The book switches back and forth between present Tokyo and three episodes of the swords' histories. This is a stumbling block; a large percentage of the early book is told from the point of view of psychopathic assholes. I assure you that Beautiful Singer's episode is short, and we thereafter only have to put up with part-time narrative from the yakuza sword master asshole who is trying to collect the set.
The strength of the book is Detective Oshiro, who gets sucked into the mess when drug lords and meter maids start dying all over Tokyo of sword wounds. Oshiro is a female Tokyo cop who's lived in the US, and is thus convincingly both in and out of her society -- at least, it was convincing to me. (I've never been farther east than the Tower of London.) Between her sexist cop boss, her family, the Tokyo crime scene, and the good-guy sword master who teaches her about the fantasy part of the plot, Oshiro winds up being an engaging viewpoint on modern Japan.
The down side is that low-magic urban fantasy isn't really my thing. This is more a cop story (with historical interludes) than a fantasy novel. This does not make it a bad book, but it wasn't quite the book I was in the mood for. So I may not pick up the sequel. But then, maybe I will.