
5:3 is the major sixth. About 15 cents or so of error.
5:4 is the major third. About 13 cents or so of error.
6:5 is the minor third. About 15 cents or so of error.
7:4 is the the first one that doesn't really have a 12-EDO equivalent, though the minor 7th is generally used, with about 31 cents of error.
7:6 similarly doesn't have an equivalent. It's about 44 cents flat of the 12-EDO minor third. In fact, most ratios with 7s are right out.
7:5 is in the ballpark of the 12-EDO tritone.
8:5 is the minor sixth. About 13 cents of error.
9:7 is a really sharp third, again no equivalent in 12-EDO.
9:8 is the major second. About 4 cents of error.
10:9 is also the major second, about 17 cents off in the other direction. (12-EDO makes no distinction between 9:8 and 10:9. That's actually fairly important, as it lets you get away with chord progressions that don't mathematically work out.)
It's really amazing to have so many decent approximations of ratios with only 12 notes. Different EDOs might have better or worse approximation of various musical intervals. It takes going all the way up to 41-EDO to find something that's better at basically everything -- it even has a more accurate 4th and 5th, which is the one thing that 12-EDO is amazingly good at.
1:1 is the unison. Not terribly interesting.
2:1 is the octave, which is exact.
3:2 is the perfect fifth. About 2 cents of error.
4:3 is the perfect fourth. Also about 2 cents of error.
5:3 is the major sixth. About 15 cents or so of error.
5:4 is the major third. About 13 cents or so of error.
6:5 is the minor third. About 15 cents or so of error.
7:4 is the the first one that doesn't really have a 12-EDO equivalent, though the minor 7th is generally used, with about 31 cents of error.
7:6 similarly doesn't have an equivalent. It's about 44 cents flat of the 12-EDO minor third. In fact, most ratios with 7s are right out.
7:5 is in the ballpark of the 12-EDO tritone.
8:5 is the minor sixth. About 13 cents of error.
9:7 is a really sharp third, again no equivalent in 12-EDO.
9:8 is the major second. About 4 cents of error.
10:9 is also the major second, about 17 cents off in the other direction. (12-EDO makes no distinction between 9:8 and 10:9. That's actually fairly important, as it lets you get away with chord progressions that don't mathematically work out.)
It's really amazing to have so many decent approximations of ratios with only 12 notes. Different EDOs might have better or worse approximation of various musical intervals. It takes going all the way up to 41-EDO to find something that's better at basically everything -- it even has a more accurate 4th and 5th, which is the one thing that 12-EDO is amazingly good at.