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BACKGROUND OF THE INVENTION
This invention generally relates to tuning musical instruments and more
specifically to a novel method for tuning certain musical instruments.
Conventionally, a person tuning a musical instrument listens to a reference
note and adjusts the instrument until its corresponding note seems
consonant with the reference note. Consciously, or not, the person tunes a
note for a specified beat rate, (which may be zero beat), with the
reference note, usually at some harmonic of either one or both the notes.
This type of tuning is possible because an equally tempered scale is based
upon simple mathematical relationships. In practice, however, pianos and
other stringed instruments do not follow simple mathematical rules. In
fact, piano tuners and builders use "harmonic" to denote a mathematical
harmonic of a note and "partial" to denote the overtone which the string
actually produces. The difference between a harmonic and a corresponding
partial is caused by "stretch". Stretch is significant. In a piano, for
instance, the second partial from a string may average 2.002 to 2.006 or
more times the fundamental frequency (i.e., the first partial). Thus, if
the fundamental notes are tuned mathematically, stretch causes the piano
to sound out of tune.
Therefore, pianos and similar instruments must be tuned differently.
Historically, a piano tuner uses a complex, iterative aural process in
which he tries to reduce errors to a minimum step-by-step. Basically, he
starts tuning a piano in a "temperament octave" by adjusting a first note
to a reference frequency, usually provided by a tuning fork. He adjusts
the remaining notes in the temperament octave by listening to partials of
notes in third, fourth and fifth intervals. For example, in striking an
interval of a third with a previously tuned lower note, the tuner adjusts
the upper note while listening to the beat between the fifth partial of
the lower note and the fourth partial of the upper note. He assumes the
proper relationship exists when he hears a predetermined beat frequency.
Listening to these partials and beat frequencies reduces errors at the
fundamental frequency because the partials multiply any error in terms of
actual frequency differences. That is, a 4 Hz error at the forth partial
represents only a 1 Hz error at the fundamental. Also, the use of partials
inherently tends to compensate for piano stretch. However, the process is
not perfect because the tuner's beat rates are calculated from harmonics
rather than partials, and the tuner usually checks the temperament octave
by retuning it using different intervals to minimize the tuning errors.
Once the tuner completes the temperament octave, he tunes other notes by
comparing partials of notes at octave intervals. He may, for example,
listen to the beat between the fouth partial of a lower, tuned note and
the second partial of the upper note while adjusting string tension for
the upper note. Lower notes are tuned similarly, although not necessarily
with octave intervals.
Each note in a piano is sounded by striking two or three strings. During
the foregoing procedure, the tuner damps out strings so only one string
actually sounds when a hammer strikes all the strings associated with that
note. After the tuner completes the procedure, he must tune the other
strings for each note by comparing either the fundamental or partial
frequencies of two strings associated with a given note.
As may be apparent, however, the entire procedure requires that a note
sustain long enough to enable the tuner to determine the beat frequency.
Obviously, the longer the interval the note sustains, the more accurately
the tuner can determine the beat frequency. In tuning, each note struck
sounds until it dies out naturally or the key is released. By "dying out",
I mean that the note can no longer be heard. Thus, the time the note
sustains limits the accuracy of aural tuning methods.
Although there are several tuning aids, no one aid has wide acceptance. In
one, a high frequency oscillator produces an output clock signal at a
selected frequency. A series of frequency dividers and an octave selector
switch provide a means for generating a reference signal at a selected
subharmonic frequency. The tuning aid combines this reference signal and a
audio signal representing the note being tuned either to generate an
audible beat note or to deflect a pointer on an indicating meter.
Unfortunately, these aids lose accuracy as the tuned note comes into
frequency with the reference. When the beat rate decreases below 20 Hz,
the audible beat note becomes inaudible. Similarly, an indicating meter
uses a frequency-to-current converter so the current level goes to zero at
a zero beat. As the current approaches zero, the visual indication becomes
less accurate. Both types of display, therefore, lose accuracy at the very
time it is most necessary.
