text: next , description will be given with respect to the preferred embodiment of the present invention . fig3 is a block diagram showing the electric configuration of the musical tone synthesizing apparatus according to the first embodiment of the present invention , wherein parts identical to those shown in fig2 will be designated by the same numerals , hence , description thereof will be omitted . in fig3 ja 1 designates a junction for carrying out the simulation of a first tone hole ( i . e ., a tone hole which is the most adjacent to the reed ). junction ja 1 multiplies coefficient r 21 by progressive wave data f 1 which obtained from a bi - directional transmission circuit bd 1 , by using a multiplier m 21 . then , the result of the multiplication is transmitted to the bi - directional transmission circuit bd 2 as progressive wave data f 2 . the junction ja 1 also multiplies coefficient r 11 by the progressive wave data f 1 by using a multiplier m 11 , and adds the result of multiplication ( r 11 f 11 ) to reflected wave data r 2 which is obtained from a bi - directional transmission circuit bd 2 by using an adder a 11 , and transmits the result of the addition ( r 2 + r 11 f 11 ) to the bi - directional transmission circuit bd 1 as reflected wave data r 1 . junctions ja 2 and additional junctions ( not shown ) simulate the other tone holes , and they are configured similar to the junction ja 1 . herein , each of coefficients r 11 , r 21 , r 12 , r 22 ( and coefficients for other junctions ) to be supplied to the corresponding multipliers m 11 , m 21 , m 12 , m 22 ( and multipliers for other junctions ) are switched by a coefficient control circuit 100 in accordance with tone hole operation data . more specifically , in the case where the first tone hole is closed , the coefficient r 21 is set to a relatively large value and the coefficient r 11 is set to a relatively small value . on the other hand , in the case where the first tone hole is opened , the coefficient r 21 is set to a relatively small value and the coefficient r 11 is set to a relatively large value . each coefficient is changed over between two values , in which one value corresponds to full - open state and the other corresponds to full - close state . alternatively , the value of each coefficient may be continuously varied in response to the opening area of the corresponding tone hole . according to this musical synthesizing apparatus of this embodiment , for example , in the case where the first tone hole is opened , output data of rom 11 is transmitted to the junction ja 1 wherein the output data is attenuated by a pre - specified attenuation ratio . next , the attenuated output data is returned toward the adder 13 . on the other hand , in a bi - directional transmission circuit bd 2 which is located at next stage , the progressive wave data from rom 11 is attenuated to a very small value . hence , in this case , the reflected wave data , which is returned to the adder 13 equals to the sum of data which are reflected at junctions ja 1 , ja 2 , ( and other junctions ) and the terminal circuit trm , wherein the data reflected at the junction ja 1 is the largest . consequently , tone pitch is determined in accordance with the reciprocation period of the data which is transmitted through the transmission circuit bd 1 . furthermore , in this case , reflected data from respective parts excepting the junction ja 1 are also returned to the adder 13 . hence , propagation of pressure wave in certain wind instrument is simulated with high - fidelity . next , in another case where the first tone hole is closed and the second tone hole is opened , output data of rom 11 is slightly attenuated at the junction ja 1 , and then reached to the junction ja 2 . such output data is transmitted through the junction ja 2 , and returned . consequently , tone pitch is determined in accordance with the reciprocation period of the data which is transmitted through the transmission circuits bd 1 , bd 2 . furthermore , in other cases where other tone holes are opened , similar operations are carried out . thus , according to the musical synthesizing apparatus of this embodiment , both of the propagation of pressure wave which is transmitted toward the terminal portion in certain wind instrument and the propagation of pressure wave which is reflected at the terminal portion and transmitted toward the reed are simulated faithfully with reduced amount of hardware or software operations . fig4 is a block diagram showing the electric configuration of the musical tone synthesizing apparatus according to the second embodiment of the present invention . first of all , the above - mentioned first embodiment contains delay circuits for both progressive wave data and reflected wave data . in contrast , in the second embodiment of the present invention , only