Means and method for automatic resonance tuning

A method and apparatus is provided for the adjustment of resonance on a freely vibrating filament by the use of piezoelectric pushers which are solid state devices whose lengths change as a result of applied voltage. The pushers are configured in such a manner that changes in the pushers' lengths are translated into changes in resonance. The pushers are controlled by feedback circuit wherein frequency of vibration is compared to an electronically generated reference. The resulting error signals are input to DC amplifiers which drive the piezoelectric pushers so as to eliminate the error.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to resonance adjustment of freely vibrating 
bodies. In particular, this invention relates to new and improved 
apparatus for automatic tuning of stringed musical instruments. 
For purposes of the following discussion, the terms "pitch" and "tune" will 
be used interchangeably and will refer to the fundamental frequency of 
vibration of an instrument's strings. 
2. Description of the Related Art 
All stringed musical instruments require tuning due to changes in physical 
conditions or changes in the characteristics of the materials from which 
the instruments are made. Many stringed instruments, such as guitars and 
violins, drift out of tune quite rapidly and musicians often need to make 
tuning adjustments during the course of a performance. 
Stringed instruments are presently manually tuned. The musician adjusts 
each string's tension (and hence its pitch) by mechanical means, such as 
worm gears. As there is no direct method for determining when a string is 
in tune, musicians must either tune their instruments "by ear" or use 
tuning aids. 
Tuning "by ear" means that the musician uses his or her judgment to 
determine if a note is in tune. It is a difficult process that requires 
the ability to discern slight variations in pitch. 
Tuning aids provide musicians with either an audio or visual reference in 
order to determine which way the string's pitch needs to be adjusted 
(higher or lower). Audio tuning aids, such as tuning forks, while 
considerably easier than tuning "by ear," still require the musician to 
judge when the string is in tune. 
Visual tuning aids, such as those disclosed in U.S. Pat. Nos. 4,023462 
(Denov et al), 4,088,052 (Hedrick) and 4,196,652 (Raskin), utilize 
electronics to measure the frequency of each string and compare it with an 
electronically generated reference frequency. A visual display is 
produced, indicating the magnitude and direction of the tuning error. The 
musician then adjusts each string to eliminate the error. Visual tuning 
aids allow individuals with very poor tone recognition skills to tune 
their instruments, but the actual tuning is still performed manually. 
There are some tuning devices and tuning apparatus which are automatic in 
nature, such as those listed in Table I, below. 
TABLE I 
______________________________________ 
Patentee U.S. Pat. No. Issue Date 
______________________________________ 
Scholz 4,375,180 March 1, 1983 
Scholz 4,426,907 January 24, 1984 
Minnick 4,584,923 April 29, 1986 
Skinn et al 
4,803,908 February 14, 1989 
______________________________________ 
Nonetheless, these automatic tuning devices and apparatus rely on methods 
which are inferior to the method of this invention. 
Both Scholz patents rely on tension sensing means for determining 
frequency. As there is no linear correlation between frequency and tension 
of a string, this method is inaccurate. 
Neither Minnick nor Skinn et al (hereinafter "Skinn") use tension sensing 
means to determine frequency; both utilize electronic means for comparing 
signals produced against reference signals. In both cases, a difference 
between signal produced and reference signal will activate motors which 
will then adjust string tension. 
There are several disadvantages to this type of method. One significant 
disadvantage is the relative bulk of such a device or apparatus when 
attached to an instrument. The size of such an apparatus or device would 
make it difficult to incorporate into a musical instrument, especially the 
smaller ones (e.g. violins). 
Another disadvantage to the methods of Minnick and Skinn is the use of 
motors to change string tensions. Since the comparison of the output and 
reference signals is electronic, the accuracy of this method is limited by 
the mechanical means of adjusting string tension. 
Both Minnick and Skinn contemplate the use of motor-driven gears to 
effectuate actual adjustment of string tension. There is an inherent 
stability and control problem in the use of gears due to the existence of 
"backlash" (i.e. the play between two meshing gears). Although this 
"backlash" can be minimized, it cannot be eliminated altogether. In the 
course of ordinary use, gears and motors become worn and periodically need 
replacement. Furthermore, motor driven gears may to slow in response for 
effective tuning due to the slow response of gear reductions, signal 
conversions, inertia and inductive phase lag. 
