U.S. patent number 3,823,390 [Application Number 05/323,609] was granted by the patent office on 1974-07-09 for musical tone wave shape generating apparatus.
This patent grant is currently assigned to Nippon Gakki Seizo Kabushiki Kaisha. Invention is credited to Takatoshi Okumura, Toshio Takeda, Norio Tomisawa, Yasuji Uchiyama.
United States Patent |
3,823,390 |
Tomisawa , et al. |
July 9, 1974 |
MUSICAL TONE WAVE SHAPE GENERATING APPARATUS
Abstract
A first memory digitally stores the levels of the spectra of the
fundamental wave and each harmonic up to the mth harmonic of
intended tone color waves, a second memory digitally stores values
X.sub.O through X.sub.N of a sinusoidal wave function at the
respective points in its one cycle sampled by a sampling number N,
and a third memory is for writing incoming information to be
thereafter read out. Digital signals (a, b, . . . z) each
representing amplitude of the respective tone color are
sequentially and repetitiously produced. The levels of the spectra
(fundamentals: a.sub.1 b.sub.1, . . . z.sub.1 ; second harmonics:
a.sub.2, b.sub.2 . . . z.sub.2 ; . . . ; mth harmonics: a.sub.m,
b.sub.m, . . . z.sub.m) for the respective tone color waves are
sequentially read from the first memory. The amplitude signals and
the level signals are respectively multiplied with each other tone
color by tone color, and thereafter are added cumulatively for each
of the fundamental waves and the harmonics to produce each
cumulative value H.sub.p = (a .times. a.sub.p) + (b .times.
b.sub.p) + . . . + (z .times. z.sub.p); where p = . . . ,m. On the
other hand, values of the sinusoidal function at the respective
address points PQ mod N, where Q = 1, . . . N, are read from the
second memory and these read out outputs are multiplied by the
respective value H.sub.p. The products of the multiplication are
added cumulatively for values H.sub.1 through Hm to obtain a signal
##SPC1## . This signal Y.sub.Q is sequentially written in an
address Q in the third memory to constitute the desired musical
tone wave shape. Then this musical tone wave shape is read out at
an appropriate rate.
Inventors: |
Tomisawa; Norio (Hamamatsu,
JA), Uchiyama; Yasuji (Hamakita, JA),
Okumura; Takatoshi (Hamamatsu, JA), Takeda;
Toshio (Hamamatsu, JA) |
Assignee: |
Nippon Gakki Seizo Kabushiki
Kaisha (Shizuoken-ken, JA)
|
Family
ID: |
11647041 |
Appl.
No.: |
05/323,609 |
Filed: |
January 15, 1973 |
Foreign Application Priority Data
|
|
|
|
|
Jan 17, 1972 [JA] |
|
|
47-6757 |
|
Current U.S.
Class: |
708/272; 984/394;
84/605; 984/393 |
Current CPC
Class: |
G10H
7/06 (20130101); G10H 7/045 (20130101) |
Current International
Class: |
G10H
7/02 (20060101); G10H 7/06 (20060101); G10H
7/04 (20060101); G10h 001/00 (); G06f 007/00 ();
G06f 013/00 () |
Field of
Search: |
;340/172.5
;84/1.01,1.02,1.03,1.28,345,DIG.29,1.27 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
"Digital Transversal Filter With Read-Only Memory," IBM Technical
Disclosure Bulletin, Vol. 15, No. 3, August 1972, pp.
976-977..
|
Primary Examiner: Henon; Paul J.
Assistant Examiner: Thomas; James D.
Attorney, Agent or Firm: Ladas, Parry, Von Gehr, Goldsmith
& Deschamps
Claims
What we claim is:
1. A musical tone wave shape generating apparatus comprising:
a. a first memory for digitally storing the levels of the spectra
of the fundamental wave and of each harmonic up to the mth harmonic
of the intended tone color waves;
b. a second memory for digitally storing values X.sub.0 through
X.sub.N of a sinusoidal wave function at respective points of a
cycle sampled by sampling number N;
c. a third memory for writing incoming information to be thereafter
read out;
d. means for sequentially and repetitively producing digital
signals (a, b, . . . z) each representing the amplitude of the
respective tone color;
e. means for sequentially reading out from the first memory the
level of each corresponding wave spectrum of each tone color in
succession at a readout rate synchronized with the rate of
production of the digital signals representing the respective tone
color amplitude to produce spectral level signals (fundamentals
a.sub.1, b.sub.1, . . . z.sub.1 ; second harmonics a.sub.2,
b.sub.2, . . . z.sub.2 ; and m.sup.th harmonics a.sub.m, b.sub.m, .