In another unit, the tuner attaches a piezoelectric transducer to a
particular string or a sounding board to produce a corresponding
electrical signal that is applied to the vertical deflection plates of a
cathode ray tube. A selector switch, crystal controlled oscillator and a
series of frequency dividers generate a selected reference signal which
energizes the horizontal deflection plates of the tube. In using this
circuit, one apparently assumes, erroneously, that a piano generates a
constant, repetitive wave form. In fact, a piano string generates an
extremely complex wave form comprising a fundamental tone and wide range
of partials, often of the same magnitude, but slightly out of tune with
each other. Furthermore, many of the component frequencies are not
necessarily constant in magnitude because a string vibrates in many modes,
each with its own damping constant. These factors cause the waveform to
change continuously, so the display is difficult to interpret.
Another problem relates to dynamic response. Initially, the amplitude of
the signal is sufficient to drive the display off the screen. As the tone
dies out, the input to the vertical deflection plates falls below the
minimum level necessary for generating a usable display. An obvious
solution is installing a variable gain amplifier to maintain the output at
a constant value. However, a circuit which provides satisfactory results
over the wide range of conditions and waveforms which the piano generates
is difficult to attain in practice. If the variable gain circuit actually
tracks the decay, it may follow the wave-form and provide a dc output
signal. Therefore, this solution is not practicable especially in view of
the non-linear parameters or conditions and the short interval for a
readable display. This effective dynamic range further complicates tuning
because adjusting a string while monitoring the display is very difficult.
Still another tuning aid receives the audio signal from a piano and
generates a corresponding electrical signal to energize the blanking or Z
axis circuitry of a cathode ray tube. A circular generator energizes X and
Y axis deflection plates with a reference frequency so the electron beam
describes a circle on the screen. If a note is in tune with the reference,
the audio signal blanks and unblanks the electron beam during the same
part of each revolution to thereby display one arcuate segment. A second
partial input signal produces two such arcuate segments; a third partial
input signal, three segments; and so forth. If a given note is not exactly
harmonically related to the reference, the segments rotate. The direction
of rotation indicates whether the note is sharp or flat while the speed of
rotation indicates the difference in frequencies. As notes in the upper
piano produce a display with a number of segments, the spaces between
adjacent sectors diminish; and the absolute frequency deviation which
produces a persistent display tends to decrease. Furthermore, alternately
blanking and unblanking the beam produces an indefinite segment
termination on the screen. When the frequency deviation is small, the
indefinite termination makes it difficult to determine whether the edges
of the segments are moving. When notes in the lower range of the piano are
tuned, the tuner must try to adjust while the tuning aid responds to
partials, since subharmonics of the reference frequency generate complete
circles on screens.
A tuning aid must provide some means for stretch compensation when it is
used to tune a piano. Thus, numerous tests have been made to evolve
standard tuning curves which provide stretch compensation. These curves
are derived by aurally tuning a large number of pianos. The measured
frequencies of the aurally tuned notes are then combined to produce
average frequencies from which one curve, or at most a limited finite set
of curves, are drawn. These curves are unsatisfactory, however, because
the actual frequencies are distributed around the average. Thus, if an
aurally tuned piano is made to conform to the standard curve, it is, by
definition, detuned. Thus, this unique quality of a given piano, i.e., its
stretch, which results from its construction, string-length, and myriad
other factors, has made the tuning aids practically unworkable in many
cases. As a result, the best piano tuners have continued to work
conventionally and do not place any significant reliance on these tuning
aids.
Therefore, it is an object of this invention to provide a new method for
tuning a piano which takes into account the stretch characteristic for
that piano.
Another object of this invention is to provide a new method for tuning a
piano which enables the use of mechanical aids.
Another objct of this invention is to provide a tuning aid which is readily
adapted for tuning a wide variety of instruments.
