In Renaissance vocal music the relatively small number of pitches is made to seem larger by virtue of the changing timbres of vowels: Properly sung, the listener will feel fundamental shifting depending on the combination of vowels sung by the several voices. When all come together on the same vowel at the same time the effect should be immediate and stunning.
It is rare that one hears a good rendering of this phenomenon, as so much music these days is tuned only harmonically, i.e., as if a vertical combination of notated pitch is the point. The same applies to string quartet playing, though, lacking text, that is more subtle. The "text" must be supplied by the individual instrumentalists allowing their several instruments to speak.
Why are classical musicians so afraid of being out of tune? Give a good listen to any good blues musician; we all have a lot to learn from them.