Another problem is the feedback associated with the gear train and electric 
motors. Hysteresis, due to gear backlash, and the phase lag inherent with 
inductive motors is likely to result in "hunting", where string tension 
adjustments overshoot the proper level and the system oscillates. None of 
the aforementioned patent publications address this problem. 
The heat generated by servo motors and especially stepper motors, shown by 
Skinn, is a significant problem. Thermal drift is probably the primary 
cause of instruments going out of tune. Placing such heat sources within 
the instrument would make short term tuning drifts inevitable. Thermal 
cycling is also detrimental to the instrument itself. 
The disadvantages pointed out in the prior art referenced above are 
overcome in this present invention by the elimination of gears and motors 
and the use of a piezoelectric element to effectuate actual adjustment of 
string tension. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, there is provided a new and 
improved device for automatically tuning stringed instruments by use of a 
piezoelectric element connected to a lever means to adjust string tension. 
The piezoelectric pushers are solid state devices whose lengths change as 
a result of applied voltage. The pushers are controlled by feedback 
circuits wherein frequency of vibration is compared to an electronically 
generated reference. The resulting error signals are input to DC 
amplifiers which drive the piezoelectric pushers so as to effectively tune 
the string. 
It is therefore an object of the present invention to provide an automatic 
tuning device which can be incorporated into any stringed musical 
instrument. 
For purposes of explaining additional objects of the invention, it is 
necessary to classify stringed instruments into two categories: (1) those 
whose strings' pitches are not altered as they are played, and (2) those 
whose strings' pitches are altered as they are played. Instruments such as 
pianos and harps belong to the first group and will be referred to as 
"fixed note" instruments. Guitars and violins are examples of the second 
and will be referred to as "adjustable note" instruments. 
When adjustable note instruments are played, the musician alters the pitch 
of the strings by shortening their effective length, usually with his or 
her fingers. These instruments also allow the musician to add vibrato, a 
cyclical variation of pitch, and otherwise distort the played frequency, 
by bending the strings. Fully automatic tuning is therefore precluded 
because tuning adjustments would interfere with the musicians' efforts to 
control each string's played frequency. Since the pitches of fixed note 
instrument strings are not altered by the musician as they are played, the 
strings' pitches can be continuously monitored and adjusted. 
It is therefore another object of the present invention to provide a 
semi-automatic tuning device for adjustable note stringed instruments 
which will tune on a demand basis. 
It is still another object of the present invention to provide fully 
automatic continuous tuning of fixed note stringed instruments. 
The basic embodiment of the invention allows for considerable variation 
with regard to configuration. It also allows for additional capabilities 
other than automatic tuning of stringed musical instruments. 
Further objects, features and advantages may be found in the following 
drawing, specification and claims.

DETAILED DESCRIPTION OF THE INVENTION 
FIGS. 1 and 2 illustrate a typical embodiment in which the invention is 
built into the tail piece 41 of an electric guitar 40. The invention is 
physically cOmprised of four subassemblies connected by wiring. Referring 
to FIG. 3, they are the String Frequency Detector 1, Electronic Module 2, 
Piezoelectric Pusher Actuator 3, and Tune Pushbutton 12. For simplicity in 
presentation, only one string 44 of the instrument 40 is illustrated; 
however, each string 44 would be identically equipped. The Tune Pushbutton 
12 would simultaneously initiate tuning in all strings 44. 
Referring again to FIG. 3, the String Frequency Detector 1 provides the 
input to the Electronic Module 2. The first element of the Electronic 
Module 2 is the Signal Conditioner 5. Conditioning consists of 
amplification and band-pass filtering. The conditioned signal is then 
input to the Comparator 7 and Signal Threshold 6. The Signal Threshold 
circuit prevents tuning adjustments when the String Frequency Detector 
signal is too weak (see further discussion below) and indicates a weak 
signal condition via LED II. The Reference Signal Generator 4 provides the 
reference signal of the desired frequency to the Comparator 7. The 
Comparator 7 produces a DC output proportional to the difference between 
the reference signal frequency and the string's actual resonance 
frequency. This error signal is then input to the Sample & Hold circuit 9 
and the Error Threshold circuit 8. The Sample & Hold circuit 9 enables 
tuning adjustments when in sampling mode and disables tuning adjustments 
when in hold mode (see further discussion below). The Error Threshold 
circuit 8 indicates an out-of-tune condition via LED I and provides a 
no-tuning-error signal to the Tune Initiate circuit 10. The Tune Initiate 
circuit 10 enables tuning when the Tune Pushbutton 12 is pushed and 
disables tuning when it receives a no-tuning-error signal from the Error 
Threshold 8. The Sample & Hold output is amplified to appropriate voltage 
by the DC Amplifier 11 whose output controls the Piezoelectric Pusher 
Actuator 3. 