SUMMARY
In accordance with this invention, a tuner first uses an electronic tuning
aid to measure the characteristic stretch of the piano. This is done by
comparing a measured partial frequency with the frequency of a
mathematical harmonic. Then, the tuner adjusts one reference note on the
piano so its fundamental is at a predetermined standard frequency. Each
successive note is tuned to a different tuning frequency which is the sum
of the nominal frequency for that note and a deviation frequency which is
calculated for that note dependent upon the characteristic stretch of that
piano. This provides a repeatable tuning method for tuning a piano to a
tuning curve which is characteristic of that piano.
This invention is pointed out with particularity in the appended claims. A
more thorough understanding of the above and further objects and
advantages of this invention may be attained by referring to the following
description taken in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a tuning aid adapted for use with this
invention;
FIG. 2 is a circuit schematic which illustrates certain details of the
circuit shown in FIG. 1;
FIG. 3 is a graphical analysis of the operation of a portion of a circuit
shown in FIG. 1;
FIG. 4 is a detailed schematic of another portion of the circuit shown in
FIG. 1;
FIG. 5, comprising FIGS. 5A and 5B, depicts a device for specifying
frequencies for successive notes in a piano;
FIGS. 6A and 6B are exploded views corresponding to FIGS. 5A and 5B to show
the device in FIG. 5 in more detal; and
FIG. 7 is a perspective view, partly in section, of a piano.
DESCRIPTION OF AN ILLUSTRATIVE EMBODIMENT
1. General Discussion
As shown in FIG. 1, my tuning aid 10 comprises an input circuit 12, a
reference circuit 14 and a detection circuit 16. The input circuit 12
comprises a microphone 18 which picks up signals generated as a musical
instrument, such as piano 11 of FIG. 7 is tuned. For example, on piano 11,
it detects the sound emanating from a struck tone generator 13, each of
which comprises one or more strings 15. The tension of strings 15 is
adjustable by tuning pins 17 in a pin block 18 thereby to vary the tension
on the string and tune the string to a given frequency. A conventional
preamplifier 20 and an active filter 22 in tuning aid 10 of FIG. 1 isolate
the signal being tuned from other signals which the microphone 18 senses.
The active filter 22 preferably is a tunable bandpass filter which has a
quality factor greater than ten. It produces an audio output signal on a
conductor 24 which connects to the detection circuit 16.
The reference circuit 14 produces a second input signal to the detection
circuit 16. A variable frequency master clock oscillator 26 covers the
twelve notes two octaves above the highest octave to be tuned, for
purposes which will become apparent later. A particular oscillator
frequency is selected by a note selector 28 which simultaneously tunes the
active filter 22. An octave selector 30 also controls the active filter 22
and further controls a frequency divider 32 which, in response to the
signals from the master clock oscillator 26, provides a square wave output
signal which is twice the frequency determined by the note selector 28 and
octave selector 30. That is, if the selectors 28 and 30 are set to select
a musical A at 440 Hz while the master clock oscillator 26 generates a
28.16 kHz output an 880 Hz signal appears on the conductor 34 leading from
the divider 32.
The detection circuit 16 has a detector 36 which receives both the audio
signal on the conductor 24 and the reference signal on the conductor 34.
It generates four output signals on output conductors 38-1, 38-2, 38-3 and
38-4. Each output is a constant-amplitude, pulse-width-modulated signal
with pulse width varying as a function of the phase difference between a
note signal on the conductor 24 derived from the instrument being tuned
and a reference signal on the conductor 34, which is the output from the
clock divider 32. The pulse repetition rate is equal to the selected
reference frequency and the rate at which the pulse width changes on each
conductor depends on the frequency difference between the note frequency
and one-half the reference frequency, the pulses on each conductor having
unvarying width if the struck note is in tune with the reference. Low-pass
filters 40 couple the pulse signals from the detector 36 to a display 42.
At any given time, a filtered dc output from a low pass filter is
proportional to the width of an input pulse. If there is a frequency
deviation, each low-pass filter output varies from 0% to 200% of its
normal value at a rate which is proportional to the frequency difference.
The display unit 42 preferably contains one pair of lamps (e.g.,
light-emitting diodes) energized by each low-pass filter output.
