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The invention relates to a method, an apparatus and a program of
determining the pitch in string instruments that are excited by plucking
or striking, wherein the vibration of a string is converted by a
transducer into an electrical signal and the electrical signal is
evaluated.
A method of this type is known from DE 43 43 411 A1. Methods of this type
are used so that, following the striking of a string in a string
instrument, information regarding the pitch that has been produced is
available for further processing as quickly as possible, i.e. insofar as
possible, before the string has reached its steady state.
Methods of this type are used predominantly in connection with
electromagnetic transducers. The prerequisite therefor is that the strings
be able to appropriately excite the electromagnetic transducer, i.e. in
the general case, they should include at least one metallic component that
will have an effect upon the electromagnetic field of the transducer and
hence be able to produce a corresponding signal at the output of the
transducer. This condition applies in the case of most so-called electric
guitars. Since this has been one of the main applications of use up to
now, there are a whole series of other methods available apart from the
above-mentioned method in DE 43 43 411 A1, with the aid of which, the
pitch of the struck or plucked string can be determined.
However, the restriction to electromagnetic transducers is disadvantageous.
Thus, players, who are used for example to an acoustic guitar wherein some
or all of the strings are formed from strings of synthetic material,
cannot partake of the advantages of a rapid synthesising procedure for the
sounds that they have produced. The same thing also applies for other
string instruments that are struck or plucked.
Here too, one would like to have the opportunity to have the corresponding
pitch information available as directly as possible following the
excitation of the string. For this, it is not just the actual or expected
frequency of vibration of the string that is to be determined. One must
also be able to evaluate the signals resulting from the movement of the
string in as simple a manner as possible.
It is in itself known to pick-up the vibrations of a string by means of a
pressure transducer. The signal resulting therefrom can then be amplified
and reproduced over a loudspeaker for example. If there is enough time
available, the signal can also be used for synthesizing purposes. However,
usage of the signals obtained thereby for a rapid synthesizing process,
along the lines of DE 43 43 411 A1 perhaps, has not been possible up to
now because the form of the signals from pressure transducers is not
suitable therefor. The development of appropriate signal handling
processes is relatively expensive. It would be more advantageous if one
could use the procedures developed for electromagnetic transducers.
Accordingly, the object of the invention is to provide ways in which the
same evaluation procedures can be utilized with different transducers.
This object is achieved in the case of a method of the type mentioned
herein above in that a pressure transducer is used as the transducer and
the electrical signal is subjected to differentiation with respect to
time.
Following the differentiation or forming the derivative with respect to
time of a signal obtained with the aid of a pressure transducer upon the
excitation of a string, there is made available a signal whose structure
has a very great similarity to the structure of an output signal from an
electromagnetic transducer. This is somewhat surprising insofar as the
output signals from electromagnetic transducers and pressure transducers
are basically of a completely different nature and hence a comparable
processibility would not have been expected. Although this has not yet
been definitely settled, it is taken for the moment that an
electromagnetic transducer produces a signal by virtue of the movement of
the string. In the widest sense therefore, we are concerned with a
movement sensor. A pressure transducer detects the actual pressure that
the string is producing. This pressure alters with the excitation of the
string and the vibrations resulting therefrom. Thus, it consists of a
constant part, which is of no further interest for the moment, and a
variable part which is producing the output signal. This pressure and
hence the output signal is proportional, in the main, to the displacement
with time of the corresponding position of the string so that one can
consider the pressure transducer as being a position sensor. Since the
movement function is a derivative of the position function with respect to
time, one can obtain a signal, which corresponds to a large extent to the
signal from an electromagnetic transducer, by differentiating the position
function with respect to time.
One thereby gains the considerable advantage that one merely has to provide
one single processing routine that can be used in conjunction with an
electromagnetic transducer as well as in conjunction with a pressure
transducer. When using a pressure transducer, one merely needs to precede
this process with one further method step, namely, the formation of the
derivative with respect to time. One is thereby spared not just from
having to develop another complete processing routine for a pressure
transducer but one also saves on the memory needed therefor and the
processing capacity needed thereby.
By means of the method provided, one is even able to transfer the
characteristic properties of differing stroking or plucking techniques.
Thus, for example, it makes a considerable difference as to whether the
player plucks the string with a plectrum which is directed perpendicularly
to the body of the guitar or whether he holds the plectrum at an angle of
approximately 45.degree. Due to the differentiation with respect to time,
the signal from the pressure transducer is in both cases (and naturally
too, for the corresponding intermediate values) transformed such that it
can be further processed in the same manner as a signal from an
electromagnetic transducer whilst retaining the same information.
Preferably, a piezo-electric transducer is used for the pressure
transducer. Piezo-electric transducers are relative small. They have a
short reaction time and accordingly contribute very little to the time
necessary for processing the electrical signals following the plucking
process.
It is of advantage if the electrical signal is digitized before being
evaluated. A plurality of processing routines are available in the digital
field with the aid of which one can deduce the pitch information from the
output signal of the transducer.
