Production Of Celeste In A Computor Organ

Abstract

Apparatus is disclosed for producing a celeste 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 notes as the computations are carried out in real time. Each amplitude is computed during a regular time interval t.sub.x by individually calculating and combining at least two sets of discrete Fourier components. The first set includes harmonically related components, generally the true pitch fundamental and overtones of each selected note. Components of the second set are offset slightly higher in frequency from those in the first set. The resultant synthesized sound resembles an organ celeste stop wherein two organ pipes, one tuned slightly sharp with respect to the other, are sounded when a note is played. In one illustrative embodiment, each set contains the same number of components, each component in the second set being slightly higher in frequency than the corresponding component of the first set. In another embodiment, the first set includes plural harmonic components, the second set contains only one component slightly offset from the fundamental of the first set.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to production of celeste in a computor organ.

2. Related Applications

The present invention is related to the inventor's copending U.S. Pat. applications No. 225,883, filed on Feb. 14, 1972, entitled COMPUTOR ORGAN and No. 298,365, filed on Oct. 17, 1972, entitled COMPUTOR ORGAN USING PARALLEL PROCESSING. Those disclosures are incorporated herein by reference.

3. Description of the Prior Art.

The celeste tones of a pipe organ are produced by a multi-rank set of pipes. One rank is set to true pitch, producing tones at the nominally correct 8-foot frequencies. The second rank consists of like sounding pipes, but tuned sharp with respect to true pitch. The frequency offset of the second rank is not consistent over the manual, but typically ranges from about 2 Hz at C.sub.3 (the note of C in the third octave) to about 4 Hz at C.sub.5. When a note is played, the listener perceives a pleasant beat note as the sounds from the two ranks interact. This gives the tone a considerable warmth.

In conventional electronic organs a celeste effect is obtained using a separate set of oscillators tuned sharp with respect to the usual analog tone generators. When mixed electrically or acoustically, the combined generator output produce a reasonable semblance of celeste. In another approach, a pseudo-celeste effect is achieved acoustically by using a slowly rotating speaker to reproduce the organ tones.

Celeste cannot easily be produced in a digital organ of the type wherein a stored musical waveshape is repeatedly read from memory at a rate determined by the fundamental frequency of the note being generated. (An instrument of this type is shown in the inventor's U.S. Pat. No. 3,515,792 entitled DIGITAL ORGAN.) A fundamental characteristic of celeste is an interference or beat effect which occurs between sounds of slightly different frequencies. To synthesize this effect requires production of a waveshape which changes in time. To achieve such synthesis in a system which repeatedly reproduces the same stored wave form requires two separate digital organs, one generating a note of true pitch, the other producing a note of slightly higher pitch. The two notes are combined, either electrically or acoustically, to produce celeste. Obviously, such implementation may double the system cost.

The principal object of the present invention is to produce a celeste effect in a computor organ of the type wherein musical notes are generated by individually calculating and combining the Fourier components comprising that note. To accomplish this, at least two sets of Fourier components, offset slightly in frequency from each other, are calculated and combined to synthesize each celeste tone. In effect, this corresponds to generating two notes, one at the true pitch and another tuned sharp. The resultant waveshape is not uniformly repititious, but changes in time; it may be thought of as the superposition of separate waveshapes associated with two notes of slightly different frequency. When this resultant waveshape is reproduced acoustically, a remarkably realistic celeste effect results.

SUMMARY OF THE INVENTION

As described in the above mentioned patent application entitled COMPUTOR ORGAN, musical notes are produced by computing in real time the amplitudes at successive sample points of a musical waveshape, and converting these amplitudes to notes as the computations are carried out. In accordance with the present invention, the amplitude at each sample point is obtained by summing at least two sets of Fourier components, one associated with the true pitch of the selected note, the other set being offset, generally slightly higher in frequency therefrom. The two sets of Fourier components thus may be considered as synthesizing respectively the true pitch and tuned-sharp ranks of a pipe organ celeste stop.

In one typical implementation, described in conjunction with FIGS. 1 and 2 below, the first set of Fourier components includes the fundamental and second through eighth harmonics of the selected note. These true pitch components are illustrated by the solid lines in the spectrum of FIG. 2. The second set of Fourier components includes a fundamental having a frequency slightly higher than that of the first set, and seven overtones harmonically related to this shifted fundamental, and hence all offset in frequency with respect to the first set. The offset or frequency-shifted components are indicated by broken lines in the spectra of FIG. 2.

The circuitry of FIG. 1 calculates both the true-pitch and frequency-offset Fourier components during each computation time interval t.sub.x. The components are summed to obtain the waveshape amplitude at the sample point currently being evaluated. The computations are repeated during successive time intervals t.sub.x to generate a waveshape which when acoustically reproduced yields a realistic celeste sound. The use of two component sets each having eight harmonics is quite satisfactory to synthesize a flute or soft string voice.