Mechanically, each lamp in a pair may be diametrically opposed in a
circle, with adjacent lamp pairs separated by 45.degree.. As becomes
apparent later, the signals which energize the lamps are in spaced
quadrature, but 180.degree. out of phase electrically. If a first lamp
pair is at full brilliance, a second lamp pair, displaced 90.degree. from
the first, is off. The lamp pairs that are displaced .+-.45.degree. from
the first are also off, for reasons I discuss later.
When an incoming note is in tune, one pair of lamps may be at or nearly at
full brilliance or two pairs may be partially lit. However, the relative
brilliance of the lamps does not change. As a result, the display appears
stationary. If there is a frequency deviation, the individual lamp pairs
reach full brilliance in one of two sequences. If the note is "sharp"
(i.e., at a higher frequency than the reference), then the lamps reach
full brilliance in a clockwise sequence; so the display appears to rotate
clockwise. When a note is flat, the sequence is reversed and the display
appears to rotate counterclockwise. As the repetition rate at which a
given set of lamps reaches full brilliance depends upon the frequency
difference, the rate at which the display appears to rotate indicates the
magnitude of the deviation.
2. Specific Discussion
The heart of the tuning aid is in the manner in which the detector 36 and
low-pass filters 40 condition input signals and display the results. Still
referring to FIG. 1, the signal that the master clock oscillator 26 and
the divider 32 place on conductor 34 has twice the frequency of the
selected note. Division by at least two in the divider 32 means that the
outputs from the master clock oscillator 26 must be four times the highest
frequencies to be measured. In one specific embodiment using a "C" as a
lower octave limit and a "B" as an upper limit, the master clock
oscillator 26 generates nominal signals in the range between 16744 and
31609 Hz. Depending on the setting of the octave selector 30, the clock
divider 32 divides the oscillator output by a factor of 2.sup.n where
1<n<8. When the octave selector 30 is set for the highest octave, the
divider 32 divides the oscillator frequency by 2, while a division by 256
occurs when the octave selector 30 is set for the lowest octave. As a
specific example, setting the note selector 28 to "A" causes the
oscillator 26 to generate a 28160 Hz signal. The frequency of the signal
on the conductor 34 and the frequency which the tuning aid will sense are
then as follows:
Signal on Frequency of Signal
Octave Number
Conductor 34 Being Measured
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8 14,080 7,040
7 7,040 3,520
6 3,520 1,760
5 1,760 880
4 880 440
3 440 220
2 220 110
1 110 55
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a. Detection Circuit 16
Now referring to FIG. 2, the signal on conductor 34 energizes the inverting
clocking terminals of JK flip-flops 50 and 52, the latter clocking input
receiving its signal through an inverter 54. The nature of the
cross-coupling shown in FIG. 2 determines the flip-flop response to
clocking signals. In this particular embodiment, the JK flip-flops 50 and
52 are cross-coupled so the set (1) and reset (0) output terminals of the
JK flip-flop 50 energize the K and J input terminals of the JK flip-flop
52, respectively. The set (1) and reset (0) output terminals of the JK
flip-flop 52 connect to the J and K input terminals of the flip-flop 50,
respectively.
Now referring to FIG. 3, GRAPH A represents the clocking signal, a square
wave that energizes the JK flip-flop 50 while Graph B is a timing chart
for the complementary clocking signal to the flip-flop 52 from the
inverter 54. Assuming for a moment that at t=0, the clocking signal to the
flip-flop 52 falls while both the flip-flops 50 and 52 are reset, the
trailing edge of the complementary clocking signal sets the flip-flop 52
and generates a clock reference signal designated as CR3 and a complement
CR4 signal as shown in GRAPHS E and F. Next, the trailing edge of the
clocking signal sets the flip-flop 50, which generates the CR1 and CR2
signals as shown in GRAPHS C and D. A succeeding clocking signal to the
flip-flop 52 resets it (GRAPHS E and F). This conditions the flip-flop 50
to be reset by the trailing edge of its next clocking signal. As a result,
it takes two cycles of the clocking signal from the conductor 34 to cycle
each CR signal from the flip-flops 50 and 52. This additional frequency
division means the four CR signals from the flip-flops 50 and 52 are at
the selected frequency. As also apparent, the CR signals are in
quadrature. Looking at the positive-going pulse edges, the sequence is
CR3-CR1-CR4-CR2, the leading edge of each pulse being spaced 90.degree. in
phase from the leading edges of preceding and following pulses. Hence, the
outputs of flip-flops 50 and 52 constitute a four-phase set of reference
signals.
