Walsh function tone generator and system
United States Patent [191 Woron 1 Apr. 22, 1975 1 WALSH FUNCTION TONE GENERATOR {73] Assignee: Allen Organ Company. Macungie.  
 [22] Filed: Dec. 12. 1972 [21] Appl. No.: 314,480  
 [52] US. Cl. 84/1111; 84/101; 84/119;  
  84/D1G. 23&#39;. 235/197 [5]] Int. Cl. G101: 3/00 [58] Field oiSearch 84/101. 1.11. 1.19. 1.04.  
 84/DIG. 23. DIG. 8. 1.21. 1.12, 123&#39;. 235/197; 179/15 BC. l SA [56] References Cited UNITED STATES PATENTS 1.956.350 4/1934 Hammond 84/123 X 3.410.948 11/1968 Ishibashi et a1. 84/l.1 l 3.505.461 3/1970 Omura ct a1 84/].01  
 3.509.454 4/1970 Gosscl 84/1111 X 3.534.144 10/1970 Ring 84/123 X 3.590.131 6/1971 Rcyers 84/1 01 3.601.518 8/1971 Hill 84/1 19 3.636.231 l/1972 Schrccongost et a1 84/123 3.702.370 11/1972 Hallman 84/101 3.743.756 7/1973 Fransscn et a1 8411.03 X  
 FOREIGN PATENTS OR APPLICATIONS 1.902.376 9/1969 Germany 84/1111 OTHER PUBLICATIONS Alan Douglas. Electrical Synthesis of Musical Tones. Electronic Engineering. July. 1953. page 278. J. W. Beauchamp. Additive Synthesis of Harmonic Musical Tones.&#34; Journal of the Audio Engineering Society. October 1966. pages 332-333.  
 Harrnuth; Henning F.. A Generalized Concept of Frequency and Some Application,&#34; IEEE Trans. on Inform. Theory. May 1968. pages 375-382.  
 Lebert. Walsh Function Generator for a Million Dif ferent Function.&#34; and Bobwatter. Analog Sequency SAL SKBNAL GE&#39;QRAYGI Analysis and Synthesis of Voice Signals. Applications of Walsh Functions Symposium and Workshop 1970. Proceeding U.Sv Dept. of Comm.. 5285 Port Royal Road. Springfield Va.. 22151 Primary Examiner-Richard B. Wilkinson Assistant Examiner-U. Weldon Attorney. Agent. or FirmSeidel. Gonda &amp; Goldhammer [57] ABSTRACT A Walsh function tone generator uses a summing means to sum a plurality of digital Walsh function signals to produce a tone outputv The Walsh function generator may be comprised of a clock circuit. a plurality of frequency dividers for dividing the output of the clock circuit and a plurality of exclusive-OR gates for generating the various orders of the Walsh function signals. The summing means may include means for weighting the various orders of the Walsh function signals. such as weighting resistors. The Walsh function tone generator as used in an electronic musical instrument may be provided with bilateral electronic switches between the output of the Walsh function generator and the input of the summing means. The electronic switches may be used in conjunction with an attack and decay generator to provide an output wave form having the desired attack and decay characteristics.  
 The purpose of the above abstract is to provide a non-legal technical statement of the disclosure of the contents of the instant patent application and thus serve as a searching-scanning tool for scientists. engineers and researchers. Accordingly. this abstract is not intended to be used in understanding or otherwise comprehending the principles of the present invention hereinafter described in detail. nor is it intended to be used in interpreting or in any way limiting the scope or fair meaning of the claims appended hereto.  