progressive wave data is delayed by delay circuits def 1 , def 2 , . . . and def m transmitted to the terminal circuit trm . each delay circuit def i ( where i = 1 to n ) have a delay time that equals to each sum of the delay times of df i and dr i in the first embodiment of the invention . thus , according to above - mentioned construction , similar operation of the first embodiment is executed . moreover , as shown in fig4 this embodiment contains a junction jb 1 instead of the junction ja 1 in fig3 . the junction jb 1 contains a low - pass filter ( lpf ) ml 11 for filtering the output data of multiplier m 11 in order to simulate the sound - loss at the tone hole . the junction jb 1 includes multipliers m 11 and m 21 having coefficients r11 and r21 respectively . thus , according to this embodiment , smaller scale of apparatus is achieved as compared with the first embodiment , by decreasing the number of delay circuits . or , in the case where the dsp is adopted for the musical tone synthesizing operation , smaller amount of software is achieved as compared with the first embodiment . fig5 is a block diagram showing the electric configuration of the musical tone synthesizing apparatus according to the third embodiment of the present invention . first of all , in the above - mentioned second embodiment , the output data of the delay circuit dff 1 is supplied to the multiplier m 11 . in contrast , in the third embodiment of the present invention , multi - stage delay circuit mff is adopted instead of the delay circuits dff 1 and dff 2 in the second embodiment . herein , the output data at n - th stage and ( n + 1 )- th stage of the mff are picked - up , and the picked - up data are multiplied by coefficients ( 1 - m ) and m at multipliers ma and mb respectively . next , the results of multiplications are added together by an adder am . then the addition result of am is supplied to an multiplier m 11 . in the multi - stage delay circuit mff , data output points ( e . g ., n - th and ( n + 1 )- th stages in fig5 ) are determined in accordance with approximate positions of tone holes formed in the wind instrument . the coefficients ( m - 1 ) and m are the coefficients which are obtained by carrying out the linear interpolation on the progressive wave data based on the output data from n - th and ( n + 1 )- th stages of mff according to the exact positions of the tone holes . each coefficient has the decimal value which ranges from 0 to 1 . therefore , data ft which is outputted from the adder am can be represented by the following formula ( 10 ). in the above formula , f ( n ) designates the output data of n - th stage , and f ( n + 1 ) designates the output data of ( n + 1 )- th stage . therefore , progressive wave data which simulates the actual pressure wave of air at the tone hole is obtained , and transmitted to the multiplier m 11 and m 21 . hence , according to this embodiment , it is possible to synthesize the musical tone corresponding to the exact positions of the tone holes . furthermore , according to this embodiment , musical tone synthesizing control corresponding to the pitch - bend and vibrato performance , is applicable . that is to say , in the case where the pitch - bend performance is simulated , coefficients ( 1 - m ) and m are varied in accordance with certain curve at the beginning of tone - generation , and they are converged to values corresponding to the actual positions of tone holes after certain time has passed . hence , at the beginning of tone - generation , the tone pitch of the sound is varied , so that the pitch - bend performance can be simulated . further , in another case where the vibrato is simulated , coefficients ( 1 - m ) and m are varied in accordance with to a certain sine curve . herein , tone pitch of the sound is varied , so that the vibrato performance can be simulated . in the embodiments described heretofore , the non - linear function is realized by rom 11 . however , it is possible to embody the non - linear function by use of random - access memory ( ram ), operation circuit and other non - linear elements . of course , the present embodiments are not limited to synthesize the wind instrument tone , hence , it is possible to synthesize the stringed instrument tone in which the size of string is not constant in one string , and also synthesize the reverberation effect applied tone and the like in the complicated three - dimensional space . as described heretofore , this invention may be practiced or embodied in still other ways without departing from the spirit or essential character thereof . therefore , the preferred embodiments described herein are illustrative and not restrictive , the scope of the invention being indicated by the appended claims and all variations which come within the meaning of the claims are intended to be embraced therein .