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BACKGROUND OF THE INVENTION
a. Field of the Invention
The present invention relates to a system for measuring the vibration
frequency of a vibrating object, and in particular it pertains to a method
for measuring the vibration frequency of a vibrating object, such as a
string of a piano, which develops harmonic vibrations, and also it
concerns a method for adjusting the vibration frequency of the vibrating
object.
B. Description of the Prior Art
A number of vibrating objects (strings) are used in a musical instrument
such as a piano. By causing vibration of such vibrating object, there has
been obtained the production of a sound having a frequency corresponding
to the fundamental frequency of the vibrating object. In such a case, the
vibration frequency of the vibrating object tends to undergo a side
variation depending on the factors such as the trifle dimensional errors
arising at the time of the manufacture of the vibrating object, the
unevenness of the quality of the material with which the vibrating object
is made, and the conditions in which the vibrating object is assembled
into a musical instrument. Accordingly, in a musical instrument wherein a
precision vibration frequency is required, there is carried out adjustment
of the vibration frequency of the vibrating object upon completion of the
assemblage of the whole musical instrument, and also periodically
thereafter. In conducting such adjustment of the vibration frequency of
the vibrating object, there has been employed in the past a tuning method
which entirely depends on the acoustic sense of a well-trained tuning
expert. Recently, however, there is relied upon the method consisting of
an electrical detection of the vibration frequency of the vibrating object
and then of carrying out the tuning in such a way that the detected value
is adjusted so as to agree with a reference value. This latter method will
hereunder be described in further detail by referring to FIG. 1. By the
use of a sensor 1 such as a microphone, the vibration frequency of a
vibrating object not shown is converted to an electric signal. This
electric signal is derived via a band-pass filter 2 having a middle point
of a pass band set at the frequency to which the vibration frequency of
the vibrating object is to be tuned in and also via an amplifier 3. The
tuning operation is carried out by a tuner by adjusting, for example, the
tuning pin of a piano in such a way that the output of the amplifier 3
will present a peak level of amplitude.
It should be noted that such a vibrating object as the strings of a piano
involves harmonic vibrations in addition to the fundamental vibration
frequency. Accordingly, the output electric signal derived from the sensor
1 contains a fundamental frequency component f and its harmonic components
nf (n=2, 3, . . . ). In such a vibrating object such as the string of a
piano, it should be noted that, in case its fundamental vibration
frequency is low (meaning it is in the bass region), the spectrum of the
harmonics is as shown in FIG. 2. That is, the amplitude level of the
harmonic component is high as distinctly contrasted by an extremely low
amplitude level of the fundamental frequency component. Moreover, the
microphone assigned to detect the vibration of the vibrating object
generally presents a poor sensitivity to the lower frequencies, and
besides, there also arise problems such as noises. As such, in conducting
the tuning of a piano string of the lower pitch range, it is difficult to
carry out a direct detection of the fundamental vibration frequency
component. The tuning of such a string requires to be done by detecting
the harmonic components. In case it is intended to tune the fundamental
vibration frequency into for example 27.5 Hz, there has been employed a
band-pass filter whose middle point of the band is set at 110 Hz which is
the frequency of the quadruple harmonic, to carry out the tunning in such
a way that the output of this band-pass filter will present a peak level.
However, in the low pitch range of sound, the difference in frequency
between the respective adjacent harmonic sounds is small and moreover,
there is a limit in the improvement of the selectively of filters.
Therefore, any two adjacent harmonic signal components undesirably jointly
pass through the band-pass filter 2. Thus, it becomes impossible to
identify which one of them is in fact the aimed harmonic component to be
measured. In an extreme instance, the tuner may erroneously tune the
vibration frequency of the vibrating object to a harmonic (n+1)f or (n-1)f
which is located just adjacent to the aimed harmonic partial nf. For
example, let us consider the instance wherein the tuner intends to tune
the vibration frequency of a vibrating object having the fundamental
vibration frequency of sound of 22.5 Hz prior to tuning so as to have the
fundamental vibration frequency of 27.5 Hz. In order to do this, let us
assume that the tuner employs a band-pass filter 2 having the filter
characteristic A whose middle point is set at 110 Hz frequency of the
quadruple harmonic. Whereupon, a signal of 90 Hz which is the quadruple
harmonic of the fundamental frequency 22.5 Hz prior to tuning and a signal
of 112.5 Hz which is the quintuple harmonic of this 22.5 Hz harmonic are
allowed to pass jointly through the filter owing to the fact that these
two frequencies are included in the width of the pass band of this
band-pass filter. Accordingly, in each of the tuning operations that the
tuner (tuning engineer) turns the tuning pin of, for example, a piano
clockwise and counterclockwise, the output signal derived will only
increase, and it becomes altogether impossible for the tuner to identify
which one of them is the quadruple harmonic sound signal which is aimed.
