U.S. patent number 3,888,153 [Application Number 05/374,680] was granted by the patent office on 1975-06-10 for anharmonic overtone generation in a computor organ.
This patent grant is currently assigned to Nippon Gakki Seiko Kabushiki Kaisha. Invention is credited to Ralph Deutsch.
United States Patent |
3,888,153 |
Deutsch |
June 10, 1975 |
Anharmonic overtone generation in a computor organ
Abstract
The production of musical notes containing anharmonic overtones
is implemented in a computor organ of the type disclosed in U.S.
patent application Ser. No. 225,883, filed Feb. 14, 1972, and now
U.S. Pat. 3,809,786. In such an instrument, the sampled amplitudes
of a musical waveshape are computed in real time by individually
calculating the amplitude contributions of the Fourier components
constituting the waveshape. In accordance with the present
invention, certain of these Fourier components are evaluated at
frequencies offset from multiples of the nominal fundamental
frequency of the note being generated. This is accomplished by
utilizing in the overtone amplitude calculations offset values
.eta..sub..nu. which establish the extent of anharmonicity of each
overtone. This results in complete freedom of control of the
anharmonicity of individual overtones. The overtone offset
(.eta..sub..nu.) 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.
Inventors: |
Deutsch; Ralph (Sherman Oaks,
CA) |
Assignee: |
Nippon Gakki Seiko Kabushiki
Kaisha (Hamamatsu-shi, JA)
|
Family
ID: |
23477784 |
Appl.
No.: |
05/374,680 |
Filed: |
June 28, 1973 |
Current U.S.
Class: |
84/625; 984/324;
984/397 |
Current CPC
Class: |
G10H
7/105 (20130101); G10H 1/06 (20130101) |
Current International
Class: |
G10H
1/06 (20060101); G10H 7/10 (20060101); G10H
7/08 (20060101); G10h 001/00 (); G10h 005/00 () |
Field of
Search: |
;84/1.01,1.03,1.24,1.25,DIG.4,DIG.5,1.11,1.19,1.22,1.23
;235/152,197 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Richard A. Schaefer, "Electronic Musical Tone Production by
Nonlinear Waveshaping," Journal of the Audio Engineering Society
(USA), Aug. 1970, Vol. 18, No. 4, pp. 413-417..
|
Primary Examiner: Wilkinson; Richard B.
Assistant Examiner: Witkowski; Stanley J.
Attorney, Agent or Firm: Ambrose & Silber
Claims
Intending to claim all novel, useful and unobvious features shown
or described, the inventor makes the following claims:
1. An electronic musical instrument for synthesizing musical tones
having anharmonic overtones, comprising:
evaluation means for individually calculating the constituent
Fourier component amplitudes F.sup.(n) of a musical waveshape in
accordance with the relationship F.sup.(n) = C.sub.n sin
(.pi./W)(nqR+.eta. .sub..nu. )
wherein R is a frequency number establishing the fundamental
frequency of the note, n=1, 2, 3, . . . , W designates the Fourier
component and .nu.=n-1 designates the overtone being evaluated,
C.sub.n is a harmonic coefficient establishing the relative
amplitude of the n.sup.th Fourier component, .eta..sub..nu.
specifies the extent of anharmonicity of the .nu..sup.th overtone,
and q is an integer incremented at regular time intervals t.sub.x,
all W of said constituent Fourier components being evaluated within
each of said intervals t.sub.x,
accumulator means for combining said separately calculated Fourier
component amplitudes to obtain during successive time intervals
t.sub.x the waveshape sample point amplitudes ##SPC4##
for successive sample points qR, and
converter means for converting said sample point amplitudes to
musical tones as said calculations are carried out.
2. An electronic musical instrument according to claim 1 further
comprising overtone offset means for providing to said evaluation
means a selected value .eta. .sub..nu. =.nu..eta. for each
evaluated overtone, wherein .eta. is a constant.
3. An electronic musical instrument according to claim 2 further
comprising overtone offset means for providing to said evaluation
means a selected value .eta. .sub..nu. =.nu..eta.=.nu.Jq for each
evaluated overtone, wherein J is a constant, the overtones of each
synthesized tone thereby being offset by a constant frequency.
4. An electronic musical instrument according to claim 1 further
comprising overtone offset means for providing to said evaluation
means a selected value, .eta..sub..nu.=.nu. (qR/k) for each
evaluated overtone, K is a constant, the overtones of each
synthesized tone thereby being offset from integral multiples of
the note fundamental frequency by a constant number of cents.
5. An electronic musical instrument according to claim 1, wherein
said evaluation means comprises:
a memory storing said harmonic coefficients C.sub.n,
a sinusoid table comprising a storage device containing a set of
sinusoid values at regular angular intervlas,
note selection switches for selecting a value R,
overtone offset means for providing a selected value .eta.
.sub..nu. for each evaluated overtone, and
Fourier component evaluation circuitry utilizing said memory and
said sinusoid table to evaluate F.sup.(n) = C.sub.n
sin(.pi./W)(nqR+.eta. .sub..nu. ) for each of the W constituent
Fourier components in accordance with the selected value R and the
provided values = .sub..nu. .
