US3888153A - Anharmonic overtone generation in a computor organ - Google Patents

Anharmonic overtone generation in a computor organ Download PDF

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Publication number
US3888153A
US3888153A US374680A US37468073A US3888153A US 3888153 A US3888153 A US 3888153A US 374680 A US374680 A US 374680A US 37468073 A US37468073 A US 37468073A US 3888153 A US3888153 A US 3888153A
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Prior art keywords
overtone
offset
adder
eta
note
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Ralph Deutsch
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Nippon Gakki Co Ltd
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Nippon Gakki Co Ltd
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Priority to GB2681574A priority patent/GB1469461A/en
Priority to IT24432/74A priority patent/IT1015405B/it
Priority to NL7408600.A priority patent/NL164983C/xx
Priority to JP7314374A priority patent/JPS5340527B2/ja
Priority to DE2431161A priority patent/DE2431161C2/de
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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10H—ELECTROPHONIC MUSICAL INSTRUMENTS; INSTRUMENTS IN WHICH THE TONES ARE GENERATED BY ELECTROMECHANICAL MEANS OR ELECTRONIC GENERATORS, OR IN WHICH THE TONES ARE SYNTHESISED FROM A DATA STORE
    • G10H7/00—Instruments in which the tones are synthesised from a data store, e.g. computer organs
    • G10H7/08—Instruments in which the tones are synthesised from a data store, e.g. computer organs by calculating functions or polynomial approximations to evaluate amplitudes at successive sample points of a tone waveform
    • G10H7/10—Instruments in which the tones are synthesised from a data store, e.g. computer organs by calculating functions or polynomial approximations to evaluate amplitudes at successive sample points of a tone waveform using coefficients or parameters stored in a memory, e.g. Fourier coefficients
    • G10H7/105—Instruments in which the tones are synthesised from a data store, e.g. computer organs by calculating functions or polynomial approximations to evaluate amplitudes at successive sample points of a tone waveform using coefficients or parameters stored in a memory, e.g. Fourier coefficients using Fourier coefficients
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10H—ELECTROPHONIC MUSICAL INSTRUMENTS; INSTRUMENTS IN WHICH THE TONES ARE GENERATED BY ELECTROMECHANICAL MEANS OR ELECTRONIC GENERATORS, OR IN WHICH THE TONES ARE SYNTHESISED FROM A DATA STORE
    • G10H1/00—Details of electrophonic musical instruments
    • G10H1/02—Means for controlling the tone frequencies, e.g. attack or decay; Means for producing special musical effects, e.g. vibratos or glissandos
    • G10H1/06—Circuits for establishing the harmonic content of tones, or other arrangements for changing the tone colour