. . z.sub.m);
f. first multiplication means for multiplying the amplitude signals
and the spectral level signals;
g. means for adding the multiplied signals accumulatively for each
fundamental wave and its harmonics to produce cumulative signal
values H.sub.p = (a .times. a.sub.p) + (b .times. b.sub.p) + . . .
+ (z .times. z.sub.p) where p = 1, 2, . . . m;
h. means for reading from the second memory values of the
sinusoidal wave function at the respective address points PQ mod N,
where Q = 0, 1, . . . N, to produce read-out signals;
i. second multiplication means for multiplying the second memory
read-out signals by the H.sub.p signals;
j. means for adding the multiplication products from said second
multiplication means cumulatively for values of H.sub.1 through
H.sub.m to obtain a signal ##SPC3##
k. means for sequentially writing signal Y.sub.Q in an address Q in
the third memory to constitute the desired musical tone wave shape;
and
l. means for reading out from the third memory the musical tone
wave shape at a desired rate.
2. A musical tone wave shape generating apparatus as defined in
claim 1 in which said means for producing digital signals
representing amplitudes of a plurality of tone-colors comprise
means provided for each tone-color and producing voltage signals
each having a level corresponding to each tone-color, gate circuits
the output side of which are connected in common connection and
which respectively receive said voltage signals, means for scanning
and thereby opening these gate circuits one after another
successively and repetitively at a predetermined rate and means for
converting analog signals from said gate circuits to digital
amplitude signals.
3. A musical tone wave shape generating apparatus as defined in
claim 2 in which said means for scanning the gate circuits comprise
a binary counter having a plurality of stages in cascade connection
and receiving a clock pulse as their input and a decoder receiving
the output of each stage of said binary counter and producing
outputs corresponding to its counting successively on its output
lines each of which is connected to one of said gate circuits.
4. A musical tone wave shape generating apparatus as defined in
claim 3 in which said first memory is a read only memory, rows of
which store the levels of spectra of the respective tone-colors and
columns of which store the levels of spectra of the fundamental
wave up to the highest harmonic.
5. A musical tone wave shape generating apparatus as defined in
claim 4 in which said means for reading out the levels of spectra
comprise means for selecting each row of said first memory in
synchronization with the scanning of said gate circuits and means
for selecting each column of said first memory sequentially and
repetitively at each cycle of scanning of said gate circuits.
6. A musical tone wave shape generating apparatus as defined in
claim 5 in which said means for selecting each column of said first
memory comprise a cascade connected second binary counter which is
connected in series to said binary counter first described and a
decoder receiving the output of each stage of said second binary
counter and producing outputs corresponding to its counting on its
output lines one after another successively and cyclicly thereby to
select each column of said first memory.
7. A musical tone wave shape generating apparatus as defined in
claim 2 in which said means for producing the signal H.sub.p
comprise adding means for adding cumulatively the products of said
first multiplication means and means for resetting the adding means
at each cycle of scanning of said gate circuits.
8. A musical tone wave shape generating apparatus as defined in
claim 6 in which said means for reading from the second memory
comprise a cascade connected third binary counter having a
plurality of stages connected in series to said second binary
counter, a multiplier for multiplying the output Q of said third
binary counter with the output P of said second binary counter and
producing an output containing a plurality of digits including the
least significant digit, and a decoder receiving the output of this
multiplier and operating in the same manner as a ring counter to
produce outputs corresponding to its counting.
9. A musical tone wave shape generating apparatus as defined in
claim 6 in which said means for producing the signal ##SPC4##
comprise adding means for adding the outputs of said second
multiplication means cumulatively and means for resetting said
adding means by the output of the last stage of said second binary
counter.
Description
This invention relates to a musical tone wave shape generating
apparatus.
A musical tone wave shape can be divided into a fundamental wave
content and one or more harmonic contents, no matter how
complicated the wave shape may appear. Conversely, a desired
musical tone wave shape can be obtained by synthesizing its
fundamental wave and one or more predetermined harmonics at an
appropriate ratio of levels. The present invention makes use of
this principle.
