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Furinkan notes that cats reached Japan by the Asuka period but were highly valued rare treasures of the upper class during the Heian period. There's a lovely article called Pet culture in Japan on Wikipedia that discusses that. Anyway, Hyakka's line has some of that added context. In Japanese, he simply mentions that they only lived in noble houses. The way of onmyo is onmyodo in Japanese. And Hakubi appears to list all five of the elements here (木火土金水).