Definitions

  • the overtone offset (17,, values may be stored in a memory, or may be generated by appropriate circuitry. In certain embodiments the offset is proportional to the frequency of the note being produced, preferably being a constant number of cents. Other embodiments include, among other things, constant frequency offset independent of time, time variant anharmonicity, offset of alternate overtones in opposite frequency directions, and overtone selection to insure correct frequency of a subjective fundamental.
  • the present invention relates to the generation of musical sounds containing anharmonic overtones in a computor organ.
  • the computor organ described in the above mentioned US. Pat. application Ser. No. 225.883 is unique in that each Fourier component of the produced musical waveshape is generated individually. As a result, frequency offsetting of individual overtones is possible, and the principal object of the present invention is to provide overtone frequency offsetting in such a computor organ.
  • the generation of musical sounds characterized by anharmonic overtones is implemented, facilitating realistic electronic synthesis of struck string instruments and of sounds characteristic of bells, chimes, violins. orchestral brass and reeds.
  • Another object is to provide a chorus or ensemble cf feet between stops of different footage generated simultaneously in a computor organ having combined footage (see the above mentioned US. patent application, Ser. No. 328,302).
  • anharmonic overtones the stops of different footage will be unlocked even when played with a single key.
  • the dominant tone of a 4-foot voice is the second overtone of an 8-foot voice.
  • By frequency offsetting this second overtone so that it is not a true harmonic of the 8 foot fundamental. the two voices are unlocked.
  • a chorus or ensemble is produced. Such unlocking of voices is totally impossible in a digital organ of the type wherein a waveshape is repetitively read from storage.
  • a further object is to provide octave decoupling by using the inventive overtone frequency offset modulation. With such modulation, two tones played on the same stop will beat, even throug their nominal fundamental frequencies are exactly in octave relationship.
  • the term *overtone is used herein to refer to one of the higher tones which together with the fundamental comprises a complex musical tonev If the overtone has a frequency which is in integral multiple of the fundamental, it is a harmonic overtone, or simply, a harmonic.” However, an overtone need not be integrally related in frequency to the fundamental, and if the overtone has a frequency which is not an integral multiple of the fundamental, it is a non-harmonic or anharmonic overtone. Thus as used herein in both the specification and claims, the term *anharmonic" means not harmonic or inharmonic.
  • each of the harmonic components F" has a frequency which is an integral multiple of the nominal fundamental frequency.
  • n designates the order of the Fourier compo ncnt
  • nqR-I-ry herein is called the overtone sample point.
  • the waveshape amplitudes X,,(qRl generally are computed at regular time intervals 1,. At each successive time interval 1, the value qR is incremented in an adder of modulo N, where N is related to the number of sample points per period of the highest frequency note produced by the instrument.
  • the fundamental amplitude F is evaluated at successive, equally separated sample points. However, for each anharmonic overtone. the distance between Sam ple points at which the amplitude of that overtone is evaluated is designated by (n-I-(n itself is changing periodically with time (i.e., is being incremented at intervals 1,, resetting at modulo N), the separation between overtone sample points. determina tive of the anharmonically of that overtone.
  • the overtone anharmonicity is independent of time.
  • each overtone has a constant frequency offset which does not vary in time. and which is the same for all notes generated by the instrument.
  • the Fourier component amplitudes are calculated in accordance with the relationship:
  • each overtone is offset by a constant number of cents, where a cent is 1/1200 of an octave.
  • FIG. 1 is a typical harmonic spectrum of a musical note produced by a computor organ employing anharmonic overtone generation.
  • FIG. 2 is an electrical block diagram of a single channel computor organ including anharmonic overtone generation in accordance with equation 3 above.
  • FIGS. 3, 4 and 5 show alternative circuits for providing overtone offset (1 values; and useful in conjunction with the computor organ of FIG. 2.
  • FIG. 6 is an electrical block diagram showing implementation of anharmonic overtone generation in a parallel processing computor organ.
  • FIG. 7 is a typical harmonic spectrum of a musical note wherein odd and even overtones are offset in opposite frequency directions.
  • FIG. 8 shows alternative circuitry for providing overtone offset values to the parallel processing computor organ of FIG. 6.
  • FIG. 9 is an electrical block diagram of a computor organ wherein constant frequency offset, anharmonic overtone generation is implemented in accordance with equation 5 above.
  • FIGS. 10 and I] are electrical block diagrams of computor organ embodiments wherein anharmonic overtones having constant cents frequency offset are generated in accordance with equation 6 above.
  • FIG. 12 is an electrical block diagram of circuitry for modulating the anharmonic overtones as a function of time.
  • FIG. 13 is a harmonic spectrum of a typical note produced by a computor organ employing anharmonic overtone generation, wherein the fundamental frequency is detuned so that the subjective fundamental recreated from offset overtones will be in tune.
  • FIG. 1 shows the harmonic spectrum of a typical musical note produced by a computor organ using anharmonic overtone generation in accordance with the present invention.
  • the spectrum contains a fundamental ll evaluated at the nominal fundamental frequency f of the note, and anharmonic overtones ]2l5 having frequencies which are not integral multiples off.
  • the first overtone 12 has a frequency Zf'l'l/ wherein u, designates the offset of this overtone with respect to the frequency 2f of the true second harmonic.