In normal operation, with the instrument in tune, the Sample & Hold circuit 
9 would be in hold mode. Its output would remain at the level of the last 
tuning adjustment, thus holding the Piezoelectric Pusher Actuator 3 in 
position to maintain tune. As the instrument is played, LED I would light 
because the Comparator 7 would be detecting large tuning errors due to the 
altering of the strings, pitches by the musician. To check the tune, the 
musician would strum the strings 44 in the "open position," that is, 
without influencing the strings' pitches by fingering them. If a string 44 
is out of tune, its Comparator's tuning error output would exceed the 
Error Threshold circuit's limit, and LED I would light. The musician would 
then initiate tuning by pressing the Tune Pushbutton 12, which would 
switch the Tune Initiate circuit 10 into tune mode. However, if the 
strings 44 are not vibrating, there would not be a sufficiently strong 
String Frequency Detector signal for proper Comparator 7 operation. The 
Signal Threshold circuit 6 is therefore needed to keep the Sample & Hold 
circuit 8 in hold mode, thus ignoring Comparator 7 output, when the String 
Frequency Detector signal is too weak. In that case, the Signal Threshold 
circuit 8 would light LED I. Upon seeing the lit LED I, the musician would 
strum the strings 44 and provide a sufficiently strong String Frequency 
Detector signal. The Signal Threshold circuit would then produce an 
adequate-signal output that would fully enable the Sample & Hold circuit's 
sample mode. In sample mode, the Comparator output is passed through the 
Sample & Hold circuit 9 to the DC Amplifier 11. The DC Amplifier output is 
then applied to the Piezoelectric Pusher Actuator 3 which alters the 
resonance frequency of the string 44, thus adjusting its tune (see 
discussion below). When the Sample & Hold circuit 9 is in sample mode, the 
entire system comprises a negative feedback circuit which acts to 
eliminate the difference between the string's resonance frequency and the 
generated reference frequency, thus tuning the string 44. 
When the tuning error has been reduced to a preset limit, the Error 
Threshold Circuit 8 produces a no-tuning-error output. The Tune Initiate 
circuit 10 then disables tuning, forcing the Sample & Hold circuit 9 into 
hold mode. 
Referring now to FIG. 2, the Piezoelectric Pusher Actuator 3 adjusts string 
resonance through a Cam 50. The Cam 50 pivots about Cam axis 51 to provide 
mechanical amplification of the Piezoelectric Pusher's range of motion. 
This amplification is desirable because it results in a maximum range of 
automatic tuning operation. The range of tuning available is a function of 
the guitar string's physical properties, and the range and force of the 
Piezoelectric Pusher Actuator 3. 
The tune of a string is determined by its fundamental resonance frequency 
of vibration, which is governed by Equation 1: 
EQU f=(1/2L)(T/M).sup.0.5 
(Musical Acoustics, Donald E. Hall) where f is the frequency, L is the 
length of the string, T is string tension and M is the string mass per 
unit length. From Equation 1, it can be seen that the string's tune is 
inversely proportional to its length (L), proportional to the square root 
of its tension (T) and inversely proportional to the square root of its 
mass per unit length (M). 
All of the strings of a guitar are the same length, approximately 0.65 m. 
The tune of each guitar string is therefore dependent on its tension and 
mass per unit length. In order to have balanced forces in the guitar neck 
42, the mass per unit length of the strings is varied so that the required 
tension is roughly equal for all strings. Rearranging Equation 1 results 
in Equation 1A: 
EQU T=M(2Lf).sup.2 
from which it can be seen that the string 44 mass per unit length (M) must 
vary in inverse proportion to the square of the frequency (f.sup.2) to 
maintain equal string 44 tensions. This is accomplished by using heavier 
strings for the lower notes. PG,8 
The tension of a string 44 is also governed by Equation 2: 
EQU T=eAE/L 
(Statics and Strengths of Materials, Stevens) where e is the string strain, 
A is the cross sectional area of the string, E is the modules of 
elasticity and L is again the string length. The string strain (e) is the 
distance the string 44 must be stretched in order to achieve tension (T). 