In the alternative embodiment of FIG. 3, a greater number of true pitch harmonics are generated, as indicated by the solid lines in the spectrum of FIG. 4. A rich string voice can be synthesized. The celeste effect is produced by a single harmonic component (shown as a broken line in FIG. 4) having a frequency slightly higher than the true-pitch fundamental. The resultant offset celeste rank has a "sinusoidal" waveform tuned sharp with respect to the first rank.

BRIEF DESCRIPTION OF THE DRAWINGS

A detailed description of the invention will be made with reference to the accompanying drawings, wherein like numerals designate corresponding parts in the several figures.

FIG. 1 is an electrical block diagram of a computor organ configured to produce a celeste effect with an equal number of Fourier components in the true-pitch and offset-frequency sets.

FIG. 2 is a harmonic spectrum associated with the computor organ of FIG. 1.

FIG. 3 is an electrical block diagram of a computor organ configured for production of celeste and wherein only a single frequency-shifted component is generated.

FIG. 4 is a harmonic spectrum associated with the computor organ of FIG. 3.

FIG. 5 is a simplified electrical block diagram of circuitry useful in conjunction with the computor organ of FIG. 3 for inhibiting production of celeste for certain selected notes.

FIG. 6 is an electrical block diagram showing celeste generation in a parallel processing 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 of the invention best is defined by the appended claims.

Structural and operational characteristics attributed to forms of the invention first described shall also be attributed to forms later described, unless such characteristics are obviously inapplicable or unless specific exception is made.

The computor organ 10 of FIG. 1 produces via a sound system 11 musical notes having a celeste quality. For each note selected by the keyboard switches 12, the computor organ 10 computes the amplitudes at successive sample points of a waveshape characterizing the selected note. Each amplitude is obtained by calculating two sets of discrete Fourier components as illustrated in FIG. 2.

Both sets of components are summed algebraically in an accumulator 13 which, at the end of each computation time interval t.sub.x contains the amplitude for the current sample point. This amplitude is provided via a gate 14, enabled by the t.sub.x signal on a line 15, to a digital-to-analog converter 16 which supplies to the sound system 11 a voltage corresponding to the waveshape amplitude just computed. Computation of the amplitude for 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. The resultant sound, synthesized from true pitch and frequency-offset harmonic components, realistically simulates a multi-rank celeste tone.

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. Each true pitch Fourier component F.sub.A.sup.(n) is calculated in accordance with the following equation:

F.sub.A.sup.(n) = C.sub.n sin (2.pi./N) nqR for q = 1, 2, 3 (1)

where R is the frequency number mentioned above, and n = 1, 2, 3, . . . A designates the Fourier component during evaluated. The value n = 1 corresponds to the fundamental, n = 2 to the second harmonic, n = 3 to the third harmonic, and so forth. The harmonic coefficient C.sub.n specifies the relative amplitude of n.sup.th Fourier component. The value of R designates each sample point of the waveshape being generated.

Similarly, each frequency-offset Fourier component F.sub.B.sup.(n) is calculated in accordance with the following equation:

F.sub.B.sup.(n) = C.sub.n ' sin (2.pi./N) nq (R + .delta.) for q = 1 2, 3 (2)

where again n = 1, 2, 3, . . . B designates which order Fourier component is being evaluated. The harmonic coefficient C.sub.n ' specifies the relative amplitude of the n.sup.th Fourier component in the shifted-frequency set. The value .delta. determines the extent of frequency-offset with respect to the corresponding true-pitch component. This value .delta. may be the same for all notes, or may be different for each note or groups of notes. Appropriate values of .delta. are stored in a memory 18 (FIG. 1) accessed in unison with the frequency number memory 17 as each keyboard switch 12 is selected.

The value N designates the number of amplitude sample points computed for the note of lowest pitch (fundamental frequency) of the computor organ 10. Satisfactory synthesis of pipe organ sounds is achieved using 32 such sample points (N = 32). Preferably the total number (A + B) of components calculated to synthesize the waveshape is equal to or less than N/2. This will satisfy the well known sampling rate requirements (related to the Nyquist criteria) of a sampled data system. In the embodiment of FIG. 1, the computor organ 10 calculates eight Fourier components (A = 8, B = 8) for each of the two sets combined to obtain each waveshape sample point amplitude. Accordingly, the sample point amplitude X.sub.o (qR) is given by the relationship: ##SPC1##

which is a form of discrete Fourier representation of a sampled periodic complex waveshape.

