US 3884108 A
A pipe organ ensemble effect results when two similar pipes, slightly out-of-tune with respect to each other, are sounded together upon selection of a single instrument key. Herein, apparatus is disclosed for producing an ensemble effect in a computor organ of the type wherein musical notes are generated by computing the amplitudes at successive sample points of a musical waveshape and converting the amplitudes to sounds as the computations are carried out in real time. Each amplitude is computed during a regular time interval tx by separately calculating a set of "combined" Fourier components which are accumulated to obtain the sample point amplitude. Each nsumming order combined Fourier component is evaluated by summming a pair of sinusoid values associated respectively with the nominal tone and the frequency offset, "out-of-tune" tone. The sum is multiplied by a harmonic coefficient to establish the relative amplitude of that combined Fourier component.
Description (OCR text may contain errors)
United States Patent Deutsch May 20, 1975 PRODUCTION OF ENSEMBLE IN A duction by Nonlinear Waveshaping, Journal of the COMPUTOR ORGAN Audio Engineering Society, (U.S.A.), August, 1970,  Inventor: Ralph Deutsch, Sherman Oaks, Volume Number 413-417 Calif.
- Primary Examiner.loseph W. Hartary  Assignee: Nippon Gakki Seiz Kabushiki Kaisha, Hamamatswshi, Japan Assistant Exammer Stanley .l. Witk0wsl i Attorney, Agent, or FzrmAmbrose & Silber  Filed: Jan. 11, 1974  App]. No.: 432,684  ABSTRACT 52 US. Cl. 84/1.24; 84/D1G. 4; 235/152; Pipe ofgan ensemble efffic} 'esults when two Similar 235/197 pipes, slightly out-of-tune with respect to each other, 51 int. Cl GlOh 1/02; GlOh /02 are Smmded F 8 Of a Single  Field of Search 84/101, 103 L24, DIG 4; ment key. Herein, apparatus is disclosed for producing 235/152 197 an ensemble effect in a computor organ of the type wherein musical notes are generated by computing the  References Cited amplitrilides aIdS;lCCSSit\/C sglmple plotins of a musical waves ape an onver ing camp 1 u es 0 soun sas UNITED STATES PATENTS the computations are carried out in real time. Each 3,305,675 2/1967 Haase 235/197 amplitude i Computed during a regular time interval S et 3 22 t by separately calculating a set of combined Fou- 531 $1972 a i t 'g 4 X rier components which are accumulated to obtain the 3:809:786 5/1974 Deutsch 84/101 Sample Point F Each order SmmbiHeFl 3,809,788 5/1974 Deutsch. 84/1'01 Fourier component is evaluated by summming a pair 3,309,739 5/1974 Deutsch 0 34/101 of sinusoid values associated respectively with the 3,809,790 5/1974 Deutsch 84/101 n m tone and the frequency Offset, 3,809,792 5/1974 Deutsch 84/124 tone. The sum is multiplied by a harmonic coefficient 3,809,876 5/1974 Byram 235/l97 to establish the relative amplitude of that combined 3,831,015 8/1974 Hoff, Jr 235/197 OTHER PUBLICATlONS Richard A. Schaeffer, Electronic Musical Tone Pro- Fourier component.
