Apparatus for use in the tuning of musical instruments

What I claim as new and desired to secure by Letters Patent of the United States is:

1. A tuning aid for musical instruments comprising:

A. an input circuit with means for detecting an audio signal in a selected range of frequencies and generating a note signal;

B. a reference circuit for transmitting a reference signal; and

C. comparison and display circuit means including:

i. means responsive to the reference signal for producing a plurality of spaced phase reference signals at a known frequency, said reference signals including a first phase reference signal, and a second phase reference signal that is other than a complement of the first phase reference signal,

ii. a phase difference detector including a logical combination means connected to receive each phase reference signal, each of said logical combination means combining the note signal and corresponding phase reference signal for transmitting a logical output signal which has a duty cycle that varies in accordance with the phase relationship between the note signal and the corresponding phase reference signal, and

iii. a plurality of display means, each display means responsive to one of the output signals for displaying the phase relationship between the note signal and the corresponding one of the phase reference signals, said plurality of display means providing a continuous display of the direction of and rate of the note signal phase change.

2. A tuning aid as recited in claim 1 wherein each of said display means comprises:

A. averaging means responsive to each logical output signal for generating an analog signal which varies as a function of the phase relationship between the note signal and a corresponding phase reference signal, and

B. at least one lamp connected with said averaging means, said averaging means varying the intensity of a corresponding lamp whereby the lamps in all of said display means reach maximum intensity in a sequence and rate which depends upon the frequency difference.

3. A tuning aid as recited in claim 2 wherein said logical combination means comprise exclusive OR circuit means responsive to the note signal and the spaced phase reference signals.

4. A tuning aid as recited in claim 3 wherein a plurality of lamps are connected in series with each of said averaging means, said lamps being equally spaced on the circumference of a circle, at least two lamps in a series set being connected to each averaging means and said lamps being equiangularly spaced about the circle, each lamp set being evenly spaced around the circle.

5. A tuning aid as recited in claim 3 wherein each said averaging means comprises a low-pass filter connected to be energized by each output signal, each low-pass filter having a cut-off frequency substantially below the lowest frequency to be tuned.

6. A tuning aid as recited in claim 1 wherein said phase detector includes means for producing the complement of each logical output signal as an additional logical output signal and each said display means comprises:

A. averaging means responsive to a logical output signal for generating an analog signal which varies as a function of phase relationship between the note signal and the corresponding one of the phase reference signals, and

B. a plurality of lamps electrically in series with said averaging means, all of said averaging means varying the intensity of the respective ones of said lamps whereby the lamps reach maximum intensity in a sequence and rate which depends upon the frequency difference.

7. A tuning aid as recited in claim 6 wherein said means for producing the spaced phase reference signals produces two signals and said plurality of display means includes four pairs of lamps equiangularly spaced on the circumference of a circle, each lamp in a pair being diametrically opposed and each pair of lamps being connected to a corresponding output from each of said averaging means.

8. A tuning aid as recited in claim 7 wherein each of said averaging means includes a low-pass filter having a cut-off frequency lower than the lowest frequency to be tuned.

9. A tuning aid as recited in claim 7 additionally comprising:

A. an other lamp,

B. a sequence monitor receiving two of the analog signals from said averaging means for generating a sequence signal, and

C. means receiving the sequence signal for enabling said other lamp.

10. A tuning aid as recited in claim 9 wherein said other lamp is connected in series with one of said lamp pairs whereby said other lamp is energized with said pair for one sequence of the analog signals.

11. A tuning aid as recited in claim 7 additionally comprising:

A. a power supply

B. a monitor circuit coupled to said power supply for generating a warning signal in response to a low voltage condition in said power supply, and

C. switch means connected to a lamp to energize said lamp in response to the warning signal.

12. A tuning aid as recited in claim 11 wherein said switch means is connected to a lamp in one of said pairs, said switch means turning on said one lamp continuously.

13. A tuning aid as recited in claim 1 wherein said reference circuit includes means for generating clocking signals and said spaced phase reference signal producing means converts the clocking signal into a pair of phase reference signals which are electrically in quadrature, said logical combination means comprising first and second exclusive OR circuits, said first exclusive OR circuit being energized by one of said phase reference signals and said note signal and said second exclusive OR circuit being energized by the other phase reference signal and the note signal.