A specific musical tone wave shape may be obtained by providing a
memory which stores this specific musical tone wave shape and
reading it from the memory. It is very difficult, however, to
change the contents once stored in the memory. In order to obtain a
plurality of different musical tone wave shapes, it is therefore
necessary to provide a plurality of memories which respectively
store one of the different wave shapes. If the number of required
musical tone wave shapes is large, a corresponding large number of
memories are required. Furthermore, a desired musical tone wave
shape will not always be obtained from one of these memories if the
desired wave shape is not stored in any of the memories.
For obtaining a musical tone wave shape, it is also possible to
provide memories which respectively store the fundamental wave and
each harmonic, read these waves from the respective memories and
synthesize them at a suitable ratio of levels. This alternative,
however, is still not quite free from the disadvantage that the
apparatus requires a large number of memories.
It is, therefore, a general object of the invention to provide a
musical tone wave shape generating apparatus capable of producing a
desired musical tone wave shape with a relatively simple
construction.
It is another object of the invention to provide a musical tone
wave shape generating apparatus capable of producing a desired
musical tone wave shape by providing a single memory storing
sinusoidal waves in digital representation, reading the fundamental
wave and each harmonic of the desired musical tone wave shape from
this single memory and synthesizing these waves at an appropriate
ratio of levels into the desired musical tone wave shape.
It is another object of the invention to provide a musical tone
wave shape generating apparatus which comprises means for
determining amplitudes of a plurality of tone-colors, a first
memory for storing digitally the levels of spectra of each
tone-color, a first addition circuit for multiplying the spectra of
the fundamental wave and harmonics of each tone-color with
corresponding volumes and adding the products of the multiplication
for each of the fundamental wave and harmonics, a second memory for
storing digitally the sinusoidal wave shape of the fundamental wave
shape for one cycle, means for providing readout address signals to
said second memory in a predetermined order and thereby reading out
each function value of the fundamental wave and harmonics, a second
addition circuit for multiplying the signals read from the second
memory with the signals from the first addition circuit and adding
the products of the multiplication each time the signal
corresponding either to the fundamental wave or the highest
harmonic is produced from the first addition circuit, means for
writing in time sequence digital signals representing the results
of the addition from the second addition circuit into a third
memory and means for reading out the contents of the third memory
at a predetermined clock rate.
It is still another object of the invention to provide a musical
tone wave shape generating apparatus which is capable of converting
an analog signal representing the amplitude of each tone-color to a
digital signal by providing a single analog-to-digital
converter.
Other objects and features of the invention will become apparent
from the description made hereinbelow with reference to the
accompanying drawings in which:
FIGS. 1a and 1b are block diagrams showing one embodiment of the
musical tone wave shape generating apparatus according to the
invention. The circuit of this embodiment is divided into two parts
by line I--I;
FIG. 2a is a graphical diagram showing the wave shape of an input
to an analog-to-digital converter;
FIG. 2b is a graphical diagram showing the levels of spectra of
each tone-color;
FIG. 3 is a graphical diagram for illustrating the reading from a
sinusoidal wave function memory;
FIG. 4 is a diagram showing one example of a wave shape stored in a
composite wave shape memory CM.
FIG. 1 is a block diagram illustrating one embodiment of the
musical tone wave shape generating apparatus according to the
invention. Clock pulses from a clock pulse generator C.sub.1 are
applied to a tone-color scanning counter TC. The tone-color
scanning counter TC consists, for example, of flip-flops of five
stages. The output of each flip-flop is applied to a decoder
D.sub.1. The decoder D.sub.1 successively produces its outputs
(e.g., negative pulses) A through Z, A . . . in accordance with the
contents of the counter TC, producing outputs in a manner similar
to a ring counter.
There are provided tone-color selection and control knobs Sa to Sz
corresponding respectively to tone colors A to Z. The amplitude of
a selected tone-color can be controlled by operating a
corresponding knob. Amplitude control devices VR.sub.a to VR.sub.z
consists, for example, of variable resistors each slider of which
is operable by the knob.