6. An electronic musical instrument according to claim 5, wherein
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 t.sub.x, the contents of said note interval
adder thereby representing qR,
argument combining circuitry for combining the values qR obtained
from said note interval adder and the values .eta..sub..nu.
provided from said overtone offset means to obtain the arguments
nqR+.eta..sub..nu. for each order n=1, 2, 3, . . . W, Fourier
component,
sin evaluation circuitry, receiving said arguments
ngR+.eta..sub..nu. from said argument combining circuitry, for
obtaining from said sinusoid table the value sin(.pi./ W)(
nqR=.eta..sub..nu. for each received argument nqR=.eta..sub..nu.
and
a harmonic amplitude multiplier for multiplying each such sin value
by the coefficient C.sub.n for the corresponding n.sup.th harmonic
component, the products of such multiplication being supplied to
said accumulator means.
7. A musical instrument according to claim 6 wherein said overtone
offset means comprises;
an overtone offset memory storing said values .eta..sub..nu.,
a memory address control for accessing from said overtone offset
memory the value .eta..sub..nu. corresponding to the n.sup.th
Fourier component being calculated, and wherein said argument
combining circuitry omprises;
a harmonic interval adder, cleared at the beginning of each time
interval t.sub.x, 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
t.sub.x, and
an adder for summing each value ngR obtained from said harmonic
interval adder with the corresponding value .eta..sub..nu. accessed
from said overtone offset memory, the resultant sum
ngR+.eta..sub..nu. being provided to said sin evaluation
circuitry.
8. An electronic musical instrument according to claim 6, wherein
said argument combining circuitry comprises;
a harmonic interval adder, cleared at the beginning of each time
interval t.sub.x,
an accumulating adder incremented by a constant amount J each time
interval t.sub.x, the contents of said accumulating adder
representing the quantity Jq, and
adder means for providing the value qR from said note interval
adder to said harmonic interval adder during calculation of the
(n=1).sup.th Fourier component and for providing the value qR=Jq to
said harmonic interval adder during calculation of each other
Fourier component, the accumulated contents of said harmonic
interval adder thus representing the argument nqR+.nu.Jq.
9. An electronic musical instrument according to claim 6, wherein
said argument combining circuitry comprises;
a harmonic interval adder, cleared at the beginning of each time
interval t.sub.x,
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, and
adder means for providing to said harmonic interval adder the value
qR from said note interval adder during calculation of the
(n=1).sup.th Fourier component and for providing the value qR+qR/K
to said harmonic interval adder during calculation of each other
Fourier component, the accumulated contents of said harmonic
interval adder thus representing the argument nqR+.nu.(qR/K).
10. An electronic musical instrument according to claim 6, wherein
said argument combining circuitry comprises;
a harmonic interval adder cleared at the beginning of each time
interval t.sub.x,
a divider for dividing the selected value R by a constant K to
provide the quotient R/K,
an accumulating adder, the value R/K being added to the previous
contents of said adder at the beginning of each time interval
t.sub.x so that the contents of said adder represents the quantity
qR/K, and
adder means for providing to said harmonic interval adder the value
qR from said note interval adder during calculation of the
(n=1).sup.th Fourier component and for providing the value qR+qR/K
to said harmonic interval adder during calculation of each other
Fourier component, the accumulated contents of said harmonic
interval adder thus representing the argument nqR+.nu.(qR/K).
11. In an electronic musical instrument of the type wherein musical
notes are generated by computing the amplitudes of a musical
waveshape at successive sample points at certain regular time
intervals from stored harmonic coefficient values, 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, the 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:
first means for establishing at said regular time intervals the
successive fundamental sample points qR at which the fundamental
component is evaluated, where R is a constant frequency number
establishing the fundamental frequency of the generated note and q
is an integer incremented as each waveshape amplitude computation
is completed,
second means for establishing, as each overtone is evaluated, an
overtone sample point nqR+.eta..sub..nu. where n designates the
order of the Fourier component being calculated, .nu.=n-1
identifies the corresponding overtone and .eta..sub..nu. designates
the extent of frequency offset of the .nu..sup.th overtone, and
means for utilizing the sample point qR established by said first
means during calculation of teh fundamental (n=1) Fourier component
and for utilizing the overtone sample points nqR+.eta..sub..nu.
established by said second means during calculation of the
individual Fourier components of order n=2 and greater.
12. 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
synthesized waveshape containing anharmonic overtones, the
fundamental component being evaluated at successive sample points
qR, where R is a constant frequency number establishing the
fundamental frequency of the generated note and g is an integer
incremented as each waveshape amplitude computation is completed,
and wherein each overtone is evaluated at an overtone sample point
nqR+.eta..sub..nu. where n designates the order of the Fourier
component being calculated, .nu.=n-1 identifies the corresponding
overtone and .eta..sub..nu. designates the extent of frequency
offset of the .nu..sup.th overtone, said instrument comprising:
a note interval adder to which the value R is added at regular
waveshape amplitude computation time intervals t.sub.x, the
contents of said note interval adder thereby specifying the
fundamental sample point qR,
overtone offset means for providing the overtone offset value
.eta..sub..nu. during calculation of the corresponding
(n=.nu.+1).sup.th Fourier component,
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+.eta..sub..nu. 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+.eta..sub..nu.,
a harmonic amplitude multiplier for multiplying said trigonometric
function by a coefficient C.sub.n establishing the relative
amplitude of the n.sup.th 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.