14. A tuning air as recited in claim 1 additionally comprising note selector means wherein said reference circuit comprises variable oscillator means responsive to said note selector means for generating a clocking signal at a selected one of a plurality of frequencies in a range greater than the highest frequency note to be tuned and said input circuit frequency detecting means in responsive to said note selector means.

15. A tuning aid as recited in claim 14 additionally including octave selector means wherein:

A. said reference circuit comprises a divider means responsive to said octave selector means for dividing said oscillator frequency, and

B. said input circuit frequency detecting means is responsive to said octave selector means.

16. A tuning aid as recited in claim 15 wherein said reference circuit comprises a unijunction transistor oscillator with a variable timing resistor and a variable timing capacitor, said oscillator additionally comprising:

A. a voltage source and resistor for coupling a normally constant voltage component to said timing resistor,

B. a variable voltage source including means for varying the voltage therefrom, and

C. summing means for combining the voltage components, the resulting total voltage being coupled to said timing resistor and capacitor whereby the timing resistor, capacitor and variable voltage source control the oscillator frequency.

17. A tuning aid as recited in claim 14 wherein said oscillator comprises:

A. a voltage responsive oscillator circuit,

B. a first voltage source for generating a constant voltage,

C. a second voltage source for generating a variable voltage component, and

D. means for summing voltage components from said first and second voltage sources whereby varying the voltage from said second voltage source changes the oscillator frequency.

18. A tuning aid as recited in claim 14 additionally including an octave selector, said input circuit detecting means comprising a tunable bandpass filter with first and second means for independently altering the resonant frequency of said filter, said note and octave selectors being connected to said first and second altering means, respectively.

19. A tuning aid as recited in claim 2 wherein:

A. said spaced phase reference signal producing means transmits a third phase reference signal that is at the same frequency as the other phase reference signals and that is other than a complement of the second phase reference signal, and

B. each of said averaging means additionally comprises means for establishing an intermediate analog signal threshold level below which the corresponding lamp is off, the intensity of a lamp, when on, varying in accordance with the difference between the analog signal and the threshold signal level, the threshold signal level being selected so that at substantially any time at least a pair of analog signals turn on lamps in corresponding ones of said display means.

20. A tuning aid as recited in claim 7 wherein each of said averaging means additionally comprises means for establishing an intermediate analog signal level below which the corresponding lamps are off, the intensity of a lamp, when on, varying in accordance with the difference between the analog signal and the threshold signal level, the threshold signal level being selected so that at substantially any time at least a pair of analog signals turn on lamps in corresponding ones of said display means.

21. A tuning aid for use in tuning the pitch of a note in a musical instrument to a desired pitch, said tuning aid comprising:

A. an input circuit for generating a binary note signal in response to an audio signal produced by the musical instrument when the note is played, the audio signal having a frequency that represents the pitch of the note and that lies in a selected range of frequencies;

B. a reference circuit for transmitting a binary reference signal at a known frequency representing the desired pitch; and

C. a detection circuit including:

i. detector means for producing a plurality of binary logical output signals, each of the output signals having a duty cycle that is variable in response to changes in the phase relationship between the binary note signal and binary reference signal, and

ii. a plurality of visual display means, each said visual display means being energized by one of the binary logical output signals, said plurality of visual display means being energized in a sequence dependent upon changes in the phase relationship of the binary note and binary reference signals, said plurality of visual display means collectively constituting a display array that continuously displays the phase relationship between the binary note and binary reference signals thereby to indicate that the note is tuned to the desired pitch when the display appears to be stationary and to indicate that the note is sharp or flat with respect to the desired pitch when the display appears to move in a first or second direction, respectively, the direction being dependent upon the sequence of energization of said visual display means and the rate of movement being dependent upon the difference between the actual and desired pitches.

22. A tuning aid as recited in claim 21 wherein said visual display means comprise lamp means.

23. A tuning aid as recited in claim 21 wherein each said visual display means comprises lamp means oppositely disposed on the circumference of a circle, said lamp means being equiangularly disposed about the circumference.