GRAPH G depicts a note signal after the signal in the conductor 24 is
conditioned in a conventional squaring circuit 56 in FIG. 2. In this
particular example, the note is in tune with the reference selected
frequency and the signal in solid lines is in phase with the CR3 signal.
In addition, an inverter 58 produces a complementary note signal which is
in phase with the CR4 signal.
Referring to FIGS. 2 and 3, the four-phase clock reference and the note
signals energize a phase modulator circuit 60 comprising two exclusive OR
circuits. The first exclusive OR circuit comprise NAND circuits 62, 64 and
66; the second, NAND circuits 70, 72 and 74. The output from a NAND
circuit 66 is designated as the ".phi.4" output; the complementary
".phi.2" output comes from the inverter 68. There are two conditions which
cause the .phi.4 signal to be at a zero level representing a FALSE output
from the exclusive OR circuit;
1. the note signal is positive and CR1 is positive, or
2. the note signal is zero and CR1 is zero. Otherwise the .phi.4 signal is
at a ONE level indicating that the exclusive OR function is met.
Similarly, the .phi.3 signal is zero when:
1. the note signal is positive and CR4 is positive, or
2. the note signal is zero and CR4 is zero. Otherwise, the .phi.3 signal is
at a ONE level. Therefore, the .phi.4 output signal indicates whether the
CR1 signal (the set condition of the flip-flop 50) and set condition of
the note signal satisfy an exclusive OR condition. Similarly, the .phi.1,
.phi.2, and .phi.3 signals indicate the exclusive OR condition of the note
signal and each of the CR3, CR2 and CR4 signals, respectively.
Still referring to FIGS. 2 and 3 and considering the note signal shown by
the solid line in GRAPH G, the note signal and set output from the
flip-flop 52 are exactly in phase. Either the NAND circuit 70 or 72 keeps
the .phi.3 output signal at a positive or logic 1 value, so the .phi.3
signal has a 100% duty cycle. Obviously, the .phi.1 output signal is
always at a logic zero or a minimum value and has a 0% duty cycle. On the
other hand, the necessary conditions to shift the .phi.4 output signal to
a positive state exist 50% of the time, so the .phi.4 and .phi.2 output
signals are complementary pulse trains at twice the selected frequency and
each has a 50% duty cycle.
Now referring back to FIG. 2, each phase output signal is passed through
one of four identical low-pass filter circuits 40, a .phi.1 filter circuit
40-1 being shown in detail. A switching circuit 78 together with diodes 93
responsive to the .phi.1 output signal provides a constant amplitude,
variable width pulse input to a conventional two-section RC low-pass
filter 80. The low-pass filter 80 normally varies its output voltage as a
function of the duty cycle to control a non-linear lamp amplifier 82
which, in turn, energizes light-emitting diodes 86 and 88.
In the particular situation shown by GRAPH G in FIG. 3, the .phi.1 output
signal (graph H is constant at zero (a 0% duty cycle). This places a
maximum positive voltage on the base electrode of the transistor amplifier
82, so the amplifier 82 keeps the diodes 86 and 88 on; and they generate a
maximum light output. However, the .phi.3 output signal (GRAPH J) and the
output of the .phi.3 filter circuit 40-3 are at maximum and minimum
levels, respectively, so diodes 90 and 92 are turned off.