Such phenomenon will be prominent in an instance wherein the fundamental
vibration frequency of the vibrating object is departed toward the lower
level side than that which is aimed.
Furthermore, in case the vibration frequency of the vibrating object is
departed so far as to be on the outside of the pass band of the band-pass
filter 2, it is utterly impossible to obtain an output. Moreover, it is
impossible also to known in which direction the vibration signal is
departed. In case it is intended to adjust the vibration frequency of a
string in particular, it often happens that the vibration frequency of the
string prior to tuning is founnd to depart considerably from the vibration
frequency which is aimed. Thus, the above-discussed problem will take
place prominently. Also, in case such conventional measuring system as
stated above is relied upon, there may arise instances wherein no output
signal is derived. Thus, this known measuring system is not suitable for
use as the vibration frequency measuring system of an automatic tuning
device which is designed to use a signal which is formed by converting the
vibration of the vibrating object to an electric signal to thereby
automatically tune the naked vibration frequency into the vibration
frequency which is aimed. Especially, in the treble (high frequency)
range, the amount of departure of the vibration frequency becomes great,
and therefore the above-discussed known measuring device will be found
difficult to operate.
SUMMARY OF THE INVENTION
It is, therefore, a primary object of the present invention to provide a
method and an apparatus for measuring, easily and accurately, the
fundamental vibration frequency of a vibrating object.
Another object of the present invention is to provide a method and an
apparatus of the type described above, whicch is capable of making an easy
and yet accurate measurement of the fundamental vibration frequency of any
vibrating object ranging from one having a high natural vibration
frequency to one having a low vibration frequency.
Still another object of the present invention is to provide an improved
method for adjusting the vibration frequency of a vibrating object such as
the strings of a piano.
These and other objects of the present invention will become apparent by
reading the following detailed description when taken in conjunction with
the accompanying drawings.
According to the improved method of the present invention, the vibration
frequency of the vibrating object is converted to an electric signal by
the use of, for example, a sensor such as a microphone, and from this
electric signal of vibration are derived the components of two adjacent
harmonic vibration frequencies (partials), and the difference between the
frequencies of these two signal components, i.e. a frequency which is
equal to the fundamental vibration frequency of the vibrating object, is
calculated.
According to an example of the present invention, the vibration of the
vibrating object is converted to an electric signal by a sensor, and this
electric signal of vibration is then inputted to a voltage-controlled
variable band-pass filter. The middle (center) frequency of the pass band
of this filter is controlled by a sweeper and is varied successively. As
this middle frequency of the filter varies successively, there
successively appears a peak in the output of this filter. The two
frequencies corresponding to adjacent two peaks are measured successively
by a frequency counter. The resulting two measured values (frequencies)
corresponding to said two peaks are stored in two memories, respectively.
The signals read out from these two memories are applied to calculators,
respectively, so that the difference in frequency between these two
signals is calculated. The resulting frequency difference thus sought
indicates the fundamental vibration frequency of the vibrating object. The
middle frequency of said filter need only be such one as can be
successively varied within the range covering the harmonic vibration
frequencies of the vibrating object to be tuned. Those degrees of adjacent
two harmonic vibrations which are derived by these filters may be
arbitrary ones. It should be understood, however, that the degrees of the
adjacent harmonic vibrations which are derived should be such that their
frequency levels are not too small relative to the fundamental vibration
frequency.
According to another example of the present invention, the vibration of the
vibrating object is converted to an electric signal by the use of a sensor
such as a microphone, and it is inputted to a pair of band-pass filters.
The middle frequency of the pass band of each of these two filters is
arranged to be in agreement with the frequencies of adjacent two harmonics
of the vibrating object. Accordingly, the differences in middle frequency
between these two filters is equal to fundamental vibration frequency of
the vibrating object. The outputs of these two filters are inputted into a
multiplier for being multiplied. The output of this multiplier indicates a
sum signal component of the two input signals applied thereto (meaning a
component representing the sum of the frequencies of the two input
signals) and a differential signal component (meaning a component
representing the difference in frequency between the two input signals).
The frequency of this differential signal component is equal to the
frequency of the vibration frequency of the vibrating object. Accordingly,
by passing the output of the multiplier through a low-pass filter and by
deriving only the differential signal component, there can be obtained the
fundamental vibration frequency of the vibrating object from the output of
this low-pass filter. For example, in case it is intended to tune a string
of a piano, the respective middle frequencies of a pair of band-pass
filters are set first at adjacent two higher harmonic vibration
frequencies which are to develop after the tuning of said string has been
completed. Whereupon, by operating a tuning pin in such a way that the
output level of the low-pass filter will become maximum, it is possible to
carry out the tuning of this string quite easily.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram showing a typical example of known system for
measuring the vibration frequency of a vibrating object.
