Bunraku theater is a traditional Japanese performing art. Bunraku puppeteering can invoke deep unconscious affective reactions from the audience, overcoming what is known as the uncanny valley effect. The authors analyze Bunraku plays, showing that the music tempo and puppet movements follow the Jo-Ha-Kyū principle, which refers to recursive and fractal artistic modulations such as changes of tempo and rhythm breaks. The authors then illustrate the difference between Bunraku and European dance and finally propose the application of Jo-Ha-Kyū in character animation design.