Abstract: A keyboard operated electronic musical instrument in which a number of tone generators are assigned to actuated keyswitches in which provisios are incorporated for simultaneously generating a combination of tones. Tones in the first family are generated with a maximum of Q harmonics by implementing a discrete Fourier transform employing stored sets of harmonic coefficients. Tones in the second family are obtained by operations on a frequency number and have a maximum of 2 Q harmonics. The second family of tones are generated in a manner that inherently provides ample noise reduction.