Since the tension (T) of all the strings 44 is roughly equal, it can be 
seen that the required strain (e) is inversely proportional to the string 
diameter (A). Thus the smallest string 44 requires the largest strain, and 
is therefore the worst case in terms of automatic tuning. 
The smallest string 44 of an electric guitar is usually tuned to E which 
corresponds to a frequency of about 330 hertz. The diameter of a typical E 
string is approximately 0.0002 m. With a density of steel of 7800 
kg/m.sup.3, the string mass per unit length is found to be: 
EQU (7800 kg/m.sup.3) (.pi.) ((0.0002 m)(1/2)).sup.2 =0.000245 kg/m. 
Solving Equation 1A for T with f=330 Hz, M=0.000245 kg/m and L=0.65 m 
results in a string tension of 4.6 kg. A typical commercial piezoelectric 
pusher (Burleigh PZL-060)has a maximum force of approximately 55 kg and a 
travel of 60 microns. With the string tension rounded up to 5 kg, the 
maximum amplification of the pusher travel is 11 and the maximum string 
strain produced by the amplified piezoelectric pusher range of motion is 
660 microns (0.00066 m). 
Combining Equations 1A and 2 and solving for strain results in Equation 3: 
EQU e=(2Lf).sup.2 (ML/EA) 
where e is the total change in string 44 length required for the string 44 
to vibrate at frequency f. With E=2.07.times.10.sup.11 Newtons/m.sup.2 for 
steel and with other values from above, the total strain needed to bring 
the E string 44 into tune is 0.0045 m. Since the available range of the 
Piezoelectric Pusher Actuator 3 is 0.00066 m, the E string must be 
manually adjusted to plus or minus seven percent (.+-.7%) of the desired 
frequency before the invention can bring the string into final tune. This 
represents a very coarse adjustment (approximately plus or minus 2 notes) 
and would generally only be necessary when initially tuning new strings. 
From the above, it can be seen that strings of lower frequency would 
require less manual coarse adjustment. 
There are a multitude of devices and alternate configurations that could be 
used for the components and subcircuits illustrated above. For example, 
the reference frequency generator 4 could consist of a quartz crystal 
oscillator coupled with a frequency divider circuit or a commercial 
integrated circuit timer chip. The comparator function 7 could be 
accomplished with a phase-locked loop amplifier or by using digital 
circuitry. The String 44 Frequency Detector 1 could be a standard magnetic 
pickup as currently used in electric guitars, a pressure transducer, or 
strain gauge. The essential element of the invention is the use of the 
piezoelectric pusher 3 in a negative feedback configuration to adjust the 
string's resonance, and hence its tune. 
While the preferred embodiment illustrated is for an electric guitar, 
incorporation with other string 44 instruments would be similar. The 
invention can be retrofitted to existing stringed instruments. Minor 
modifications to the invention would allow additional capabilities which 
include, but are not limited by: 
1. Automatic string excitation during the tuning cycle 
In the preferred embodiment illustrated, the musician must manually excite 
the strings to provide adequate signal strength to the Electronics Module 
2; however, with the addition of appropriate circuitry, the Piezoelectric 
Pusher Actuator 3 could be utilized to excite the strings 44. In this 
configuration, the first step of the tuning sequence would be a burst of 
AC voltage applied to the piezoelectric pushers of sufficient power and 
duration to start the strings 44 vibrating. The tuning process would then 
continue as described above. Other means of automatic excitation, such as 
the addition of separate piezoelectric pushers for string 44 excitation, 
are available. 
2. Automatic key changes 
With additional circuitry, the invention could tune the strings to 
different notes, thus changing the instrument's key, on the basis of 
switch selection, etc. from the musician. 
3. Enhanced sound capabilities 
With additional circuitry, the invention could provide programmed 
distortions of the string's pitches. An example of this is automatic 
vibrato which can be achieved by superimposing an AC signal over the 
piezoelectric pusher DC control voltage. The magnitude and frequency of 
the AC signal would be selected by the musician and would determine the 
character of the vibrato. 
The foregoing description has been directed to particular embodiments of 
the invention in accordance with the requirements of the Patent Statutes 
for the purposes of illustration and explanation. It will be apparent, 
however, to those skilled in this art that many modifications and changes 
will be possible without departure from the scope and spirit of the 
invention. It is intended that the following claims be interpreted to 
embrace all such modifications.