 20 Claims, 10 Drawing Figures MTENTEE AFR 22585 susnsurs SAL SIGNAL GENERATOR SAL(3,t) CLOCK T 28 f&#39; F 2? 34 26 F SAL(?,t)  
  FLIP FLOP SAL(5,t) 30 4 $54 73 48 FLIP SAL(6,U FLOj 36 40 fi sAum) gig; 2x22;  
  ,t 46 SA (8,t)  
 j 56 swam SAL(IO,t)  
 FIG. 3 SALU 1,0  
  42 5 SAL(I2,t)  
 I SALHEIJ) I SAL(I4,t)  
 PATENIEUmzema 3878&#39;749 sum u or g I L I ELECTRONIC SWITCH &#39;w\,-4|  
  H j FIG. 4  
 ELECTRONIC SWITCH &#39;vwo I N62 F ELECTRONIC SWITCH -WW-l I ELECTRONIC SWITCH I ELECTRONIC SWITCH 80 I-FILTER T OUTPUT H j P ELECTRONIC SWITCH W b I F ELECTRONIC SWITCH W4 SAL t ELECTRONIC SWITCH h 82 O 72 \TTACK AND DECAY GEN PAIENIEDIPRZZ I975 ELECTRONIC SWITCH ELECTRONIC SWITCH ELECTRONIC SWITCH &#39;I- ELECTRONIC SWITCH saw 5 or g SWITCH IGO ELECTRONIC SWITCH ELECTRONIC ACE.  
 c; KEY  
 0 3- B&#39;GEDACKT TONE GENERATOR NC? SIGNAL MODULATING GENERATOR CIRCUIT FIG. HA  
 WALSH FIQNCTION TONE GENERATOR AND SYSTEM BACKGROUND OF THE INVENTION The present invention relates to a Walsh function tone generator and system. More particularly. the present invention relates to a Walsh function tone generator in which predetermined Walsh functions are summed in order to generate a predetermined tone.  
  Heretofore tone generators and especially tone generators used in electronic musical instruments were built using capacitive and inductive elements based on the sine and cosine functions. The capacitive and inducti\e elements used in these tone generators were both bulky and expensive. This is especially true at the lower frequencies which are used in the production of music.  
  In accordance with the present invention. Walsh functions are used too synthesize complex wave shapes such as audio wave shapes. Walsh functions per se have been known for some time. For example. reference may be had to the following articles and others fora detailed mathematical discussion of Walsh functions: A Closed Set of Orthogonal Functions.&#34; Am. J. Math.. \&#39;ol. 55. pp. 544. I933: A Generalized Concept of Frequency and Some Applications.-- IEEE Transactions on Information Theory. \&#39;ol. lTl-l. May. I968 and Applications of Walsh Functions in Communications. IEEE Spectrum. November. I96  
  The walsh functions form a complete. orthogonal sys tern of functions. In this respect. they are similar to the complete. orthogonal system of functions formed by the sine and cosine functions. The Walsh functions are comprised of two functions which are known as the sal function and the cal function. The sal function is somewhat analogous to that of the sine function in that they arc asymmetric or odd functions. The cal function and the cosine function are somewhat analogous in that they are symmetric or even functions.  
  The sal and cal functions of the Walsh function family may he of an unlimited number of orders. This is somewhat similar to the sine or eosinc signals which may be of an unlimited number of different frequencies. The notation used herein is sal (S. 1) or cal (5. (I wherein the 5&#34; indicates the order of the sal or cal function and the &#34;1&#34; indicates that it is a function of time.  
  A significant advantage in the use of Walsh functions is that the Walsh functions are essentially binary. That is. the Walsh function signals have only two levels or conditions. The fact that a Walsh function may have only two conditions at any point other than a point of discontinuity is a significant advantage since it allows the use of modern digital integrated circuit technology to produce any desired complex wave form. The use of integrated circuit technology enables the generation of a large number of Walsh functions on a single integrated circuit chip.  
 SUMMARY OF THE INVENTION The present invention provides a new and unobvious tone or wave form generation means which is particularly useful in electronic musical instruments. The term tone as used herein means any single frequency tone or any complex wave form. The present invention provides a significant advantage in that the tone may be generated by the use of digital electronic techniques Briefly. in accordance with the present invention. there is provided an apparatus for producing a musical tone having means for generating a plurality of digital Walsh function signals and means for summing prede termined ones of the plurality ofdigital Walsh function signals in order to produce a tone output. Predetermined ones of the plurality of digital Walsh function signals may be weighted by predetermined amounts prior to summing if the desired tone so requires.  
  In accordance with a more detailed aspect of the invention. a digital Walsh function signal generator may be comprised of a clock circuit feeding a plurality of frequency dividers. The output of the clock circuit and the outputs of the frequency dividers are fed to a plurality of exclusive-OR logic circuits. The walsh function signals at the outputs of the escIusive-OR- logic circuity are fed to electronic switches. The digital Walsh function signals control the electronic switches gating an attack and decay modulated keying signal. The outputs of the electronic switches may be weighted by means of weighting resistors or other suitable means. The weighted Walsh function signals are then summed in a summing ltl&#39;IIPllfIct&#39;.  
