Normally, a piano has notes that are a half tone apart. If you take two pianos and tune one of them a quarter tone sharp, you can use them to play 24 tone equal temperament. These videos demonstrate 3 quarter tone piano pieces by Charles Ives.
24 tone equal temperament is a somewhat controversial tuning. It's similarity to 12 tone equal temperament makes it an obvious choice for study, but many people don't like it. They point out that the in between notes tend to be rather dissonant. This tuning is regarded by some as one of the least interesting. Well, I haven't formed any strong opinions about it myself. I have had very little success with it, so far, but I recently had some ideas that may be productive. I can say that I like these pieces and hope you will enjoy them, too.
Charles Ives-3 Quarter Tone Pieces-Largo
Charles Ives-3 Quarter Tone Pieces-Allegro
Charles Ives-3 Quarter Tone Pieces-Chorale