12 Claims, 3 Drawing Figures I n l? sin (nq R++) a],
sinn 12 ee 37 58 f w q f i-mRMomc sinusoio TFIBLE I L SINUSOID TABLE 1 22 AMPL'TUDE MULTIPLIER as l l ar 23 C" f g-i) MEMORY ADDRESS MEMORY minimizes 4 fl'-'l mb'md DEconsq DE -005R coUNTER j HARMONIC i; COEFFICIENT cp 33 3a 44 l 23 I5 PIG MEMORY ADDER f I4 Low FREQUENCY 32L j DIVIDER 29 44 1 DIGITAL To nqR/k 29 1 ANALQG HRRMONIC INTERVAL "EMORY CONVEQTER ADDRESS oivioziz ADDER 27 L, nqQ/K' a 45 9 g :1 47 26 GATE 24 scum: svsrEM q]? 20 L I! NOTE 'NTERVAL tx FREQUENCY NUMBER -17 MEMORY no DUE? DECODERDRESS L (MODULO 2w) ,8 R MEMOIZY 50 FREQUENCY 'NSFRUME'NT To DMDER 52 OFFSET i MEMORYH KEYBOARD 'ro ADDER 38 FIIIENIEI] W20 5 RELATIVE AMPLITUDE I I I I I l l I I I I I I I I I I I I I I I I I SHEET 10F 2 lac-.1.
l I I I I I I I I l I I I I I I I I l I I I I I I f f 8f 9f f IIf I2f I3f I4f ISf I6f FREQUENCY [0Q ,I IG 3 fag 3/ TO I-IAnMoNIc q]? Tr AMPLITUDE 4O sm n (q,R+ 6O 38 5ln-W- nqjl MULTIPLIER sINusoID TABLE SINUSOID TABLE I 3! MEMORY ADDRES MEMORY ADDRESS DECODER DECODEI? f) 58 57 n f 28 mg? CLEAR HARMONIC INTERVAL HARMONIC INTERVAL CLEAR ADDER 55 maps? 7 ap cp GATE 26 GATE 20 54% ADDED R NOTE INTERVAL A9135? ,7
DIVIDER A I I K 8L GATE 4 FREQiEEIfiS RVNUMBER t' I l5 s INSTRUMENT KEYBOARD SWITCHES wimanwm 3,884,108
SHEET 2 OF 2 muq Hr C5 PRODUCTION OF ENSEMBLE IN A COMPUTOR ORGAN BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the production of ensemble in a computor organ.
2. Related Applications This invention is related to the inventors copending US. patent applications Ser. No. 225,883 filed on Feb. 14, 1972 entitled COMPUTOR ORGAN now US. Pat. No. 3,809,786, Ser. No. 298,365 filed on Oct. 17, 1972 entitled COMPUTOR ORGAN USING PARALLEL PROCESSING nowU.S. Pat.No. 3,809,788, Serv No. 321,231 filed on Jan. 5, 1973 entitled PRODUCTION OF CELESTE IN A COMPUTOR ORGAN now US. Pat. No. 3,809,792, and Ser. No. 374,680 filed on June 28, 1973 entitled ANI-IARMONIC OVERTONE GEN- ERATION IN A COMPUTOR ORGAN.
3. Description of the Prior Art An ensemble effect is produced in a pipe organ by using two or more ranks of pipes, one of which is tuned to the nominally correct 8-foot frequency while another is slightly out-of-tune. When a single keyboard switch is depressed, both the in-tune and out-of-tune pipes are sounded. The resultant beat frequencies are most pleasant to the listener. An ensemble effect using two sets of pipes also is known as tone doubling. More complex effects are achieved using three or four sets of pipes to produce trio or quartet" ensemble.
In conventional electronic organs an ensemble effect is obtained by using separate sets of oscillators offset in frequency with respect to the nominal tone generators. When mixed electronically or acoustically, the combined generator outputs produce a reasonable facsimile of ensemble. Alternatively, two separate and complete electronic organ systems, detuned with respect to each other and used to drive different speakers, may be used to produce ensemble. Such approaches are expensive, and virtually rule out trio or quartet ensemble as beyond acceptable cost limits.
An object of the present invention is to implement ensemble in a computer organ. The system add-on is inexpensive and readily facilitates doubling, trio or quartet ensemble effects.
