circuit 71 consists of 2n 1 delay units connected sequentially to one another where n is given by an integer the delay intervals u03c4 k of the data d k k is equal to or larger than n and equal to or smaller than n output from delay circuit 71 are given by equ 26 below the multipliers m k k is equal to or larger than n and equal to or smaller than n multiplies each d k by a corresponding c k k is equal to or larger than n and equal to or smaller than n then adder circuit 72 adds the products obtained by the above multiplication operation the coefficients c k are determined so that the total of the 2n 1 coefficients is equal to 1 and c k is equal to c k given the above conditions and equ 27 the frequency response function shown in equ 28 is obtained equ11 the above equation equ 28 is reformed to the following form by introducing equation equ 27 the amplification characteristics a w of the above filter is expressed by equ 30 below the phase characteristics p w of the filter and delay interval u03c4 are expressed by equ 31 and equ 32 below respectively the above equations show that the delay interval of the filter is independant of the coefficients c k by virtue of this characteristic of the filter mentioned above variation of timbre without changing the pitch becomes possible a musical sound synthesizer can be created by making use of a delay circuit as described in the first or second preferred embodiments.