13. An electronic musical instrument according to claim 12 wherein
said overtone offset means includes circuitry which provides values
.eta..sub..nu.=.nu. (qR/K) where K is a constant, so that each
overtone is offset by an extent which is proportional to the
fundamental frequency of the note being generated.
14. An electronic musical instrument according to claim 12 wherein
said overtone offset means includes circuitry which provides values
.eta..sub..nu.=.nu..eta. where .nu. is a constant.
15. An electronic musical instrument according to claim 12 wherein
said overtone offset means includes circuitry which provides offset
values .eta..sub..nu.=.nu.Jq where J is a constant, so that said
overtones are offset by constant frequency amounts independent of
the note being generated and independent of time.
16. An electronic musical instrument according to claim 12
including:
means for evaluating the (n=1).sup. th Fourier component at a
frequency f' different from the nominal fundamental frequency f of
the note being generated and for evaluating the (.nu.=1).sup. th
overtone at a frequency 2f'+.eta..sub.1 =2f.
17. An electronic musical instrument according to claim 12 further
comprising;
means for time modulating at least some of the offset values
.eta..sub..nu. to produce time variant anharmonic overtones.
18. 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 designating the successive sample points qR at which said
waveshape is sampled, the number R establishing the fundamental
frequency of said waveshape, the value q being an integer
incremented at regular amplitude computation intervals t.sub.x,
means for providing certain offset values .eta..sub..nu.
establishing the extent of anharmonicity of the corresponding
Fourier components,
means, responsive to the designated sample point qR and to the
provided values .eta..sub..nu., for obtaining each constituent
Fourier component a trigonometric function value corresponding to
an argument nqR+.eta..sub..nu., where n designates the order of the
Fourier component being evaluated and .nu.=n-1,
means for scaling each obtained trigonometric function by a
coefficient C.sub.n to establish the relative amplitude of the
corresponding n.sup.th Fourier component, and
means for accumulating the scaled trigonometric function values
during each computation cycle to establish the waveshape sample
point amplitude, and further comprising:
converter and sound system means for converting the waveshape
amplitudes established in said accumulating means to musical notes
as the amplitude computations are carried out, and
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 ##SPC5##
where x.sub.o (qR) is the waveshape sample point amplitude and W
designates the number of Fourier components included in each
amplitude computation.
Description
BACKGROUND OF THE INVENTION
1. Related Applications
The present invention is related to the following copending U.S.
patent applications:
Ser. No. 225,883 COMPUTOR ORGAN, filed Feb. 14, 1972, and now U.S.
Pat. No. 3,809,786.
Ser. No. 298,365 COMPUTOR ORGAN USING PARALLEL PROCESSING, filed
Oct. 17, 1972, and now U.S. Pat. No. 3,809,788.
Ser. No. 321,231 PRODUCTION OF CELESTE IN A COMPUTOR ORGAN, filed
Jan. 5, 1973, and now U.S. Pat. No. 3,809,792.
Ser. No. 328,302 IMPLEMENTATION OF COMBINED FOOTAGE STOPS IN A
COMPUTOR ORGAN, filed Jan. 31, 1973, and now U.S. Pat. No.
3,809,790.
The latter three applications are commonly owned by Nippon Gakki
Seizo Kabushiki Kaisha, the owner of the present application.
2. Field of the Invention
The present invention relates to the generation of musical sounds
containing anharmonic overtones in a computor organ.
3. Description of the Prior Art
The unique tonal quality of certain conventional musical
instruments is attributable to the presence of overtones which are
not true harmonics of the note being played. This anharmonicity of
the overtones is particularly characteristic of struck string
instruments such as the piano and harpsichord. In the past,
electronic synthesis of musical sounds containing non-harmonic
overtones has been seriously impeded by limitations inherent in
known tone generation systems.
For example, in electronic organs of the type using separate
oscillators for each note, overtones which are integral multiples
of the oscillator fundamental frequency are readily obtainable.
However, production of non-harmonic overtones requires a separate
oscillator for each anharmonic or frequency offset overtone, adding
considerably to instrument cost. In digital organs of the type
wherein a complex waveshape is stored in memory and read out
repetitively at a frequency established by the selected note,
individual harmonics cannot be separately controlled. Although the
stored waveshape may be characteristic of a sound having
non-harmonic overtones, the waveshape is fixed. It is impossible to
modulate dynamically the overtone anharmonicity, thereby preventing
synthesis of certain musical sounds.
The computor organ described in the above mentioned U.S. 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 effect between
stops of different footage generated simultaneously in a computor
organ having combined footage (see the above mentioned U.S. patent
application, Ser. No. 328,302). By using anharmonic overtones, the
stops of different footage will be unlocked even when played with a
single key. For example, in such a system 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.
In accordance with usual musical terminology, the term "overtone"
is used herein to refer to one of the higher tones which together
with the fundamental comprises a complex musical tone. 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.
SUMMARY OF THE INVENTION
These and other objectives are achieved by providing anharmonic
overtone generation systems for a computor organ of the type
described in the above mentioned U.S. patent application Ser. No.