It is particularly preferred hereby that the digitilization process be
effected at a constant sampling rate and that the differentiation be
effected by forming the differences between sampling values which are
mutually spaced apart in time by a constant predetermined amount. One is
thereby saved from the additional processing step of forming a quotient.
By virtue of the constant temporal spacings, the formation of the
difference is sufficient for obtaining the same information as would
otherwise emerge from a digital differentiation process.
It is particularly preferred hereby that the spacing be selected such that
there is an increase from 10% to 90% of the maximum value of the signal in
the interval formed thereby, at least for one predetermined state of
tension in the string. The choice of spacing depends on two important
factors: the sampling rate and the slope of the signal. If one selects the
spacing such that there is an increase from about 10% to about 90% of the
maximum value of the signal in this time, then, to a close approximation,
one can proceed on the basis that the differentiation at this spacing will
provide a relatively exact picture of the information contained in the
signal with respect to further processability as a signal from an
electromagnetic transducer. If the spacing is smaller, then the fraction
of signal peaks declines in comparison with the high frequency noise or
interference peaks that are always present in a signal of this type. If
the spacing is too great then the derivative no longer has an
approximately Gaussian shape as is wanted but rather, is in the form of a
trapezoid whereby the similarity to the signal from an electromagnetic
transducer is again impaired. The slope of the signal is dependent, inter
alia, on the frequency of the tone that is being produced by the string.
Since different strings are generally provided in a string instrument for
producing different pitches, the temporal spacing for the different
strings may also be of different amounts. Different sounds can also be
produced with a single string. In the case of a guitar for example,
different taps or frets are provided for this purpose. It is sufficient
hereby for example, if one selects the middle one of the tones that are
producible by the corresponding string, or, the tone produced most
frequently by the string as determined by experience, as being the basis
for the temporal spacing.
In a particularly preferred embodiment, it is provided that, following the
differentiation, the temporal spacing of the pulses or groups of pulses in
the form of plucked-transients be detected and evaluated as a transit time
or a transit time difference in order to produce a signal representing the
pitch. If one effects an evaluation in this manner, one no longer has to
wait until the string has reached its steady state. By virtue of the
differentiation, one can also obtain the so-called plucked-transients from
the output signal of the pressure transducer i.e. those in the pulses or
groups of pulses of a wave excitation that runs to and fro on a string
before a steady state of the string occurs. By virtue of the transit times
or transit time difference of these plucked-transients, a signal can then
be obtained that contains the pitch information.
It is preferred hereby that the polarity of the pulses or groups of pulses
should also be detected and that a signal be determined from the temporal
sequence of the pulses or groups of pulses which represents the position
at which the string is being excited. One thereby also obtains information
regarding the location of the excitation. With the aid of this
information, one can better incorporate the manner of expression and the
way in which the player plays into the synthesizing process for the
signals.
The invention will be described hereinafter by means of a preferred
embodiment taken in conjunction with the drawing.
Therein
FIG. 1 shows a schematic view of a string instrument having two strings,
FIG. 1a shows a schematic view of the string of FIG. 1 suspended between
two points,
FIGS. 2a and 2b show schematic waveforms when a string is struck with a
plectrum in a first position
FIGS. 3a and 3b show the corresponding waveforms when a string is struck
with a plectrum at an angle of 45.degree.,
FIG. 4 shows a block diagram of an apparatus for recognition of a tone
pitch,
FIG. 5 shows an apparatus for recognition of tone pitch using a program
stored on a CD-ROM and
FIG. 6 shows the main steps of the program stored on the CD-ROM of FIG. 5.
FIG. 1 shows in schematic manner, a body 1 of a guitar having a bridge 2
over which pass two strings 3, 4. In reality, a guitar has substantially
more strings, six or twelve for example. However one string suffices for
the purposes of explanation.
A strut 5, 6 is provided on the bridge 2 for each of the strings 3, 4. A
respective piezo-electric element 7, 8 serving as a pressure transducer is
arranged between the supports 5, 6.
Each piezo-electric element 7, 8 is provided with two terminals 9, 10 (only
those for the piezo-electric element 7 are illustrated). A voltage
proportional to the pressure on the piezo-electric element 7 can be tapped
off from the terminals 9, 10.
Moreover, the electromagnetic transducers 11, 12 are also illustrated in
schematic manner. Electromagnetic transducers 11, 12 of this type are
arranged very closely under the appertaining strings 3, 4 i.e. at a
distance of one mm for example. They are only sketched there so as to
enable a comparison between the output signals of the piezo-electric
transducers 7, 8 and the output signals of the electromagnetic transducers
11, 12 to be made. In reality, a guitar or a similar musical instrument
will either have electromagnetic transducers 11, 12 or piezo-electric
elements 7, 8.