In the embodiment of FIG. 1, equation 3 is implemented by computing the amplitude value x.sub.o (qR) for each sample point during a fixed time interval t.sub.x established by a clock 20 and a counter 21. During each interval t.sub.x individual Fourier components are calculated in successive time intervals designated t.sub.cp1 through t.sub.cp16 respectively. During the first eight intervals t.sub.cp1 through t.sub.cp8 .sub.' the eight true-pitch components (solid lines in FIG. 2) are calculated in accordance with equation (1) above. The eight frequency-shifted components (broken lines in FIG. 2) are calculated during the subsequent calculation intervals t.sub.cp9 through t.sub.cp16 .sub.' in accordance with equation (2) above. All of the calculated components are summed in the accumulator 13, the contents of which, representing the amplitude value x.sub.o (qR), is gated to the digital-to-analog converter 16 at the end of the computation cycle t.sub.x.

To this end, the clock 20 provides timing pulses at intervals t.sub.cp via a line 22 to the counter 21. The counter 21 preferably is of modulo 16, and provides outputs t.sub.cp1 through t.sub.cp16 on the lines designated with corresponding numbers. The signals t.sub.cp1 through t.sub.cp8 all are provided via an OR-gate 23 onto a line 24 to control calculation of the true-pitch components. Similarly, the signals t.sub.cp9 through t.sub.cp16 all are supplied via an OR-gate 25 to a line 26 which controls calculation of the frequency-offset components. The t.sub.cp16 signal, slightly delayed in a delay unit 27, provides the t.sub.x signal on the line 15 indicating the end of the computation cycle.

To calculate each true-pitch harmonic component, the frequency number R associated with a selected note is supplied from the memory 17 via a line 28 and a gate 29 to a note interval adder 30. The gate 29 is enabled by the t.sub.x signal, so that the contents of the adder 30 is incremented each computation interval, and represents the value (qR) designating the waveshape sample point currently being evaluated.

At each interval t.sub.cp1 through t.sub.cp8 .sub.' the value (qR) is gated from the adder 30 via a line 32 and a gate 33 to a harmonic interval adder 34 which is cleared by the t.sub.x signal at the beginning of each computation cycle. Accordingly, during the first eight calculation cycles, the contents of the adder 34 represents the value nqR (for n = 1, 2, 3, . . . 8) designating which true-pitch harmonic component currently is being evaluated.

An address decoder 35 accesses from a sinusoid table 36 the value sin (2.pi./N) nqR corresponding to the argument nqR received via a line 35' from the harmonic interval adder 34. The sinusoid table 36 may comprise a read only memory storing values of sin (2.pi./N) .theta. for 0 .ltoreq. .theta. .ltoreq. N at intervals of D, where D is called the resolution constant of the memory.

The value sin (2.pi./N) nqR, supplied via a line 37, is multiplied by the coefficient C.sub.n for the corresponding n.sup.th harmonic by a multiplier 38. The multiplication product represents the amplitude F.sub.A.sup.(n) of the n.sup.th true-pitch harmonic component, and is supplied via a line 39 to the accumulator 13. The appropriate coefficient C.sub.n is accessed from a harmonic coefficient memory 41, described in more detail below, under direction of a memory address control unit 42 also receiving the computation interval signals t.sub.cp1 through t.sub.cp8 from the line 24.

After the eighth true-pitch component has been calculated, the harmonic interval adder 34 is cleared. To accomplish this, the the t.sub.cp8 signal, slightly delayed by a delay unit 44, is supplied via a line 45 to the "clear" input of the adder 34.

To compute the frequency-offset components, the value .delta. associated with the selected note is accessed from the memory 18 and added to the frequency number R for that note by an adder circuit 46. The sum (R + .delta.) is supplied to a second note interval adder 47 via a gate 48 actuated by the computation interval signal t.sub.x on the line 15. Accordingly, the note interval adder 47 during each computation interval will contain the sum q(R + .delta.). This value q(R + .delta.) in effect represents the sample point of a waveshape having a fundamental slightly higher in frequency, by an amount designated by .delta., than the true-pitch fundamental of the same note.

At each interval t.sub.cp9 through t.sub.cp16 the value q(R + .delta.) is supplied via a line 49 and a gate 50 to the harmonic interval adder 34. Accordingly, the contents of the adder 34 represents a quanitity nq(R + .delta.) for n = 1, 2, 3, . . . 8 where n now indicates the harmonic order of the frequency-shifted Fourier components illustrated by the broken lines in FIG. 2.

The memory address decoder 35 now accesses from the sinusoid table 36 the value sin (2.pi./N) nq(R + .delta.) corresponding to the argument nq(R + .delta.) received from the harmonic interval adder 34 on the line 37. This sin value, supplied via the line 37, is multiplied by the appropriate harmonic coefficient C.sub.n ' obtained from the harmonic coefficient memory 41. The memory address control 42 now receives the signals t.sub.cp9 through t.sub.cp16 on the line 26, insuring that the appropriate values C.sub.n ' are supplied to the multiplier 38.