225,883. In such an instrument, musical notes are generated by
computing the amplitudes at successive sample points of a musical
waveshape and converting the amplitudes to musical sounds as the
computations are carried out in real time. For each sample point
qR, the constituent harmonic amplitudes F.sup. (n) are calculated
individually, then combined to obtain the waveshape amplitude
X.sub. o (qR). The computations are carried out in accordance with
the following discrete Fourier representation of a sampled periodic
complex waveshape: ##SPC1##
wherein R is a frequency number which establishes the fundamental
frequency of the generated note, n= 1,2,3 . . . , W designates the
harmonic or Fourier component being evaluated, and C.sub. n is a
harmonic coefficient establishing the relative amplitude of the
n.sup. th harmonic. In a computor organ which implements equation
1, each of the harmonic components F.sup. (n) has a frequency which
is an integral multiple of the nominal fundamental frequency.
In accordance with one embodiment of the present invention (see
FIG. 2) individual Fourier component amplitudes F.sup. (n) are
calculated according to the relationship:
F.sup. (n) = C.sub. n sin(.pi./W)(nqR+.eta..sub..nu.) for q= 1,2,3
. . . (Eq. 2)
wherein n designates the order of the Fourier component, .nu.=n- 1
designates the overtone being evaluated, and .eta..sub..nu.
specifies the extend of frequency offset or anharmonically of the
.nu..sup.th overtone. The fundamental (n= 1) component usually is
evaluated at the nominal fundamental frequency of the generated
note, so that .eta..sub..nu. =.eta..sub.o = 0. For each anharmonic
overtone, the corresponding value of .eta..sub.o will be non-zero.
Should .eta..sub..nu.=0 for a particular value of .nu., the
corresponding .nu..sup.th overtone will not be offset in frequency,
but will be a true harmonic of the note being generated. The term
nqR+.eta..sub..nu. herein is called the overtone sample point.
The Fourier component amplitudes F.sup.(n) are summed to obtain the
resultant waveshape sample point amplitude X.sub. o (qR). That is:
##SPC2##
Note that in the special case when .eta..sub..nu.=0 for all values
of .nu., none of the overtones are anharmonic and equation 3
becomes identical to equation 1 above.
An interesting ramification of equations 2 and 3 is that the amount
of frequency offset of each overtone is not fixed in time; rather,
the extent of anharmonically itself varies periodically. This can
be understood if equation 2 is rewritten in the following form:
##SPC3##
In the computor organ, the waveshape amplitudes X.sub. o (qR)
generally are computed at regular time intervals t.sub. x. At each
successive time interval t.sub. x 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.sup. (1) is evaluated at
successive, equally separated sample points. However, for each
anharmonic overtone, the distance between sample points at which
the amplitude of that overtone is evaluated is designated by
(n+(.eta..sub..nu.)/qR) R. Since q itself is changing periodically
with time (i.e., is being incremented at intervals t.sub. x,
resetting at modulo N), the separation between overtone sample
points, determinative of the anharmonically of that overtone, also
will change with time. That is, the extent of anharmonicity of each
overtone will be periodic. Moreover, the periodicity of the
anharmonicity will be smaller at the high frequency end of the
scale (where the R values are greater) than at the low frequency
end. It is this effect which facilitates, inter alia, octave
decoupling in the computor organ.
In alternative embodiments of the invention, the overtone
anharmonicity is independent of time. Thus, in the computor organ
of FIG. 9, 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. In this embodiment, the Fourier component
amplitudes are calculated in accordance with the relationship:
F.sup. (n) = C.sub. n sin (.pi./W) (nqR+.eta..sub..nu.') = C.sub. n
sin (.pi./W) (nqR+ .nu. Jq) for q= 1,2,3, . . . (Eq. 5)
wherein .eta..sub..nu.' = .nu.Jq and J is a constant; preferably J
= 2.sup.- .sup.k with k being an integer. A characteristic of such
embodiment is that the extent of overtone offset is the same for
all keys on the manual. Thus, the first overtone of each note may
be displaced by say +2Hz from the nominal second harmonic
frequency, regardless of what note is being played.
In the preferred forms of the invention shown in FIGS. 10 and 11
the overtone anharmonically does not vary in time, but is a
function of the note being generated. In these embodiments, each
overtone is offset by a constant number of cents, where a cent is
1/1200 of an octave. Each Fourier component amplitude is calculated
by the equation: F.sup. (n) = C.sub. n
sin(.pi./W)(nqR+.eta..sub..nu.") =C.sub. n
sin(.pi./W)(nqR+.nu.(qR/K)) (Eq. 6)
wherein .eta..sub..nu."=.nu.(qR/K) and K is a constant; preferably
K= 2.sup. Z with Z being an integer. Instruments using such
constant cents overtone offset have a particularly pleasing sound
over the entire range of the keyboard.
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 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 (.eta.) 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 11 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.
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 also shall be attributed to forms
later described, unless such characteristics obviously are
inapplicable or unless specific exception is made.