24. A tuning aid as recited in claim 22 wherein each of said lamp means comprises a pair of light emitting diodes.

Description Submit all comments and votes

BACKGROUND OF THE INVENTION

This invention generally relates to tuning musical instruments and more specifically to apparatus which simplifies tuning procedures.

Conventionally, a person listens to a reference note and adjusts a musical instrument until its note seems consonant with the reference note. Consciously, or not, the person tunes a note for a zero beat with the reference note, usually at some coincident harmonic or partial of either one or both the notes.

This type of tuning, known as Interval Tuning, is possible because a conventional scale is based upon mathematical relationships. In practice, however, pianos and other stringed instruments do not follow simple mathematical rules. The overtones, or partials, generated by a given note are more than integral multiples of the fundamental. This deviation, termed "stretch", may be defined as the difference between a partial and corresponding harmonic (e.g., the second partial and theoretical second harmonic frequency) or a note. Stretch is significant. In a piano, for instance, the second partial from a string averages 2.002 to 2.006 or more times the fundamental frequency. Thus, if the fundamental notes are tuned mathematically, stretch causes a piano to sound out of tune.

Therefore, pianos and similiar instruments must be tuned differently. The general approach is a complex, iterative process in which a tuner tries to reduce errors to a minimum step-by-step. Basically, a piano tuner starts tuning a piano in a "temperament octave" by adjusting a first note to a reference frequency. He adjusts the remaining notes in the temperament octave by listening to partials of 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 obtains a predetermined beat frequency between these coincident partials.

Listening to these partials reduces errors at the fundamental frequency because the partial errors are multiplied in terms of actual frequency differences. That is, a 4 Hz error at the fourth 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 and the tuner usually checks the temperament using different intervals and retunes it as necessary to minimize the tuning errors.

Once the tuner completes the temperament octave, he tunes other notes by comparing partials while playing octave intervals. He may, for example, listen to the beat between the fourth 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.

Most piano notes have two or three strings. During the foregoing interval timing 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 interval tuning procedure, he must tune the other strings for each note to be in unison with the first string comparing corresponding partials 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.

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 an 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 and especially 1 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 with a fundamental frequency and partials slightly out of tune with each other but often of the same magnitude. Furthermore, the component frequencies are not necessarily constant in relative 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 waveform 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 harmonic input signal produces two such arcuate segments; a third harmonic 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 segment 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 harmonics, since subharmonics of the reference frequency generate complete circles on screen.

Apparently, another reason professional piano tuners are reluctant to use prior aids is that each piano is tuned uniquely, so a generalized tuning aid that responds to the fundamental frequency of the note being tuned does not really help the tuner. The unique quality of each piano stems from its construction, string length, wear on hammers, and myriad other factors. As a result, piano tuners continue to work conventionally and do not place any significant reliance on mechanical aids.

Therefore, it is an object of my invention to provide a tuning aid which is readily adapted for tuning a wide variety of instruments.

SUMMARY

In accordance with my invention, a tuner selects a specific note and a specific octave on the tuning aid. He strikes a note. A microphone picks up the sound, and a filter passes only the selected frequency. The tuning aid converts the signal to a square-wave note signal. A reference clock provides an output which is converter to a multi-phase reference signal. The tuning aid compares the note signal against each reference phase signal to generate multiple pulse signals with the pulse width of each representing the phase difference between the note signal and a respective one of the phase reference signals.

Other circuitry converts these pulse signals to multiple dc signals which individually energize different lamps. The lamps may be equiangularly spaced on a circumference with lamps in diametrically opposed pairs. The magnitude of the dc signals are normally proportional to the respective pulse widths. Accordingly, when a note signal is in phase with one of the phase reference signals, one pair of lamps is at maximum brightness. Any frequency deviation causes pairs of lamps to reach full brilliance in succession, so the display looks like a rotating light bar. The direction of rotation indicates the direction of deviation while the speed of rotation indicates the magnitude of the deviation.