 BRIEF DESCRIPTION OF THE DRAWINGS For the purpose of illustrating the invention. there are shown in the drawings forms which are presently preferred; it being understood. however. that this invention is not limited to the precise arrangements and instrumentalitics shown.  
  FIG. I is a schematic diagram in block diagram form of an apparatus in accordance with the present IIIYCI&#39;I&#39; tion.  
  FIG. 2 is a drawing of wave forms generated in practicing the present invention.  
  FIGS. 3 and 4 are schematic diagrams. partially in block diagram form. ofan embodiment of an apparatus in accordance with the present invention.  
  FIG. 4A is a schematic diagram. partially in block diagram form. of another embodiment of the apparatus of FIG. 4 in accordance with the present invention.  
  FIG. 5 is a schematic diagram. partially in block diagram form. showing the electronic switches of FIG. 4 in greater detail.  
  FIG. 6 is a schematic diagram of exclusive-OR logic circuitry in accordance with the present invention.  
  FIG. 7 is a table illustrating one of the principles of the present invention.  
 m FIG. 8 is a schematic diagram in block diagram form of an electronic musical instrument in accordance with the present invention.  
  FIG. 8A is a schematic diagram in block diagram form of another embodiment of an electronic musical instrument in accordance with the present invention.  
 DESCRIPTION OF THE PREFERRED EMBODIMENTS function generator 13. The cal function generator produces a cal function outputs cal (1.1). cal (a. r). The cal outputs are weighted by variable resistors [4 in order to provide the cal coefficients a I I ala respectively. The sal function generator 13 produces sal function output signals sal (1.!) .sal (n.1l. Similarly. variable resistors I6 provide the desired weighting of the sal function output signals. The cal function signals. sal function signals and wal (O. I) function signal are summed in summing amplifier I8 to produce the desired wave form output depending upon the setting of the variable resistors 14. I6 and 20.  
  In general. both sal and cal signals are needed to synthesize an arbitrary wave shape. Ho\vc\ er. in the case of the generation of musical tones which are intended for perception by a human ear. certain optimizations may be made so that only sal signals. for example. may be required to synthesize the desired audio tones. It is known that the ear can perceive changes in amplitude of various harmonics in a musical tone. However. changes in the relative phasing of the harmonics in the audio sound create very little change in the perception ofthe sound by a human ear. Therefore. phasing of har monics in the desired musical tone may be arranged in such a way as to optimize the synthesis. It has been found that arranging the phasing in the tone or sound so that each harmonic is in phase with the fundamental produces an audio wave shape which may be generated using only sal signals. In addition. Wal lo. I). the dc. term is not needed. Therefore. the use of sal functions alone is sufficient to produce good quality audio tone or music. The wave forms of the first sixteen orders of sal signals are shown in FIG. 2.  
  As discussed above. the Walsh functions form a com pletc. orthogonal system of functions. The Walsh functions are adaptable to a Fourier type of analysis. In other words. Walsh-Fourier series expansions of functions in terms of the Walsh cal and sal functions have been defined in the literature and Walsh-Fourier transforms have been derived. Therefore. a significant advantage of using Walsh functions in the generation of tones is that methods exist for calculating the orders of sal or cal functions required and the amplitude ofthcse functions. or in other words. the value of the weighting resistors for the particular cal or sal function.  
  Referring now to FIGS. 3 and 4. there is shown another embodiment of the present invention. In FIG. 3. there is shown a sal signal generator for generating the first sixteen sal signals as shown in FIG. 2. As shown in FIG. 3. a clock circuit 22 is provided. The output of clock circuit 22 is a pulse signal having a frequency or repetition rate which is a predetermined number of times the fundamental frequency ofthe tone being generated. Asa specific example in FIG. 3. the output of the clock circuit would be sixteen times the fundamental frequency of the tone being generated.  
  The output of the clock circuit is fed via line 24 to flip-flop circuit 26. one input of exclusive-OR gate 28 and the output line labeled sal (16. I). That is. in the specific example being illustrated. the output of the clock circuit forms the sixteenth order sal signal. The clock signal on line 24 in FIG. 3 is labeled E.  
