An electronic musical instrument wherein, by merely depressing one key, the tone pitch corresponding to that key varies periodically with cyclic repetition at a specific rate. The pitch variation is made on the octave basis by periodically shifting digits of binary signals of plural bits which designate readout addresses of a musical tone waveform. Various patterns of the pitch variation can be obtained by suitably setting a pattern of shifting of the digits of the binary signals. The patterns include an "up mode" in which the pitch slides successively toward higher pitches one octave interval at a time and then, upon reaching a predetermined octave, immediately returns to the original pitch and subsequently the same operation is repeated, and a "turn mode" in which the pitch slides successively toward higher pitches one octave interval at a time and, upon reaching a predetermined octave, slides successively in the reverse direction until it returns to the original pitch and subsequently the same operation is repeated. The patterns further include a "jump mode" in which, when a plurality of keys are successively depressed, the pitches of the succeedingly depressed keys slide in conformity with the octave slide of the first depressed key and a "random mode" in which, when a plurality of keys are successively depressed, the octave slide of the respective keys is made independently and separately from each other. In a case where plural keys are depressed, the "up mode" or the "turn mode" can be selectively combined with the "jump mode" or the "random mode". The speed of the octave slide is determined by the rate of the clock pulse employed in the instrument and, accordingly, a clock pulse of a rate corresponding to a note to be played is selectively used.