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 constructed in accordance with my 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 the circuit shown in FIG. 1;

FIG. 4 is a detailed schematic of another portion of the circuit shown in FIG. 1;

FIG. 5A shows a specific embodiment of the input circuit in FIG. 1;

FIG. 5B shows a simplified block diagram of the filter circuit in FIG. 5A;

FIG. 6A is a schematic of a modification which can be made to FIG. 2; and

FIGURE 6B shows how this modification alters the display arrangement in FIG. 2.

DESCRIPTION OF AN ILLUSTRATIVE EMBODIMENT

1. General Discussion

As shown in FIG. 1, my tuning aid 10 comprises an input circuit 12 and a comparison and display circuit including a reference circuit 14 and a detection circuit 16. The input circuit 12 includes a microphone 18 which picks up signals generated as a musical instrument is tuned. For example, on a piano, it detects the sound emanating from a struck note. A conventional preamplifier 20 and an active filter 22 isolate the signal being tuned from other signals which the microphone 18 senses (i.e., an active bandpass filter). The filter 22 preferably is a tunable filter which has a quality factor greater than 10 . Such bandpass filters are known in the art. The filter 22 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 12 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 in the form of a two-pole switch which simultaneously tunes the active filter 22 by changing one or more tuning resistors therein. An octave selector 30 also controls the active filter 22 by changing capacitors therein and is in the form of a three-pole switch. The selector 30 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 [hereinafter A(440)], resistors and capacitors in the filter 22 tune it to a center frequency of 440 Hz while the master clock oscillator 26 generates a 28.16 kHz output and 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 is proportional to the width of an input pulse. If there is a frequency deviation, each low-pass filter output varies up and down between 0 to 200% of its normal value at a rate which is proportional to the frequency difference.

The display unit 42 preferably contains an array of lamp means in which one pair of lamps (e.g., light-emitting diodes) is 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 lamps in space quadrature are 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 difference, the individual lamp pairs reach full brilliance in one of two sequences. If the note is "sharp" (i.e., at a higher frequency than one-half the reference frequency), 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 difference.

2. Specific Discussion

The heart of this invention 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 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 frequency of the output signal 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.ltoreq.n.ltoreq.8. When the octave selector 30 is set for the highest octave, the divider 32 divides the oscillator frequency by 2, while 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 ______________________________________ 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 ______________________________________

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 from 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 binary 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 complementary clocking signal to the flip-flop 52 falls while both the flip-flops 50 and 52 are reset, the trailing, or falling, 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 complementary 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, or falling, 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 given plurality of four CR signals from the flip-flops 50 and 52 each 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 means for generating a given plurality of spaced phase reference signals at a known frequency.

GRAPH G depicts a binary note signal after the signal on 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 binary four-phase clock reference signals and the binary note signal energize a phase modulator circuit 60 which combines the note signal and each clock reference signal logically. Although logical AND and other logical combinations are adapted for use in this invention, very good results are obtained with a circuit 60 comprising two exclusive OR circuits. The first exclusive OR circuit comprises NAND circuits 62, 64 and 66; the second, NAND circuits 70, 72 and 74. The outputs 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 output signal to be at a zero level representing a FALSE output from the exclusive OR circuit:

1. the binary note signal is positive and CR1 is positive, or

2. the binary 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 binary note signal is positive and CR4 is positive or

2. the binary 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 the binary note signal satisfy an exclusive OR condition. Similarly, the .phi.1, .phi.2 and .phi.3 signals indicate the exclusive OR condition of the binary note signal and each of the CR3, CR2 and CR4 signals, respectively.

Still referring to FIGS. 2 and 3 and considering the binary 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-modulated output signal is passed through one of four identical energizing circuits such as low-pass filter circuits 40, a .phi.1 filter circuit 40-1 being shown in detail. A switching circuit 78 together with diodes 93 is responsive to the .phi.1 output signal and 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 enchance 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 low-pass 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 that 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 has 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 depending upon the phase relationship between the note signal and correspondng phase reference signal. 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 duty cycle of the .phi.1 signal 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 40-1 will have reached the same value, so that diodes 86 and 88 will also be at about half brilliance. When the diodes 86 and 88 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 5 to 10 Hz, the display becomes 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 piano 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 semi-tone.