While I'm not the biggest Devil May Cry fan, having only played this and DmC, I can definitely appreciate the work put in by primary composer Tetsuya Shibata, as well as Shusaku Uchiyama, Kota Suzuki, Akihiko Narita, Rei Kondoh, Chamy Ishikawa and Shinichiro Satoh whom also contributed.
With hard rock/heavy metal tones for battle scenes giving the perfect scenario to beat down any demon in any way you like to dark and gothic overtones for an incredible atmospheric approach to exploring areas and wondering how to solve a puzzle efficiently to gain that SSS ranking at the end of a section.
The game I feel, has something for a lot of people. The main theme "Out of Darkness" is a beautiful, operatic opening which greatly shows off the vocal talents of Aubrey Ashburn, as well as describe the connection between Nero and Kyrie and the battles they face to be together.
The music definitely suits the atmosphere of the game and delivers on the demon slayer aspect.