You guys aren't disagreeing exactly. acjohnson55 mentioned "Medieval and Renaissance" but you're just talking about the Renaissance, and the Medieval-to-Renaissance transition is the interesting part (I think acjohnson55 just got the timing a bit wrong). The major third as a consonant interval became accepted in the early Renaissance. Most medieval composers considered thirds to be dissonant, which makes medieval music sound strange to modern listeners because things don't resolve as we expect them to, with phrases often ending on open fourths or fifths instead of triads (though to be fair, their third was somewhat different than ours because of changes in temperament over time).