On the other hand, the .phi.2 and .phi.4 output signals (GRAPHS I and K)
have a 50% duty cycle. In order to enhance the display, the filters are
constructed so the lamps in a pair do not light until the duty cycle of an
output signal falls below some threshold representing a duty cycle less
than 50%. Specifically, the diodes 93 in the switching circuit 78 clip the
input signal to a value which equals the forward breakdown voltage of two
diodes (i.e., about 1.2 volts total with silicon diodes). The lowpass
filter 80 is constructed so that at approximately a 50% duty cycle, the
filter output cannot forward bias the base-emitter junction of the
amplifier 82 so the light-emitting diodes the amplifier controls do not
conduct. When the duty cycle reaches a value which causes the filter
output to forward bias the base-emitter junction, the amplifier 82 turns
on and the corresponding diodes conduct whereupon the diodes emit light at
a level which is proportional to the current through the amplifier.
If the note signal shown in GRAPH G merely shifts slightly in phase,
without changing frequency, as shown by the dotted lines, the .phi.1
output signal no longer as a 0% duty cycle signal. Hence, the energizing
current through the diodes 86 and 88, which responds to the duty cycle for
the .phi.1 output signal, decreases. If the phase-shift is to the right as
shown by the dashed lines in GRAPH G, the .phi.2 output signal duty cycle
increases, so diodes 94 and 96 remain off. In this particular case, the
.phi.3 duty cycle decreases, but remains above a 50% duty cycle, so the
diodes 90 and 92 also remain off. However, the .phi.4 signal has a duty
cycle which is less than 50% so the diodes 98 and 100 turn on slightly.
GRAPH L shows the signal from the squaring circuit 56 when the note signal
frequency is greater than the standard frequency. GRAPHS C through F and L
show that each output signal duty cycle varies in time. For the time
interval shown, it is apparent from GRAPH M that the .phi.4 duty cycle is
increasing from a minimum. Meanwhile, the duty cycle of the .phi.2 output
signal (GRAPH O) is decreasing from a maximum. As time continues, the
.phi.4 output signal will reach a maximum duty cycle and then return to a
minimum; and the variation is substantially linear with time. Similarly,
the duty cycle of .phi.1 output signal (GRAPH N) is decreasing from 50%
while the .phi.3 output signal (GRAPH P) is increasing from 50%. As a
result, the light output from diodes 98 and 100 decreases while diodes 86
and 88 turn on with their brightness increasing as the .phi.1 signal and
duty cycle continues to decrease.
Furthermore, the light output from diodes 98 and 100 continues to decrease
until the threshold is reached, whereupon they turn off. At about the time
they reach one-half brilliance, however, the output from the filter
circuit 40-2 will have reached the same value, so that diodes 94 and 96
will also be at about half brilliance. When the diodes 94 and 96 reach
full brilliance, the tuner sees what appears to have been a rotation of a
light bar 45.degree. clockwise and this apparent rotation continues, so
that the display appears as a bar which rotates at one-half the beat
frequency.
When the beat frequency exceeds about 5Hz, the display is persistent to the
eye. However, at this beat frequency, each low-pass filter begins to
attenuate its output so the maximum current level, and the average energy
level to the lamps, decreases. This reduces the average brilliance of the
lamps. So when the display is persistent, the tuner adjusts a string to
increase brilliance. At about 25 Hz, there is enough filter attenuation to
turn all the lamps off. This poses no problem, however, because a 25 Hz
difference is readily detectable by ear. At the low end of the piano, it
represents an octave while at the high end of the piano it represents a
tuning error of 10% of a semitone. It is apparent that the individual
input pulses of each of the filter circuits, such as the filter 80 in
filter circuit 40-1, do not affect, directly, the light emitting diodes.
This is because the pulses themselves are at the clock frequency and the
minimum clock frequency is greater than the cut-off frequency of the low
pass filters.
b. Master Clock Oscillator 26
For the tuning aid to be effective, there should be some provision to vary
the frequency of the master clock oscillator 26 shown in FIG. 1. The
oscillator 26 generates signals in accordance with the known mathematical
relationships of the equally tempered scale. Course and fine pitch
variation controls 44 and 46 (FIG. 1) enable a tuner to vary the frequency
of all the notes up to 1/2 a semi-tone in either direction, while
preserving the correct relationship among the notes.