  The output of flip-flop circuit 26 is a pulse output signal having a frequency one-half of that ofthe Clt ck circuit 22 output. The output signal of flip-flop circuit 26 is labeled D. The output signal D of flip-flop circuit 26 is fed to flipflop 30. one input of exclusive-OR gate 28.  
 one input ofexclushe-OR gate 32. one input of exclusi e-OR gate 34. and directly to the output labeled sal (8. I).  
  The output signal of flip-flop circuit 30 is labeled C. The C signal has a frequency one-fourth that ofthe output of clock circuit 22. The signal C is fed to flip-flop circuit 36. one input ofexclusive-OR gate 32. one input of exclusive-OR gate 38. one input of exclusive-OR gate 40. one input of exclusive-OR gate 42. one input ofcxclusive-OR gate 44. and directly to the output line labeled sal (4. r).  
  The output signal of flip-flop circuit 36 is labeled B. The output signal B has a frequency or pulse repetition rate of one eighth that of signal E which is the output of clock circuit 22. Signal B is fed to the input of flipflop circuit 46. In addition. signal 8 is fed to one input of exclusiveOR gates 54. 40. 48 and S0 and directly to the output labeled sal (2. r).  
  The output of flip-flop circuit 46 is a signal A having a frequency of one-sixteenth that of signal E. The output signal A offlip-flop circuit 46 is fed to one input of exclusive-OR gates 52. 54. 56 and 44. In addition. signal A is fed directly to the output labeled sal (I. I).  
  There is shown in FIG. 7 a table for indicating which of the signals A. B. C. D and E are to be combined by modulo two addition in order to produce the various sal signals. As shown in FIG. 7. the top row indicates the order of the sal function. The letters in the various columns indicate that those signals must be combined by modulo two addition in order toi produce the particular order of sal function indicated at the top of the particular column. For example. the first order sal function is simply the signal A. The eleventh order sal function is produced by the modulo two addition of signals A. B. C. D and E. Similarly. the table in FIG. 7 indicates the derivation of all of the first sixteen orders of sal signals.  
  Referring now to FIG. 6 in conjunction with FIG. 3. there is shown the exclusivcOR circuitry for generating the third order sal signal. This circuitry is shown alone in FIG. 6 and in conjunction with the remaining exclusive-OR circuitry in FIG. 3. It may be seen that signals A and B are applied to exclusive-OR gate 54. An exclusive-OR gate. as is well known. produces a sig nal output when there is a signal present on one of its inputs but not both. Therefore. cxclusive-OR gate 54 produces an output when either signal A or signal 8 is present. but not when both signals A and Bare present. The output oifexclusive-OR gate 54 is fed as one input to exclusive-OR gate 38. Exclusive-OR gate 38 receives as its second input the signal C. Exclusive-OR gate 38 therefore produces an output when either one or three of the signals A. B and C are present. In a similar man our. the other orders of sal functions are generated by the occurrence of an odd number of signals indicated in the particular column in FIG. 7.  
  It is believed unnecessary to trace and discuss every line in FIG. 3 since the operation of the circuitry is apparent in view of the above discussion. However. the generation of the ninth order sal signal will also be traced out as an additional example of the operation of the circuitry shown in FIG. 3. Sal (9. r) is the output signal of exclusive-OR gate 56. Exclusive-OR gate 56 receives as one ofits inputs signal A which is the output of flip-flop circuit 46. The other input of exclusive-OR gate 56 is received from the output of exclusive-OR gate 28. Exclusive-OR gate 28 receives signals D and E as its inputs. Therefore. the output signal sal (9.1) is the modulo two addition of signals A. D and E as indicated in FIG. 7. i  
  The output sal signals of the sal signal generator shown in FIG. 3 may be fed directly to the summing means 18 as illustrated with respect to FIG. I. In the al&#39; ternative. the output sal signals of the sal signal generator may be fed to an electronic switching network as shown in FIG. 4. The electronic switching network shown in FIG. 4 provides a means of attack and decay modulating the tone to be produced. Selected ones. some or all. of the sal out puts generated by the circuitry shown in FIG. 3 will be applied to the gate electrodes of the electronic switches shown in FIG. 4.  