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 11 evaluated at the nominal fundamental frequency f of
the note, and anharmonic overtones 12- 15 having frequencies which
are not integral multiples of f. The first overtone 12 has a
frequency 2f+ .nu..sub.1, wherein .nu..sub.1 designates the offset
of this overtone with respect to the frequency 2f of the true
second harmonic. Similarly, the typical non-harmonic overtones 13,
14 and 15 are evaluated at respective frequencies 3f+.nu..sub.2,
4f+.nu..sub.3 and 16f+.nu..sub.15 which are offset by the amounts
.nu..sub.2, .nu..sub.3 and .nu..sub.15 from the frequencies 3f, 4f
and 16f of the true third, fourth and sixteenth harmonics. (In FIG.
1, the solid lines designate Fourier components actually generated
by the computor organ; the dotted lines indicate the harmonics
which are not generated.)
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. In general,
circuitry and operation of the computor organ 18 is as described in
the U.S. patent application, Ser. No. 225,883. However, the
computor organ 18 includes an overtone offset (.nu.) memory 19, an
.nu. memory address control 20 and an adder 21 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 calculating the discrete Fourier components
associated with amplitudes at successive sample points of a
waveshape characterizing the selected note. The components are
algebraically summed in an accumulator 23 which, at the end of each
computation time interval t.sub. x contains the amplitude at the
current sample point. This amplitude is provided via a gate 24,
enabled by the t.sub. x 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
of the 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 tonal quality of the
produced musical note is established by the set of harmonic
coefficients c.sub. n stored in a memory 28 and used in computing
the Fourier components at each sample point. In general, the use of
16 Fourier components (W= 16) is quite satisfactory for
synthesizing musical instrument sounds.
The computor organ 18 implements equation 3 by computing the
amplitude value X.sub. o (qR) for each sample point during a time
interval t.sub. x. The individual Fourier component amplitudes
F.sup. (n) (see equation 2) for each of the W= 16 components are
calculated separately during successive time intervals t.sub. cp1
through t.sub. cp16 established by a clock 31 and a counter 32. At
the first interval t.sub.cp1 the amplitude F.sup. (1) of the
fundamental is calculated. This value F.sup. (1) is placed in the
accumulator 23. At the interval t.sub.cp2 the amplitude F.sup. (2)
of the second Fourier component (i.e., the first overtone) is
computed and added to the accumulator 23 contents. At time
t.sub.cp3 the second overtone amplitude F.sup. (3) 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.sub. o (qR) for the sample point designated by
the value qR.
As noted earlier, the waveshape amplitude X.sub. o (qR) in the
accumulator 23 is gated to the digital-to-analog converter 26 at
the end of the computation interval t.sub. x. 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 amplitudes
F.sup. (n) are calculated for the sample point designated by the
new value of qR. Eventually the entire waveshape will be generated,
the sound system 21 reproducing the musical note as the amplitude
computations are carried out.
In the system of FIG. 2, 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 t.sub. x
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 t.sub. x signal on the line 25.
Preferably, the adder 33 is of modulo N where N is the product of
the R number for any note times the number of points per period of
that note.
To calculate each Fourier component, the values nqR (for n = 1,2, .
. . , W) are obtained in a harmonic interval adder 35 which is
cleared before each amplitude computation cycle. Upon occurrence of
the first t.sub.cp1 clock pulse of a new 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. At each
subsequent t.sub.cp clock pulse, the value qR is added to the
previous contents of the adder 35. As a result, the harmonic
interval adder 35 will contain the value nqR for the n.sup. th
order Fourier component currently being evaluated. Preferably the
harmonic interval adder 35 also is of modulo N.
To implement production of anharmonic overtones, the frequency
offset value .eta..sub..nu. of the .nu..sup.th overtone is added to
the value nqR by the adder 21. The value nqR is obtained from the
harmonic interval adder 35 via a line 38. The output of the adder
21, provided on a line 41, thus represents the sum
(nqR+.eta..sub..nu.).
The frequency offset value .eta..sub..nu. is supplied to the adder
20 from the overtone offset (.eta.) memory 19 via a line 42. The
.eta. memory 19 is accessed by the address control circuit 20 which
receives the timing pulse t.sub. cp1 - t.sub. cp16 via a line 43
from the counter 32. Thus, e.g., at the time t.sub. cp2 during
which the second (n= 2) Fourier component (i.e., the first
overtone) is being calculated, the t.sub.cp2 signal on the line 43
will cause the address control 20 to access the overtone offset
value .eta..sub.1 from the memory 19.
The value sin (.pi./W) (nqR+.eta..sub..nu.) corresponding to the
argument (nqR+.eta..sub..nu.) received via the line 41 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 (.pi./W .phi. for 0 .ltoreq. .phi. .ltoreq. 2W at
intervals of D, where D is called the resolution constant of the
memory.
The value sin .pi./W (nqR+.eta..sub..nu.) supplied via a line 48,
is multiplied by the coefficient C.sub.n for the corresponding
n.sup.th Fourier component by a multiplier 50. The multiplication
product represents the amplitude F.sup. (n) of the n.sup. th
Fourier component and is supplied via the line 51 to the
accumulator 23. The appropriate coefficient C.sub. n is accessed
from the harmonic coefficient memory 28 by an address control 35
which receives the calculation timing signals via the line 43.
