A tape cassette that includes a rotatable drum having a centrally disposed tape storage device and a surrounding circumferential wall with one or more openings therein through which tape passes from the storage device to and helically around the outer surface of the wall and then back inside the drum. A cooperating recorder/reader head is mounted outside the drum in alignment with the tape to record/read a slant track thereon as the drum rotates. The tape storage device may be indexable to to incrementally advance the tape along the wall surface, or the head may be indexable so as to incrementally move across the tape, each time the drum completes one revolution, to thereby record/read a succession of slant tracks as the drum rotates through successive revolutions. Such a cassette offers the combined advantages of a fast-access disk and a mass-storage tape.