The problem with a piano sound is that every note has a different mix of harmonics and harmonic envelopes so you really need a sample for each note. You can just about get away with stretching one sample over an octave but that is it.
I would, and have on many occasions, use a MIDI sound module. My favorite is the Yamaha MU10, long since obsolete but still available on eBay. You feed MIDI signals directly into it which the Arduino can generate. It also does other great sounds.
Failing an external MIDI sound module many computers have software sound generators. Garage band on the Mac has lots of sound you can trigger in this way. You need a helper application called Hairless ( it is free ) to convert the normal serial connection from an Arduino into MIDI.
There is a project here where I used the MU10 to make a chaotic pendulum trigger MIDI notes. There is a video with some of the sounds on it.