In the embodiment of FIG. 2, arbitrary values of .eta..sub..nu. may
be stored in the memory 19. The values may be the same or different
for each overtone. The value .eta..sub..nu. for a certain overtone
may be zero in which case a true harmonic with no frequency offset
will be evaluated.
The overtone offset (.eta.) 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 (.eta.) values can be user programmed into this integrated
circuit memory. The adder 21 may comprise a Signetics type 8268
integrated 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.sub. n 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.
TABLE A ______________________________________ Component
Conventional inter- (FIG. 2) grated circuit*(or other reference)
______________________________________ Frequency (a) SIG 8223
field-programmable number read only memory memory 27 (ROM) [p.37]
(b) TI SN5488A, SN7488A 256-bit ROM[p.9-235] (c) Also can be imple-
mented using a diode arroy memory, as per U.S. patent No. 3,377,513
to Ashby et al. Note interval (a) SIG. 8260 arithme- adder 33 tic
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 25. adder 35 Component
Integrated Circuit Gates 24,34,37 TI SN5408, SN5409 quadruple AND
gates [p.6-17] Sinusoid table (a) TI TMS4405 sinu- 46 and memory
soid table and address decoder 47 addressing cir- cuitry (b) TI
TMS4400 ROM containing 512 words of 8-bits [p.14-188] pro- grammed
to store sin values Harmonic coefficient (a) SIG 8277 sixteen-
memory 28 and memory bit shift address control 35 register[p.121];
address control implemented by connecting t.sub.c clock line 21
(FIG.1) to the shift register input which controls shift. (b) TI
SN54166 series shift registers [p.9-134] (c) Also can be
implimented using a read only memory such as SIG 8223 which
includes address control circuitry Harmonic Amplitude (a) May be
implement- Multiplier 50 ed as shown in application sheet SIG
catalog, p.28 using SIG 8202 buffer registers and 8260 arith- metic
element (b) Also can be implemented using SIg 8243 scaler [p.65]
Accumulator 23 (a) SIG. 8268 or TI SN5483, SN7483 full adders
connected as shown in Flores.sup.1, section 11.1 "Accumulators".
______________________________________ * TI = Texas Instrument Co.
[Page references are to the TI "Integrated Circuiits Catalog for
Design Engineers," first Edition, January, SIG = Signetics,
Sunnyvale, California [Page references are to the SIG "Digitial
8000 Series TTL/MSI" catalog, copyright .sup.1 Flores, Ivan "
Computer Logic" Prentice-Hall, 1960.
FIG. 3 shows a modified version of the computor organ 18 which also
implements equation 3. In this embodiment, .eta..sub..sub..nu.
=.nu..eta. for each overtone. Thus the first (.nu.=1) overtone has
an offset established by a value of .eta. stored in a register 53.
The second (.nu.=2) overtone is evaluated with an offset 2.eta.,
and each higher order overtone has an offset .nu..eta..
With this arrangement, the .eta..sub..nu. values need not be stored
individually in a memory, but can be calculated during the
waveshape amplitude computation cycle. Thus the overtone offset
memory 18 and address control 19 shown in FIG. 2 are not used;
rather the overtone offset values .nu..eta. are provided via a line
42' to the adder 40 (FIG. 2) by the circuit of FIG. 3. The value
.nu..eta. is accumulated in an adder 54 which is cleared at the end
of each computation cycle by the t.sub. x signal on the line 25.
During the first calculation interval t.sub. cpl, when the
fundamental is being evaluated, the contents of the adder 54 is
zero so that no offset is introduced; thus the (n= 1) component
will be evaluated at the true fundamental frequency of the note
being generated.
To provide the overtone offset values .nu..eta., the value .eta.
stored in the register 53 is added repetitively to the previous
contents of the adder 54 at successive overtone calculation times
t.sub. cp2 through t.sub.cp16. To this end, the value .eta. is
supplied to the adder 54 via a gate 56 enabled by the corresponding
timing signals on a line 43' from the counter 32. Occurrence of the
timing signal t.sub.cp2 causes the value .eta. to be transferred
from the register 53 to the adder 54. Accordingly, the value
.eta..sub.1 =.eta. will be provided via the line 42' to the memory
address decoder 47 of FIG. 2 during calculation of the first
overtone. During successive calculation intervals t.sub. cp3
through t.sub. cp16 , the value .eta. will be added successively to
the adder 54 contents, so that the required value .nu..eta. will be
supplied to the computor organ 18.
The value of .eta. stored in the register 53 (FIG. 3) is arbitrary.
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 .eta. which are functions of the selected
note. In the embodiment of FIG. 4, the note dependent overtone
offset value .eta. = 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 .eta. = R/K to the
register 53 via a line 60. In this embodiment, 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 circuit incorporates a
function element 61 which implements an arbitrary transfer function
.eta.=f(R). The circuit 61 receives the selected frequency number R
from the memory 27 and provides via a line 60' to the register 53
(FIG. 3) the value .eta.=f(R). Note that 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 computor organ
of the type disclosed in the U.S. patent application, Ser. No.
298,365. Such an implementation is shown in FIG. 6 wherein the
computor 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 66B.
