I have to use studio reference headphones with my Audya to take advantage of the full dynamic range offered by real audio, although it might not be so important on the Korg.
If you don't want anything too big then I love
Sennheiser HD 25-1 II as they are small and portable, but if you plan to use phones for long periods of time you might want to look at something more comfortable, perhaps
Sony MDR 7509HD which had very good reviews. Of course if money is no object there is only one choice in my book: the superb
Sennheiser HD800.