(yeah, that is kinda punny)

OK so let's say I make a recording of "Rhapsody in Blue" and then want to play that recording in a public setting. Do I just give Harry Fox $0.09 for every time the song plays or is there a different way to go about this? - It would not be 'for sale' but it would be 'broadcast', in a setting that may be considered 'public', as part of the overall production.
OR because people will buy tickets to this, with a limited number of seats, would it be considered a 'private event' that would be exempt from this question?
This is all hypothetical, of course. . .
PS The song in question I believe to be outside of the public domain until the year 2038, or so sez the Interweb.