SUMMARY OF THE INVENTION In a COMPUTOR ORGAN of the type described in the above mentioned patent application Ser. No. 225,883, now US. Pat. No. 3,809,786, musical notes are produced by computing in real time the amplitudes X (qR) at successive sample points qR of a musical waveshape, and converting these amplitudes to notes as the computations are carried outv In accordance with the present invention, each sample point amplitude is computed during a regular time interval according to the relationship where q is an integer incremented each time interval 1,, the value n=1,2,3, W represents the order of the combined Fourier component being evaluated, C is a coefficient establishing the relative amplitude of the n" component and R is a number specifing the period of the waveshape. The resultant musical sounds will have an ensemble effect characterized by the presence of beats between two notes separated in frequency by the amount (1R (Eq. 21
where is a positive or negative constant.
The resultant musical notes produced by the computor organ will have a harmonic spectrum typified by that of FIG. 1. Therein the solid lines represent the Fourier components F r f at the nominally correct pitch. The broken lines designate the Fourier components F f' of the out-of-tune note, these being offset in frequency by an amount nqR/ from the corresponding true-pitch component but equal in amplitude thereto. The amplitude of the waveshape constituted by the two sets of components of FIG. 1 is represented by:
which is the equivalent of Equation 1.
Equation 1 readily is implemented in a computor organ since only one multiplication by C, is required to evaluate each combined Fourier component, and only a single summation is needed to establish each sample point amplitude X,,(qR). The waveshape amplitude contributions of the true and offset components are not separately evaluated and summed, as would be the case if Equation 3 were implemented. Accordingly, rather than requiring complete duplication of substantially the entire computor organ, including duplicate harmonic amplitude multipliers and accumulators, ensemble is obtained by the provision of straightforward circuitry for obtaining another sin value.
In the system disclosed herein, each combined Fourier component is calculated by dividing the quantity nqR by the constant adding nqR to the quotient, and obtaining the value simr/W(nqR+(nqRba) from a memory table of sinusoid values. Concurrently the value sin(1r/W)nqR is separately evaluated. The two sin values are added together, and the sum is multiplied by the associated harmonic coefficient C The resultant combined Fourier component amplitudes are summed in an accumulator to obtain the waveshape sample point amplitude. The system may be replicated to obtain trio or quartet ensemble.
Advantageously the constant K=2'" where m is an integer. Accordingly, in a binary implementation, division may be accomplished by right-shifting the quantity nqR (or alternatively, qR) in a shift register. The
3 amount of frequency offset Af is a matter of desig choice, but typically is between about 6 and I2 cents, where a cent is one-hundredth of a semitone (i.e.. there are 1,200 cents per octave). This constant-cents offset provides a greater deviation for high-pitched notes and a lesser deviation for low notes, resulting in a pleasing ensemble effect.
BRIEF DESCRIPTION OF THE DRAWINGS A detailed description of the invention will be made with reference to the accompanying drawings, wherein like numerals designate comprising parts in the several figures.
FIG. 1 is a harmonic spectrum typical of an ensemble effect.
FIG. 2 is an electrical block diagram of a computor organ configured to produce an ensemble effect.
FIG. 3 is an electrical block diagram of an alternative implementation of ensemble in a computor organ.
DESCRIPTION OF THE PREFERRED EMBODIMENTS The following detailed description is of the best presently contemplated modes of carrying out the invention. This description is not to be taken in a limiting sense, but is made merely for the purpose of illustrating the general principles of the invention since the scope ofthe invention best is defined by the appended claims.
Structural and operational characteristics attributed to forms of the invention first described also shall be attributed to forms later described, unless such characteristics obviously are inapplicable or unless specific exception is made.