The output of the multiplier 38 on the line 39 represents the value F.sub.B.sup.(n) of the frequency-offset component currently being calculated. This value is supplied to the accumulator 13 where it is summed with the previously calculated true-pitch and frequency-shifted components. When all eight frequency-shifted components have been evaluated (i.e., after interval t.sub.cp16) the contents of the accumulator 13 represents the value x.sub.o (qR) as given by equation (3) above. The t.sub.x signal gates this value x.sub.o (qR) via the digital-to-analog converter 16 to the sound system 11, and clears the accumulator 13 in readiness for computation of the next sample point amplitude. As the computations are carried out, the sound produced by the system 11 corresponds to the selected notes with a pleasing celeste effect.

The memory 41 advantageously comprises a read only memory containing harmonic coefficient values C.sub.n and C.sub.n ' appropriate to produce a note of desired tonal quality. The values C.sub.n may be the same as, or different from the values C.sub.n ' for like harmonics. In the former instance (C.sub.n = C.sub.n ') each frequency-offset harmonic component (broken lines in FIG. 2) will have an amplitude equal to the corresponding true-pitch component. This in effect will synthesize a pipe organ sound wherein both celeste ranks are of like tonal quality. Alternatively, the values C.sub.n may differ from the corresponding value C.sub.n ', producing a sound wherein the two celeste ranks have different voices.

The following Table I indicates typical values of C.sub.n and C.sub.n ' for a flute voice and a soft string voice respectively wherein both celeste ranks are of like voice (C.sub.n = C.sub.n ') and for a celeste stop having ranks of different tonal quality (C.sub.n .noteq. C.sub.n ').

TABLE I __________________________________________________________________________ Value Stored in Memory __________________________________________________________________________ Flute Soft String Mixed Voice Harmonic Coefficient (Relative Amplitude) Decibel Equivalent (Relative Amplitude) db Equivalent (Relative Amplitude) db __________________________________________________________________________ Equivalent C.sub.1 127 0 127 0 127 0 C.sub.2 0 -50 40 -10 40 -10 C.sub.3 4 -30 16 -18 16 -18 C.sub.4 0 -50 36 -11 36 -11 C.sub.5 0 -50 6 -27 6 -27 C.sub.6 0 -50 4 -30 4 -30 C.sub.7 0 -50 5 -29 5 -29 C.sub.8 0 -50 1 -44 1 -44 C.sub.1 ' 127 0 C.sub.2 ' Same Same 0 -50 C.sub.3 ' as as 4 -30 C.sub.4 ' C.sub.1 --C.sub.8 C.sub.1 --C.sub.8 0 -50 C.sub.5 ' respectively respectively 0 -50 C.sub.6 ' 0 -50 C.sub.7 ' 0 -50 C.sub.8 ' 0 -50 __________________________________________________________________________

The harmonic coefficient memory 41 and address control 42 together may be implemented using a single integrated circuit read only memory such as the Signetics type 8223. Such unit accepts a binary coded addressing signal. Correspondingly, the counter 21 may comprise a Signetics type 8281 16-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.sub.cp1 through t.sub.cp16 signal lines shown in FIG. 1. The type 8223 memory may be programmed to store the harmonic coefficients listed in Table I above, or other values of C.sub.n and C.sub.n ' appropriate to produce other celeste voices.

The frequency number memory 17 and the .delta. memory 18 likewise may be implemented using the same or separate conventional integrated circuit read only memories such as the Signetics type 8223. The following table shows typical values for the frequency number R and .delta. values for the notes between C.sub.3 and C.sub.5.

TABLE II ______________________________________ Note R .delta. Frequency Offset of Shifted Fundamental(Hertz) ______________________________________ C.sub.3 0.0341 0.005 2.00 C .sub.3 0.0361 0.005 2.10 D.sub.3 0.0382 0.006 2.20 D .sub.3 0.0405 0.006 2.25 E.sub.3 0.0429 0.006 2.35 F.sub.3 0.0455 0.006 2.45 F .sub.3 0.0482 0.006 2.50 G.sub.3 0.0510 0.007 2.60 G .sub.3 0.0541 0.007 2.70 A.sub.3 0.0573 0.007 2.75 A .sub.3 0.0607 0.007 2.85 B.sub.3 0.0643 0.008 2.95 C.sub.4 0.0681 0.008 3.00 C .sub.4 0.0722 0.008 3.10 D.sub.4 0.0765 0.008 3.20 D .sub.4 0.0810 0.009 3.30 E.sub.4 0.0858 0.009 3.40 F.sub.4 0.0909 0.009 3.45 F .sub.4 0.0963 0.009 3.55 G.sub.4 0.1021 0.009 3.60 G .sub.4 0.1081 0.010 3.70 A.sub.4 0.1146 0.010 3.75 A .sub.4 F 0.010 3.85 B.sub.4 0.1286 0.010 3.90 C.sub.5 0.1362 0.011 4.00 ______________________________________

in the foregoing table, the frequency numbers are based on N = 32 sample points per period for the note C.sub.7, and assume a monophonic instrument as shown in FIG. 1. The listed .delta. values will provide the frequency-offset between the true-pitch and frequency-shifted fundamental components also specified in Table II. The .delta. values are a design choice selected to provide a pleasing celeste. In the example of Table II, different groups of notes have like frequency offset. As mentioned before, this is not necessary, and all notes could have the same offset, or each note could have a different frequency offset.