  • the typical non-harmonic overtones l3, l4 and are evaluated at respective frequencies 3f+u ift-v and loft-11, which are offset by the amounts v v and 1/ from the frequencies 31', 4f and 16f of the true third, fourth and sixteenth harmonics.
  • the solid lines designate Fourier components actually generated by the computor organ; the dotted lines indicate the harmonics which are not generatedl
  • Musical notes having non-harmonic overtones are produced by the computor organ 18 (FIG. 2) which implements anharmonic overtone generation in accordance with equation 3 above ln general, circuitry and operation of the computor organ 18 is as described in the US. patent application, Ser. No. 225,883.
  • the computor organ 18 includes an overtone offset (1 memory 19, an v memory address control 20 and an adder 2] which implement frequency offsetting of selected Fourier components.
  • the computor organ 18 of FIG. 2 operates to produce via a sound system 21 a musical note selected by the keyboard switches 22. This is accomplished by cal culating the discrete Fourier components associated with amplitudes at successive sample points of a waveshape characterizing the selected note. The compo nents are algebraically summed in an accumulator 23 which. at the end of each computation time interval t, containsthe amplitude at the current sample point. This amplitude is provided via a gate 24, enabled by the I signal on a line 25, to a digital-to-analog converter 26 which supplies to the sound system 21 a voltage corresponding to the waveshape amplitude just computed. Computation ofthe amplitude at the next sample point subsequently is initiated. so that the analog voltage supplied from the converter 26 comprises a musical waveshape generated in real time.
  • 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 22.
  • a set of such frequency numbers corresponding to the notes of the instrument is stored in a frequency number memory 27.
  • the computor organ l8 implements equation 3 by computing the amplitude value X,,(qR) for each sample point during a time interval l
  • the amplitude F" of the fundamental is calculated. This value F is placed in the accumulator 23.
  • the amplitude P of the second Fourier component i.e. the first overtone
  • the second overtone amplitude F is calculated and added to the accumulator 23.
  • the routine is terminated when all W Fourier components have been evaluated. Upon such termination. the algebraic sum contained in the accumulator 23 will correspond to the amplitude X,,(qR) for the sample point designated by the value qR.
  • the waveshape amplitude X (qR) in the accumulator 23 is gated to the digital-to-analog converter 26 at the end of the computation interval 1,.
  • the accumulator 23 then is cleared by the signal on the line 25, and computation of the amplitude at the next sample point subsequently is initiated.
  • the value qR is incremented and the W harmonic component ampli tudes F' are calculated for the sample point designated by the new value of qR.
  • the entire waveshape will be generated, the sound system 21 re producing the musical note as the amplitude computations are carried out.
  • a note interval adder 33 contains the value qR identifying the sample point at which the waveshape amplitude currently is being evaluated. This value qR is incremented at the beginning of each computation interval 1, by adding the selected freguency number R to the previous contents of the adder 33. The selected value R is supplied to the adder 33 via a gate 34 enabled by the I signal on the line 25.
  • the adder 33 is of modulo N where N is the prodact of the R number for any note times the number of points per period of that note.
  • the values nqR (for n 1,2. W) are obtained in a harmonic interval adder 35 which is cleared before each amplitude computation cycle.
  • the current value qR contained in the note interval adder 33 is entered into the harmonic interval adder 35 via a line 36 and a gate 37.
  • the value qR is added to the previous contents of the adder 35.
  • the harmonic interval adder 35 will contain the value nqR for the n'" order Fourier component currently being evaluated.
  • the harmonic inter' val adder 35 also is of modulo N.
  • the frequency offset value 1 of the v' overtone is added to the value nqR by the adder 2].
  • the value nqR is obtained from the harmonic interval adder 35 via a line 38.
  • the frequency offset value 1 is supplied to the adder 20 from the overtone offset (1;) memory 19 via a line 42.
  • the 1 memory 19 is accessed by the address control circuit 20 which receives the timing pulse !,.,,,-l,.,, via a line 43 from the counter 32.
  • the signal on the line 43 will cause the address control 20 to access the overtone offset value m from the memory [9.
  • the value sin (Tr/W) tnqR+17 corresponding to the argument (nqR+n received via the line 4] from the adder 20 is accessed from a sinusoid table 46 by an address decoder 47.
  • the sinusoid table 46 may comprise a read only memory storing values of sin (IT/W d) for d: s 2W at intervals of D. where D is called the resolution constant of the memory.
  • the value sin YT/W (itqRlYJ supplied via a line 48. is multiplied by the coefficient C for the corresponding n' Fourier component by a multiplier 50.
  • the multiplication product represents the amplitude F" of the 11" Fourier component and is supplied via the line 51 to the accumulator 23.
  • the appropriate coefficient C is accessed from the harmonic coefficient memory 28 by an address control 35 which receives the calculation timing signals via the line 43.
  • arbitrary values ofn may be stored in the memory 19.
  • the values may be the same or different for each overtone.
  • the value 17,, for a certain overtone may be zero in which case a true harmonic with no frequency offset will be evaluated.
  • the overtone offset (1 memory 19 and the associated address control 20 advantageously may be implemented using a single integrated circuit such as the Signetics type 8223 programmable read only memory. Full word decoding is included in this integrated circuit chip, which accepts a binary address input.
  • a binary counter such as the Signetics integrated circuit type 8281 advantageously is used as the counter 32; the buss 43 may comprise the binary output lines from that counter.
  • Any desired overtone offset (17) values can be user programmed into this integrated circuit memory.