As shown in FIG. 4, the master clock oscillator 26 comprises a unijunction
transistor 150 in a relaxation oscillator circuit. A
temperature-compensating resistor 152 connects "base 2" to a conductor 154
from a power supply. An output resistor 155 is between "base 1" and
ground. Two elements generally control the oscillator frequency -- a
variable capacitor 156 and a variable resistor 158.
To set the oscillator initially, the capacitor 156 is adjusted so that the
oscillator 26 generates its highest required frequency. This is done with
the resistor 158 at a minimum value. Usually the resistor 158 comprises a
switched resistance ladder network which enables the frequency for each
setting of the note selector 28 to be adjusted independently. During
calibration, the frequencies are adjusted for the correct mathematical
relationship. A buffer amplifier 160 couples the signal from the output
resistor 155.
The capacitor 156 and resistor 158 constitute two distinct means for
varying the frequency of the oscillator 26. The oscillator 26 includes a
third means for independently varying frequency. As known, the unijunction
transistor 150 discharges when the emitter voltage reaches a threshold
which is a substantially constant percentage of the voltage between the
bases. The time is takes the capacitor voltage to reach that threshold is
a function of the resistor and capacitor values and the voltage applied to
the tuning circuit.
In the oscillator 26 in FIG. 4, this voltage appears across a capacitor 166
and is equal to the voltage on the conductor 154 minus the voltage across
a resistor 162. The voltage across the resistor 162 depends on the current
through it and the current has two components. A first component is
constant for a given setting of the note selector 28 and depends upon the
voltage on the conductor 154 and the series impedance of the resistors 162
and 158.
The second component is variable in response to the setting of the pitch
controls. A conductor 164 carries this second component. As the pitch
controls increase this component, the voltage drop across resistor 162
increases so the voltage across capacitor 156 decreases. As a result, the
oscillator frequency decreases.
The remaining circuitry shown in FIG. 4 provides the variable second
current component. A first resistor network comprising a resistor 172
couples the conductor 164 to the wiper of a potentiometer 174, the
potentiometer 174 being energized from the conductor 154. Variations in
the position of the coarse pitch control 44 offset the wiper arm from a
normal position. Positioning the fine pitch control 46 similarly alters
the wiper arm on a potentiometer 176 also energized from the conductor
154. A resistor 178 couples this wiper arm to the conductor 164.
The qualitative effect of varying either wiper arm position is the same.
The component values are chosen so that a given physical displacement of
the coarse pitch control 44 produces a larger offset than the same
displacement of the fine pitch control 46. Therefore, the following
discussion relates only to the operation of the coarse pitch control 44.
Two relationships exist in this circuit. First, as apparent, the voltage on
the conductor 154 is greater than the voltage on the conductor 164.
Secondly, resistor 172 is at least an order of magnitude larger than
resistor 162.
At a zero voltage offset position, there is a zero voltage drop across the
resistor 172 so only the first current component flows through the
resistor 162. If the coarse pitch control 44 is moved, the second current
component from the conductor 164 changes the voltage across the resistor
162 and the capacitor 156.
Both pitch controls vary the frequency as a percentage of the base
frequency, so these controls can be calibrated in "cents" difference to
raise or lower the resulting frequency, assuming that the oscillator is
calibrated with the potentiometers 174 and 176 at their mid-points.
The tuning aid shown in FIG. 1 is sensitive and accurate. Tests show that
the display has visible motion when the phase shift is less than
10.degree., with the accuracy being dependent upon the time the tuning aid
senses the tone and the stability of both the tone and note. This means
that the tuning aid senses a frequency difference which produces less than
a 10.degree. phase shift over the interval the note signal exists. When
operated from a battery power supply, the tuning aid is very stable. Tests
against a tuning fork show no displacement after 10 seconds of tone. This
increased sensitivity and stability have enabled me to analyze how pianos
are tuned conventionally and evolve two new ways to tune a piano.
c. Tuning Methods
Piano tuners use different tests as they tune a piano to compensate for
stretch. Each tuner, however, uses the same tests as he tunes each piano.
Generally, therefor | | |
