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It's Fun to Play the Piano ... Please Pass It On!
Freud asked, and I see men are still asking. Even the great Sherlock Holmes found this all but impossible to interpret... and I suspect they like it that way.
However, some detective work of your own could help the odds. A look at her music collection, for instance; noticing what radio station she listens to; asking her friends or siblings (though they may give you away); even asking her.
If she thinks you've tried to please her and have thought about what she likes (and dislikes), I think that could help you. Bring out a bouquet of flowers from a place of concealment (not red roses, though) and present it to her when you play--- that helps make an impression. Some piece you really love and can play well, that expresses your own feelings, will at least get you credit for a good effort (and she will remind her husband of it, many times, in the future).
Bottom line: she either likes you, or she doesn't. So, give it a shot. Nothing ventured, nothing gained.
I believe the piece Bluespianofan might be referring to is Comptine d'un autre été by Yann Tiersen. It is a very moving piece of music. This is the piece that made me want to learn how to play piano! Any girl will melt for this one (I'm a little partial to Tiersen)! I also agree with Rob and Jeff...YOU'VE gotta love whatever piece you pick. She will hear the emotion you play it with. Good luck! I'd be curious to know which one you end up going with!
Pick a piece based on how she dresses and which sociologic group she belongs to : Emo, rock chick, chav, geek, wigger, nerd, keener and so forth which should also give a clue to the music she admits to listening to...
Checkout VKGOESWILD channel on youtube. She'll send sheet music for a small donation...
If target is Emo or Rock oreinted the how about Nine inch Nails' "Hurt" or Placebo/Kate Bush "Running up that hill" or Nirvana's "Heart Shaped Box".
Why try and impress. Do what you want to do. Play that wonderful discordant sonata by Xenaxis, or Prokofiev with lots of discord and fortissomos, and bewildering chromatics. Really forget the girl. Blot her out and ignore her. If she's a beauty she'll be intrigued. But if you get steamed up you won't concentrate on your playing and you'll be likely to come over as a sap.
Great topic - it's generated a lot of good suggestions that I appreciate having. My suggestion is "The Summer Wind" - the theme to the movie Summer of 42. The sheet music version is a good intermediate version.