An audio signal generation apparatus comprising: a plurality of channels each including a sample counter adapted to perform counting operation at a given rate, each of the channels being configured to generate a waveform sample value based on retrieving, from a memory (WM, RB), of a sample value of an original waveform based on a count value of the sample counter; a control section configured to set, independently for each of the channels, the rate and an initial value for the sample counter of the channel and control start and stop of the counting operation of the sample counter, so that a partial portion of the original waveform corresponding to a count range from the set initial value to a count stop point is reproduced in the channel; and an overlap adder controlled by said control section, wherein said control section is configured to set the initial values in individual ones of a set of channels, selected from among the plurality of channels, such that sample values at different sample positions of the original waveform are retrieved from the memory in individual ones of the set of channels, and control said overlap adder to add up a plurality of samples generated in the set of channels, whereby sample values of an audio waveform signal with a plurality of partial portions of the original waveform, which are to be reproduced in the set of channels, partially overlapping each other are output from said overlap adder, characterized in that said overlap adder includes adders provided in corresponding relation to the channels, and the adder of each of the channels is configured to add up a waveform sample value generated by the channel and an output signal of the adder of another channel in accordance with control by the control section. a plurality of channels each including a sample counter adapted to perform counting operation at a given rate, each of the channels being configured to generate a waveform sample value based on retrieving, from a memory (WM, RB), of a sample value of an original waveform based on a count value of the sample counter; a control section configured to set, independently for each of the channels, the rate and an initial value for the sample counter of the channel and control start and stop of the counting operation of the sample counter, so that a partial portion of the original waveform corresponding to a count range from the set initial value to a count stop point is reproduced in the channel; and an overlap adder controlled by said control section, wherein said control section is configured to set the initial values in individual ones of a set of channels, selected from among the plurality of channels, such that sample values at different sample positions of the original waveform are retrieved from the memory in individual ones of the set of channels, and control said overlap adder to add up a plurality of samples generated in the set of channels, whereby sample values of an audio waveform signal with a plurality of partial portions of the original waveform, which are to be reproduced in the set of channels, partially overlapping each other are output from said overlap adder, characterized in that said overlap adder includes adders provided in corresponding relation to the channels, and the adder of each of the channels is configured to add up a waveform sample value generated by the channel and an output signal of the adder of another channel in accordance with control by the control section.