In the alternative embodiment of FIG. 3, the computor organ 10' calculates 15 true-pitch Fourier components F.sub.A.sup.(n) (for n = 1, 2, 3, . . . ,15) and a single component F.sub.B.sup.(1) offset slightly higher in frequency than the true-pitch fundamental. The associated harmonic spectrum is shown in FIG. 4. The true-pitch components are calculated during the time intervals t.sub.cp1 through t.sub.cp15.sub.' and the offset component is evaluated at the calculation interval t.sub.cp16.

To this end, the corresponding t.sub.cp1 through t.sub.cp15 outputs from the counter 21' are supplied via an OR-gate 52 and a line 53 to the gate 33. Thus the value nqR in the harmonic interval adder 34' is incremented at each of these 15 consecutive calculation intervals. Accordingly, the true-pitch component values F.sub.A.sup.(n) for n = 1,2, . . .,15 successively are provided on the line 39' for summation in the accumulator 13. After the 15th true-pitch component F.sub.A.sup.(15) has been calculated, the harmonic interval adder 34' is cleared by the t.sub.15 signal, slightly delayed by a delay unit 54.

The single frequency-offset component is calculated during the interval t.sub.cp16. At the beginning of each computation cycle, the value .delta. associated with the selected note is accessed from the memory 18' and supplied via a gate 55 to an interval adder 56. The value .delta. is added to the previous contents of the interval adder 56, so that the output on a line 57 represents the value q.delta.. This is summed with the value qR from the note interval adder 30 by an adder 58 to obtain the value q(R + .delta.). At the calculation interval t.sub.cp16, the value q(R + .delta.) is supplied from the adder 58 via a gate 59 to the harmonic interval adder 34' upon occurrence of the t.sub.cp16 signal on a line 60. Since the adder 34' previously was cleared by the delayed t.sub.15 signal, the resultant contents of the adder 34' will be simply q(R + .delta.).

The memory address decoder 35 then accesses from the sinusoid table 36 the value sin (2/N) q(R + .delta.) corresponding to the argument q(R + .delta.) received from the adder 34'. That sin value, provided via the line 37', is multiplied by the corresponding coefficient C.sub.1 ' to provide the value F.sub.B.sup.(1) = C.sub.1 ' sin (2.pi./N) q(R + .delta.). This value F.sub.B.sup.(1) is added in the accumulator 13 to the sum of the previously calculated 15 true-pitch components, to provide the sample point amplitude ##SPC2##

This value of x.sub.o (qR) then is gated via the digital-to-analog converter 16 to the sound system 11. Again there results a note having pleasant celeste characteristics.

FIG. 4 shows a typical harmonic spectrum of the celeste sound produced by the computor organ 10' of FIG. 3. The 15 true-pitch components are indicated by the solid lines, and the single frequency-offset component by the broken line. The relative amplitudes of the various components of course determine the tonal quality of the produced sound. By way of example, a rich string sound may be produced using the harmonic component values C.sub.n and C.sub.1' listed in the following Table III. These values are stored in the harmonic coefficient memory 41' and appropriately accessed by the memory address control 42' which receives the calculation interval signals on the lines 53 and 60.

TABLE III ______________________________________ Harmonic Value Stored in Memory Coefficient Rich String Voice (Relative (Decibel Amplitude) Equivalent) ______________________________________ C.sub.1 80 -4 C.sub.2 80 -4 C.sub.3 101 -2 C.sub.4 127 0 C.sub.5 32 -12 C.sub.6 36 -11 C.sub.7 25 -14 C.sub.8 18 -17 C.sub.9 28 -13 C.sub.10 16 -18 C.sub.11 13 -20 C.sub.12 7 -25 C.sub.13 5 -28 C.sub.14 3 -33 C.sub.15 3 -33 C.sub.1 ' 127 0 ______________________________________

Celeste may be implemented for all notes of the organ, or only for some notes. Thus in the embodiment of FIG. 3, celeste is produced for each note between C.sub.3 and C.sub.5. Celeste may be inhibited, as by appropriate logic 62, when a note between C.sub.1 and B.sub.3 or between D.sub.5 and C.sub.7 is selected.

