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An 1884 newspaper interview1) suggests that Sweet Bye and Bye was the first title produced:
“The Superintendent at this point conducted the reporter to his private workshop, which was carefully locked, and exhibited the first made of the new music boxes. […] Here he placed in his model a roller of music like that of a Swiss box (except that the pins were bedded in wood instead of metal) and turned a small crank. Sweet Bye and Bye was the result in full resonant tones.”