Intonation Correction
Within a chord, most pitches (particularly the 3rd or the 7th) are naturally sharp or flat. I recommend a tool with which a user could correct the intonation of a particularly note or even an automatic feature that would adjust pitches based on the given chord. This would greatly improve the playback feature. For examples of how partials need corrected I've attached a chart (credit to http://briansacawa.com) 
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Comments
Just temperament is a particularly specialist thing.
Musicians have been using temperaments to allow an instrument to play in more than one key since the Renaissance.
If you really want to be restricted to music that cannot modulate successfully then you could try this plugin.
http://musescore.org/en/project/autotuneselection
But, if you alter the pitches to "improve" playback, won't this result in it sounding different from you keyboard (unless you tune it, too, for each chord)? Or am I missing something?
In reply to But, if you alter the pitches by underquark
True, but the difference is much more defined on the playback, which has a much poorer tone (the better the tone, the less out of tune it will sound). Besides, that only applies to percussive instruments (e.g. the piano). Wind musicians who would read the music would naturally (or, depending on skill level, intentionally) alter their pitch in the same way.