Illustrative celeste inhibit circuitry 62 is shown in FIG. 5. The lines C.sub.1 and B.sub.3 and B.sub.5 through C.sub.7 from the corresponding keyboard (or pedal) switches 12 are supplied on an OR-gate 63. When a note between C.sub.3 and C.sub.5 is played, a low output is present on the line 64 from the OR-gate 63, indicating that celeste is to be implemented. This low signal is inverted by an inverter 65 to produce on a line 66 a high signal which enables a pair of AND-gates 67, 68. The gates 67, 68 thus provide the t.sub.cp15 and t.sub.cp16 signals respectively to the delay unit 54 and the gate 59, as shown in FIG. 3. Normal celeste production occurs.

When a note between C.sub.1 and B.sub.3, or between B.sub.5 and C.sub.7 is played, the output of the OR-gate 63 on the line 64 is high. This functions as described below to inhibit celeste production. During the calculation interval t.sub.cp16 the offset harmonic component F.sub.B.sup.(1) is not generated. Instead, a 16th (n = 16) true-pitch harmonic F.sub.A.sup.(16) is produced.

When the output of the OR-gate 63 is high, the output of the inverter 65 is low, and the AND-gates 67, 68 are disabled. The t.sub.cp15 is not supplied to the delay unit 54, hence the harmonic interval adder 34' is not cleared at the end of the t.sub.cp15 interval. Further, the high signal on the line 64 enables an AND-gate 69, which provides the t.sub.cp16 pulse via an OR-gate 70 to the gate 33. As a result, during the time interval t.sub.cp16 the value (qR) is added to the contents of the harmonic interval adder 34', so that the contents becomes nqR = 16qR. As a result, the sin value corresponding to that argument (16qR) is accessed from the sinusoid table 36 and to the harmonic amplitude multiplier 38.

Similarly, the t.sub.cp16 signal is provided via the AND-gate 69 to the memory access control 42'. This causes access from the harmonic coefficient memory 41' of the value C.sub.16 (that is, the harmonic coefficient for the 16th true-pitch harmonic). As a result, the true-pitch harmonic F.sub.A.sup.(16) is provided to the accumulator 13. The resultant waveshape is obtained from 16 true-pitch harmonics and no frequency-offset components; this corresponds exactly to the production of a true-pitch note without celeste.

As shown in FIG. 6, production of a celeste readily is implemented in a computor organ 75 using parallel processing. The organ 75, like the instrument of FIG. 1, calculates the same number of true-pitch and frequency-shifted components. The advantage of using parallel processing is that both sets of Fourier components are calculated concurrently, so that the system clock rate may be one-half that required for the computor organ 10 of FIG. 1. As discussed in the above mentioned patent application entitled COMPUTOR ORGAN USING PARALLEL PROCESSING, this significant reduction in computation rate more readily permits the computor organ to be implemented using conventional integrated circuitry.

Referring to FIG. 6, the computor organ 75 includes a first processing channel 76a in which the values F.sub.A.sup.(n) for the true-pitch components are calculated, and a second, like parallel processing channel 76b wherein the values F.sub.B.sup.(n) are calculated for the frequency-shifted components. System timing is established by a clock 77 having a rate one-half that of the clock 20 in FIG. 1. The output pulses t.sub.cp ' from the clock 77 advance a binary counter 78 of modulo 8. The output of the counter 78 on the lines 79a, 79b, 79c comprises a binary signal representing the respective counts t.sub.cp1 ' through t.sub.cp8 '.

At the first interval t.sub.cp1 ' the low order, true-pitch Fourier component F.sub.A.sup.(1) is calculated in the channel 76a and concurrently the low order frequency-shifted component F.sub.B.sup.(1) is calculated in the channel 76b. These components, present on the respective lines 80, 81 are summed by an adder 82 and supplied via a line 83 to an accumulator 13, gate 14, digital-to-analog converter 16 and sound system 11 like that of FIG. 1. At consecutive intervals t.sub.cp2 ' through t.sub.cp8 ' successive pairs of true-pitch and frequency-shifted components F.sub.A.sup.(n) and F.sub.B.sup.(n) for values n = 2,3, . . . 8 are computed, summed in the adder 82 and supplied to the accumulator 13. In this manner, both sets of Fourier components are computed during eight time intervals t.sub.cp ', each of which intervals t.sub.cp ' is twice as long as the calculation interval t.sub.cp of the FIG. 1 system.

The various components of the parallel processing organ 75 will be recognized by reference to FIG. 1. However, separate harmonic interval adders 34a, 34b are used to accumulate the totals nqR and nq(R + .delta.) respectively. Both adders 34a, 34b are cleared by the t.sub.x signal derived via a delay unit 84 from the t.sub.cp8 ' signal. The values qR from the note interval adder 30a and q(R + .delta.) from the note interval adder 30b respectively are gated to the harmonic interval adders 34a and 34b via gates 33a and 33b enabled at each calculation interval t.sub.cp1 ' through t.sub.cp8 '.

