The Grand-Daddy of All "Music Minus One" Records...
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...is "My Pretty Girl" by Charles Fulcher and his Orchestra, Columbia 551-D, recorded in Atlanta in 1925. Look it up on RedHotJazz.com. About three-quarters of the way through this side, which is awfully hot, the band gozinta a stop-time chorus- which NOBODY takes! The time is left open, and unless you are completely devoid of musical imagination, you "hear" a horn solo, a tap-dance chorus, a scat vocal - anything to fill the gaps. The record just cries out for someone to join in. Actually, it's very "Zen," though I'm sure this was well before John Cage's "4:33." I play along with it all the time.
BTW, there are also some acetate recordings from 1943 of Charlie Parker playing tenor sax (!) along with records by Hazel Scott and Benny Goodman, with seamless, transcendent results. These came out on LP about 1986. Albert, what if the "perpetrator" happens to be an artist of immeasurably greater stature than the ones on the original record(s)?