  • the adder 21 may comprise a Signetics type 8268 inte' grated circuit adder. Integrated circuitry useful for implementing the other components of the computor organ 18 are described in the related applications listed above. Similarly, typical values of R and C are tabulated in those related applications. The following Table A lists typical conventional integrated circuits that may be employed as certain of the components of the instrument shown in FIG. 2.
  • Also can he implimented using a read only memory such as SIG 8223 which includes address control circuitry May he implemented as shown in application sheet SIG catalog. p.28 using SIG B202 buffer registers and R260 arithmetic element Also can be implemented using Slg 8243 sealer [p.65]
  • FIG. 3 shows a modified version of the computor organ 18 which also implements equation 3.
  • 1 v1y for each overtone.
  • the m values need not be stored individually in a memory. but can be calculated during the waveshape amplitude computation cycle.
  • the overtone offset memory I8 and address control 19 shown in FIG. 2 are not used; rather the overtone offset values w; are provided via a line 42' to the adder 40 (FIG. 2) by the circuit of FIG. 3.
  • the value in is accumulated in an adder 54 which is cleared at the end of each computation cycle by the 1, signal on the line 25.
  • the contents of the adder 54 is zero so that no offset is introduced;
  • the value 1 is supplied to the adder 54 via agate S6 enabled by the corresponding timing signals on a line 43' from the counter 32. Occurrence of the timing signal 1, causes the value 1 to he transferred from the register 53 to the adder 54. Accordingly. the value 11 1 will he provided via the line 42' to the memory address do coder 47 of FIG. 2 during calculation of the first over tone. During successive calculation intervals r,.,, through r the value 1 will be added successively to the adder 54 contents. so that the required value my will be supplied to the eomputor organ I8.
  • n stored in the register 53 is or bitrary. It may be constant for all notes of the scale; or it may differ for different notes.
  • FIGS. 4 and 5 show circuits for providing to the register 53 values of 1 which are functions of the selected note.
  • the note dependent overtone offset value '1) R/K is obtained by dividing the frequency number R by a constant k. This is implemented by a divider 59 which receives the R number via a line 27' from the frequency number memory 27 and which supplies the quotient r; R/K to the register 53 via a line 60.
  • the overtone offset will be a constant number of cents. but however the anharmonicity will vary periodically in time since the waveshape amplitude is computed in accordance with equation 3 above.
  • FIG. 5 shows a more generalized system for producing frequency proportional overtone anharmonicity.
  • the divider 59 (FIG. 4) is a specialized embodiment of the general circuitry of FIG. 5.
  • Anharmonic overtone generation in accordance with equation 3 likewise can be implemented in a parallel processing eomputor organ of the type disclosed in the US. patent application. Ser. No. 298.365. Such an implementation is shown in FIG. 6 wherein the eomputor organ 65 includes two parallel processing channels 66A. 66B. Half of the Fourier components utilized in the waveshape amplitude computation are calculated in one channel 66A. and the remaining components are evaluated concurrently in the other channel 668.
  • separate overtone offset (mmemorics I9A. I9B and related 17 memory address control circuits 20A. 20B are provided in the respective channels 66A. 668.
  • the values nqR for certain values of n are supplied via a line 38A during consecutive calculation time intervals I through I,.,,,. to an adder 21A.
  • the appropriate overtone offset values 1;. are provided to the adder 21A from the memory IJA, so that the output of the adder 21A represents the quantities nqR+17,. for the set of Fourier components evaluated in the hannel 66A.
  • This output. on a line 41A is provided to the sinusoid table and address decoder 46A.
  • the remaining Fourier components are similarly evaluated in the parallel channel 668. wherein corresponding circuit blocks are identified by like numerals followed by the letter
  • the Fourier components present concurrently on the lines 48A and 48B are summed in an adder 67 and provided to an accumulator.
  • digital-to-analog converter and sound system (not shown) analogous to those shown in FIG. 2.
  • Different sets of Fourier components may be evaluated in the two processing channel 66A, 668.
  • the overtone offset memory 19A will contain the values 1 through 1;; which are accessed at the respective time intervals through I
  • the overtone offset memory 19B will contain the values m through 17, which are accessed at the consecutive time intervals r,.,,, through I when the corresponding 8th through 15th overtones (i.e., the 9th through 16th Fourier components) are evaluated.
  • the overtone offset memory 19A will contain the values 17 .11 1 17
  • the overtone offset memory I9B will contain the values n n- 17;, 0.
  • overtones are frequency offset in the same sense. Some of the overtones may be offset sharp and others flat. This is illustrated by the harmonic spectrum of FIG. 7, wherein the odd overtones (even Fourier components) are offset sharp and the even overtones are offset flat. Production of such notes readily is implemented by the FIG. 9 eomputor organ embodiment described in the preceeding paragraph. Negative offset (1 values are stored in the memory 19A and positive 1 values are stored in the memory 198. With this arrangement. e.g., will be calculated using a positive value 7 to provide an anharmonic overtone 70 (FIG. 7) which offset is sharp. The second overtone 71, evaluated in the processing channel 668, will be flat.
  • a system analogous to that shown in FIG. 3 may be used to provide overtone offset values to the parallel processing eomputor organ of FIG. 6.
  • Such an arrangement. shown in FIG. 8, is useful in the embodiment wherein the low order Fourier components are evaluated in one channel 66A and the high order components are evaluated in the other channel 668.
  • the ap limbate 1/ values are supplied to the adders 21A, 218 (FIG. 6) from respective accumulating adder circuits 72A. 728 which are cleared at the end of each computation cycle; the overtone offset memories 19A, 19B are not used.
