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Ok if I wanted to be Gertie Cummings than do you think that "If Momma was married" from Gypsy is a good choice?
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Sorry if I'm posting this too late to be helpful--it's been a long time since I've seen Gypsy, so I'm not too familiar with that song. For Gertie any song would work, because she really doesn't sing in the show. For Ado Annie, if you're not familiar with "Oklahoma" you could probably sing something from "Annie Get Your Gun", or if you're sticking with Gypsy, maybe "Everything's Coming Up Roses"--pick a fun song that could be seen as a show-stealer (in other words, if choosing between a belt and a ballad, choose a belt). If you were auditioning for Laurie I'd say go for a ballad, because she's the romantic lead. But for Ado Annie, pick a belt, and for Gertie anything's good.
Another thought, if you're familiar with other Rodgers and Hammerstein musicals (Sound of Music, South Pacific, King and I--most of the classics), those might be good choices. Sometimes directors like to hear either a song from the show or in the same style as the show you're auditioning for.