Thanks for the links - will definitely check them out.
Tan Dun is of course pretty well known for "Hero" and especially for "Crouching Tiger, Hidden Dragon" which is one of my personal favorites.
What I like about traditional Japanese music is the "formality" of it, for the lack of a better word. Modern Japanese music like for movie scores can be completely different, though. Two examples:
"Rising Sun", which features a "modern" jazz/thriller soundtrack, but integrating Japanese motives and instruments flaring up here and there. Perhaps not the best soundtrack for isolated listening but it works fantastic in the movie and gives it a very particular atmosphere.
The other "example" is the constant battle in my head for the last 25 years: "Which anime soundtrack is better: The one from Akira or the one from Ghost in the Shell?"
The correct answer to this question is of course: "Yes"
Akira: Kaneda's Theme (some violence, 3:30 - 5:20 )
GitS: Making of Cyborg (some nudity), recycled in part in this sequence: Ghost City