  • the value 81 is gated from the register 74 via a gate 77 to the adder 728.
  • the overtone offset value 81 is susplied via the line 428 to the adder 218 in the computor organ 65; during this interval the eighth overtone is being evaluated in the channel 663.
  • the value 1 is provided via the gate 75 and the line 76 to the adder 728 wherein the values 91 through 151; will be accumu lated.
  • a different implementation of anharmonic overtone generation is employed in the computor organ 80 of FIG. 9.
  • This embodiment provides constant frequency offset of the overtones, independent of time. in accordance with equation above.
  • the computor organ 80 produces musical notes having a harmonic spectrum similar to that shown in FIG. I, but wherein the fundamental is evaluated at the true fundamental frequency f of the note being generated and each overtone l2, l3 has a frequency nf+ 111 where v n I.
  • the frequency number R of the selected note is gated to the note interval adder 33 at the beginning of each waveshape amplitude computation cycle.
  • the note interval adder 33 provides on the line 36 the value qR.
  • this value qR is supplied via a gate SI to a non'accumulating adder 82.
  • the second input to the adder 82 is zero, so that the value qR is supplied via the line 83 to the harmonic interval adder
  • the first Fourier component is evaluated at the nominal fundamental frequency of the selected note.
  • the value Jq is supplied to the adder 82 via a gate 84 and a line 85, so that the value (qR-l-Jq) is provided via the line 83 to the harmonic interval adder 35.
  • the arguments (nqR+vJq) will be presented to the memory address decoder 47 via the line 41 during the consecutive Fourier component calculation intervals.
  • the sin values corresponding to these arguments will be provided via the line 48' from the sinusoid table 46 to a harmonic interval multiplier 50, accumulator 23, digital-to-analog converter 26 and sound system 21 like that of FIG. 2.
  • the constant J is stored in a register 87 (FIG. 9).
  • the value J is added to the previous contents of an accumulating adder 88 (of modulo N) upon occurrence of the computation cycle timing signal I, which enables a gate 89.
  • the contents of the adder 88 thus represents the value Jq.
  • a computor organ 90 which implements equation 6 above is shown in FIG. 10.
  • each an harmonic overtone is offset by an amount which is a constant number of cents.
  • the anharmonicity is inde pendent of time.
  • the value qR from the interval adder 33 is supplied to the harmonic interval adder 35" at the interval t via a gate 9] and a non-accuniulating adder 92 the other input of which is zero during this 1 interval.
  • the value z Rfls'. where K is a constant. is added to the value qR in the adder 92 and the sum (qR-H qR/K)) is supplied via the line 93 to the harmonic interval adder 35".
  • the arguments tnqR+v(qR/K)) are provided to the sinusoid table 46, exactly in accordance with equation 6 above.
  • the value qR/k is obtained by dividing the value qR from the line 36 by the constant K in a divider circuit 94.
  • the constant K 2 where z is an integer of I or greater.
  • the divider circuit 94 may comprise a shift register, since right shifting is the equivalent of dividing by a power of 2.
  • the divided qR/k is provided to the adder 92 via a line 95 and agate 96 which is enabled by the calculation timing signals 1, through provided via a line 97 from the counter 32.
  • the computor organ of FIG. I] implements equation 6 above in an alternative manner.
  • the frequency number R obtained on the line 27' is divided by the constant K in a divider circuit 100.
  • the dividend R/K is gated to an accumulating adder 101 of modulo N via a gate 102 enabled by the t signal on the line 25.
  • the output of the adder 101, present on a line 103 represents the quantity qR/K
  • FIG. 9, l0, and 11 are shown in single processing channel computor organs, similar arrangements can be implemented in parallel processing instruments. In such instance, separate harmonic interval adders would be provided in each processing channel. To such adders would be supplied the appropriate values qR+JQ or qR-l-q(R/K) for generation in each channel of selected subsets of the desired anharmonic overtones.
  • the frequency offset values 17 themselves may be modulated at a low frequency, typically on the order of 6 Hz, to produce a vibrato-like effect.
  • This can be implemented using the circuitry of FIG. 12 wherein the value 1; to be time modulated is supplied via a line [05 to an adder 106.
  • the output of an oscillator I07 operating at the modulation frequency is converted to a digital signal by an analog-to-digital (A/D) converter I08 the digital output of which is summed with the value 1 by the adder 106.
  • the output of the adder 106 on a line 109 comprises a time varying overtone offset value 17(1').
  • FIG. 12 may be used in conjunction with the computor organ 18 of FIG. 2 by inserting the adder I06 (FIG. l2) in series with the line 42 (FIG. 2). That is. the line 42 would be opened. the 1 values from the overtone offset memory l9 would be provided to the line I05, and the time modulated ⁇ alues nlj') on the line 109 would be supplied to the adder 2].
  • the time modulation circuit of FIG. 12 may be used with the computor organ embodiments of FIGS. 9. 10 or ll.
  • the adder 106 (FIG. 12) may be inserted in the line 85 (or the line 88') of FIG. 9 to time modulate the overtone offset value Jq.
  • the circuit of FIG. [2 may be inserted in the line 95 of FIG. 10 or the line [03 of FIG. ll to time modulate the offset value qR/k in these embodiments.
  • a characteristic of human hearing is that the car hecomes less sensitive at low frequencies. Because of this roll off" of hearing ability. the first overtone ofa note having low fundamental frequency may appear to the listener to have a greater amplitude than the fundamental. In such instance. the listener may subjectively sense the fundamental at a frequency which is half that ofthe first overtone. Thus at the low frequency end of the keyboard range. a note having anharmonic overtones may seem sharp or flat because the listener is detecting the fundamental subjectively at half of the first overtone frequency. For example. referring to the harmonic spectrum of FIG.
