The inventive circuitry extends the harmonic content of musical tones produced by a computor organ of the type disclosed in U.S. Pat. No. 3,809,786. A memory stores values of an algebraic approximation of the summation of the amplitudes of a set of Fourier components of order higher than those separately evaluated by the computor organ itself. As each musical waveshape sample point amplitude is computed by the computor organ, the stored summation approximation value for the corresponding sample point is accessed from the memory. This accessed value is appropriately scaled, and is added to the sum of the lower order Fourier component contributions that are calculated by the computor organ. The resultant sample point amplitudes are converted to musical tones in real time. In an illustrative embodiment, musical tones having the spectral content of a sawtooth wave are produced.