A tone source apparatus is provided for an electronic musical instrument. It comprises a memory circuit which has a plurality of addresses and is so arranged that where at least one cycle of a musical tone waveform is divided into p units and a waveform in each section range is represented by a formula containing the abscissa as its variable, a coefficient and a section range quantum number of each formula is memorized in the form of digital signals in the corresponding address. Also included are a clock pulse oscillator, a counter means for counting output clock pulses of the clock pulse oscillator, and a coincidence circuit serving to generate the coincidence signal when the output digital signal of the counter means and a digital signal of the section range quantum number memorized in the memory circuit coincide with one another. A decoder designates the next stage address in order by output signals of the coincidence circuit. A calculation circuit is used for calculating a digital signal from the counter means and a coefficient digital signal from the designated address. A D-A convertor converts the output digital signal of the calculation circuit into a corresponding analog signal. The addresses in the memory circuit have memory portions which memorize as digital signals respective coefficients of n degree multiple term formulae for respective section ranges, and respective section range quantum numbers.