The timing signals t.sub.cp1 ' through t.sub.cp8 ' are derived from the binary counter 78 output using a binary-to-octal decoder 85. The eight lines from the decoder 85, containing the respective signals t.sub.cp1 ' through t.sub.cp8 ' all are connected to an OR-gate 86 the output of which, on a line 87, enables the gates 33a and 33b.

Separate harmonic coefficient memories 41a, 41b and associated address control units 42a, 42b are used in the respective channels 76a, 76b. Each may be implemented using a Signetics type 8223 read only memory or the equivalent, the address control portion of which directly receives the binary coded count on the lines 79a - 79c. The memory 41a contains the true-pitch harmonic coefficients C.sub.n and the memory 41b stores the coefficients C.sub.n ' for the frequency-shifted components. These values may correspond to those set forth above in Table I.

Although the embodiments shown in the drawings each calculate two sets of Fourier components, the invention is not so limited. Thus three or more sets of components could be evaluated and summed to obtain each sample point amplitude. In such case, all three sets may be slightly offset in frequency from each other. Further, even in the two set embodiments, it is not required that the components of either set correspond in frequency to the true pitch of the selected note. Thus, e.g., one set may be tuned slightly below true pitch, the other slightly above. Advantageously, but not necessarily, the musical instruments disclosed herein are implemented digitally.

TABLE A __________________________________________________________________________ Conventional Inte- Component grated Circuit* (or (FIG. 1) other reference) Remarks __________________________________________________________________________ Frequency (a)SIG 8223 field-pro- number grammable read only memory 17 memory (ROM) [p. 37] Typical values of R (b)TI SN5488A, SN7488A and .delta. are 256-bit ROM [p. 9-235] listed in Table II of specification .delta. memory 18 Note interval (a)SIG. 8260 arithmetic adders 30,47 logic element [p. 37] (b)SIG. 8268 gated full adder [p. 97] (c)TI SN5483, SN7483 4-bit binary full adders [p. 9-271] (may be connected as shown in Flores.sup.1 Section 11.1 to accumulate sum) Harmonic Same as note interval interval adder 30 adder 34 R+.delta. Adder 46 SIG. 8268 gated full adder Gates 14,29,33, TI SN5408, SN5409 48,50 quadruple AND gates [p. 6-17] Sinusoid table (a)TI TMS4405 sinusoid 36 and memory table and addressing address decoder 35 circuitry Roundoff, if required, may (b)TI TMS4400 ROM be implemented containing 512 words per Ledley.sup.2 of eight-bits [p. 14-188] section 4-6. programmed to store sin values Harmonic (a)SIG 8223 read only coefficient memory which in- See Table I for memory 41 cludes address examplary and memory control circuitry contents address control 42 (b)TI SN54166 series shift registers [p.9-134] Harmonic (a)May be implemented Amplitude as shown in appli- Multiplier cation sheet, SIG 38 catalog, p.28 using SIG 8202 buffer registers and 8260 arithmetic element (b)Also can be implemented using SIG 8243 scaler [p.65] Accumulator 13 (a)SIG 8268 or TI SN5483, SN7483 full adders connected as shown in Flores.sup.1, section 11.1 "Accumulators". Counter 21 (a)SIG 8281 sixteen-state binary counter [p. 123], and a SIG 8250 binary- to-octal decoder Clock 20 Any oscillator __________________________________________________________________________ *TI=Texas Instrument Co. [Page references are to the TI "Integrated Circuits Catalog for Design Engineers", First Edition, January, SIG=Signetics, Sunnyvale, California [Page references are to the SIG "Digital 8000 Series TTL/MSI" catalog, copyright 1971 Flores, Ivan "Computer Logic" Prentice-Hall, 1960 Ledley, Robert "Digital Computer and Control Engineering" McGraw-Hill, 1960

Claims

Intending to claim all novel, useful and unobvious features shown or

1. Apparatus for production of celeste in a computor organ comprising:

first means, operative during repetitive computation intervals, for separately calculating a first set of Fourier components associated with the musical waveshape of a first note of one pitch; and second means, also operative during said repetitive computation intervals, for separately calculating a second set of Fourier components associated with the musical waveshape of a second note having a pitch slightly offset in frequency with respect to said first note,

means for combining the calculated components of said first and said second sets within each computation interval to establish a sample point amplitude of a resultant musical waveshape the shape of which varies in time as a result of the frequency difference between said first and second notes,

means operative at the end of each computation interval for incrementing the effective sample point for which said resultant waveshape amplitude is established, and

means for converting said resultant waveshape amplitudes to sounds in real

2. Celeste production apparatus according to claim 1 wherein said calculating and combining is performed digitally, wherein said means for converting includes a digital-to-analog converter and a sound system for reproducing the output from said converter, and wherein each component amplitude is established by a set of coefficients stored digitally, the relative amplitudes of said components establishing the tonal quality of