The computor organ of FIG. 2 produces via a sound system 11 musical notes having an ensemble quality.' For each note selected by the keyboard switches 12, the instrument 10 computes the amplitudes at successive sample points of a waveshape characteristic of ensemble. The computations are performed in accordance with Equation 1. The combined Fourier components are summed algebraically in an accumulator 13 which, at the end of each computation time interval 2,, contains the amplitude at the current sample point. This amplitude is provided via a gate 14, enabled by the t, signal on a line 15, to a digital-toanalog converter 16 which supplies to the sound system 11 a voltage corresponding to the waveshape amplitude just computed. Computation of the amplitude at the next sample point subsequently is initiated, so that the analog voltage supplied from the converter 16 comprises a musical waveshape generated in real time and having ensemble characteristics. The period of the computed waveshape, and hence the fundamental frequency of the generated note, is established by a frequency number R selected by the keyboard switches 12. A set of such frequency numbers corresponding to the notes of the instrument is stored in a frequency number memory 17. At the end of each computation interval t,, the frequency number R associated with a selected note is supplied via a gate 18 and added to the previous contents of a note interval adder 19. Thus the contents of the adder l9, supplied via a line 20, represents the value (qR) designating the waveshape sample point currently being evaluated. Preferably the note interval adder 19 is of modulo 2W, where Wis the highest order Fourier component evaluated by the system 10. Satisfactory pipe organ synthesis is achieved when W=l6 combined Fourier components are evaluated by the system 10.
System timing is established by a clock 22 and a counter 23 of modulo 16. During each waveshape amplitude computation interval t, the clock 22 provides 16 timing pulses I to the counter 23. The counter 23 in turn provides consecutive timing pulses t,.,,, through t which enable calculation of the corresponding l6 combined Fourier components. The t signal on the line 15 is derived from the t signal slightly delayed in a delay unit 24.
Each of the calculation timing pulses r through r is supplied via an OR gate 25 to a gate 26. This gate 26 provides the value qR to a harmonic interval adder 27 whichis cleared at the end of each amplitude computation interval t Thus the contents of the harmonic interval adder 27 is incremented by the value (qR) at each calculation interval 2 through 1 so that the contents of the adder 27 represent the quantity (nqR). This value is available on a line 28.
An address decoder 30 accesses from a sinusoid table 31 the value sin(1r/W)nqR corresponding to the argument nqR received via the line 28. The sinusoid table 31 may comprise a read only memory storing values of sin(1r/W) for 0 s d) s W/2 at intervals of D, where D is called the resolutionconstant of the memory. With this arrangement, the value sin(1r/W)qR will be supplied on a line 31 from the sinusoid table 31 during the first calculation interval r During the next interval r the value sin(1r/W)2qR will be present on the line 31'. Thus in general, the value sin(1r/W)ngR will be provided from the sinusoid table 31 for the particular if" order component specified by the timing interval output from the counter 23.
Concurrently, the value sin(1r/W)(nqR+(nqR/K) is evaluated in the following manner. The quantity (nqR) present on the line 28 and supplied via a switch 29 and a contact 29a is divided by the constant in a divider circuit 32. .The quotient is summed with the value (nqR) in an adder 33 to provide on a line 34 the argument (nqR+(nqR/ A separate memory address decoder 35 and sinusoid table 36 (similar to the decoder 30 and the table 31) are used to supply on a line 37 the value sin(1r/W)(nqR +(nqRA3) corresponding to the argument provided on the line 34.
The sin values present on the line 31' and 37 are summed in an adder 38 and the sum is supplied via a line 39 to a harmonic amplitude multiplier 40. There, the sum of the sin values is multiplied by theappropriate coefficient C supplied from a harmonic coefficient memory 41. The product, supplied via a line 42 to the accumulator 13, corresponds to the combined Fourier component F of the order n currently being evaluated. Thus within each amplitude computation interval 2,, the 16 combined Fourier components of order n=l through n=Wl6 will be provided to the accumulator 13 during the corresponding consecutive calculation time intervals r through r At the end of the interval I the accumulator 13 thus will contain the waveshape sample point amplitude x,,(qR) for the sample point currently being evaluated. As described earlier, the sample point amplitudes obtained in the accumulator 13 are converted to an analog signal by the converter 16 and reproduced by the sound system 11 to provide musical notes having an ensemble effect.
