This fact about musical perception is indeed a necessary condition
for music as we know it to be possible, since having one interval
uniformly in tune makes other intervals uniformly out of tune.
A large part of the history of western music since the late middle
ages has been the history of different compromises that have been
made with regard to getting different intervals in tune. In particular,
12 equal interval tuning, which has been standard in western music
since about 1800, tunes the fifth flat enough to make the major third
less hideously sharp than it would be if all fifths were tuned pure,
as they were in the “Pythagorean” tuning of medieval music, but not
as flat as is needed to make the major thirds pure, as they were
in the “meantone” tuning of renaissance and baroque music.