In the embodiment of FIG. 6, separate overtone offset
(.eta.)memories 19A, 19B and related .eta. memory address control
circuits 20A, 20B are provided in the respective channels 66A, 66B.
In the channel 66A the values nqR for certain values of n are
supplied via a line 38A during consecutive calculation time
intervals t.sub. cp1 through t.sub. cp8 to an adder 21A. The
appropriate overtone offset values .eta..sub..sub..nu. are provided
to the adder 21A from the memory 19A, so that the output of the
adder 21A represents the quantities nqR+.eta..sub..nu. for the set
of Fourier components evaluated in the channel 66A. This output, on
a line 41A, is provided to the sinusoid table and address decoder
46A, which provides the values sin(nqR+.eta..sub..nu.). These sin
values are multiplied by the appropriate harmonic coefficients
C.sub. n supplied from a memory 28A by a harmonic amplitude
multiplier 50A to produce on a line 48A the Fourier component
values F.sup. (n) = C.sub. n sin .pi./W (nqR+.eta..sub..nu.) for
those components evaluated in the channel 66A.
The remaining Fourier components are similarly evaluated in the
parallel channel 66B, wherein corresponding circuit blocks are
identified by like numerals followed by the letter "B." 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, 66B. For example, the first eight (n=
1,2,3, . . . , 8) low order Fourier components may be calculated in
the channel 66A, and the high order (n= 9,10,11, . . . , 16)
Fourier components in the channel 66B. In this case, the overtone
offset memory 19A will contain the values .eta..sub.1 through
.eta..sub.7 which are accessed at the respective time intervals
t.sub. cp2 through t.sub. cp8 . The overtone offset memory 19B will
contain the values .eta..sub.8 through .eta..sub.15 which are
accessed at the consecutive time intervals t.sub. cp1 through
t.sub. cp8 when the corresponding 8th through 15th overtones (i.e.,
the 9th through 16th Fourier components) are evaluated.
In another embodiment, the odd (n= 1,3,5, . . . , 15) Fourier
components may be evaluated in the channel 66A and the even (n=
2,4,6, . . . , 16) Fourier components (corresponding to the odd
overtones) may be calculated in the other channel 66B. In that
case, the overtone offset memory 19A will contain the values
.eta..sub.2,.eta..sub.4,.eta..sub.6 . . . .eta..sub.14 the overtone
offset memory 19B will contain the values .eta..sub.1,.eta.
.sub.3,.eta. .sub.5 . . . .eta..sub.15.
It is not necessary that all overtones be 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 computor organ
embodiment described in the preceeding paragraph. Negative offset
(.eta.) values are stored in the memory 19A and positive .eta.
values are stored in the memory 19B. With this arrangement, e.g.,
will be calculated using a positive value .eta..sub.1 to provide an
anharmonic overtone 70 (FIG. 7) which offset is sharp. The second
overtone 71, evaluated in the processing channel 66B, will be
flat.
A system analogous to that shown in FIG. 3 may be used to provide
overtone offset values to the parallel processing computor 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 66B. The appropriate .nu. values are supplied to
the adders 21A, 21B (FIG. 6) from respective accumulating adder
circuits 72A, 72B which are cleared at the end of each computation
cycle; the overtone offset memories 19A, 19B are not used.
A pair of registers 73, 74 respectively store the values .eta. and
8.eta.. During the first calculation interval t.sub.cp1 the
contents of the adder 72A is zero. Accordingly, the fundamental
(n=1) Fourier component is evaluated in the channel 66A with no
frequency offset (i.e., at the nominal fundamental frequency of the
generated note) During each successive interval t.sub.cp2 through
t.sub.cp8 the value .eta. is gated to the adder 72A via a line 76
and added to the previous contents of that adder. Thus the adder
72A will contain the values .eta.,2.eta.,3.eta., . . . 7.eta. at
the corresponding times that the first through seventh overtones
are evaluated in the channel 66A. These values .nu..eta. are
supplied via the line 42A to the adder 21A in the computor organ of
FIG. 6. For channel 66B, at time t.sub.cp1 the value 8.eta. is
gated from the register 74 via a gate 77 to the adder 72B. Thus
during the calculation interval t.sub.cp1 the overtone offset value
8.eta. is susplied via the line 42B to the adder 21B in the
computor organ 65; during this interval the eighth overtone is
being evaluated in the channel 66B. On successive calculation
intervals t.sub.cp2 through t.sub.cp8, the value .eta. is provided
via the gate 75 and the line 76 to the adder 72B wherein the values
9.eta. through 15.eta. will be accumulated. These are the
appropriate offset values utilized by the channel 66B for
evaluation of the high order overtones.
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 5 above. The computor organ 80
produces musical notes having a harmonic spectrum similar to that
shown in FIG. 1, but wherein the fundamental is evaluated at the
true fundamental frequency f of the note being generated and each
overtone 12, 13 . . . 15 has a frequency nf+.nu..eta. where
.nu.=n-1.
