Abstract: An electronic musical instrument has a keyboard including a plurality of scale keys and a plurality of chord keys. Musical sounds are generated by a programmable frequency divider network capable of producing different output frequencies, depending on which keys of the keyboard are activated. A decoding means connects the keyboard and the programmable frequency divider network to supply signals which cause the programmable frequency divider network to produce different output frequencies, depending on which keys of the keyboard are activated. Means connect the scale keys and the chord keys for altering signals supplied from the chord keys to the programmable frequency divider network, depending on which scale keys are activated. On this basis, compatible chords may be generated with the chord keys for a melody being played with the scale keys. The frequency divider network utilizes lowest common multiples and prime numbers, which substantially eliminates the potential for producing dissonant sounds.