Each slider of the amplitude control devices is connected to the
drain of corresponding transistors TR.sub.a to TR.sub.z which
respectively constitute gate circuits. The sources of these
transistors TR.sub.a to TR.sub.z are connected in common connection
to the input terminal of an analog-to-digital converter AD. The
gates of the transistors TR.sub.a to TR.sub.z are respectively
connected to the output terminals of the decoder D.sub.1.
When the decoder D.sub.1 is actuated to successively produce its
outputs A, B, . . . Z, A, B . . . , the transistors of the gate
circuit successively and cyclicly conduct in the order of TR.sub.a,
TR.sub.b, . . . TR.sub.z, TR.sub.a, . . . . If the tone-color
selection and control knobs Sa to Sz are respectively set at
predetermined positions, voltages corresponding to the set
positions of these knobs are successively applied to the input of
the analog-to-digital converter AD. These applied voltages
constitute a wave shape such as shown in FIG. 2a where voltage a
corresponds to the knob S.sub.a, voltage b to the knob S.sub.b, . .
. and voltage z to the knob S.sub.z respectively. These voltages
are converted in the analog-to-digital converter AD to digital
signals consisting of a suitable bit number, e.g., 5 and thereafter
applied to the input terminals on one side of a multiplication
circuit ML.sub.1.
The output of the last stage of the scanning counter TC is applied
to a harmonic scanning counter HC. The harmonic scanning counter HC
consists, for example, of flip-flops of five stages the outputs of
which are applied to a decoder D.sub.2. The decoder D.sub.2
successively produces outputs 1, 2, . . . 32, 1, . . . in
accordance with the contents of the scanning counter HC. Each of
these outputs is used for designating a specific column of a
tone-color spectra memory RM.
The tone-color spectra memory RM consists, for example, of a read
only memory (ROM) and stores the levels of a fundamental wave
component and higher harmonic wave components of each tone-color A,
B, C, . . . Z. Each component of the tone-colors A through Z
(hereinafter called "spectrum") has a level such as shown in FIG.
2b. In FIG. 2b, small letters a, b, c, . . . z respectively
represent the components of the tone-colours A, B, C . . . Z. The
numeral 1 affixed to these small letters represents the fundamental
wave, the numeral 2 the second harmonic, . . . and the numeral 32
the 32nd harmonic respectively. Accordingly, a.sub.1, for example,
represents the level of the fundamental wave component of the
tone-color A.
The spectra a.sub.1 through a.sub.32, b.sub.1 through b.sub.32, . .
. ; z.sub.1 through z.sub.32 are respectively stored in the
tone-color spectra memory RM as digital information. The spectra
a.sub.1 through a.sub.32 ; b.sub.1 through b.sub.32 ; . . . ;
z.sub.1 through z.sub.32 are respectively stored in each row.
Hence, the spectra a.sub.1, b.sub.1 . . . z.sub.1 are stored in the
first column, the spectra a.sub.2, b.sub.2. . . z.sub.2 in the
second column and the spectra a.sub.32, b.sub.32 . . . z.sub.32 in
the 32nd column.
Each output line of the decoder D.sub.1 is connected also to the
tone-color spectra memory RM, and each output of the decoder
D.sub.1 selects a row of specific information stored in the memory
RM. More specifically, when the output A is produced from the
decoder D.sub.1, the row of the spectra a.sub.1, a.sub.2, . . .
a.sub.32 is selected by this output A, whereas when the output 1 is
produced from the decoder D.sub.2, the first column is selected by
this output 1. Hence the spectrum a.sub.1 is read out.
As the decoder D.sub.1 operates to produce the outputs A, B, . . .
, Z, A, . . . successively and repetitively, the column selecting
signal from the decoder D.sub.2 is shifted to a next column at each
cycle of the operation of the decoder D.sub.1. Accordingly, the
spectra are successively and repetitiously read from the tone-color
spectra memory RM in the order of a.sub.1, b.sub.1, through z.sub.1
; a.sub.2, b.sub.2 through z.sub.2 ; a.sub.3, b.sub.3 through
z.sub.3 ; . . . z.sub.32 ; a.sub.1, b.sub.1 . . . . These spectra
are read out in the form of digital information consisting of a
suitable number of bits, e.g., 8, and are applied to the input
terminals on the other side of the multiplication circuit
ML.sub.1.