  • This effect can be overcome by selecting the values of R and r; for low frequency notes such that the subjective fundamental will coincide with the nominal fundamental frequency of the note.
  • the frequency number R is selected so that the fundamental component H1 is evaluated by the computor organ at a fre quencyj which is flat with respect to the nominal fundamental frequencyfof the note being generated.
  • the listener will hear a subjective funda mental H3 at half the frequency of the first overtone. i.e., at exactly the nominal frequencyfof the selected note.
  • the actual fundamental component lll, although flat. will be sensed only slightly because of the hearing roll off.
  • the note will seem to the listener to be in tune. and to have the desired anharmonic overtone quality.
  • An electronic musical instrument for synthesizing musical tones having anharmonic overtones comprising:
  • accumulator means for combining said separately calculated Fourier component amplitudes to obtain during successive time intervals I, the waveshape sample point amplitudes for successive sample points qR, and
  • converter means for converting said sample point amplitudes to musical tones as said calculations are carried out.
  • said evaluation means comprises:
  • a memory storing said harmonic coefficients C a sinusoid table comprising a storage device containing a set of sinusoid values at regular angular intervlas.
  • overtone offset means for providing a selected value 1; for each evaluated overtone, and
  • said Fourier component evaluation circuitry comprises:
  • a note interval adder for adding said selected value R to the previous contents of said note interval adder at the beginning of each time interval 1,, the contents of said note interval adder thereby representing qR.
  • a harmonic amplitude multiplier for multiplying each such sin value by the coefficient for the corresponding n'" harmonic component. the products of such multiplication being supplied to said accumulator means.
  • said overtone offset means comprises;
  • an overtone offset memory storing said values 1 a memory address control for accessing from said overtone offset memory the value 17,, corresponding to the n" Fourier component being calculated. and wherein said argument combining circuitry omprises;
  • a harmonic interval adder cleared at the beginning of each time interval r,. for repetitively adding the value qR obtained from said note interval adder to the previous contents of said harmonic interval adder. the contents of said harmonic interval adder thereby representing ngR where n equals the number of such repetitive additions since the beginning of each time interval 1;.
  • said argument combining circuitry comprises;
  • a harmonic interval adder cleared at the beginning of each time interval 1,.
  • a harmonic interval adder cleared at the beginning of each time interval r,.
  • a divider for dividing the value qR obtained from said note interval adder by a constant K. the output of said divider representing the value qR/k.
  • each amplitude being computed by individually calculating a set of constituent Fourier components of said waveshape.
  • each Fourier component being calculated by multiplying a trigonometric function of the Fourier component sample point by a harmonic coefficient value which establishes the relative amplitude of that component. and wherein these amplitudes are converted to musical notes as the computations are carried out in real time.
  • said improvement wherein at least some of said Fourier components are overtones that are evaluated at frequencies offset from multiples of the fundamental frequency of said generated note so that said instrument will produce a synthesized waveshape containing anharmonic overtones.
  • said instrument comprising:
  • an overtone sample point nqR-l-n designates the order of the Fourier com ponent being calculated.
  • An electronic musical instrument of the type wherein musical notes are generated by computing the amplitudes of a musical waveshape at successive sample points and converting these amplitudes to musical notes as the computations are carried out in real time and wherein a plurality of generalized Fourier components are calculated separately and combined to obtain each waveshape amplitude. at least some of said Fourier components being overtones that are evaluated at frequencies offset from multiples of the fundamental frequency of said generated note to produce a synthe sized waveshape containing anharmonic overtones. the fundamental component being evaluated at successive sample points qR.
  • a note interval adder to which the value R is added at regular waveshape amplitude computation time intervals 1,, the contents of said note interval adder thereby specifying the fundamental sample point qR.
  • overtone sample point means including a harmonic interval adder cleared before each computation cycle, and cooperating with said note interval adder and said overtone offset means, for establishing the overtone sample point nqR-Pn at which each overtone is evaluated,
  • a trigonometric function table comprising a memory storing values of a trigonometric function at regular angular intervals, and means for obtaining from said table a trigonometric function the argument of which corresponds to said overtone sample point nqR+n a harmonic amplitude multiplier for multiplying said trigonometric function by a coefficient C,, establishing the relative amplitude of the n'" Fourier component, and
  • an accumulator cleared at the beginning of each computation cycle, for accumulating said scaled trigonometric functions, the contents of said accumulator at the completion of each computation cycle thereby representing said waveshape amplitude.
  • An electronic musical instrument according to claim 12 including:
  • An electronic musical instrument further comprising;
  • Apparatus for synthesizing musical sounds by computing in real time the amplitudes at successive sample points of a waveshape having anharmonic Fourier components comprising:
  • means for accumulating the scaled trigonometric function values during each computation cycle to establish the waveshape sample point amplitude and further comprising:
  • note selection switches for selecting the number R which establishes the waveshape fundamental frequency and hence determines the musical note being generated, said apparatus implementing the equation lqR) C sin (nqRt-n included in each amplitude computation.