  The foregoing describes the generation of Walsh sal functions. Walsh function generators for generating cal functions or both cal and sal functions are known to those skilled in the art. See. for example. Lebert. Walsh Function Generator for a Million Different Functions. Applications of Walsh functions Symposium and Workshop. I970 Proceedings. United States Department of Commerce. pages 52-54.  
  Referring now in detail to FIG. 4 in conjunction with FIG. 5. there is shown a plurality of electronic switch means 60 each having a control gate input line 62. Electronic switch means 60 functions as a bilateral single pole double throw switch. Electronic switch means 60 is shown in greater detail in FIG. 5 wherein it is seen that each electronic switch means 60 includes a first electronic single pole single throw switch 64 and a second electronic single pole single throw switch 66. The control gate input 68 of electronic switch 66 is provided with an inverter 70. Asa specific example ofsuitable hardware. electronic switch 60 may be a complemcntary-symmetry metal-oxide semiconductor of the type (D 4UI6A Quad Bilateral Switch manufactured by RCA. However. this specific example of hardware is not intended to be limiting and any other suitable electronic switch may be used in practicing the invention.  
  Referring back now to FIG. 4. there is shown a key or key switch 72 which operatively controls attack and decay generator 74. The output of attack and decay generator 74 is a wave form as shown at 76. The wave form output of attack and decay generator 74 is applied to one of the inputs ofeach electronic switch means 60 directly and is applied to the other input of each of the electronic switch means 60 through analog inverter 78.  
  The sal output signals from the sal signal generator shown in FIG. 3 are applied to the control gate input lines either directly or through digital inverters 80. The presence or absence of an inverter is determined by whether the component sal function making up the tone is to have a positive or negative coefficient.  
  There is shown in FIG. 4 wave form 82 which is generated on line 84 for an attack and decay wave form 76 as shown at the output of attack and decay generator 74 and a sal signal on control gate input line 62. As may be seen from wave form 82. electronic switch means 60 effectively gates either the attack and decay wave form 76 or its inverse from analog inverter 78 in response to the sal signal appearing on control gate input line 62.  
  The outputs ofthe electronic switch means 60 are fed through weighting resistors 86 to summing amplifier 88. The output of summing amplifier 88 is fed to filter 90. Filter 90 may be a low pass filter which eliminates any high frequency noise due to the digital nature of Ill the sal signals. The output of filter 90 is the desired tone.  
  Referring now to FIG. 4A. there is shown another embodiment of an electronic switching arrangement which does not require the use of inverters to produce the inverted coefficient. The embodiment shown in FIG. 4A uses both inverting and non inverting input terminals of an operational amplifier in order to produce an output corresponding to both positive and negative coefficients.  
  The attack and decay wave form is applied to each of the electronic switches l5I-l53 and [61-163 via line 150. The inverted attack and decay wave form is applied to each of the electronic switches 151453 and I6I-I63 via line I60. The dotted lines between elec&#39; tronic switches I52 and I53 indicate that numerous other electronic switches may be used depending upon the tone to be produced. Similarly. the dotted lines between electronic switches ]62 and 163 indicate that any desired number of electronic switches may be used to supply the non-inverting terminal of operational amplifier I80.  
  Sal signals which are to have inverted coefficients would be applied to control gate input lines 154456 of electronic switches 151-153. respectively. Sal signals which would correspond to non-inverted signals in the output tone are applied to control gate input lines 164-166 of electronic switches I6l-I63. respectively.  
  The gated outputs of electronic switches II 53 are applied to the inverting input I78 through their weighting resistors 157-159. respectively. The gated outputs of electronic switches l6ll63 are applied to the non-inverting input terminal I79 ofoperational amplifier 180 through weighting resistors 167-169. respectively. As is well known. operational amplifier I will produce a signal appearing on non-inverting input 179 in amplified form and the signal appearing on inverting input 178 in an inverted and amplified form. The output of operational amplifier I80 is applied to a filter circuit (not shown) and used in a manner similar to the output of amplifier 88 in FIG. 4.  
