A musical tone signal generating apparatus has waveform memory WM which stores a plurality of compressed data sets obtained by compressing, by linear prediction, sample values obtained by sampling musical tones. The musical tone signal generating apparatus has cache circuit 740 which reads out compressed data from waveform memory WM within an assigned computing period in response to instructions to generate a musical tone, and decoding circuit 750 which decodes the compressed data and outputs the decoded data as the data indicative of a sample value. The musical tone signal generating apparatus has CPU 901 inputs tone pitch information indicative of a tone pitch of a musical tone which is to be generated, identifies waveform data which is to be read out by cache circuit 740 from waveform memory WM and determines, in accordance with the identified waveform data, the length of the computing period which is to be assigned.