This paper describes a novel music playback interface, called Musicream, which lets a user unexpectedly come across various musical pieces similar to those liked by the user. With most previous ``query-by-example'' interfaces used for similarity-based searching, for the same query and music collection a user will always receive the same list of musical pieces ranked by their similarity and opportunities to encounter unfamiliar musical pieces in the collection are limited. Musicream facilitates active, flexible, and unexpected encounters with musical pieces by providing four functions: the music-disc streaming function which creates a flow of many musical-piece entities (discs) from a (huge) music collection, the similarity-based sticking function which allows a user to easily pick out and listen to similar pieces from the flow, the meta-playlist function which can generate a playlist of playlists (ordered lists of pieces) while editing them with a high degree of freedom, and the time-machine function which automatically records all Musicream activities and allows a user to visit and retrieve a past state as if using a time machine. In our experiments, these functions were used seamlessly to achieve active and creative querying and browsing of music collections, confirming the effectiveness of Musicream.