More often than not Takemitsu's music pushes the boundaries whilst never undermining the other elements of a film. And when he was more conventional (as at Kurosawa's behest in the Mahler-influenced "Ran") he was also excellent.
The genius of modern Japanese music of the twentieth century. Aside from his excellent soundtracks mixing European avant garde and Japanese folk traditions, his orchestral music and music for guitar is fantastic! Personally, Takemitsu, Nino Rota and Bernard Herrmann feel like the reigning gods in the world of soundtrack composers who expose people like John Williams for the hacks they are!