As discussed above, in connection with Equation 2 and FIG. 1, the frequency separation between the true pitch and out-of-tune" notes is established by the constant The value is a design choice, but in a binary system the constant advantageously is an integral power of 2. For example, a pleasing ensemble effect is achieved when the constant K=28=25 6. This results in a frequency offset AF of about 7 cents. Pleasing ensemble also is achieved when K=2=128, which provides a frequency offset AF of about 13 cents. A rinky-tink effect is achieved when K=26=64, yielding a frequency offset of about 26 cents.
In a binary implementation in which K=2", the divider 32 may comprise a shift register which right-shifts the quantity nqR by m digits. Since a right shift of one bit position is equivalent to division by 2, a shift of in positions is equivalent to division by 2'". Commercially available integrated circuit, parallel-in, parallel-out shift registers such as the Texas Instrument Co. type 7495 may be employed as the divider 32.
The invention is not limited to binary systems, thus the value need not be a power of 2, and need not be abinary or decimal integer. The constant K may be positive or negative. In the latter instance, the out-oftune Fourier components will be lower in frequency (i.e., flat) with respect to the true pitch components. The value K may be preset into the divider 32, or alternatively may be selected by the musician to adjust the ensemble frequency offset to a desired value.
The constant K need not be the same value for all notes produced by the instrument 10. Alternatively, different values of may be used for each note or sets of notes. For example, individual values of K may be stored in a memory 43 which is accessed in response to keyboard note selection when a switch 43' is closed. Thus when any keyboard switch 12 is depressed, the value K corresponding to the selected note is accessed from the memory 43 and provided to the divider 32 for utilization during ensemble production. In such embodiment the memory 43 may be implemented using an integrated circuit programmable read only memory such as the Signetics SIG 8223 or the Texas Instruments type SN5488A. As another alternative, the value may be time variant. For example, a low frequency oscillator 44 connected to the divider 32 via a switch 44 may be used to vary the value at a periodic or non-periodic rate, resulting in a concomitant time-varying ensemble frequency offset.
The harmonic coefficient memory 41 advantageously comprises a read only memory containing values C appropriate to produce a note of desired tonal quality. For example, table I below sets forth typical harmonic coefficient values for obtaining a diapason tone. The value C corresponding to the n Fourier component currently being evaluated is accessed from the memory 41 by a memory address control unit 45 which receives the calculation interval timing pulses r through t from the counter 23. Thus, e.g., when the timing pulse 1 is received, the control unit 45 causes the harmonic coefficient C to be accessed from the memory 41 and supplied to the multiplier 40.
TABLE I Continued DIAPASON Coefficient (Relative (Decibel Amplitude) Equivalent) C 36 l 1 C 23 1 5 C6 25 1 4 C1 8 24 u 8 -24 C9 4 31 10 4 -31 C11 2 38 12 2 38 13 2 38 14 1 42 C 1 42 C 1 42 The harmonic coefficient memory 41 and address control 45 together may be implemented using a single integrated circuit read only memory such as the Signetics type 8223. Such a unit accepts a binary coded addressing signal. Correspondingly, the counter 23 may comprise a Signetics type 8281 l6-state binary counter, the binary output of which may be supplied directly to the address control input of the type 8223 memory. A Signetics type 8250 binary-to-octal decoder may be used in conjunction with the type 8281 counter to provide the separate t through t signal lines shown in FIG. 2. The type 8223 memory may be programmed to store the harmonic coefficients listed in table I above, or other values of C appropriate to produce other tones.
