Abstract: M-ary angle modulation is used to record digital data at high density on a disk. In one embodiment, data symbols are encoded by assigning each data symbol a phase representation in terms of a carrier signal, the disk is physically altered in such a manner as to represent the carrier signal, and, at defined intervals, a phase angle of the carrier signal is changed by one of M of possible phase increments, where M equals two to the power of a number of data bits in a data symbol. M data bits are therefore recorded per each of the defined intervals. In another embodiment, a frequency of the carrier signal is changed to have one of M possible frequencies.