  Referring now to FIG. 8. there is shown in block diagram form an electronic musical instrument such as an electronic organ. There is shown a master clock 92 which produces a pulse output having a frequency which is N times the highest note frequency to be produced. The output of master clock 92 is fed to a top octave synthesizer 94. Top octave synthesizers are wellknown in the art. commercially available and need not be described herein in detail. Top octave synthesizer 94 produces frequency output signals having frequencies of N times the frequencies of the notes C C D... l3, and C In an embodiment as described with respect to FIGS. 3 and 4, N would equal 16. However. N may equal any suitable number sufficient to give the desired degree of accuracy. That is. as N increases. the accuracy of the tone produced also increases.  
  The output of top octave synthesizer 94 which is la beled NC. is fed to cascaded frequency dividers 96. The other outputs of top octave synthesizer 94 would be fed to similar sets of cascaded dividers.  
  The outputs of the dividers 96 are fed to Walsh signal generators 98. The outputs of the Walsh signal genera tors are fed to keying-modulating networks I00. The keying-modulating networks 100 receive an input from keyboard 102. The keying-modulating networks 100 perform the function as described with respect to FIG. 4.  
  The outputs of the keying-modulating networks 100 are fed to summing-voicing circuits 104. The summingvoicing circuits I04 receive an input from the stop switches 106 which determine the voice of the tone to be produced (that is. the combination of weighting resistors 8(1). The outputs of the summing-voicing circuits are applied to speaker 108 through amplifier I10.  
  Referring now to FIG. 8A. there is disclosed another embodiment of a musical instrument in accordance with the present imention. la the embodiment shown in FIG. 8A. a top octave synthesizer is not required. In accordance with the embodiment of FIG. 8A. a complete tone generator is used for each key-stop combination. A (I, -8 foot Gedackt tone generator is shown at 202 in FIG. 8A. Additional stops playing a (I note would be provided by additional tone generators tuned and \oiced accordingly The embodiment shown in Fl(]. SA has the musical advantage that the various notes are independent or in other words are not phase locked.  
  Referring now more particularly to H6. 8A. there is shown a clock 204 which provides a frequency at N times the (I. note frequency. The output ofclock circuit 204 is fed to Walsh signal generator 206. The output of Walsh signal generator 206 is fed to keying modulating circuit 208. Keying-modulating circuit 208 receives an input from the C key or key switch 210. The output of keying-modulating circuit 208 is fed to summing-voicing circuit 2 It). The output of summingvoicing circuit 2) is fed through the 8 foot (icdackt stop switch 212 to amplifier 214. Amplifier 214 also receivcs output signals from the other tone generators lnnt shown) in the musical instrument. The output of amplifier 214 is fed to speaker 216. Speaker 216 com \crts the amplified electrical signals into musical sound waves.  
  It will be apparent to those skilled in the art that various changes and modifications may he made within the spirit ofthe above teachings. For example. although the operation has been disclosed in detail with respect to sail functions. it is apparent that cal functions could be used as well. Various other types of logic may be used to generate the Walsh functions and various other keying and switching techniques may be used. Furthermore. the illustration of two embodiments ofelectronic musical instruments are only selected examples. and it is apparent that many variations may be made within the spirit of the present invention.  
  In view of the above. the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof and. accordingly. reference should be made to the appended claims. rather than to the foregoing specification as indicating the scope of the invention.  
  I claim: 1. Apparatus for producing a musical tone. compris ing:  
 means for summing predetermined ones of the plu rality of digital Walsh function signals to produce a musical tone output.  
  2. Apparatus in accordance with claim I including means for weighting predetermined ones of said digital Walsh functions by predetermined amounts. said weighting means being connected between said digital walsh function generating means and said summing means.  
  3. Apparatus in accordance with claim I wherein said digital Walsh function signal generating means includes means for generating a predetermined number of orders of cal function signals.  
  4. Apparatus in accordance with claim 1 wherein said digital Walsh function signal generating means includes means for generating a predetermined number of orders of sal function signals.  
  5. Apparatus in accordance with claim 1 wherein said digital Walsh function signal generating means includes means for generating a first predetermined number of cal function signals and a second predetermined numher of sal function signals.  
  6. Apparatus for producing a musical tone. comprising:  
 a clock circuit;  
 a predetermined number of frequency dividers. said frequency dividers producing submultiplcs of the clock frequency output of said clock circuit;  
 gating means for producing output signals in response to predetermined combinations of input sig nals from said clock circuit output and said frequcncy divider outputs to generate a predetermined number of orders of Walsh function signals:  
 means for generating a modulating envelope for modulating the Walsh function signals:  
 a predetermined number ofelectronic switch means.  
 said electronic switch means receiving said modulating envelope. said electronic switch means gating the modulating envelope in response to predetermined ones of the output Walsh function signals of said gating means: and  
 summing means. said summing means summing the gated outputs of said electronic switch means.  