The frequency number memory 17 likewise may be implemented using a conventional integrated circuit read only memory such as the Signetics type 8223. The following table II shows typical values for the frequency number R for the notes between C and C The note interval adder 19, the harmonic interval adder 27 and the accumulator 13 may be implemented using conventional integrated circuit full adders such as the Signetics type 8268 or the Texas Instrument Co. type SN5483 or SN7483. These may be connected as shown in the section entitled Accumulators of the textbook Computer Logic by Ivan Flores, Prentice- Hall, 1960, to accumulate the sum. Each sinusoid table 31, 36 and memory address decoder 30, 35 may comprise a conventional integrated circuit read only memory, such as the Texas Instrument Co. type TMS4400 programmed to store sin values. A useful integrated circuit having prestored sinusoid table and addressing circuitry also is available from the Texas Instrument Co. as a type TMS4405 device. A single sinusoid table could be time-shared in place of separate tables 31 and 36. The harmonic amplitude multiplier 40 may be implemented as shown in the application sheet on page that the Contents of the adder 56 represents the quan- 28 of the Signetics catalog entitled Digital 8000 tity n(qR/K) for the n" order component currently Series TTL/MSI, copyright 1971, using Signetics being evaluated. This value is supplied via a line 57 to SIG 8202 buffer registers and 8260 arithmetic elea memory address decoder 58 and a sinusoid table 59 ment. The multiplier 40 also could be implemented identical in function and operation to the decoder 35 sing a Signetics 8243 sealer. and sinusoid table 36 of FIG. 2. The obtained value sin(1r/W)n(qR+(qR/K)) is supplied via a line 60 to the A trio ensemble effect can be achieved by the adder 38 Where it is su ed With the value computer organ using the optional circuitry shown sin( pr sent n the ine 32. The sum is supin FIG. 2 and actuated when the switch 29 is set to en- 10 plied ia the line 3 to the harmonic amplitude multigage the contact 2912. Trio ensemble is produced in a plier 40 (FIG. 2). The remaining circuitry of the instrupipe organ by simultaneously sounding three pipes ment 10A is identical to that of FIG. 2, and operates which are frequency offset with respect to each other. correspondingly to provide musical sounds having an The effect is synthesized in the instrument 10 by imple- H ensemble quality.
menting the following equation: Intending to claim all novel, useful and obvious fea- W W W X (QR) =1 F Y P .(n)
true i Offset 2 offset W W W n n nctR 1T R X C slnnqR+ I C s1n(nqR+,-')+ v C sin n 'R+ n=l n w n21 n w K i n w 9 K W "T R C J. q 1*; nqR
n21 n [s1n nqR+sln (nqR+ K s1n (r1q R+ (Eq, 5)
wherein F gffset, represents the Fourier components tures shown or described, the applicant claims: associated with a third tone. These components are off- 30 1. In an electronic musical instrument wherein the Set q lf by'ah amount "q from thfi COITe" amplitudes of a waveshape are computed at regular Spohdlhg h' 'p hp time intervals from stored harmonic coefficients, e he of Equation Shows that h Same musical notes being produced from said computed amaSEelh'?ltlon 1 except for addmoh of the thud 51h termplitudes as said computations are carried 'out in real This value sin(n-/W)(nqR+(nqR/K)) is evaluated by the components designated 46 through 49 in FIG. 2. Specifically, the value (nqR) from the line 28 is divided by the constant K in a divider circuit 46 which may be lmplmerited m hi g as theglvder 83 time interval t each combined Fourier compoquonent ls Summe Wlt 6 Va ue y at} 3 er v 4O nent being thesum of a first constituent Fourier 47. A memory address decoder 48 and a sinusoid table component at the nominal true-pitch of the se- 49 (similar to the decoder 30 and SlIlUSOld table 31) are used to obtain the value sin(7T/W)(-n R+(n R for lected note and a second constituent Fourier comq q ponent offset in frequency from the corresponding the argument provided by the adder 47. This sin value h f t F h is supplied via the line 50 to the adder 38 where it is true'pltc Us Constituent curler componentt e time, the improvement for producing an ensemble effect comprising:
first means for evaluating a set of combined Fourier components during subintervals within each summed with the other sin terms, present on the lines first and 9 Constituent Fourier COmPQIeMS of 32 and 37, associated with the true-pitch and first offset Crr eSpndmg 9 havmg an efiual amphwde components of corresponding order. The sum of the tabhshed by Sald Stored harmome components" three sin values then is multiplied by the coefficient C an aeehmulatoh Connected to reeelve Sald eomblhed in the multiplier 40 and added to the previous contents Fowler eempohehts from e first e i for of the accumulator 13. At the end of each computation eumulahhg ah the the eomhlhed Founer p interval 1,, the accumulator 13 will contain the wavehems evaluated during each interval 1 to Obtain a shape amplitude for the current sample point, evalu waveshape amplitude for a certain sample point, ated in accordance with equation 5. As successive sam ample point means Operative at the end of each inple point amplitudes are obtained in the accumulator 5 tel'val I o enting he effective sample 13, they are converted to analog form and reproduced point (qR) for which said resultant waveshape'amby the sound system 11 to produce musical notes havplitude is established and for supplying the effecing a trio ensemble effect. I tive sample point (qR) value to said first means,
