An electronic musical instrument which produces musical notes synthesized based on logic orthogonal functions stored in digital form. A coefficient corresponding to a tone selected by a tone selector is read out of a memory to calculate a logic orthogonal function, for example, a composite coefficient of a Walsh Hadamard matrix. The composite coefficient is applied to a plurality of waveshape calculators to calculate the amplitude value of a waveshape of the required tone and the waveshape calculators are actuated at the timing predetermined times the period of the musical note selected by the depressed key. Any desired musical waveshape can be produced by setting the coefficient corresponding thereto and the spectral structure of the waveshape can be changed with the lapse of time. Polyphonic tone synthesis is achieved by intermittent operation of the waveshape calculators to produce a wide variety of musical sounds. Further, a depressed key data detector is provided for detecting non-encoded key data. Columns of a key switch matrix are selected by a ring counter and a predetermined time slot is provided by a priority selector in accordance with priority of rows having key switch closure signals and a pulse having the phase angle of the row is produced in the time slot. This pulse is extracted together with a frame pulse and a clock to detect key data. The key data are assigned to a plurality of assignment units one after another and, thereafter, waveshape calculation is carried out in each of a plurality of systems.