>>>In the chanting of certain sutras I have noticed how the group collectively settles on a major third followed by a minor third out of sheer improvisation.<<<

Back when my mum used to drag me to these very wacky Charismatic Catholic prayer meetings (late 1970s), people would fall into tongues and eventualy sing in tonuges. the same Major third/minor third pattern tended to develop. Every now and then though, you'd get a different pattern with an augmented fourth and other "perfect" chords but your third/third pattern was the norm. it'd take a few minutes to develop and then would rise and fall in a repeatable pattern.