In the computor organ 80 (FIG. 9), 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. Thus the
note interval adder 33 provides on the line 36 the value qR. At
each component calculation interval t.sub.cp1 through t.sub.cp16,
this value qR is supplied via a gate 81 to a non-accumulating adder
82. During the initial interval t.sub.cp1 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 35'. As a result, the first Fourier
component is evaluated at the nominal fundamental frequency of the
selected note. At each successive calculation interval t.sub.cp2
through t.sub.cp16 the value Jq is supplied to the adder 82 via a
gate 84 and a line 85, so that the value (qR+Jq) is provided via
the line 83 to the harmonic interval adder 35'. As a result, the
arguments (nqR+.nu.Jq) 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. To obtain the values Jq, the constant J is stored in a
register 87 (FIG. 9). Preferably, but not necessarily, the value
J=2.sup..sup.-k where k is an integer of 1 or greater. 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
t.sub.x 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. In this embodiment each anharmonic overtone is offset by
an amount which is a constant number of cents. The anharmonicity is
independent of time.
To evaluate the fundamental without frequency offset, the value qR
from the interval adder 33 is supplied to the harmonic interval
adder 35" at the interval t.sub.cp1 via a gate 91 and a
non-accumulating adder 92 the other input of which is zero during
this t.sub.cp1 interval. On each of the successive overtone
calculation intervals t.sub.cp2 through t.sub.cp16, the value qR/K,
where K is a constant, is added to the value qR in the adder 92 and
the sum (qR+(qR/K )) is supplied via the line 93 to the harmonic
interval adder 35". As a result, the arguments (nqR+.nu.(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. Preferably the
constant K=2.sup.z , where z is an integer of 1 or greater. In a
digital system, 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 a gate 96 which is enabled by the calculation timing signals
t.sub.cp2 through t.sub.cp16 provided via a line 97 from the
counter 32.
The computor organ 90' of FIG. 11 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. At the
beginning of each computation cycle, the dividend R/K is gated to
an accumulating adder 101 of modulo N via a gate 102 enabled by the
t.sub.x signal on the line 25. Thus the output of the adder 101,
present on a line 103, represents the quantity qR/K). As in the
embodiment of FIG. 10, the constant K preferably is given by
K=2.sup.z where z is an integer of 1 or greater.
During the first calculation interval t.sub.cp1 when the
fundamental is evaluated, only the value qR on the line 36 from the
note interval adder 33 is supplied via the gate 91 and the
non-accumulating adder 92' (FIG. 11) to the harmonic interval adder
35". Thus the (n=1).sup.th Fourier component is evaluated at the
nominal fundamental frequency of the generated note. During each
successive calculation interval t.sub.cp2 through t.sub.cp16 the
value q(R/K) from the adder 101 is supplied to the adder 92' via
the gate 96' for addition to the value qR which also is gated to
the adder 92'. The sum (qR+q(R/K)) is supplied on the line 93',
resulting in evaluation of the desired constant cents offset
anharmonic overtones.
The embodiments of FIG. 9, 10, 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+q(R/K) for generation in each
channel of selected subsets of the desired anharmonic
overtones.
Particularly interesting effects are achieved by modulating the
anharmonic overtones a function of time. For example, the frequency
offset values .eta. 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 .eta. to be time modulated is supplied via a line 105 to an
adder 106. The output of an oscillator 107 operating at the
modulation frequency is converted to a digital signal by an
analog-to-digital (A/D) converter 108 the digital output of which
is summed with the value .eta. by the adder 106. The output of the
adder 106 on a line 109 comprises a time varying overtone offset
value .eta.(t).
The circuit of FIG. 12 may be used in conjunction with the computor
organ 18 of FIG. 2 by inserting the adder 106 (FIG. 12) in series
with the line 42 (FIG. 2). That is, the line 42 would be opened,
the .eta. values from the overtone offset memory 19 would be
provided to the line 105, and the time modulated values .eta.(f) on
the line 109 would be supplied to the adder 21.
Alternatively, the time modulation circuit of FIG. 12 may be used
with the computor organ embodiments of FIGS. 9, 10 or 11. For
example, 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. Likewise, the circuit of FIG. 12 may be inserted in the line 95
of FIG. 10 or the line 103 of FIG. 11 to time modulate the offset
value qR/k in these embodiments.
A characteristic of human hearing is that the ear becomes less
sensitive at low frequencies. Because of this "roll off" of hearing
ability, the first overtone of a 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 of the 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. 1, the listener may
sense a subjective fundamental at a frequency 1/2(2f+.eta..sub.1)=
f+.eta..sub.1 /2 slightly sharp with respect to the actual
fundamental frequency f.
This effect can be overcome by selecting the values of R and .eta.
for low frequency notes such that the subjective fundamental will
coincide with the nominal fundamental frequency of the note. This
is illustrated by the harmonic spectrum of FIG. 13. The frequency
number R is selected so that the fundamental component 111 is
evaluated by the computor organ at a frequency f' which is flat
with respect to the nominal fundamental frequency f of the note
being generated. The offset value .eta..sub.1 is selected so that
the first overtone 112 will be produced at a frequency
2f=2f'+.eta..sub.1 which is exactly twice the nominal fundamental
frequency f. As a result, because of reduced hearing ability at the
low frequencies, the listener will "hear" a subjective fundamental
113 at half the frequency of the first overtone, i.e., at exactly
the nominal frequency f of the selected note. The actual
fundamental component 111, 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.
* * * * *