FIG. 2 is a chart showing the amplitude levels of the fundamental
frequency, and harmonics presented by a vibrating low-pitch string of a
piano.
FIG. 3 is an illustration for explaining the action of the known system
shown in FIG. 1.
FIG. 4 is a block diagram showing an example of the system for measuring
the vibration frequency of a vibrating object according to the present
invention.
FIG. 5 is a block diagram showing another example of the system according
to the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
An example of the present invention will be described by referring to FIG.
4. Reference numeral 4 represents a sensor for detecting the vibration of
a vibrating object not shown and for converting the detected vibration to
an electric signal. This sensor 4 may be an ordinary microphone. The
output of this sensor 4 is inputted into an amplifier for being amplified,
and the resulting amplified output, in turn, is inputted into a
voltage-controlled variable bandpass filter 6. The middle frequency of the
pass band of this filter 6 is controlled by a sweep 7, and this middle
frequency varies successively. This sweeper 7 is one that produces, for
example, a sawtooth voltage. The filter 6 outputs several harmonic
vibration signals during the sweeping period of said sweeper 7. More
specifically, for example, at each time the frequencies of the respective
harmonic signals shown in FIG. 2 come into agreement with the middle
frequency of the filter 6, there develops a peak amplitude level in the
output of this filter 6.
Numeral 9 represents a frequency counter to which the output of the filter
6 is inputted. This frequency counter 9 measures the frequency of the
output signal of the filter 6 at each development of peak in the output of
this filter 6. More specifically, the frequencies of adjacent two harmonic
vibrations of the vibrating object are measured by this frequency counter
9. This frequency counter 9 is triggered by the output of a peak-detector
8 assigned for detecting the peak of the output of the filter 6, and
measures the frequency of the output of the filter 6. When this frequency
counter 9 is triggered upon its receipt of an output of the peak-detector
8, the frequency counter 9 measures the output of the filter 6, and feeds
the result of the measurement to a first memory 12 via a switching circuit
11 for being stored in this first memory 12. A delay circuit 10 delays the
action of the peak-detector 8, and after the completion of the storing
action of the first memory 12, this delay circuit 10 feeds a changeover
signal to the switching circuit 11. Whereupon, the frequency counter 9 is
electrically connected to a second memory 13 via the switching circuit 11.
It should be understood that, simultaneously with the changeover action of
the switching circuit 11, the contents of the frequency counter 9 are
cleared. When, thereafter, the peak of the next-produced output of the
filter 6 is detected by the peak-detector 8, the frequency counter 9
measures the frequency of this next-produced output of the filter 6, and
feeds via the switching circuit 11 the results of the measurement to said
second memory 13 to be stored therein. In this way, the frequencies of
adjacent two harmonic vibrations of the vibrating object are stored in the
first memory 12 and the second memory 13, respectively. When, in this
state, the sweeping period of the sweeper 7 terminates and when,
accordingly, the sawtooth output thereof undergoes a decay, this decay is
differentiated by a differentiater circuit 15, and its differentiation
signal is fed to a calculator 14. Upon receipt of this differentiation
signal, the calculator 14 calculates the difference in frequency between
the adjacent two harmonic vibrations stored in the first and the second
memories 12 and 13, and produces an output at its output terminal 16. More
specifically, a signal indicating the fundamental vibration frequency of
the vibrating object is derived at said output terminal 16. The calculator
14 may be arranged to be operative so that, for example, it multiplies the
outputs of the memories 12 and 13, and outputs the lower frequency
component among the result of this multiplication. This will become
apparent from the description of the example of FIG. 5 which will be made
later.
In summary, in the instant example, the harmonic vibration signals of the
vibrating object are successively derived by a voltage-controlled variable
band-pass filter 6 whose middle frequency of pass band are varied
successively; and, among the harmonic vibration signals thus derived, the
frequencies of any adjacent two signals are measured; and by seeking the
difference in the measured two frequencies, the fundamental vibration
frequency of the vibrating object is obtained. Accordingly, the adjacent
two harmonic vibrations which are measured for the purpose of seeking the
fundamental vibration frequency of the vibrating object can be arbitrarily
selected from among the numerous harmonic vibrations. It will be
desirable, however, to set the output conditions of the sweeper 7 so that,
in case it is intended to measure such a fundamental vibration frequency
of, for example, a low-pitch string of a piano as having the spectrum
shown in FIG. 2, the fundamental vibration frequency is sought by the use
of any adjacent two harmonics among the third to sixth harmonics having
large energy levels.
In the description made above, the frequency counter 9, the first and the
second memories 12 and 13, and the calculator 14 may be of either a
digital type or an analog type.
Next, description will be made on another example of the present invention
by referring to FIG. 5.
