Where can I find non-hokey traditional music (Latin chant/choir, Japanese/Chinese, Irish)

Everytime I find traditional music, it usually the kind of stuff you'd hear you're grandparents play on their record player. I guess you could say I'm looking for fairly contemporary traditional styled music. Specifically Latin Choir (Preferably without a strong, detectable religious tone, but whatever) and Japanese (Featuring traditional instruments, especially Taiko drums).

Bands, Albums/compilations, websites, I'll take anything.