When the decoder D.sub.1 produces the output A, a signal a is
applied through the analog-to-digital converter AD to one of said
input terminals on one side of the multiplication circuit ML.sub.1
and the signal a.sub.1 is applied from the tone-color spectra
memory RM to one of said input terminals on the other side of the
circuit ML.sub.1. Consequently, the multiplication circuit ML.sub.1
effects the calculation a .times. a.sub.1 (a times a.sub.1) and
provides the result of the calculation to an addition circuit
AC.sub.1. When the decoder D.sub.1 produces the output B, the
multiplication circuit ML.sub.1 likewise effects the calculation b
.times. b.sub.1, providing the result to the addition circuit
AC.sub.1. Subsequently, results of calculations c .times. c.sub.1,
d .times. d.sub.1, . . . z .times. z.sub.1 are provided to the
addition circuit AC.sub.1. The addition circuit AC.sub.1
cumulatively adds the outputs of the multiplication circuit
ML.sub.1 successively applied thereto and is reset by the output of
the last stage of the tone-color scanning counter TC at each cycle
of operation of the decoder D.sub.1. Accordingly, the addition
circuit AC.sub.1 effects the following calculation and thereafter
is reset:
H.sub.1 = (a .times. a.sub.1) + (b .times. b.sub.1) + . . . + (z
.times. z.sub.1)
As the decoder D.sub.1 completes one cycle of its operation and
starts a next cycle, the decoder D.sub.2 produces the output 2. The
multiplication circuit ML.sub.1 effects calculations a .times.
a.sub.2, b .times. b.sub.2, c .times. c.sub.2. . . z .times.
z.sub.2 in the same operation principle as has been described
above. The addition circuit AC.sub.1 effects the following
calculation and thereafter is reset:
H.sub.2 = (a .times. a.sub.2) + (b .times. b.sub.2) + . . . + (z
.times. z.sub.2)
The addition circuit AC.sub.1 subsequently makes the following
calculations:
H.sub.3 = (a .times. a.sub.3) + (b .times. b.sub.3) + . . . + (z
.times. z.sub.3)
H.sub.32 = (a .times. a.sub.32) + (b .times. b.sub.32) + . . . + (z
.times. z.sub.32)
The signals H.sub.1 through H.sub.32 are successively applied to a
temporary memory HM where they are stored temporarily and
thereafter are successively applied to the input terminals on one
side of a multiplication circuit ML.sub.3.
These signals H.sub.1 through H.sub.32 are signals which are
produced from both the amplitudes of the tone-color selection and
control knobs and the levels of the spectra. The signal H.sub.1
represents the level of the fundamental wave of a combined
resultant musical tone wave shape to be obtained. The signal
H.sub.2 represents the level of the second harmonic of the musical
tone wave shape. Similarly, the other signals H.sub.3 . . .
H.sub.32 respectively represent the levels of the third and
subsequent harmonics of the musical tone wave shape.
The reference characters SM designate a sinusoidal wave function
memory which consists, for example, of a read only memory (ROM). A
sinusoidal wave shape of one cycle is sampled by a suitable
sampling number, e.g., 64, and values of amplitudes X.sub.0,
X.sub.1, . . . X.sub.63 at respective sampling points are stored in
the memory SM in the form of digital information consisting of a
suitable number of bits, e.g., 8.
Each wave shape amplitude is read from the memory SM by means of a
device comprising a sample address scanning counter SC, a
multiplication circuit ML.sub.2 and a decoder D.sub.3. The reading
of the wave shape amplitudes will be described in detail
hereinbelow.
The sample address scanning counter SC consists, for example, of
flip-flops of six stages. The output of the harmonic scanning
counter HC is applied to the first stage of the counter SC. Each
bit output of the counter SC (hereinafter referred to as a
fundamental wave phase address Q.) is applied to the input
terminals on one side of the multiplication circuit ML.sub.2. Each
bit output of the counter HC (hereinafter referred to as a harmonic
address P.) is applied to the input terminals on the other side of
the multiplication circuit ML.sub.2. The multiplication circuit
ML.sub.2 multiplies the address P with the address Q and produces a
read out address R .ident. P.sup.. Q mod 64 by taking out six
consecutive digits including the least significant digit and
discarding the overflow outputs of more significant digits than
these six digits. The states of the addresses P, Q, P .times. Q, R,
etc., are shown in Table I where the address P, Q, P .times. Q and
R are represented in decimal numbers only.
__________________________________________________________________________
Harmonic Fundamental P.times.Q Read out Sinusoidal Harmonic
Composite address wave phase address wave level wave (P) address (R
.tbd. P.sup.. Q function (H.sub.P) shape (Q) mod 64) (X.sub.PQ mod
64) sample value (Y.sub.Q)
__________________________________________________________________________
1 0 0 0 X.sub.0 H.sub.1 2 0 0 X.sub.0 H.sub.2 3 0 0 X.sub.0 H.sub.3
Y.sub.0 4 0 0 X.sub.0 H.sub.4 . . . . . . . . . . . . . . . 32 0 0
X.sub.0 H.sub.32 1 1 1 1 X.sub.1 H.sub.1 2 2 2 X.sub.2 H.sub.2 3 3
3 X.sub.3 H.sub.3 Y.sub.1 . . . . . . . . . . . . . . . 32 32 32
X.sub.32 H.sub.32 1 2 2 2 X.sub.2 H.sub.1 2 4 4 X.sub.4 H.sub.2 3 6
6 X.sub.6 H.sub.3 Y.sub.2 . . . . . . . . . . . . . . 32 64 0
X.sub.0 H.sub.32 1 3 3 3 X.sub.3 H.sub.1 2 6 6 X.sub.6 H.sub.2 3 9
9 X.sub.9 H.sub.3 Y.sub.3 . . . . . . . . . . . . . . . 32 96 32
X.sub.32 H.sub.32 . . . . . . 1 63 63 63 X.sub.63 H.sub.1 2 126 62
X.sub.62 H.sub.2 Y.sub.63 3 189 61 X.sub.61 H.sub.3 . . . . . . . .
. . 32 2016 0 X.sub.0 H.sub.32
__________________________________________________________________________
If the address Q is a decimal number 0 while the address P changes
from 0 to 31, the products P .times. Q are all zero and therefore
the outputs R of the multiplication circuit ML.sub.2 are all zero.
Accordingly, the decoder D.sub.3 produces only the output 0 thereby
selecting the address 0 of the sinusoidal wave function memory SM.
The memory SM produces the signal X.sub.0 which is applied to one
of the input terminals on the other side of the multiplication
circuit ML.sub.3. While the address P changes from 1 to 32, the
signals H.sub.1, H.sub.2, H.sub.3 . . . H.sub.32 are successively
applied to the input terminals on one side of the multiplication
circuit ML.sub.3 in the manner described above in synchronization
with the change of the address P. Thus, the multiplication circuit
ML.sub.3 effects calculations H.sub.1 .times. X.sub.0, H.sub.2
.times. X.sub.0 . . . , H.sub.32 .times. X.sub.0 and provides the
results successively to an addition circuit AC.sub.2. The addition
circuit AC.sub.2 makes the following addition and provides the
result of the addition in the form of a signal having a suitable
number of bits, e.g., 12 to a composite wave shape memory CM to be
described later:
Y.sub.0 = (H.sub.1 .times. X.sub.0) + (H.sub.2 .times. X.sub.0) + .
. . + (H.sub.32 .times. X.sub.0)
When the addition circuit AC.sub.2 has finished the calculation of
Y.sub.0, it is reset by an overflow output of the harmonic scanning
counter HC to prepare for a next calculation.
The values P .times. Q and R when the address Q is decimal numbers
1, 2, 3 . . . 63 are shown in Table I. The multiplication circuit
ML.sub.3 and the addition circuit AC.sub.2 effect calculations in
the same operation principle as described above. Thus, the output
of the addition circuit AC.sub.2 is represented generally by the
equation ##SPC2##
This Y.sub.Q represents the Qth sample value of a composite musical
tone wave shape to be obtained. More specifically, the sampled wave
shape amplitudes of the fundamental wave, the second harmonic, . .
. the 32nd harmonic can be substantially read from the sinusoidal
wave function memory SM by using the above described read out
address R and, as a result, the signals representing the sampled
amplitudes of the composite musical tone wave shape are
successively produced from the addition circuit AC.sub.2. This will
be explained more in detail with reference to FIGS. 3(a), (b), (c)
and (d).
In FIG. 3, the diagram (a) shows the fundamental wave, the diagram
(b) the second harmonic, the diagram (c) the third harmonic and the
diagram (d) the fourth harmonic respectively. The harmonics higher
than the fourth harmonic are obtained by addressing the fundamental
wave shape stored in the sinusoidal wave function memory SM in a
suitable manner. The horizontal axis which is used as a time base
for the second harmonic shown in FIG. 3(b) is double that of the
fundamental wave in length for the same period of time. Likewise,
the horizontal axis in FIG. 3(c) is three times and the one in FIG.
3(d) four times as long as that of the fundamental wave for the
same period of time.
When the address Q is 0, the sinusoidal wave function X.sub.0 is
read from the memory SM both for the fundamental wave and each
harmonic. The signals H.sub.1`, H.sub.2 . . . H.sub.32 are
multiplied one after another with X.sub.0 and the products are
added together to obtain the sum Y.sub.0. It will be understood
from the foregoing that this Y.sub.0 is a composite signal of the
fundamental wave and each harmonic at the address 0, each component
wave being provided with its predetermined level.
When the address Q is 1, the functions X.sub.1, X.sub.3, X.sub.4 .
. . X.sub.32 are successively read from the memory SM for the
fundamental wave, second, third, fourth and thirty-second harmonics
respectively. These functions are multiplied with the signals
H.sub.1 through H.sub.32 and thereafter are added together to
produce the sum signal Y.sub.1. This signal Y.sub.1 is a composite
signal of the fundamental wave and each harmonic at the address 1,
each component wave being provided with its predetermined
level.
When the address Q is 2, the functions X.sub.2, X.sub.4, X.sub.6,
X.sub.8 . . . X.sub.0 are read from the memory SM and the sum
signal Y.sub.2 is obtained.
Likewise, the composite signals Y.sub.3, Y.sub.4 . . . Y.sub.63 are
obtained as the address Q becomes 3, 4, . . . 63.
It will be apparent from the foregoing that the signals Y.sub.0
through Y.sub.63 respectively represent composite sample values of
the fundamental wave and each harmonic.
The composite wave shape memory CM which consists, for example, of
a random access memory (RAM) stores the above described signals
Y.sub.0 through Y.sub.63 applied from the addition circuit AC.sub.2
at its predetermined addresses. When the signal Y.sub.0 is applied
from the addition circuit AC.sub.2, the address Q is simultaneously
applied to the decoder D.sub.4. Thereupon a write address output
selecting the address 0 is applied from the decoder D.sub.4 to the
memory SM to store the signal Y.sub.0 at the address 0. Likewise,
the signals Y.sub.1, Y.sub.2, . . . Y.sub.63 are stored in the
addresses 1, 2, . . . , 63.
Thus, the composite musical tone wave shape of one cycle such as
shown in FIG. 4 consisting of the sample values Y.sub.0 through
Y.sub.63 is stored in the composite wave shape memory CM in the
form of digital signals.
Pulses of N.sup.. f Hz (N = 2.sup.n, and f represents the frequency
of the fundamental wave of the musical tone wave shape to be
obtained.) are applied from a clock pulse generator C.sub.2 to a
counter RC of n(e.g., six) stages. Each bit output of the counter
RC is applied to a decoder D.sub.5 which in turn applies a read out
address to the composite wave shape memory CM in accordance with
the contents of the counter RC. ACcordingly, as the clock pulses
are applied to the counter RC, the read out addresses 0 . . . 63, 0
. . . are applied successively and repetitively from the decoder
D.sub.5 to the composite wave shape memory CM, whereby the signals
Y.sub.0, Y.sub.1. . . Y.sub.63, Y.sub.0 . . . consisting of a
suitable number of bits, e.g., 12, are successively read from the
memory CM and applied to a digital-analog converter DA. This
converter DA is provided for converting the digital signals Y.sub.0
through Y.sub.63 to analog signals.
Thus, a musical tone wave shape which is a composite wave shape of
each tone-color consisting of the spectra stored in the memory RM
and provided with the amplitude determined by one of the tone-color
selection and control knobs S.sub.a through S.sub.z is taken out of
an output terminal T.sub.0.
In the foregoing embodiment, kinds of the tone-color and the
sampling number of each memory have been explained only by way of
example and these may of course vary according to necessity.
Further, the tone-color spectra memory RM may be constructed of a
random access memory (RAM) so that spectrum information may be
variably written through a suitable reading device.
* * * * *