In the comments to the question Why is the fourth against the bass considered a dissonance?, I wrote
A 5:4 third was considered dissonant until musical tastes changed and declared it consonant.
To which @phoog replied
In the days in which major thirds were considered dissonant, Pythagorean tuning prevailed. Those were 81:64 thirds, not 5:4.
What was the process of (major) thirds shifting from dissonances to consonances, and did the change in tuning play a significant role in that shift?