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  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Engineering & Computer Science (AREA)
  • Acoustics & Sound (AREA)
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  • Algebra (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
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  • Electrophonic Musical Instruments (AREA)
US374680A 1973-06-28 1973-06-28 Anharmonic overtone generation in a computor organ Expired - Lifetime US3888153A (en)

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Application Number Priority Date Filing Date Title
US374680A US3888153A (en) 1973-06-28 1973-06-28 Anharmonic overtone generation in a computor organ
GB2681574A GB1469461A (en) 1973-06-28 1974-06-17 Anharmonic overtone generation in a computor organ
IT24432/74A IT1015405B (it) 1973-06-28 1974-06-25 Apparato per la generazione di iper toni anarmonici in un organo calco latore
NL7408600.A NL164983C (nl) 1973-06-28 1974-06-26 Electronisch muziekinstrument voor het voortbrengen van niet-harmonische boventoon.
JP7314374A JPS5340527B2 (de) 1973-06-28 1974-06-26
DE2431161A DE2431161C2 (de) 1973-06-28 1974-06-28 Tonerzeugungseinrichtung für ein elektronisches Musikinstrument

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US374680A US3888153A (en) 1973-06-28 1973-06-28 Anharmonic overtone generation in a computor organ

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US (1) US3888153A (de)
JP (1) JPS5340527B2 (de)
DE (1) DE2431161C2 (de)
GB (1) GB1469461A (de)
IT (1) IT1015405B (de)
NL (1) NL164983C (de)

Cited By (22)

* Cited by examiner, † Cited by third party
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DE2629697A1 (de) * 1975-07-03 1977-01-20 Nippon Musical Instruments Mfg Elektronisches musikinstrument
US4048480A (en) * 1975-04-30 1977-09-13 Minot Pierre J M Generators of anharmonic binary sequences
US4103582A (en) * 1976-04-02 1978-08-01 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument
US4112803A (en) * 1975-12-29 1978-09-12 Deutsch Research Laboratories, Ltd. Ensemble and anharmonic generation in a polyphonic tone synthesizer
US4135422A (en) * 1976-02-12 1979-01-23 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument
US4175464A (en) * 1978-01-03 1979-11-27 Kawai Musical Instrument Mfg. Co. Ltd. Musical tone generator with time variant overtones
US4177706A (en) * 1976-09-08 1979-12-11 Greenberger Alan J Digital real time music synthesizer
US4215614A (en) * 1977-12-13 1980-08-05 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instruments of harmonic wave synthesizing type
US4246823A (en) * 1977-11-01 1981-01-27 Nippon Gakki Seizo Kabushiki Kaisha Waveshape generator for electronic musical instruments
US4257303A (en) * 1978-07-31 1981-03-24 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument of partials synthesis type
US4345500A (en) * 1980-04-28 1982-08-24 New England Digital Corp. High resolution musical note oscillator and instrument that includes the note oscillator
US4416180A (en) * 1979-08-24 1983-11-22 Sony Corporation Wave synthesizing apparatus
US4437377A (en) 1981-04-30 1984-03-20 Casio Computer Co., Ltd. Digital electronic musical instrument
US4616546A (en) * 1981-10-15 1986-10-14 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument forming tones by wave computation
US4633749A (en) * 1984-01-12 1987-01-06 Nippon Gakki Seizo Kabushiki Kaisha Tone signal generation device for an electronic musical instrument
US4811644A (en) * 1985-02-26 1989-03-14 Kabushiki Kaisha Kawai Gakki Seisakusho Electronic musical instrument for generation of inharmonic tones
US4984496A (en) * 1987-09-08 1991-01-15 Allen Organ Company Apparatus for deriving and replicating complex musical tones
US5900570A (en) * 1995-04-07 1999-05-04 Creative Technology, Ltd. Method and apparatus for synthesizing musical sounds by frequency modulation using a filter
US5936182A (en) * 1997-06-25 1999-08-10 Kabushiki Kaisha Kawai Gakki Seisakusho Musical tone synthesizer for reproducing a plural series of overtones having different inharmonicities
US6091269A (en) * 1995-04-07 2000-07-18 Creative Technology, Ltd. Method and apparatus for creating different waveforms when synthesizing musical sounds
EP1039442A2 (de) * 1999-03-25 2000-09-27 Yamaha Corporation Verfahren und Vorrichtung zur Wellenformkomprimierung und Erzeugung
FR2960688A1 (fr) * 2010-06-01 2011-12-02 Centre Nat Rech Scient Procede et systeme de synthese de signaux periodiques anharmoniques et instrument de musique comprenant un tel systeme

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5224515A (en) * 1975-08-07 1977-02-24 Nippon Gakki Seizo Kk Electronic instrument
JPS584359B2 (ja) * 1975-10-21 1983-01-26 ヤマハ株式会社 デンシガツキ
IT1105041B (it) * 1977-08-15 1985-10-28 Norlin Ind Inc Perfezionamento negli strumenti musciali elettronici a tastiera
DE2936935A1 (de) * 1978-09-14 1980-04-24 Nippon Musical Instruments Mfg Elektronisches musikinstrument

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US3809788A (en) * 1972-10-17 1974-05-07 Nippon Musical Instruments Mfg Computor organ using parallel processing
US3831015A (en) * 1972-06-08 1974-08-20 Intel Corp System for generating a multiplicity of frequencies from a single reference frequency

