A musical controversy is sending shockwaves through Motown -- two singers belting out their versions of the Temptations classic "My Girl" ... in an a cappella duel to the death!!!!

It all started when Harvey Levin hit the famous Hitsville Museum in Detroit Tuesday ... and was so moved by the experience of being the legendary Motown recording studio, he broke out in song ... accompanied by some sort of warped Temptations dance move.

The next day, David Ruffin Jr. -- son of Temptations lead singer David Ruffin -- challenged Harvey to a sing-off ... while standing in a back alley, somewhere in L.A.

So, we gotta ask ...