In the alternative embodiment of FIG. 3, the comand puter organ 10A also produces ensemble sounds in ac- 6O 'meahs, Connected to recelve waveshape hcordance with equation I. In this implementation, the tudes from Sald accumuiatoh for cohvertmg Sald value (qR) on the line 20 is divided by the constant resultaht waveshape amplitudes to Sounds, Said in a divider 53. The quotient is summed with the value Converting being Carried out, in real time as Said R) i an dd 54 to Obtain the Sum (qR+(qR/K))' At waveshape amplitudes are computed, the sounds so each calculation interval r through this sum is 65 Produced exhibiting an ensemble effectp id d i a gate 55 to a h i interval adder 5 2. A musical instrument according to claim I wherein like the adder 27. The harmonic interval adder 56 is Said Sample Point ns sta es a sample point cleared at the end of each computation interval t so Value I Where q is an Integer nt d a t rval t and R is a constant frequency number establishing the nominal fundamental frequency of the pro duced note, and wherein said first means comprises;
trigonometric function circuitry, utilizing the sample point value qR, for evaluating a pair of like trigonometric functions the arguments of which correspond respectively to the sample point nqR of the true pitch first constituent Fourier component and to the sample point (nqR+(nqR/K)) of the second constituent Fourier component, where n designates the order of each combined Fourier component, and is a constant establishing the extent of frequency offset of said second constituent Fourier component, I i an adder, receiving the evaluated trigonometric function from said circuitry, for summing said pair of trigonometric functions for each order n, and a multiplier connected to said adder and receiving said stored harmonic components, for multiplying each trigonometric function sum from said adder by the harmonic coefficient for the corresponding order n, the product being the combined Fourier component value which is supplied to said accumulator.
3. As an electronic musical instrument exhibiting an ensemble effect:
first means for computing at regular time intervals 1 the amplitudes X (qR) of a waveshape, where q is an integer incremented each time interval t,, in accordance with the relationship wherein n=l ,2, 3, Wdesignates the order of the Fourier components included in each waveshape amplitude computation, wherein C is a coefficient establishing the relative amplitude of the corresponding n'" component, wherein R is a number specifying the period of said waveshape, and wherein is a constant establishing the ensemble frequency offset, and
second means responsive to said first means for providing ensemble tones from said computed amplitudes, and wherein said first means comprises;
a coefficient memory storing said harmonic coefficients C,,,
at least one sinusoid table comprising a memory storing values of sin(1r/W) qS for (1) s W/2 at intervals of D where D is a resolution constant,
a frequency number memory containing values of R associated with selectable musical notes and note selection circuitry for accessing from said frequency number memory the value R for each selected note,
first sinusoid evaluation circuitry connected to one of said sinusoid tables to calculate sin(1r/W)nqR for each value n=l,2,3, W in accordance with the selected value R. all of said calculations being performed within each interval t second sinusoid evaluation circuitry connected to a sinusoid table to calculate sin(1r/W)(nqR+(nqR/K)) for each value 11-1 .23
. W in accordance with the selected value R and said constant K, all of said calculations being performed within each interval t,,
a first adder, said first and second evaluation circuitry concurrently providing to said adder the respective values sin(.1r/ W)nqR and Sil'l(7T/W(nqR+(i16[R/K)) for the same order n. said respective sin values being summed by said adder, a harmonic amplitude multiplier connected to receive from said coefficient memory the harmonic coefficient C, corresponding to said same order n of the sin values summed by said adder, and operative to multiply the sin value sum from said adder by said received coefficient c,,, and
an accumulator for algebraically summing, during each interval 2,, the products from said multiplier for all values n=l,2,3, Wto obtain each waveshape amplitude X (qR).
