Looking for new genres...

Looking to add something new to my CD collection,.. to meet new genres. What could match the following criterias: to be Music with capital letter, but not to belong directly to Jazz, Blues, Classics, or Folk (derivatives are acceptable)?
For example: MA has several recordings, which originally are folk-based, but in reality are too complex and rich musical pieces to be called Folk. Another thing would be "Requiem for my friend" by Preisner - beautiful and modern work, nicely derived from Classics but isn't belonging to it...
Do you have anything like those?..