3. Celeste production apparatus according to claim 1 wherein components of said first set are calculated at effective waveshape sample points separated by qR wherein R is a frequency number establishing the fundamental period of said first note and q is an integer incremented at the end of each computation interval and wherein components of said second set are calculated at effective waveshape sample points separated by q(R + .delta.) wherein .delta. is a value designating the amount of frequency

4. Celeste production apparatus according to claim 1 comprising:

a clock for establishing said repetitive computation intervals,

a frequency number memory storing values R which establish the effective waveshape sample point separation for corresponding notes,

a .delta. memory storing harmonic offset values .delta. for selectable notes,

a keyboard for selecting notes to be produced by said apparatus, actuation of a key on said keyboard causing memory readout of the R and .delta. values for the selected note,

note interval adders for establishing values of (qR) and q(R + .delta.) for selected notes during successive computation intervals, where q is an integer incremented by said means for incrementing, and wherein said first means comprises

circuitry, cooperating with said note interval adders, for evaluating said first set F.sub.A.sup.(n) of Fourier components in accordance with the relationship

F.sub.A.sup.(n) = C.sub.n sin (2.pi./N) nqR

and wherein said second means comprises circuitry, also cooperating with said note interval adders, for evaluating said second set F.sub.B.sup.(n) of Fourier components in accordance with the relationship

F.sub.B.sup.(n) = C.sub.n ' sin (2.pi./N) nq (R + .delta.)

wherein A and B represent the number of Fourier components includes in said respective first and second sets, components in said second set being shifted in frequency with respect to said first set by an amount established by said values .delta., wherein C.sub.n and C.sub.n ' are coefficients indicating the relative amplitude of the corresponding n.sup.th component in the respective first and second set, and wherein N

5. As a musical instrument exhibiting a:

first means for computing at regular time intervals t.sub.x the amplitudes x.sub.o (qR) of a waveshape, where q is an integer incremented each time interval t.sub.x, in accordance with the relationship ##SPC3##

wherein A and B represent the number of Fourier components included in respective first and second sets defining said waveshape, components in said second set being shifted in frequency with respect to components of said first set by an amount established by .delta., wherein C.sub.n and C.sub.n ' are coefficients establishing the relative amplitudes of the corresponding n.sup.th components in the respective first and second sets, wherein R is a number specifying the period of said waveshape, and wherein N is a system constant, said first means comprising;

a coefficient memory storing said harmonic coefficients C.sub.n and C.sub.n ',

a sinusoid table comprising a memory storing values of sin (2.pi./N) .theta. for 0 .ltoreq. .theta. .ltoreq. N at intervals of D where D is a resolution constant,

a frequency number memory containing values of R associated with selectable musical notes, a .delta. memory containing values of .delta. associated with said notes, and note selection circuitry for accessing from said frequency number and .delta. memories the values R and .delta. for each selected note,

harmonic component evaluation circuitry utilizing said coefficient memory and said sinusoid table to calculate

F.sub.A.sup.(n) = C.sub.n sin (2.pi./N) nqR (n = 1,2, . . .A)

for each of the A Fourier components in said first set in accordance with the selected value R, and to calculate

F.sub.B.sup.(n) = C.sub.n ' sin (2.pi./N) nq(R + .delta.) (n = 1,2, . . .B)

for each of the B Fourier components in said second set in accordance with the selected values R and .delta., and

an accumulator for algebraically summing the calculated values F.sub.A.sup.(n) and F.sub.B.sup.(n) to obtain each waveshape amplitude X.sub.o (qR), and

second means responsive to said first means for providing celeste tones

6. A musical instrument according to claim 5 wherein said calculations are performed digitally, wherein said second means includes a digital-to-analog converter and a sound system for converting said obtained waveshape amplitudes to musical sounds exhibiting a celeste effect, successive cycles of said obtained waveshape being of different

7. A musical instrument according to claim 5 wherein said first means includes:

a clock and counter defining calculation subintervals within said regular interval t.sub.x, components of said first and second sets being

8. A musical instrument according to claim 5 together with means for preventing calculation of components in said second set when notes having

10. A musical instrument according to claim 9 wherein C.sub.n = C.sub.n '

11. A musical instrument according to claim 9 wherein C.sub.n .noteq.

12. A musical instrument according to claim 5 wherein B = 1, the frequency of the single component in said second set being slightly higher than the

13. A musical instrument according to claim 5 wherein N represents the number of waveshape sample points for the tone of lowest fundamental

14. A musical instrument according to claim 5 wherein the components of said first set are harmonically related in frequency to the true pitch of a selected note and wherein each component of said second set is offset slightly higher in frequency from the corresponding component of said

15. A musical instrument according to claim 5 wherein the values .delta. are selected so that the frequency offset of the (n = 1).sup.th component

16. A musical instrument according to claim 5 wherein said first means includes parallel processing channels for concurrently calculating components of said first and second sets.