4. A musical instrument according to claim 3 having first and second like sinusoid tables, said first and second evaluation circuitry respectively utilizing said first and second sinusoid tables.
5. A musical instrument according to claim 3 wherein said first means further comprises;
a note interval accumulating adder of modulo 2W,
first gate circuitry connected to said frequency number memory and to said note interval adder for supplying to said note interval adder at each interval t, the value R accessed from said frequency number memory, so that the contents of said note interval adder represents the quantity (qR), and wherein said first and second evaluation circuitry are connected to receive said quantity (qR) from said note interval adder.
6. A musical instrument according to claim 5 wherein said first evaluation circuitry comprises;
a first harmonic interval accumulating adder cleared at the end of each interval t second gate circuitry for supplying to said first harmonic interval adder the quantity (qR) from said note interval adder during successive subintervals of each interval t so that the contents of said first harmonic interval adder successively represent the quantity (nqR) for different values of n, and
first circuitry utilizing one of said sinusoid tables to obtain the values sin('rr/W)nqR for each argument (nqR) supplied from said first harmonic interval adder.
7. A musical instrument according to claim 6 wherein said second evaluation circuitry comprises;
a divider connected to receive the contents (nqR) of said first harmonic interval adder and to divide said value (naR) by said constant K,
a second adder for summing the outputs of said divider and said first harmonic interval adder to obtain the arguments (nqR+(nqR/K)), and
second circuitry utilizing one of said sinusoid tables to obtain the values sin(1r/ W)(nqR+(nqR/K)) for each argument supplied from said adder.
8. A musical instrument according to claim 7 for providing trio ensemble, further comprising;
a second divider connected to receive the contents (nqR) of said first harmonic interval adder and to divide said value (nqR) by a constant K different from K,
another adder for summing the outputs of said second divider and said first harmonic interval adder to obtain the argument (nqR+(nqR/K')), and
third circuitry utilizing one of said sinusoid tables to obtain the values sin(1r/W)(nqR+(nqR/K)) for each argument supplied from said other adder, and
1 1 wherein said first adder sums the three sin values provided by first, second and third utilizing circuitry.
9. A musical instrument according to claim 7 wherein said value K=2"" Where m is an integer, and wherein said divider comprises a binary shift register which accepts said value (nqR) in binary and to right shift said value by m binary positions to perform said division by K.
10. A musical instrument according to claim 6 wherein said second evaluation circuitry comprises;
a divider connected to receive the contents (qR) of said note interval adder and to divide said value (qR) by said constant K,
an adder for summing the outputs of said divider and said note interval adder to obtain the value (q 'q /K)- a second harmonic interval adder cleared at the end of each interval t second gating circuitry for providing said obtained value (qR+(qRK)) to said second harmonic interval adder during successive subintervals of said interval t so that the contents of said second harmonic interval adder successively represent the arguments n(qR+(qR/K)) for different values of n, and
second circuitry utilizing a sinusoid table to obtain the values sin(1r/W)n(qR/K)) for each argument supplied from said second harmonic interval