Assume that A and B are singing together and that the correct sound is sin(w). But A does sin(w+d) and B does sin(w+c), with d and c small comparing to w. Then the sum sound would be
sin(w+d)+sin(w-c)= 2sin[w+0.5(d-c)]cos[0.5(d-c)].
since d-c is very small so this is approximately 2sin(w). This says that if several bad singers are not all bad in the same direction they can correct each other. One can see this in high school performance :)