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US3004460A (en) * 1956-12-31 1961-10-17 Baldwin Piano Co Audio modulation system
US3007361A (en) * 1956-12-31 1961-11-07 Baldwin Piano Co Multiple vibrato system
US3049959A (en) * 1957-11-22 1962-08-21 Baldwin Piano Co Obtaining ensemble and celeste effects in electrical musical instruments
US3147333A (en) * 1960-07-27 1964-09-01 Baldwin Co D H Audio modulation system
US3157725A (en) * 1961-06-01 1964-11-17 Baldwin Co D H System for processing musical spectra
US3305675A (en) * 1962-06-19 1967-02-21 Kurt H Haase Wave form synthesizing apparatus
US3479440A (en) * 1966-08-15 1969-11-18 Baldwin Co D H Randomly-perturbed,locked-wave generator
US3636337A (en) * 1969-10-29 1972-01-18 Fmc Corp Digital signal generator for generating a digitized sinusoidal wave
US3633017A (en) * 1970-01-07 1972-01-04 Sperry Rand Corp Digital waveform generator
US3809786A (en) * 1972-02-14 1974-05-07 Deutsch Res Lab Computor organ
US3831015A (en) * 1972-06-08 1974-08-20 Intel Corp System for generating a multiplicity of frequencies from a single reference frequency
US3809788A (en) * 1972-10-17 1974-05-07 Nippon Musical Instruments Mfg Computor organ using parallel processing
US3809789A (en) * 1972-12-13 1974-05-07 Nippon Musical Instruments Mfg Computor organ using harmonic limiting
US3809792A (en) * 1973-01-05 1974-05-07 Nippon Musical Instruments Mfg Production of celeste in a computor organ
US3809790A (en) * 1973-01-31 1974-05-07 Nippon Musical Instruments Mfg Implementation of combined footage stops in a computor organ
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Cited By (25)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4048480A (en) * 1975-04-30 1977-09-13 Minot Pierre J M Generators of anharmonic binary sequences
US4748888A (en) * 1975-07-03 1988-06-07 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument including waveshape memory and modifiable address control
DE2629697A1 (de) * 1975-07-03 1977-01-20 Nippon Musical Instruments Mfg Elektronisches musikinstrument
US4112803A (en) * 1975-12-29 1978-09-12 Deutsch Research Laboratories, Ltd. Ensemble and anharmonic generation in a polyphonic tone synthesizer
US4135422A (en) * 1976-02-12 1979-01-23 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument
US4103582A (en) * 1976-04-02 1978-08-01 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument
US4177706A (en) * 1976-09-08 1979-12-11 Greenberger Alan J Digital real time music synthesizer
US4246823A (en) * 1977-11-01 1981-01-27 Nippon Gakki Seizo Kabushiki Kaisha Waveshape generator for electronic musical instruments
US4215614A (en) * 1977-12-13 1980-08-05 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instruments of harmonic wave synthesizing type
US4175464A (en) * 1978-01-03 1979-11-27 Kawai Musical Instrument Mfg. Co. Ltd. Musical tone generator with time variant overtones
US4257303A (en) * 1978-07-31 1981-03-24 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument of partials synthesis type
US4416180A (en) * 1979-08-24 1983-11-22 Sony Corporation Wave synthesizing apparatus
US4345500A (en) * 1980-04-28 1982-08-24 New England Digital Corp. High resolution musical note oscillator and instrument that includes the note oscillator
US4437377A (en) 1981-04-30 1984-03-20 Casio Computer Co., Ltd. Digital electronic musical instrument
US4616546A (en) * 1981-10-15 1986-10-14 Nippon Gakki Seizo Kabushiki Kaisha Electronic musical instrument forming tones by wave computation
US4633749A (en) * 1984-01-12 1987-01-06 Nippon Gakki Seizo Kabushiki Kaisha Tone signal generation device for an electronic musical instrument
US4811644A (en) * 1985-02-26 1989-03-14 Kabushiki Kaisha Kawai Gakki Seisakusho Electronic musical instrument for generation of inharmonic tones
US4984496A (en) * 1987-09-08 1991-01-15 Allen Organ Company Apparatus for deriving and replicating complex musical tones
US5900570A (en) * 1995-04-07 1999-05-04 Creative Technology, Ltd. Method and apparatus for synthesizing musical sounds by frequency modulation using a filter
US6091269A (en) * 1995-04-07 2000-07-18 Creative Technology, Ltd. Method and apparatus for creating different waveforms when synthesizing musical sounds
US5936182A (en) * 1997-06-25 1999-08-10 Kabushiki Kaisha Kawai Gakki Seisakusho Musical tone synthesizer for reproducing a plural series of overtones having different inharmonicities
EP1039442A2 (de) * 1999-03-25 2000-09-27 Yamaha Corporation Verfahren und Vorrichtung zur Wellenformkomprimierung und Erzeugung
EP1039442A3 (de) * 1999-03-25 2003-08-20 Yamaha Corporation Verfahren und Vorrichtung zur Wellenformkomprimierung und Erzeugung
FR2960688A1 (fr) * 2010-06-01 2011-12-02 Centre Nat Rech Scient Procede et systeme de synthese de signaux periodiques anharmoniques et instrument de musique comprenant un tel systeme
WO2011151598A1 (fr) * 2010-06-01 2011-12-08 Centre National De La Recherche Scientifique (C.N.R.S) Procede et systeme de synthese de signaux periodiques anharmoniques et instrument de musique comprenant un tel systeme

Also Published As

Publication number Publication date
DE2431161C2 (de) 1983-07-07
NL164983C (nl) 1981-02-16
GB1469461A (en) 1977-04-06
NL7408600A (de) 1974-12-31
JPS5340527B2 (de) 1978-10-27
JPS5036109A (de) 1975-04-05
IT1015405B (it) 1977-05-10
DE2431161A1 (de) 1975-01-16
NL164983B (nl) 1980-09-15

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