  7. Apparatus in accordance with claim 6 including means for weighting the gated outputs of said electronic switch means.  
  8. Apparatus in accordance with claim 6 wherein said frequency dividers are flip-flops.  
  9. Apparatus in accordance with claim 6 wherein said gating means is comprised of exclusive-OR gates.  
  10. Apparatus in accordance with claim 6 wherein said electronic switch means receive the modulating envelope from an attack and decay generator. said attack and decay generator receiving a signal input from a key switch.  
  11. Apparatus in accordance with claim 9 wherein each of said electronic switch means is comprised of a first and a second electronic switch. said first and second electronic switches each being provided with an input. an output and gate terminal. the modulating envelope being applied to the input terminals of each of said first and second electronic switches. a predeter mined Walsh function signal being applied to said gate terminal of said first electronic switch and said gate ter minal of said second electronic switch through an inverter circuit.  
  [2. Apparatus in accordance with claim 6 wherein said gating means produces sal signals.  
  13. Apparatus in accordance with claim 6 including inverters for inverting predetermined ones of the Walsh function signal outputs of said gating means.  
  14. Apparatus in accordance with claim 6 wherein said summing means includes an operational amplifier provided with a non-inverting input terminal and an inverting input terminal. predetermined ones of the gated outputs of said electronic switch means being applied to said non-inverting input terminal and other predete rmined ones of the gated outputs of said electronic switch means being applied to said inverting input terminal.  
 15. An electronic musical instrument. comprising:  
 a clock circuit:  
 a top octave synthesizer. said top octave synthesizer receiving the output of said clock circuit and gen erating a predetermined number of frequency signal outputs having frequencies equal to N times the top octave frequencies;  
 a predetermined number of sets of frequency dividcrs. one set of frequency dividers being provided for each lop octave frequency signal output. each set of frequency dividers being provided with a pre determined number of frequency dividers; predetermined number of Walsh function generators for generating Walsh function signals in re sponse to predetermined combinations of the top octave frequency signal output and the outputs of the frequency dividers in a set:  
 means for generating a modulating envelope for modulating the Walsh function signals:  
 means for combining the modulating envelope with the Walsh function signals;  
 means for summing the modulated Walsh function signals: and  
 means for transducing the summed Walsh function signals into sound waves.  
  In. An electronic musical instrument in accordance with claim [5 wherein said generating means generates a modulating signal to provide a desired attack and/or decay keying signal.  
 fill  
  17. Apparatus in accordance with claim 15 including means for voicing the output of said summing means.  
 18. An electronic musical instrument. comprising:  
 a plurality of tone generators. each of said plurality of tone generators providing a predetermined tone output in response to being keyed. each of said plurality of tone generators being provided with a clock circuit. a Walsh tone generator. a keyingmodulating circuit and a summing circuit means. said clock circuit producing an output having a frequency equal to a predetermined number of times the basic tone frequency output ofthe tone generator. said Walsh signal generator receiving the output of said clock circuit. said keyingmodulating circuit receiving an input from a key corresponding to the particular generator and the output of said Walsh signal generator. the output of the keyingmodulating circuit being applied to a summing circuit means. said summing circuit means producing a predetermined tone output;  
 amplifier means. said amplifier means receiving the tone output ofeach of said plurality of tone generators: and  
 transducer means for converting the electrical output of said amplifier to a sound wave.  
  [9. An electronic musical instrument in accordance with claim 18 wherein said summing circuit means includes a voicing means.  
  20. Apparatus for producing a musical tone. comprising:  
 clock means for generating a clock signal at a frequency which is a predetermined number times the fundamental frequency of the musical tone to be generated;  
 means for receiving the clock signal and for generating a plurality of digital Walsh function signals;  
 weighting means for \veighting predetermined ones of said Walsh function signals by predetermined amounts; and  
 means for summing predetermines ones ofthe plural ity of weighted digital Walsh function signals to produce a musical tone output.  
 * s s we: