U.S. patent number RE32,862 [Application Number 06/774,092] was granted by the patent office on 1989-02-14 for electronic musical instrument.
This patent grant is currently assigned to Nippon Gakki Seizo Kabushiki Kaisha. Invention is credited to Masatada Wachi.
United States Patent |
RE32,862 |
Wachi |
February 14, 1989 |
Electronic musical instrument
Abstract
More than one sub-intervals or time-windows are provided in a
one-cycle period of a musical tone selected at a keyboard of an
electronic musical instrument. Each time-window passes a sine wave
having a frequency predetermined for the time-window. The envelope
of the spectrum of a time-window is determined by the shape and the
width of the time-window, and the envelope of the spectrum of a
sine wave passed from the time-window will become the convolution
of the spectrum of the time-window and the frequency of the sine
wave. The total area of the frequency spectrum included as
frequency components of a musical tone can be covered by several
time-windows, each having a different length and passing a sine
wave of a different frequency. An amplitude control means controls
the amplitude of each sine wave independently. The controlled
amplitude level determines the spectrum intensity of the frequency
region influenced by the corresponding sine wave. When the levels
of all the sine waves are properly controlled, the resultant
harmonic contents will be a desired one which produces a desired
tone quality.
Inventors: |
Wachi; Masatada (Hamamatsu,
JP) |
Assignee: |
Nippon Gakki Seizo Kabushiki
Kaisha (Hamamatsu, JP)
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Family
ID: |
14378304 |
Appl.
No.: |
06/774,092 |
Filed: |
September 9, 1985 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
67693 |
Aug 20, 1979 |
04282790 |
Aug 11, 1981 |
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Foreign Application Priority Data
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Aug 29, 1978 [JP] |
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53-104345 |
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Current U.S.
Class: |
84/693 |
Current CPC
Class: |
G10H
7/10 (20130101); G10H 2250/261 (20130101) |
Current International
Class: |
G10H
7/10 (20060101); G10H 7/08 (20060101); G10H
001/08 (); G10H 007/00 () |
Field of
Search: |
;84/1.01,1.03,1.09,1.11,1.19,1.21-1.28 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Witkowski; Stanley J.
Attorney, Agent or Firm: Spensley Horn Jubas &
Lubitz
Claims
What is claimed is:
1. An electronic musical instrument comprising:
means for repeatedly generating a waveshape having a frequency
which changes as a function of time from the start point of said
waveshape, said start point of said waveshape being synchronized
with a predetermined phase point of the fundamental period of a
musical tone to be generated and said waveshape being terminated
within a period of said fundamental period of said musical
tone;
an amplitude control means for controlling the amplitude of said
waveshape in correspondence with said frequency changing as a
function of time within said fundamental period; and
a sound system means for producing a musical tone from the output
of said amplitude control means.
2. An electronic musical instrument according to claim 1 wherein
said means for repeatedly generating a waveshape generates a
constant amplitude sine wave, the frequency of said sine wave
having a harmonic relation with the fundamental frequency of said
musical tone, and the frequency ratio in said harmonic relation
being changed at predetermined time points in the progress of time
from said start point of said waveshape within said fundamental
period.
3. An electronic musical instrument according to claim 1 wherein
said means for repeatedly generating a waveshape generates an
amplitude modulated sine wave, the frequency of said sine wave
having a harmonic relation with the fundamental frequency of said
musical tone, and the frequency ratio in said harmonic relation
being changed at predetermined time points in the progress of time
from said start point of said waveshape within said fundamental
period.
4. An electronic musical instrument according to claim 1 wherein
said means for repeatedly generating a waveshape is provided with
parallel operating waveshape generators, and each one waveshape
generator generates a waveshape which is assigned to said waveshape
generator, the start point of said assigned waveshape being
synchronized with a predetermined phase point of the fundamental
period of a musical tone to be generated and said waveshape being
terminated within a period of said fundamental period of said
musical tone.
5. An electronic musical instrument according to claim 1 wherein
said means for repeatedly generating a waveshape generates a
waveshape which is a predetermined time function in the progress of
time from said start point of said waveshape, the shape of said
predetermined time function being unchanged in a predetermined
range of the changes of said fundamental frequency of a musical
tone to be generated.
6. An electronic musical instrument for producing a musical tone
having a fundamental with a period To, comprising:
time-window generation means for producing a consecutive set of
time-window signals each establishing a respective time interval
which is a different fractional portion of said fundamental period
To,
first sine wave generation means, cooperating with said time-window
generation means, for generating during each respective established
time interval a sine wave signal having a frequency that is a
different harmonic of said fundamental,
coefficient generation means, cooperating with said time-window
generation means and said sine wave generation means, for
respectively independently scaling said generated sine wave signals
by a separate coefficient for each time interval, and
sound conversion means for converting said scaled sine wave signals
to a musical tone.
7. An electronic musical instrument according to claim 6 wherein
said time-window generation means produces time window signals
establishing respective time intervals which are different integral
fractional portions of said fundamental period To, and wherein said
first sine wave generation means generates sine wave signals each
having a frequency that is harmonically related to said fundamental
in accordance with the inverse of said integral fraction of the
corresponding time interval.
8. An electronic musical instrument according to claim 6 further
comprising:
second sine wave generation means, also cooperating with said
time-window generation means, for generating during each of said
established time intervals a second sine wave signal having a
frequency which is a different harmonic of said fundamental from
the harmonic generated by said first sine wave generation means
during the same established time interval, said second sine wave
signals also being scaled and combined with said scaled sine wave
signals from said first sine wave generator for use by said sound
conversion means.
9. A digital electronic musical instrument comprising:
accumulator means for repetitively accumulating with a fixed
modulus at a set clock rate a selected frequency number related to
the fundamental frequency of a musical tone,
a wave shape memory storing sampled amplitudes of a sine wave,
decoder means, responsive to the contents of said accumulator, for
producing a set of time interval control signals respectively
establishing time intervals that are different fractional portions
of the period of said fundamental frequency,
bit shift circuitry, cooperating with said decoder means, for
causing the contents of said waveshape memory to be accessed using
as sample point specifying addresses different subsets of said
accumulator contents in accordance with the value of said time
interval control signals, and
digital-to-analog conversion means for converting the accessed
sampled amplitudes from said waveshape memory to musical tones.
10. A digital electronic musical instrument according to claim 9
further comprising:
coefficient generator means for providing a set of amplitude scale
factors,
selector means, cooperating with said decoder means, for selecting
a scale factor from said set in accordance with the value of said
time interval control signals, and
scaler means, cooperating with said waveshape memory, for scaling
the accessed sampled amplitudes from said waveshape memory by the
selected scale factor and providing the resultant scaled amplitudes
to said conversion means.
11. An electronic musical instrument according to claim 10 wherein
said coefficient generator means provides successively different
sets of ampltiude scale factors as a function of time from
initiation of musical tone production.
12. An electronic musical instrument according to claim 9 further
comprising:
at least one additional sine waveform memory means, accessed by
directly using a subset of the accumulator contents as the sample
point specifying addresses, for producing at least a fundamental
frequency sine wave continuously throughout all of said established
time intervals, said continuously produced sine wave being combined
with the accessed sampled amplitudes from said waveshape memory for
input to said conversion means.
13. An electronic musical instrument according to claim 12 further
comprising:
another additional sine waveform memory means for producing a sine
wave at twice the fundamental frequency continuously throughout all
of said established time intervals, which sine wave also is
combined with said accessed sampled amplitudes for input to said
conversion means.
14. An electronic musical instrument according to claim 9 wherein
said waveshape memory stores sampled amplitudes of a sine wave
which is amplitude modified to gradually increase and then decrease
in envelope amplitude through one or more sine wave periods, said
accessed sampled amplitudes thereby constituting a Hanning
time-window modulated sine wave signal.
15. A digital electronic musical instrument comprising:
accumulator means for accumulating with a fixed modulus a selected
frequency number related to the octave of a musical tone, said
accumulating being repetitively initiated in synchronism with the
fundamental period of said musical tone,
a waveshape memory storing sampled amplitudes of a sine wave,
decoder means, responsive to the contents of said accumulator and
to said musical tone octave for producing a set of time interval
control signals respectively establishing time intervals that are
different fractional portions of the period of said fundamental
frequency, there being fewer of such established time intervals for
musical tones of progressively higher octave,
bit shift circuitry means, cooperating with said decoder means, for
causing the contents of said waveshape memory to be accessed using
as sample point specifying addresses different subsets of said
accumulator contents in accordance with the value of said time
interval control signals, and
digital-to-analog conversion means for converting the accessed
sampled amplitudes from said sine waveshape memory to musical
tones.
16. A digital electronic musical instrument according to claim 15
wherein said produced time interval control signals cause said bit
shift circuitry means to access sampled amplitudes constituting a
sequence of sine waves that are progressively higher harmonics of
the fundamental of said musical tone, lower order harmonics being
deleted from said sequence for notes of progressively higher
octave. .Iadd.
17. An electronic musical instrument according to claim 1
wherein:
said means for repeatedly generating a waveshape comprises:
means for generating uniformly progressing phase angle information
beginning from a predetermined phase point of the fundamental
period of a musical tone to be generated,
phase modifying means for modifying the generated uniformly
progressing phase information, and
a waveshape memory storing samples of a sinusoidal waveshape, and
means for reading out the same in accordance with said modified
phase information from said phase modifying means, the frequency of
said read out waveshape effectively changing as the generated phase
information is modified during said fundamental period; and
wherein said amplitude control means comprises;
means, responsive to said uniformly progressing phase angle
information, for providing amplitude control information which
varies with time within said fundamental period, and
multiplier means for multiplying the waveshape sample values read
out from said waveshape memory by said amplitude control
information, the output of said multiplier means being supplied to
said sound system means. .Iaddend. .Iadd.
18. An electronic musical instrument comprising:
means for repeatedly generating a waveshape having a frequency
which changes as a function of time from the start point of said
waveshape, including:
means for generating uniformly progressing phase angle information
beginning from a predetermined phase point of the fundamental
period of a musical tone to be generated,
phase modifying means for modifying the generated uniformly
progressing phase information, and
a waveshape memory storing samples of a sinusoidal waveshape, and
means for reading out the same in accordance with said modified
phase information from said phase modifying means, the frequency of
said read out waveshape effectively changing as the generated phase
information is modified during said fundamental period; and
amplitude control means for controlling the amplitude of said
waveshape in correspondence with said frequency changing as a
function of time within said fundamental period, including:
means, responsive to said uniformly progressing phase angle
information, for providing amplitude control information which
varies with time within said fundamental period, and
multiplier means for multiplying the waveshape sample values read
out from said waveshape memory by said amplitude control
information; and
sound system means for producing a musical tone from the output of
said multiplier means. .Iaddend. .Iadd.19. An electronic musical
instrument according to claim 18 wherein said means for repeatedly
generating a waveshape terminates each repeated generation in less
than a period of said fundamental period of said musical tone.
.Iaddend.
Description
BACKGROUND OF THE INVENTION
The present invention relates to an electronic musical instrument,
and more particularly, to an electronic musical instrument wherein
tones are produced through digital processings.
In recent years, the technology of integrated circuits has
undergone a remarkable progress, resulting in the development of
various digital technics for generating musical tones. For one
example, there is disclosed in the prior art an electronic musical
instrument, in which a waveshape is stored in digital
representations and is repetitively read out at a selectable rate,
therefrom producing a musical note.
But this method for producing a musical note has disadvantages in
that the quality of the produced musical tone is fixed by the
waveshape which is previously stored, and that, for different tone
qualities, different memories must be provided for storing
different waveshapes. And, moreover, this method for producing a
musical note is not suitable to change the generated tone quality
as a function of time.
For another example, there is known in the prior art a musical
instrument wherein a desired waveshape is synthesized by adding the
fundamental frequency component and the harmonic components. But
this method of synthesizing a tone waveshape has a disadvantage in
that a large number of harmonic components must be processed when a
precise amplitude control is required up to a higher degree of
harmonics to obtain a high grade control for the tone quality. When
many harmonic components are processed in a time division system,
the system clock frequency must be increased in proportion to the
number of the harmonic components, and when parallel processings
are introduced to lower the clock frequency, parallel processing
circuits must be provided resulting in the increase of the
structure of the equipment.
SUMMARY OF THE INVENTION
Therefore, the general object of the invention is to eliminate
these disadvantages inherent in the heretofore known method of
producing a musical tone and to provide an electronic musical
instrument in which desired harmonic components can be produced by
a simple circuit arrangement, and the spectrum distribution of the
harmonic components can be easily controlled to produce a musical
tone having any desired tone quality selectable from a wide variety
of tone qualities.
More particularly, one object of this invention is to provide an
electronic musical instrument in which a specified frequency band
which includes plural harmonic components is generated by a single
circuit, and the spectrum intensity of all the harmonic components
in the frequency band is controlled simultaneously by a single
circuit.
Another object of this invention is to provide a means to
determine, in accordance with the design of the musical instrument,
the width of each frequency band in which the spectrum intensity is
controlled simultaneously by a single circuit.
Still another object of this invention is to provide a means to
minimize the side-lobe spectrum distribution and thus reduce the
undesired mutual influences in the control of the harmonic
components.
Further, an important object of this invention is to produce
harmonic components in which the line spectra which indicate the
component frequencies and the envelope shape of the spectrum which
determines the intensities of the line spectra can be independently
controlled.
Other and further objects, features and advantages of the invention
will appear more fully from the following description taken in
connection with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows an example of a tone waveshape and time-windows
generated in an embodiment of this invention.
FIGS. 2A and 2B show examples of a spectrum corresponding to a sine
waveshape which passes through a rectangular time-window.
FIG. 3 is a spectrum diagram illustrating the spectrum envelope of
the waveshape shown in FIG. 1.
FIG. 4 shows another example of a tone waveshape and time-windows
generated in another embodiment of this invention.
FIG. 5 is a spectrum diagram illustrating the spectrum envelope of
the waveshape shown in FIG. 4.
FIG. 6 is a block diagram of an embodiment of this invention.
FIG. 7 is a circuit diagram illustrating an example of the decoder
shown in FIG. 6.
FIG. 8 is a circuit diagram illustrating another example of the
decoder shown in FIG. 6.
FIG. 9 is a connection diagram illustrating the internal connection
of the bit shifter means shown in FIG. 6.
FIG. 10 is a block diagram showing an example of the coefficient
generator shown in FIG. 6.
FIG. 11 is a block diagram of another embodiment of this
invention.
FIG. 12 shows an example of waveshapes generated in an embodiment
of this invention.
FIG. 13 is a block diagram illustrating still another embodiment of
this invention.
FIG. 14 shows another example of waveshapes generated in another
embodiment of this invention.
FIG. 15 is a spectrum diagram illustrating the spectrum envelope of
the waveshapes shown in FIG. 14.
FIG. 16 is a block diagram illustrating still another embodiment of
this invention.
FIG. 17 shows an example of the relation between the line spectra
and the spectrum envelope in an embodiment of this invention.
FIG. 18 is a block diagram illustrating still another embodiment of
this invention.
FIG. 19 shows an example of waveshapes generated by the embodiment
shown in FIG. 18.
FIG. 20 is a circuit diagram illustrating an example of the decoder
shown in FIG. 18.
FIG. 21 is a block diagram illustrating still another embodiment of
this invention.
FIG. 22 is a block diagram illustrating an example of the waveshape
generator shown in FIG. 21.
FIG. 23 is a block diagram illustrating an example of the
coefficient generator shown in FIG. 21.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to FIG. 1, there are shown a tone waveshape and
consecutive time intervals or time-windows generated in an
embodiment of this invention.
The abscissa in FIG. 1 represents the time t, while the ordinate
represents the amplitude of the waveshape. The generated tone
waveshape is indicated by TW, and the time intervals or time
windows are indicated by W.sub.1, W.sub.2, W.sub.3, W.sub.4, and
W.sub.5 respectively. The period of the musical tone to be produced
is indicated by T.sub.O, and the tone waveshape TW is equal to A
sin 4(2.tau./To)t from t=0 to t=t.sub.1 =T.sub.O /2, to A sin
8(2.tau./To)t from t=t.sub.1 to t=t.sub.2 =t.sub.1 +T.sub.O /4, to
A sin 16(2.tau./To)t from t=t.sub.2 to t=t.sub.3 =t.sub.2 +T.sub.O
/8, to A sin 32(2.tau./To)t from t=t.sub.3 to t=t.sub.4 =t.sub.3
+T.sub.O /16, and to A sin 64(2.tau./To)t from t=t.sub.4 to
t=t.sub.5 =T.sub.4 +T.sub.O /32.
In a general expression, a sine wave of frequency k/T.sub.O is
generated for a duration of 2T.sub.O /k at each repetition cycle of
the period t.sub.0, where k=4, 8, 16, 32, 64, . . . This is
equivalent to the output of the time-windows, when the input of the
time-windows are continuous sine waves of A sin k(2.tau./To)t and
the time-windows pass the sine waves only for the durations of
2T.sub.O /k at each repetition cycle of the period T.sub.O. For
this reason, the rectangular pulses W.sub.1, W.sub.2, W.sub.3,
W.sub.4, and W.sub.5 in FIG. 1 are called time-windows or
time-window functions.
The tone waveshape TW of FIG. 1 can be easily analysed to a Fourier
series. In order to obtain a general concept, the Fourier series of
the tone waveshape TW will be deduced as a sum of the convolutions
of the continuous sine wave frequencies and the frequency spectrums
of the time-windows.
FIGS. 2A and 2B show examples of a spectrum corresponding to a sine
wave passed through a rectangular time-window. The abscissas of
FIGS. 2A and 2B represent the frequency f, while the ordinates
represent the spectrum intensity. The curve S.sub.1k shows the
spectrum envelope of a rectangular time-window having a width of
2T.sub.O /k, and S.sub.2k shows the line spectrum of a sine wave
represented by A sin k(2.tau./To)t. S.sub.3k is the convolution of
S.sub.1k and S.sub.2k, and shows the spectrum envelope of the sine
wave A sin k(2.tau./To)t which is passed through the rectangular
time-window.
It is well known that the spectrum envelope of a rectangular pulse
can be represented by a formula sin x/x. When the time-window is
cyclically repeated with the repetition period of T.sub.O, the
frequency spectrum of the time-window will be composed of a series
of line spectra beginning from f=O (meaning a direct current
component) and spaced by a regular frequency interval of f.sub.O
=1/T.sub.O. And when the width of the time-window is not changed,
the spectrum envelope remains the same for different values of the
repetition period T.sub.O. In the example illustrated by FIGS. 2A
and 2B, the spectrum envelopes S.sub.1k is shown for k=8, and the
series of the line spectra is denoted by dotted points on the
frequency axis. When the spectrum of the time-window is a series of
line spectra, the spectrum of the sine wave which is passed through
the time-window is also a series of line spectra which is
calculated as the convolution of the line spectrum k/To and the
series of line spectra of the time-window.
FIG. 3 is a spectrum diagram illustrating the spectrum envelope of
the waveshape TW shown in FIG. 1. In FIG. 3, the abscissa
represents the frequency f in logarithmic scale and the ordinate
represents the spectrum intensity. S.sub.4, S.sub.8, S.sub.16,
S.sub.32, and S.sub.64 are respectively the spectrum envelopes
corresponding to the portions of the waveshape TW of the
frequencies of 4/T.sub.O, 8/T.sub.O, 16/T.sub.O, 32/T.sub.O, and
64T.sub.O. It will be apparent from the descriptions in connection
with FIGS. 2A and 2B that the spectrum envelope of the tone
waveshape TW in FIG. 1 will become as shown in FIG. 3.
The tone waveshape TW in FIG. 1 can be easily generated by a simple
digital circuit, the intensity of the generated frequency spectrum
is decreased in inverse proportion to the value of k presenting a
desirable frequency characteristic of 6 db attenuation per octave,
and the amplitude of each sine wave corresponding to a timewindow
can be independently controlled by a single control circuit in a
time division system. These characteristics of the tone waveshape
are advantageous to obtain a desired tone quality.
The bandwidth of the frequency spectrum (for example the bandwidth
from f=O to f=k/2T.sub.O of the spectrum envelope S.sub.1k in FIGS.
2A and 2B) corresponding to a time window can be easily changed, as
the bandwidth is inversely proportional to the time width of the
time-window. As was described in the foregoing paragraph, the
amplitude of each sine wave corresponding to a time-window can be
independently controlled, and therefore, the change of the width of
a time-window means the change of the frequency band which can be
independently controlled. In other words, the degree of the
frequency resolution in the control of the harmonic components, can
be changed by changing the time width of the time-window. In the
embodiments of this invention as will be described in the following
paragraphs, the degree of the frequency resolution is predetermined
at a value which is most suitable for the design purpose, by
determining the time widths of the time-windows.
FIG. 4 shows another example of a tone waveshape and time-windows
generated in another embodiment of this invention. In FIG. 4, the
same notations with FIG. 1 have the same meanings. In the example
of FIG. 1, a sine wave of A sin k(2.tau./To)t passes a time-window
having a time width of 2T.sub.O /k, and in the example of FIG. 4, a
sine wave of A sin k(2.tau./To)t passes a time-window having a time
width of T.sub.O /k. Therefore, in the example of FIG. 4, k=2, 4,
8, 16, 32, and 64 correspond to the time-window W.sub.1, W.sub.2,
W.sub.3, W.sub.4, W.sub.5, and W.sub.6 respectively. In the example
of FIG. 1, two complete cycles of a sine wave pass the
corresponding time-window, while, in the example of FIG. 4, only
one complete cycle of a sine wave passes the corresponding
time-window. Therefore each spectrum envelope corresponding to each
time-window in FIG. 4, has a double bandwidth compared to the
corresponding spectrum envelope of the time-window in FIG. 1.
FIG. 5 is a spectrum diagram illustrating the spectrum envelope of
the tone waveshape shown in FIG. 4, S(W.sub.1).about.S(W.sub.6) in
FIG. 5 shows the spectrum envelopes of the sine waves which pass
time-windows W.sub.1 .about.W.sub.6 respectively. As described in
connection with FIG. 3, the spectrum envelope shown by FIG. 5 has
also 6 db attenuation per octave characteristic and the spectrum
intensity is decreased by 6 db for each one step from S(W.sub.1) to
S(W.sub.6), the intensity of S(W.sub.6), for example, being 1/32 of
the intensity of S(W.sub.1). In FIG. 5 and also in all the
following drawings, however, the spectrum envelope curves are
represented with this 6 db per octave attenuation compensated
(neglected) in order to show the curves more distinctly.
One example of the means for generating the tone waveshape TW in
FIG. 4 will now be described. FIG. 6 is a block diagram of an
embodiment of this invention. In FIG. 6, 11 is a keyboard, 12 is a
frequency number memory, 13 is an accumulator, 14 is a coefficient
generator, 2 is a sine wave memory of 512 words, 3 is a decoder, 4
is a bit shifter, 5 is a selector, 6 is a multiplier, 7 is a
digital to analog converter (hereinafter will be abbreviated as
DAC), and 8 is a sound system.
When a key is depressed at the keyboard 11, the information of the
key is received by the frequency number memory 12 which outputs the
digital number F.sub.0 corresponding to the fundamental frequency
assigned to the key. This digital number F.sub.O is cumulatively
added in the accumulator 13 at a rate equal to the frequency of the
clock pulse .phi., and consequently the accumulator overflows a
carry pulse CA from the MSB (most significant bit) of the
accumulator. .Iadd.Thus the accumulator 13 provides uniformly
progressing phase angle information. .Iaddend.The modulus of the
accumulator 13 and the frequency of the clock pulse .phi. are so
designed as to make the frequency of the carry pulse CA equal to
the fundamental frequency f.sub.O assigned to the key.
.Iadd.Accordingly, the phase angle information begins when the
modulus of the accumulator is reached, which corresponds to a
predetermined phase point of the fundamental period 1f.sub.O of the
musical tone to be generated. .Iaddend.The fundamental frequency
f.sub.O is proportional to the number F.sub.O, and different values
of F.sub.O for different keys are predetermined and stored in the
frequency number memory 12.
The significant 10 (ten) bits of the accumulator 13 are used to
address the sine wave memory 2 and also to generate the gating
signal for the decoder 3. In FIG. 6 and also in the following
drawings, the number of bits constituting a word which is
transmitted on a signal line is designated by a numeral at the side
of the block line crossed by a short dash.
.Iadd.From the above two paragraphs, it will be appreciated that
the digital number F.sub.0 as it is accumulated by the accumulator
13 constitutes the uniformly progressing phase angle information
representing at any point in time a particular phase of the sine
wave stored in memory 2. It will also be appreciated that the
progressing phase angle information is reset and repeats at a
frequency f.sub.0 (the fundamental frequency of the tone to be
produced) determined by the value of the digital number F.sub.0.
.Iaddend.
From the significant 10 bits of the output of the accumulator 13,
the MSB is excluded and other 9 bits are received by the bit
shifter 4. The decoder 3 and the bit shifter 4 are provided in
order to change the frequency of the sine wave which is read out
from the sine wave memory 2, when the time-window changes from
W.sub.1 to W.sub.6 as shown in FIG. 4. .Iadd.Thus the frequency of
the read out sine waveshape effectively changes as the generated
phase information is modified by the cooperation of the decoder 3
and the bit shifter 4 during the fundamental period. .Iaddend.It
will be easily understood that the frequency of the sine wave
readout will be 2f.sub.O when all the 9 bits which are received by
the bit shifter 4 are used to address the sine wave memory 2.
FIG. 7 is a circuit diagram illustrating an example of the decoder
3 shown in FIG. 6. The decoder 3 receives the 6 bits (c.sub.9,
c.sub.8, c.sub.7, c.sub.6, c.sub.5, and c.sub.4) from the
significant 10 bits (c.sub.9 .about.c.sub.O) of the output of the
accumulator 13, and generates the time windows W.sub.1, W.sub.2,
W.sub.3, 4.sub.4, W.sub.5, and W.sub.6 as shown in FIG. 4. In FIG.
7, 301.about.306 are inverters, 311.about.316 are AND gates, and
the small circles at the cross points of the vertical and
horizontal lines mean that the circled horizontal lines constitute
the input lines to the gate situated at the end of the vertical
line. (In the following drawings, similar expressions are used.) It
will be apparent that the gates shown as the time-windows
W.sub.1.about.W6 in FIG. 4 are generated by the circuit shown in
FIG. 7.
FIG. 8 is a circuit diagram illustrating another example of the
decoder 3 shown in FIG. 6. In FIG. 8, 32 is a 7 stage ring-counter,
321.about.326 are AND gates, 33 is an OR gate, c.sub.9
.about.c.sub.4 are the same with the notations in FIG. 7, CA shows
the carry pulse from the accumulator 13, and KON is the key-status
signal of the key which is operated at the keyboard 11. The
ring-counter 32 is set at the initial state by the KON signal when
a key is operated and is shifted by the output of the OR gate 33.
It is apparent that the gates shown in FIG. 4 as the time-windows
W.sub.1 .about.W.sub.6 are generated at the corresponding stages of
the ring-counter 32.
FIG. 9 is a connection diagram illustrating an example of the
internal connection of the bit shifter 4 in FIG. 6. The input to
the bit shifter 4 is the 9 bits (c.sub.8 .about.c.sub.O) taken from
the significant 10 bits (c.sub.9 .about.c.sub.O) with the MSB
(c.sub.9) excluded. The control input to the bit shifter 4 is the
time-window W.sub.1 .about.W.sub.6 from the decoder 3. The output
of the bit shifter 4 is the 9 bits (a.sub.8 .about.a.sub.O) which
address the sine wave memory 2. The connections between c.sub.8
.about.c.sub.O and a.sub.8 .about.a.sub.O are changed in accordance
with the time-windows W.sub.1 .about.W.sub.6 as shown in FIG. 9.
Thus, in the duration of W.sub.1, there are connections between
c.sub.8 and a.sub.8, c.sub.7 and a.sub.7, . . . , and a sine wave
of frequency 2f.sub.O is readout from the sine wave memory 2. And,
in the duration of W.sub.2, there are connections between c.sub.7
and a.sub.8, c.sub.6 and a.sub.7, . . . , a.sub.O being always at
logic "0", and the sine wave memory 2 is readout at even-numbered
addresses (that is, 256 words out of 512 words memory) to generate
a sine wave of frequency 4f.sub.O. .Iadd.Thus the decoder 3 and bit
shifter 9 cooperate to modify the uniformly progressing phase
information generated from the accumulator 13. The waveshape memory
2 is read out in accordance with this modified phase information.
.Iaddend.In this way, the output from the sine wave memory 2 will
become as shown by the tone waveshape TW in FIG. 4.
FIG. 10 is a block diagram showing an example of the coefficient
generator 14 in FIG. 6, and 140 is a coefficient memory, 141 is a
changeover switch for the coefficient memory 140, 142 is a counter,
143 is a clock generator which generates a clock pulse at a
relatively low repetition rate, 144 is a NAND gate, and 145 is an
AND gate. As described in connection with FIG. 6, the time-windows
W.sub.1 .about.W.sub.6 are changed successively at the output of
the decoder 3, and the frequency of the sine wave which is readout
from the sine wave memory 2 is successively changed. In synchronism
with the change of the frequency of this sine wave, the coefficient
which determines the amplitude of the corresponding sine wave is
successively changed at the selector 5, and the selected
coefficient is transmitted to the multiplier 6 where the
coefficient controls the amplitude of the corresponding sine wave.
.Iadd.Thus the selected coefficients constitute amplitude control
information, which vary with time within the fundamental period
1/f.sub.O. This variation occurs in response to the uniformly
progressing phase angle information provided by the accumulator 13
to the decoder 3, since the decoder 3 and the selector 5 select
different values of amplitude coefficients in response to the
changed values of the phase angle information. .Iaddend.In the
embodiment shown in FIG. 6, 6 (six) coefficients b.sub.1
.about.b.sub.6 which correspond to the 6 time-windows W.sub.1
.about.W.sub.6 are transmitted from the coefficient generator 14 to
the selector 6.
In order to obtain a desired tone quality, these coefficients must
be set at proper values, and to realize the variation of the tone
quality as a function of time to imitate a natural musical
instrument, these coefficients must be changed as functions of
time. Moreover, the form of the time function which determines the
tone quality must be changed when the nature of the generated tone
quality is to be changed. To meet these requirements, the
coefficient memory 140 has several sets of the memories of
coefficients b.sub.1 .about.b.sub.6 for which different values are
stored at different addresses. The player of the musical instrument
selects any one set of these coefficient memories by the switch
141.
The coefficient memory 140 is addressed by the contents of the
counter 142, and the selected sets of the coefficients b.sub.1
.about.b.sub.6 which change as the address is changed, are readout.
The counter 142 is progressed by a clock pulse of a suitable
frequency from the clock generator 143. It is assumed that the
output frequency of the clock generator 143 is adjustable. Also it
is assumed that the maximum value of the address of the coefficient
memory 140 is designed to coincide with the maximum value of the
contents of the counter 142, and when all the bits of the counter
142 become at logic "1", the AND gate 145 is cut off by the output
of the NAND gate 144, thereby inhibiting the input of the clock
pulse to the counter 142. When the signal KON indicates that a key
is newly depressed at the keyboard 11, the counter 142 is cleared.
Thus, the coefficients b.sub.1 .about.b.sub.6 are readout, with
these 6 coefficients in parallel, for the duration where the signal
KON indicates that the key is in a depressed state, or from the
time when the signal KON indicates that a key is newly depressed to
the time when the clock pulse input is inhibited by the AND gate
145. These coefficients b.sub.1 .about.b.sub.6 are received by the
selector 5.
As the coefficients b.sub.1 .about.b.sub.6 control the amplitudes
of the sine waves in the time-windows W.sub.1 .about.W.sub.6 in
FIG. 4 respectively, the intensities of the spectrum envelopes
S(W.sub.1).about.S(W.sub.6) in FIG. 5 are controlled by the
respective coefficients b.sub.1 .about.b.sub.6. This means that, in
this embodiment of the invention, a single multiplier 6 can control
the intensities of the spectrum envelopes
S(W.sub.1).about.S(W.sub.6) independently.
The output of the multiplier 6 is converted to an analog voltage by
the DAC 7, and this analog voltage is further converted to a
musical sound in the sound system 8. The DAC 7 and the sound system
8 are well known and will need no further explanations.
As described in the foregoing paragraphs concerning the comparison
between FIG. 1 and FIG. 4, the time width of a time-window in FIG.
4 is relatively small for the period of the sine wave which passes
through the time-window, and therefore, the bandwidth of an
independently controllable spectrum envelope is relatively wide,
with the adjoining envelopes overlapping to each other as shown in
FIG. 5. In other words, the frequency resolution in the control of
the spectrum intensity is relatively poor for the tone waveshape TW
in FIG. 4.
When an improvement in the frequency resolution is desired, the
ratio of the time width of a time-window to the period of the
corresponding sine wave is to be increased. For example, the tone
waveshape TW in FIG. 1 has an improved frequency resolution
compared to the tone waveshape which is generated by the circuit
shown in FIG. 6.
FIG. 11 is a block diagram of another embodiment of this invention,
and the same numerals indicate the same or the like components with
FIG. 6, and will need no further descriptions. And, 20 is a sine
wave memory of, for example, 1024 words capacity, 21 is a sine wave
memory of 512 words capacity, 22 is a sine wave memory of 256 words
capacity, 61, 62, 63 are respectively multipliers, and 64 is an
adder.
The significant 10 bits (c.sub.9 .about.c.sub.0) from the
accumulator 13 address the sine wave memory 20 to readout a
continuous sine wave of frequency f.sub.0, the 9 bits (c.sub.8
.about.c.sub.0) taken from the 10 bits (c.sub.9 .about.c.sub.0)
address the sine wave memory 21 to readout a continuous sine wave
of frequency 2f.sub.0. The 8 bits (c.sub.7 .about.c.sub.0) taken
from the 9 bits with the c.sub.8 bit excluded, are received by the
bit shifter to readout the tone waveshape TW in FIG. 1 from the
sine wave memory 22.
The circuit of the decoder 3 in FIG. 11 is similar to the circuit
shown in FIG. 7 or FIG. 8, provided that the decoder 3 in FIG. 11
is devoid of the circuits corresponding to the time-window W.sub.6,
since the tone waveshape TW in FIG. 1 has only five time-windows
W.sub.1 .about.W.sub.5. Thus, the inverter 306 and the AND gate 314
in FIG. 7 are not necessary for the decoder 3 in FIG. 11; and for
the decoder 3 in FIG. 11, the AND gate 326 in FIG. 8 is not
necessary and the ring-counter is a six stage counter. Therefore,
the input to the decoder 3 in FIG 11 is the significant 5 bits
(c.sub.9 -c.sub.5) and the output is the 5 time-windows W.sub.1
.about.W.sub.5.
The internal connection of the address switching means 4 in FIG. 11
is similar to the connection shown by FIG. 9, but the c.sub.8 bit
in the input, the a.sub.8 bit in the output, and the connection for
the time-window W.sub.6 are devoid in the bit shifter 4 in FIG.
11.
Further, the coefficient generator 14 of FIG. 11 has a circuit
similar to the circuit shown by FIG. 10, but the coefficient
generator 14 of FIG. 11 generates not only the 5 coefficients
b.sub.2 .about.b.sub.6 for the time-windows W.sub.1 .about.W.sub.5
but also the coefficients b.sub.0, b.sub.1 corresponding to the
output from the sine wave memories 20, 21. The coefficients b.sub.2
.about.b.sub.6 are transmitted to the selector 5, and the
coefficients b.sub.0, b.sub.1 are respectively transmitted to the
multipliers 61, 62.
In these circuit connections, the sine wave memory 22 is readout in
a similar way in which the sine wave memory 2 in FIG. 6 is readout,
except that the sine wave memory 22 is readout for two repeated
sine wave cycles per each one time-window, generating the tone
waveshape TW in FIG. 1. And the spectrum envelopes corresponding to
these time-windows W.sub.1 .about.W.sub.5 become as shown by
S.sub.4 .about.S.sub.64 in FIG. 3. The amplitudes of these spectrum
envelopes S.sub.4 .about.S.sub.64 are controlled at the multiplier
63 by the corresponding coefficients b.sub.2 .about.b.sub.6. From
the comparison between FIG. 3 and FIG. 5, it is clear that the
embodiment illustrated by FIG. 11 can produce narrower frequency
bands of independently controllable spectrum envelopes than the
embodiment illustrated by FIG. 6. But, as shown by FIG. 3, the tone
waveshape TW of FIG. 1 which is readout from the sine wave memory
22 of FIG. 11 contains very weak spectrum intensities for the
frequency components f.sub.0, 2f.sub.0, the sine wave memories 20,
21 are provided to generate these two frequency components f.sub.0,
2f.sub.0, and the output of these sine wave memories 20, 21 are
amplitude-controlled at the multipliers 61, 62 by the coefficients
b.sub.0, b.sub.1 respectively.
The output values of these multipliers 61, 62, 63 are added at the
adder 64 and the resultant is converted to an analog voltage by the
DAC 7.
In the embodiment shown in FIG. 11, there are provided three sine
wave memories 20, 21, and 22. But it is apparent that one single
sine wave memory can be readout in a time division system to
generate the three different waveshapes by a minor modification in
the memory reading circuit.
In the embodiments shown by FIG. 6 and FIG. 11, the accumulator 13
is used to generate the addressing signal having a repetition
frequency f.sub.0, and the tone waveshapes TW shown in FIG. 1 and
FIG. 4 are readout from the sine wave memories 2 and 22, but it is
clear that this invention is not limited to a particular method for
generating the tone waveshape TW, and any heretofore known method
of generating a tone waveshape can be used in this invention.
Further, in the embodiments of FIG. 6 and FIG. 11, rectangular
time-windows are used. In a rectangular time-window, the total time
width can be effectively used for gating a sine wave, but the
spectrum envelope of a rectangular time-window is widely spreaded
as shown by S.sub.1k in FIG. 2. Especially, the spectrum
intensities in the so-called side-lobe region are fairly strong for
a rectangular time-window. The first zero of the spectrum intensity
of a rectangular time-window is at the frequency k/2T.sub.0 as
shown by FIG. 2, and the spectrum envelopes beyond this frequency
are called side-lobe spectrum envelopes, while the spectrum
envelope within this frequency is called a main-lobe spectrum
envelope. By this character of a rectangular time-window, the
intensity control for a desired main-lobe spectrum envelope is
accompanied by an undesired intensity change in the side-lobe
spectrum envelopes, deteriorating the frequency resolution in the
spectrum intensity control.
In order to eliminate this demerit, a time-window which has a
sufficiently attenuated side-lobe spectrum is to be used. But it
must be remembered that such a time-window with a sufficiently
attenuated side lobe spectrum requires a longer time width for a
same main-lobe spectrum bandwidth than a rectangular time-window
does. In other words, the efficiency of the time width is decreased
when the shape of a time-window is changed from a rectangular
shape.
FIG. 12 shows an example of waveshapes generated in an embodiment
of this invention. In FIG. 12, the abscissa represents the time t,
the waveshapes TW.sub.1, TW.sub.2 are sine waves of frequency
f.sub.0, 2f.sub.0 respectively, the waveshape TW.sub.4 shows the
waveshape of four complete cycles of a sine wave of frequency
4f.sub.0 which is passed through a Hanning time-window of time
width T.sub.0. The waveshape TW.sub.8 shows the waveshape of four
each complete cycles of sine waves of frequencies 8f.sub.0,
16f.sub.0, 32f.sub.0, 64f.sub.0 which are passed through Hanning
time-windows of time widths of T.sub.0 /2, T.sub.0 /4, T.sub.0 /8,
and T.sub.0 16.
FIG. 13 is a block diagram illustrating an embodiment of this
invention to generate tone waveshapes shown by TW.sub.1, TW.sub.2,
TW.sub.4 and TW.sub.8 in FIG. 12. In FIG. 13, the same numerals
denote the same or the like components with FIG. 11, and will need
no further description. The waveshape memory which stores the
waveshape TW.sub.4 of FIG. 12 in 1,024 words in represented by 23,
and 24 is another waveshape memory which stores the portion from
t=0 to t=T.sub.0 /2 of the waveshape TW.sub.8 of FIG. 12 in 512
words. As shown by the waveshape TW.sub.8, the time widths of the
time-windows are changed successively to T.sub.0 /2, T.sub.0 /4,
T.sub.0 /8, and T.sub.0 /16, corresponding to the time-windows
W.sub.1, W.sub.2, W.sub.3, and W.sub.4 in FIG. 1 (devoid of the
time-window W.sub.5 of FIG. 1), and therefore the decoder 3 in FIG.
13 is devoid of the circuit corresponding to the time-windows
W.sub.5 and W.sub.6 from the circuit shown by FIG. 7 or FIG. 8, and
the internal connections of the address switching means 4 in FIG.
13 is devoid of the connections corresponding to the time-windows
W.sub.5 and W.sub.6 from the connections shown by FIG. 9. It will
be apparent that the tone waveshapes TW.sub.1, TW.sub.2, TW.sub.4,
and TW.sub.8 in FIG. 12 are respectively readout from the sine wave
memories 20, 21, and the waveshape memories 23, 24 in FIG. 13. The
waveshapes TW.sub.4 and TW.sub.8 can be considered as the
waveshapes which are produced when pure sine waves are passed
through the corresponding Hanning time-windows, and therefore, the
spectrum envelopes for these waveshapes can be calculated from the
convolution of the spectrum envelope of the Hanning time-window and
the line spectrum of the corresponding pure sine wave. The total
time width of the time-windows of the tone waveshapes TW.sub.4 and
TW.sub.8 in FIG. 12 is twice as long as the total time width of the
time-windows for the tone waveshape TW in FIG. 1, and the shape of
the time-windows in FIG. 12 can be considered as Hanning windows as
shown by the dotted lines in TW.sub.4 and TW.sub.8. It will be
clear from the Fourier analysis of a Hanning window that the
side-lobe spectrum which was fairly strong for a rectangular
time-window as shown by S.sub.1k in FIG. 2, is sufficiently
attenuated for a Hanning window and that the bandwidth of the
main-lobe spectrum envelope for the Hanning window in FIG. 12 is
the same with that for the rectangular window in FIG. 1, since the
time width of the Hanning window in FIG. 12 is twice as wide as the
time width of the rectangular window in FIG. 1.
The output of the sine wave memories 20, 21 are
amplitude-controlled by the corresponding coefficients at the
multipliers 61, 62 as described in connection with FIG. 11, the
output of the waveshape memory 23 (the tone waveshape TW.sub.4 of
FIG. 12) is amplitude-controlled at the multiplier 65 by the
coefficient b.sub.2, and the output of the waveshape memory 24 (the
tone waveshape TW.sub.8 of FIG. 12) is amplitude-controlled at the
multiplier 63 by the corresponding coefficients b.sub.3
.about.b.sub.6. Therefore, each spectrum envelope which can be
independently controlled by any of these coefficients b.sub.2
.about.b.sub.6 in the circuit of FIG. 13 has more sufficiently
attenuated side-lobe spectrum envelope than the corresponding
spectrum envelope which can be independently controlled by the
corresponding one of the coefficients b.sub.2 .about.b.sub.6 in the
circuit of FIG. 11. In this meaning, it can be said that the
embodiment shown in FIG. 13 has a better frequency resolution in
the control of the spectrum intensities.
From the comparison between FIG. 6 and FIG. 11, and that between
FIG. 11 and FIG. 13, it will be understood that the time width of a
time-window must be increased to increase the frequency resolution
in the control of spectrum intensities, that a rectangular window
must be avoided to suppress the side-lobe spectrum envelopes which
are detrimental to the frequency resolution, and that the number of
the parallel operating waveshape memories (in general, the parallel
operating waveshape generators must be increased to increase the
frequency resolution in the control of the spectrum
intensities.
FIG. 14 shows another example of waveshapes generated in another
embodiment of this invention. In FIG. 14, the same notations with
FIG. 1 have the same meanings, and TWA shows a tone waveshape which
will hereafter be called as series A, while TWB shows another tone
waveshape which will hereafter be called as series B. When FIG. 14
is compared with FIG. 1, it will be apparent that the ratio of the
time width of each time-window to the period of the corresponding
sine wave of TWA in FIG. 14 is two times that of TW in FIG. 1, and
the ratio of the time width of each time-window to the period of
the corresponding sine wave of TWB in FIG. 14 is one and half times
that of TW in FIG. 1. Therefore the bandwidths of the spectrum
envelopes for the tone waveshapes TWA and TWB will become
respectively one half and two thirds of the bandwidths of the
spectrum envelopes shown as S.sub.8, S.sub.16, S.sub.32, and
S.sub.64 in FIG. 3.
FIG. 15 is a spectrum diagram illustrating the spectrum envelopes
for the tone waveshapes shown by TWA and TWB in FIG. 14. This
spectrum diagram of FIG. 15 is represented with the 6db/octave
attenuation compensated as described in connection with FIG. 5.
S(TWA) and S(TWB) are the spectrum envelopes for the tone
waveshapes TWA and TWB respectively, and
S(W.sub.1A).about.S(W.sub.4A) of S(TWA) and
S(W.sub.1b).about.S(W.sub.4B) of S(TWB) show the spectrum envelopes
for the tone waveshapes which pass the time-windows W.sub.1
.about.W.sub.4 of FIG. 14 respectively.
When FIG. 15 is compared with FIG. 3, it will be apparent that the
tone waveshapes TWA and TWB have narrower frequency bands of the
spectrum envelopes which increase the resolution in the spectrum
control, but which give rise to spectrum void regions where
spectrum intensities are very weak as shown by S(TWA) or S(TWB) in
FIG. 15. Therefore, both tone waveshapes TWA and TWB in FIG. 14 are
simultaneously generated to eliminate these spectrum void regions
throughout the whole frequency region. Further, as shown in FIG.
15, the frequency components at frequencies f.sub.0, 2f.sub.0,
3f.sub.0, and 4f.sub.0 are not included in either one of the
spectrum envelopes S(TWA) and S(TWB), and these frequency
components must be generated by other circuits.
FIG. 16 is a block diagram illustrating still another embodiment of
this invention, and the same numerals with FIG. 11 show the same or
the like components which will need no further explanations. And in
FIG. 16, the circuits after the output of the adder 64 are not
shown in the drawing, since these circuits are the same with the
corresponding circuits in FIG. 11.
Further, the keyboard 11, the frequency number memory 12, the
accumulator 13 shown in FIG. 11 and the decoder 3 shown in FIG. 13
are also provided in the circuit of FIG. 16, but these components
are not shown in FIG. 16 for brevity of the drawing, and only the
transmission lines for the accumulator output and the decoder
output W.sub.1, W.sub.2, W.sub.3, W.sub.4 are indicated. The
circuit of FIG. 16 has a coefficient generator corresponding to the
coefficient generator 14 in FIG. 11, and the coefficient generator
in FIG. 16 (not shown in the drawing) generates 12 coefficients
b.sub.0 .about.b.sub.6 and a.sub.1 .about.a.sub.5. The transmission
lines for these coefficients are shown in FIG. 16.
And 25 in FIG. 16 is a memory of 3 periods of a sine wave which
stores the 3 periods in 1,024 words, 26 is a sine wave memory of
128 words, 27 is an another memory of 3 periods of a sine wave
which stores the 3 periods in 512 words, and 66, 67, and 68 are
multipliers respectively.
In the circuit of FIG. 16, there are also provided a selector 51
for series A, a selector 52 for series B, bit shifter 41 for series
A, and bit shifter 42 for series B in order to produce both tone
waveshapes TWA and TWB simultaneously. The function of the selector
51 or 52 is the same with that of the selector 5 in FIG. 13, and
the internal connection of the bit shifter 42 is the same with that
of the bit shifter 4 in FIG. 13. The bit shifter 41 has a similar
connection with that of the bit shifter 42, but is devoid of the
circuits related to the input bits c.sub.8, c.sub.7 and the output
bits a.sub.8, a.sub.7, since the storage capacity of the sine wave
memory 26 is 128 words.
In the same way as described in connection with FIG. 11 and FIG.
13, sine waves of frequencies f.sub.0, 2f.sub.0, 3f.sub.0, and
4f.sub.0 are generated respectively from the sine wave memories 20,
21, the memory of 3 periods of a sine wave 25, and the sine wave
memory 22; and the tone waveshapes TWA and TWB in FIG. 14 are
generated respectively from the sine wave memory 26 and the memory
of 3 periods of a sine wave 27.
The sine waves of frequencies f.sub.0, 2f.sub.0, 3f.sub.0, and
4f.sub.0 are independently amplitude-controlled at the multipliers
61, 62, 66, and 67 by the coefficients b.sub.0, b.sub.1, a.sub.1,
and b.sub.2. The frequency components in the spectrum envelopes
S(W.sub.1A).about.S(W.sub.4A) in FIG. 15 are independently
amplitude-controlled at the multiplier 63 by the coefficients
b.sub.3 .about.b.sub.6 respectively, and the frequency components
in the spectrum envelopes S(W.sub.1B).about.S(W.sub.4B) in FIG. 15
are independently amplitude-controlled at the multiplier 68 by the
coefficients a.sub.2 .about.a.sub.5 respectively.
When FIG. 15 is compared with FIG. 3 or FIG. 5, it will be said
that, in the embodiment shown by FIG. 16, the frequency resolution
in the spectrum control is substantially improved.
In all embodiments heretofore shown, the time width of any of the
time-windows is equal to one part of the fundamental period T.sub.0
divided by a predetermined integer, and the ratio of the period of
the sine wave which passes the time-window to the period T.sub.0 is
also maintained at an integer. But, in general, the time width of
any of the time-windows and the period of the sine wave which
passes the sine wave can be determined independently from the
period T.sub.0.
For example, when the time width of a time-window is 2T.sub.W /k
where T.sub.w is arbitrary provided with T.sub.W <T.sub.0, the
frequency of the sine wave which passes the time-window of 2T.sub.W
/k width is k/T.sub.W, and k=4, 8, 16, 32, and 64 maintaining the
relation T.sub.0 >(2T.sub.W /4+2T.sub.W /8+2T.sub.W 16+2T.sub.W
/32+2T.sub.W /64), it will be clear that a tone waveshape which is
similar to the tone waveshape TW in FIG. 1 is generated. And it is
apparent that the spectrum envelope which is obtained by the
Fourier analysis of this tone waveshape contains only line spectra
which are integral multiples of the frequency f.sub.0 =1/T.sub.0,
because the repetition period of this tone waveshape is T.sub.0
regardless of the value of T.sub.W.
FIG. 17 shows an example of the relation between the line spectra
and the spectrum envelope in an embodiment of this invention, and
there are shown the spectrum envelope S.sub.W and the line spectra
when a sine wave Asin4(2.tau./T.sub.W)t is passed through a
rectangular window having 2T.sub.W /4 time width with a repetition
period T.sub.0 where T.sub.W >T.sub.0. In FIG. 17, the abscissa
is the frequency f, and the spectrum envelope S.sub.W has its peak
at the frequency f=4/T.sub.W as will be easily understood from the
descriptions in connection with FIG. 2, while all the frequency
components included are the harmonics for the frequency f.sub.0
=1/T.sub.0 as shown by 3f.sub.0, 4f.sub.0, 5f.sub.0, 6f.sub.0, . .
. in FIG. 17.
The example of the spectrum envelope S.sub.W shown in FIG. 17
corresponds to the spectrum envelope S.sub.4 shown in FIG. 3. It
will be clear that other spectrum envelopes corresponding to the
spectrum envelopes corresponding to the spectrum envelopes S.sub.8
.about.S.sub.64 in FIG. 3 may also be produced and that the shapes
of these produced spectrum envelopes are determined by the time
widths 2T.sub.W /k, while the line spectra included in these
spectrum envelopes are all the harmonics of the frequency f.sub.0
=1/T.sub.0.
FIG. 18 is a block diagram illustrating still another embodiment of
this invention, and FIG. 19 shows an example of waveshapes
generated by the embodiment shown by FIG. 18.
In the embodiment shown by FIG. 18, it is assumed that a bit
shifter 43 addresses the sine wave memory 22 to readout a same tone
waveshape in a same octave, and changes the addressing to readout
different tone waveshapes for different octaves are shown in FIG.
19. The repetition frequency of any of these tone waveshapes is
always coincident with the frequency f.sub.0, and the start point
of the tone waveshape is controlled to coincide with a
predetermined phase point of the period T.sub.0.
It is also assumed that, in the embodiment of FIG. 18, the musical
tones are generated in a range of 4 octaves, that is, the octave
No. 1(OC1), the octave No. 2(OC2), the octave No. 3(OC3), and the
octave No. 4(OC4). The tone waveshapes readout from the sine wave
memory 22 in the 4 different octaves are shown in FIG. 19 by
TW(OC1), TW(OC2), TW(OC3), and TW(OC4) respectively. In FIG. 19,
the abscissa represents the time t and the ordinate represents the
amplitude A. The musical tone frequencies corresponding to these 4
tone waveshapes TW(OC1).about.TW(OC4) are denoted respectively by
T.sub.01 .about.T.sub.04 in FIG. 19. This embodiment of FIG. 18 is
characterized in that, when the musical tone frequency is changed
in a same octave (that is, when the time width of any one of
T.sub.01 .about.T.sub.04 is changed), the corresponding tone
waveshape of the waveshapes TW(OC1).about.TW(OC4) remains
unchanged.
In all these tone waveshapes TW(OC1).about.TW(OC4) in FIG. 19, the
highest frequency of the sine waves which pass the time-windows
remains constant. This means that the highest frequency component
included in the spectrum envelopes corresponding to the tone
waveshapes TW(OC1).about.TW(OC4) is the same, the spectrum envelope
for the tone waveshape TW(OC1) corresponding to the spectrum
envelope S.sub.4 .about.S.sub.64 in FIG. 3, the spectrum envelopes
for the tone waveshapes TW(OC2), TW(OC3), and TW(OC4) respectively
corresponding to spectrum envelopes S.sub.8 .about.S.sub.64,
S.sub.16 .about.S.sub.64, and S.sub.32 .about.S.sub.64 in FIG. 3.
The frequency components which have frequencies higher than the
spectrum envelope S.sub.64 in FIG. 3 are inaudible and have little
influence on the tone quality. Therefore, the tone waveshapes are
changed for different octaves as shown in FIG. 19 in order to
simplify the waveshape generation circuit.
In FIG. 18, the same numerals with FIG. 11 show the same or the
like components, and 15 is an encoder which receives the
information of the tone frequency assigned to the key depressed on
the keyboard 11 and generates the octave code OCC for indicating
the octave to which the tone frequency belongs and the note code
NTC for indicating the name of the note of the tone frequency. The
octave code OCC is composed of 2 bits for indicating the desired
one of the 4 kinds of octaves OC1.about.OC4 which are previously
described, and the note code NTC is composed of 4 bits for
indicating the desired one of the 12 different names of the note.
The numerals 121 and 122 are frequency number memory No. 1 and
frequency number memory No. 2 respectively. Each of these frequency
number memories 121 and 122 corresponds to the frequency number
memory 12 in FIG. 11, the frequency number memory 121 receiving the
octave code OCC from the encoder 15 for producing the value F.sub.W
corresponding to the input OCC, and the frequency memory 122
receiving the octave code OCC and the note code NTC for producing
the value F.sub.0 which is the same with the output F.sub.0 of the
frequency number memory 12 of FIG. 11. The numerals 16 and 17
respectively denote multipliers which will be described in later
paragraphs. When both the multiplier inputs as indicated by WOW and
VIB in FIG. 18 are unity, the outputs of these multipliers 16 and
17 are respectively F.sub.W and F.sub.0. Two accumulators, each
corresponding to the accumulator 13 of FIG. 11, are provided, 131
being accumulator No. 1 and 132 being accumulator No. 2. The
accumulator 131 accumulates the value F.sub.W at the clock
frequency .phi. and the 8 bits (c.sub.7 .about.c.sub.0) of this
accumulator 131 address the sine wave memory 22 through the address
switching means 43. A set-reset type flipflop is denoted by 18. The
accumulator 132 generates a carry pulse CA which has the musical
tone frequency in a same way as the accumulator 13 in FIG. 6, and
this carry pulse CA clears the accumulator 131 through the flipflop
18. Thus, the address from the accumulator 131 to readout the sine
wave memory 22 changes in synchronism with the carry pulse CA, and
therefore, the start points of the waveshapes TW(OC1).about.TW(OC4)
are synchronized with the start points of the corresponding musical
tone periods T.sub.01 .about.T.sub.04 as shown in FIG. 19. The
decoder 30 in FIG. 18 corresponds to the decoder 3 in FIG. 11, and
the bit shifter 43 in FIG. 18 corresponds to the bit shifter 4 in
FIG. 11.
Further, in the circuit of FIG. 18, there are provided the
coefficient generator 14, the sine wave memories 20 and 21, the
multipliers 61 and 62, the adder 64, the DAC 7, and the sound
system 8 in the same way as shown in FIG. 11, although these
components are not shown in FIG. 18 for the sake of the brevity of
the drawing, the sine wave memories 20 and 21 (not shown in FIG.
18) are addressed by the output of the accumulator 132.
FIG. 20 is a circuit diagram illustrating an example of the decoder
30 shown in FIG. 18. In FIG. 20, the same numerals with FIG. 7 show
the same or the like components, the same notations have the same
meanings, and there are also provided AND gates 34, 35, 36, and OR
gates 37, 38. As in FIG. 7, the decoder 30 receives the higher 5
bits (c.sub.9 .about.c.sub.5) from the output of the accumulator
131, and transmitts the time-window W.sub.1 .about.W.sub.5 from the
AND gates 311.about.315. But in the decoder 30, the 2 bits of the
octave code OCC are decoded to signals OC1.about.OC3 which
represent the octaves, and in accordance with the octave, the
time-windows W.sub.1 .about.W.sub.5, W.sub.1 .about.W.sub.4,
W.sub.1 .about.W.sub.3, or W.sub.1 and W.sub.2 are transmitted
through the OR gates 34, 35, and 36. The output frequency of the
accumulator 131 becomes higher as the octave is raised, resulting
in a narrower time width of a time-window. For example, the time
width of the time-window W.sub. 1 in the octave OC4 is equal to
that of the time-window W.sub.4 in the octave OC1.
The internal connection of the bit shifter 43 is the same with that
of the bit shifter 4 in FIG. 11, provided that the switchings in
the bit shifter 43 are only among the time-windows which are
received from the decoder 30, since the number of the time-windows
which are transmitted from the decoder 30 changes in accordance
with the octave as shown by FIG. 19.
Thus, one of the tone waveshapes selected in accordance with the
octave code OCC from TW(OC1).about.TW(OC4) shown in FIG. 19 are
readout from the sine wave memory 22. The selector 5 in FIG. 18 is
the same with the selector 5 in FIG. 11, provided that only the
coefficients corresponding to the time-windows which are received
from the decoder 30 are transmitted to control the amplitudes of
the corresponding waveshapes of the waveshapes
TW(OC1).about.TW(OC4) in FIG. 19 at the multiplier 63, since the
number of the time-windows which are transmitted from the decoder
30 changes in accordance with the octave.
Accordingly, the spectrum envelope of the tone waveshape readout
from the sine wave memory 22 of FIG. 18 in the octave OC1 will
become equivalent to the spectrum envelope S.sub.4, S.sub.8,
S.sub.16, S.sub.32, and S.sub.64 of FIG. 3, and the fundamental
tone frequency changes in the range of one octave with the
frequency f.sub.O of FIG. 3 as the highest limit of the fundamental
tone frequency; in the octave OC2, the spectrum envelope will
become equivalent to the spectrum envelope S.sub.8, S.sub.16,
S.sub.32, and S.sub.64 of FIG. 3, the fundamental tone frequency
changes in the range 2f.sub.O .about.f.sub.O ; in the octave OC3,
the spectrum envelope will become equivalent to the spectrum
envelope S.sub.16, S.sub.32, and S.sub.64 of FIG. 3, and the
fundamental tone frequency changes in the range 4f.sub.O 2f.sub.O ;
and in the octave OC4, the spectrum envelope will become equivalent
to the spectrum envelope S.sub.32 and S.sub.64 of FIG. 3, and the
fundamental tone frequency changes in the range 8f.sub.O
4f.sub.O.
At the multiplier 63, each sine wave is independently
amplitude-controlled by the corresponding one of the coefficients
b.sub.2 .about.b.sub.6. This means that, in the octave OC1, each
part S.sub.4 .about.S.sub.64 of the spectrum envelope of FIG. 3 is
amplitude-controlled by the corresponding coefficient b.sub.2
.about.b.sub.6 ; in the octave OC2, each part S.sub.8
.about.S.sub.64 of the spectrum envelope of FIG. 3 is
ampltiude-controlled by the corresponding coefficient b.sub.3
.about.b.sub.6 ; in the octave OC3, each part S.sub.16
.about.S.sub.64 of the spectrum envelope of FIG. 3 is
amplitude-controlled by the corresponding coefficient b.sub.4
.about.b.sub.6 ; and in the octave OC4, each part S.sub.32,
S.sub.64 of the spectrum envelope of FIG. 3 is amplitude controlled
by the coefficient b.sub.5 or b.sub.6.
It will be easily understood from the relation between the spectrum
envelope S.sub.W and the line spectra in FIG. 17 that a vibrato
effect or wow-wow effect which accompany the spectrum variation can
be obtained by giving a small variation to the frequency f.sub.W
=1/T.sub.W and/or f.sub.O =1/T.sub.O.
The multiplier 16 in FIG. 18 multiplies the value F.sub.W by a
coefficient (the coefficient shown by WOW in the drawing) which
changes as a function of time by a small amount around the center
value of unity, and this multiplication changes the frequency
f.sub.W by a small amount around the center frequency, resulting in
the lateral shift (shaft along the frequency axis) of the spectrum
envelope S.sub.W of FIG. 17. When the output of the multiplier 17
is fixed during the variation of the output of the multiplier 16,
the lateral positions (positions on the frequency axis) of the line
spectra do not change in the changing spectrum envelope S.sub.W,
and therefore, a wow-wow effect is obtained in which the relative
intensities of the line spectra are changed.
The multiplier 17 of FIG. 18 multiplies the value F.sub.O with a
coefficient (the coefficient shown by VIB in the drawing) which
changes as a function of time by a small amount around the center
value of unity, and this multiplication changes the frequencey
f.sub.O by a small amount around the center frequency. When the
output of the multiplier 16 is fixed during the variation of the
output of the multiplier 16, the lateral positions of the line
spectra are changed in the fixed spectrum envelope S.sub.W in FIG.
17, and a vibrato effect is obtained.
It has been described that the frequency number memory 121 stores
the values of F.sub.W for all the octaves, but it will be apparent
that only the value of F.sub.W for the lowest octave (OC1) is
stored in the memory 121 and the values of F.sub.W for higher
octaves may be produced by shifting the bits or a bit of the value
of F.sub.W for the octave OC1. In this case the memory 121 will
become very simple when the value of F.sub.W =1.0 is stored in the
memory. Further the memory 121 and the multiplier can be combined
as an arithmetic circuit for operating the calculation (1+.DELTA.).
(oct-1), where .DELTA. is a WOW coefficient and oct is the number
representing the order of the octave.
In all the embodiments heretofore described, sine waves are passed
through time-windows to generate tone waveshapes, but it will be
apparent that this invention is not limited to a particular method
for generating tone waveshapes.
Further, in all the embodiments heretofore described, the frequency
of the sine wave passing through time-windows is changed by
stepwise; but it will be clear that a similar effect can be
obtained by gradually changing the sine wave frequency.
FIG. 21 is a block diagram illustrating still another embodiment of
this invention, and the same numerals with FIG. 6 represent the
same or the like components which need no further descriptions. The
waveshape generator 28 in FIG. 21 generates a sine wave of a
gradually changing frequency with the start point synchronized by
the carry pulse CA from the accumulator 13. This sine wave of
gradually changing frequency is terminated before the succeeding
carry pulse CA.
The coefficient generator in FIG. 21 is denoted by 19, which
generates a gradually changing coefficient (corresponding to the
coefficients b.sub.1 .about.b.sub.6 of FIG. 6) synchronized with
the change of the sine wave frequency from the waveshape generator
28 and cyclically repeated with the frequency of the carry pulse CA
in the whole duration of the KON signal.
The circuit to generate a sine wave of a gradually changing
frequency is well known in the technological field of the frequency
modulation in a communication equipment or of the frequency sweep
in a signal generator equipment. Any of these heretofore known
circuits can be used as the waveshape generator 28 of FIG. 21.
FIG. 22 is a block diagram illustrating an example of the waveshape
generator 28 shown in FIG. 21. The sine wave memory 2 in FIG. 22 is
the same with the sine wave memory 2 in FIG. 6, and 123 is a
frequency number memory corresponding to the frequency number
memory 121 of FIGS. 18, 281 and 282 are respectively AND gates, 283
is an OR gate, 284 is an inverter, 285 is a shift register, 286 is
a multiplier, and 287 is a flipflop.
The value R corresponding to the pitch of the musical tone assigned
to the key which is depressed at the keyboard 11, is readout from
the frequency number memory 123 and are accumulated in the
accumulator 133 through the AND gate 281 and the OR gate 283. But
the value R is added to the accumulator 133 only when the carry
pulse CA is transmitted from the accumulator 13 (FIG. 21) to the
AND gate 281. In other times, the value of R' which is circulated
from the output of the OR gate 283, through the multiplier 286, the
shift register 285, the AND gate 282 to the input of the OR gate
283, and which is multiplied by a constant k at the multiplier 286
for each one circulation, is accumulated in the accumulator 133.
Thus, the value of R' is increased exponentially and the frequency
of the sine wave readout from the sine wave memory 2 addressed by
the higher bits of the accumulator 133 is increased
exponentially.
The flipflop 287 is set by the carry pulse from the multiplier 286
and is reset by the carry pulse CA from the accumulator 13, in
order to synchronize the start point of the waveshape readout from
the sine wave memory 2 with a predetermined phase of the musical
tone and terminate the waveshape within the period of the musical
tone.
FIG. 23 is a block diagram illustrating an example of the
coefficient generator 19 in FIG. 21, and the same numerals with
FIG. 10 represent the same or the like components which will need
no further descriptions. The coefficient memory which corresponds
to the coefficient memory 140 in FIG. 10 is denoted by 146 in FIG.
23, and 191 is an envelope number memory, 192 is an accumulator,
193 is an AND gate, and 194 is a set-reset type flipflop.
While the coefficients b.sub.1 .about.b.sub.6 are generated in
parallel from the coefficient generator 14 of FIG. 10, the
coefficient readout from the coefficient generator 19 in FIG. 21,
gradually changes in synchronism with the change of the sine wave
frequency readout from the waveshape generator 28. Thus, the
coefficient memory 146 of FIG. 23 is addressed by the counter 142
in a same way as the coefficient memory 140 of FIG. 10 is addressed
by the counter 142, and the coefficient memory 146 is also
addressed by the contents of the accumulator 192 which changes in
synchronism with the change in the output frequency of the
waveshape generator 28. The AND gate 193 sets the flipflop 194 when
all bits of the accumulator 192 are at logic "1", and the carry
pulse CA from the accumulator 13 resets the flipflop 194, and
thereby the coefficient, which changes in synchronism with the
change of the output frequency of the waveshape generator 28 and
which also changes as a function of time from the start point of
the KON signal, is readout from the coefficient memory 142. The
output from the envelope number memory 191 is a digital value
corresponding to the pitch of the musical tone assigned to the key
depressed at the keyboard 11, and this output is accumulated in the
accumulator 192. The relation between the output from the envelope
number memory 191 and the digital value R from the frequency number
memory 123 of FIG. 22 keeps the predetermined relation beteen the
change of the coefficient generated from the coefficient generator
19 and the change of the output frequency from the waveshape
generator 28.
As the spectrum envelope of a sine wave with a gradually changing
frequency is well known in the field of the spectrum analysis of a
frequency modulated signal, detailed descriptions are abbreviated.
But it will be easily understood that the gradual change in the
frequency is more advantageous for the suppression of undesired
harmonic components which are generated by an abrupt change in the
frequency.
Although the foregoing descriptions of this invention have been on
several particular embodiments, this invention is not limited to
these particular embodiments and many modifications can be made
without departing from the scope and spirit of this invention to
provide a musical instrument in which the spectrum envelope can be
independently controlled by a simple circuit.
* * * * *