The vibration of the vibrating object is converted to an electric signal by
a sensor 44 such as a microphone. The electric signal is inputted to a
pair of band-pass filters 45 and 46, respectively. The middle frequencies
of these filters 45 and 46 are set at the frequencies of adjacent two
harmonic vibrations of the vibrating object whose fundamental frequency is
to be measured. For example, let us assume that the vibrating object
consists of a string of a piano whose vibration frequency is to be
adjusted to 27.5 Hz. As shown in FIG. 3, let us assume that the middle
frequency of one 45 of the pair of filters 45 and 46 is set at 82.5 Hz
(third harmonic) and that the middle frequency of the other filter 46 is
set at 110 Hz (fourth harmonic). By doing so, it will be understood that
if the fundamental vibration frequency of the vibrating object which is
intended to be adjusted to 27.5 Hz is noted to depart from this value,
only one of the two filters 45 and 46 will produce an output or neither
one of these filters will produce an output. The filters 45 and 46 will
produce outputs simultaneously only when the fundamental vibration
frequency of the piano string is brought into agreement with 27.5 which is
the aimed frequency.
The multiplier 47 is assigned to conduct mathematical multiplication of the
output signals X and Y of the two filters 45 and 46. The output signal Z
of the multiplier 47 is expressed by the following equation:
Z = X . Y
= a.sub.x cos(2.pi.f.sub.x t + .theta..sub.x) . A.sub.y cos(2.pi.f.sub.y t
+.theta..sub.y)
= 1/2 A.sub.x . A.sub.y { cos[ 2.pi. (f.sub.x + f.sub.y) t + .theta..sub.x
+ .theta..sub.y ] + cos[ 2.pi.(f.sub.x - f.sub.y) t + .theta..sub.x -
.theta..sub.y ]}
wherein:
A.sub.x, A.sub.y represent the amplitudes of the signals X and Y;
f.sub.x, f.sub.y represent the frequencies of the signals X and Y; and
.theta..sub.x, .theta..sub.y represent the phases of the signals X and Y.
More specifically, in case the fundamental vibration frequency of the
vibration object, i.e. the string of a piano, has been correctly adjusted,
the output signal Z of the multiplier 47 contains the sum-up signal
components (f.sub.x + f.sub.y) of: the 82.5 Hz frequency (f.sub.x) of the
third harmonic and the 110 Hz frequency (f.sub.y) of the fourth harmonic,
and also contains the difference signal component (f.sub.x - f.sub.y) of
these two frequencies. Accordingly, by passing this output of the
multiplier 47 which contains the aforesaid signal components through a
low-pass filter 48 to remove the sum-up signal components (f.sub.x +
f.sub.y) from the output of the multiplier 47, there will be derived at
the output terminal 49 thereof a difference signal component which is a
signal having a frequency equal to the fundamental vibration frequency of
the piano string.
As discussed above, arrangement is made so that vibration signal of a
vibrating object is fed to a multiplier through two filters whose middle
frequencies are different from each other by an amount of the fundamental
frequency of the vibrating object, and that only a lower frequency
component from among the frequencies contained in the output of the
multiplier is derived through a low-pass filter. Whereby, it will be
understood that, by operating a fundamental vibration frequency adjusting
means of the vibrating object, i.e. a tuning means of a piano string, it
is possible to surely and easily adjust the fundamental vibration
frequency of the vibrating object to the aimed frequency.
In this instant example, arrangement is provided so that the outputs of a
pair of filters are multiplied by a multiplier. It should be understood,
however, that arrangement may be provided to operate in such a way that
the output levels of the two filters are directly observed to adjust the
fundamental vibration frequency of the vibrating object.
According to this instant example, arrangement is provided so that, when
the fundamental vibration frequency of the vibrating object comes into
agreement with the aimed frequency, the output level of the low-pass
filter 18 becomes maximum. As such, by the use of a control means
constructed so that the vibration frequency adjusting means, i.e. a tuning
pin, of a vibrating object, i.e. a piano string, is operated in accordance
with the output level of a low-pass filter, it is possible to
automatically adjust the fundamental vibration frequency of the vibrating
object.
In a similar way, in the example of FIG. 4 also, there may be provided a
control unit for operating the vibration frequency adjusting means, e.g. a
tuning pin, of a vibrating object, e.g. a piano string, so as to bring the
frequency of the output of the calculator 14 into agreement with a
reference frequency, whereby it is possible to automatically adjust the
frequency of the vibrating object.
As stated above, according to the present invention, the fundamental
vibration frequency of a vibrating object is obtained from the difference
in frequency between adjacent two harmonic vibrations of a vibrating
object. Therefore, even in the event that the fundamental vibration
frequency of the vibrating object departs considerably from a reference
frequency, it is possible to unmistakingly measure and adjust the
fundamental vibration frequency.
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