FIG. 1a shows schematically the string 3 which is strung between a fixed
clamping point constituted by strut 5 and a clamping point 15 at which the
tension can be set. The string 3 stretches over a guitar neck (not shown)
on which there are arranged various frets 14. Shown by an arrow 13 is one
fret on which the string 3 is pressed down. This fret together with the
strut 5 determines the effective length L of the string 3. The
electromagnetic pick-up 11 is arranged under the string. By means of a
triangle 17, which is intended to symbolize a plectrum or a similar
plucking implement, a position of excitation for the string 3 is shown. If
the string 3 is now plucked or struck at this position of excitation a
standing wave of the frequency which is characteristic of the pitch is not
established directly. Rather, a transient process begins, which can be
described in a simplified way by saying that two pulses designated A and B
run to the left and the right from the position of excitation. The pulse A
runs to the left as far as the fret 13 on which the string is held down.
There it is reflected, with phase reversal and runs back once more. In the
same way the pulse B runs to the right as far as the clamping point
consisting of the strut 5, where it is reflected, with phase reversal and
runs back once more. The pulses or waves, running to and fro, overlay one
another and after a short time they form the standing wave with which the
string 3 oscillates.
The pulses A and B run past the electromagnetic pick-up 11 which is very
close to the strut 5 and is assumed here to coincide locally with the
strut 5.
A corresponding time diagram is shown in FIG. 2a. It can be seen here that
the pulse designated B which is intended to have a positive amplitude
crosses the pick-up 11 at a time t1.
At time t2 the pulse designated A which was reflected at the fret 13 and
phase-inverted arrives at the electromagnetic pick-up 11. Finally at time
instant t3 the electromagnetic pick-up 11 senses again the pulse B after
it has travelled over the string a second time and after having been
phase-inverted for the second time at fret 13.
The velocity of motion or the travelling velocity of the pulses A and B on
the string 3 is known. The active length of the string 3 and hence the
tone pitch can be determined from the time difference T1, which is, the
difference between the times t1 and t3. Since T1 is the time required for
traversing the string two times the effective length L of the string can
be calculated as L=v.multidot.T1/2, where v is the travelling velocity of
the pulses.
The total length L of the string 3 is intersected by the plucking point
into two parts a and b in such a manner, that a+b=L. In order to determine
the position of the plucking point the time interval T2 between time
instant t1 and time instant t2 must be evaluated. The arrival of the pulse
A at the electromagnetic pick-up 11 is delayed with regard to the first
arrival of the pulse B because the pulse A first travels away from the
electromagnetic pick-up and has therefore to travel a way which is longer
than the way to be travelled by the pulse B. The additional way which must
be travelled by pulse A is equal to 2a. Therefore the distance a can be
calculated as a=v.multidot.T2/2.
When a string is struck or plucked at a predetermined position of
excitement, the signal waveform is very dependent on the type of
excitation even in the case of a constant exciting force. This will be
made clear with the aid of FIGS. 2 and 3. FIG. 2 shows signal waveforms in
the case of excitation by a plectrum which is held approximately
perpendicularly to the surface of the body 1. FIG. 3 shows the
corresponding waveforms when a string is struck by a plectrum which is
held at an angle of 45.degree. to the body 1. Hereby, the signal waveform
that occurs on the electromagnetic transducer 11, 12 is illustrated in the
parts a of the Figures, whilst the signal waveform that occurs on the
terminals 9, 10 of the piezo-electric element 7 or 8 is illustrated in the
parts b of the Figures.
If the plectrum is held somewhere between the two extreme positions, the
signal waveform changes accordingly and will adopt an intermediate value
between the two signal waveforms illustrated. This applies for the
electromagnetic transducer as well as for the piezo-electric element.
All four signal waveforms are only illustrated schematically. They serve
for the purpose of explaining the effects occurring in a qualitative
manner.
The piezo-electric element 7, 8 is a pressure sensor that determines the
instantaneous pressure of the string which is tensioned over the strut 5,
6 on the piezo-electric element 7, 8. The pressure on the piezo-electric
element 7, 8 has a constant part which is dependent on the basic tension
in the string and is of no interest here for the moment, and a variable
part which produces the electrical signals. This pressure is proportional
to the instantaneous displacement of the string. One can deduce therefrom
that the piezo-electric element 7, 8 can be used here as a position
sensor.
By contrast, the electromagnetic transducer 11, 12 is a movement sensor
because it produces an electrical voltage when a corresponding string 3, 4
is moved in an inhomgeneous magnetic field of the transducer magnets. This
presupposes of course that the string can interact with this field. As a
rule, strings made of synthetic material are not able to do this.
Rathermore, metal strings and in particular steel strings are required.
Thus, while the piezo-electric element 7, 8 is a position sensor, the
electromagnetic transducer is a movement sensor.
The movement is the derivative with respect to time of the position signal.
If one views the piezo-electric element 7, 8 as a movement sensor, then
the electromagnetic transducer 11, 12 forms a speed sensor. One can thus
derive the output signal of the piezo-electric element 7, 8 with respect
to time in both cases and obtain a signal which is very similar to that
from the electromagnetic transducer 11, 12.
FIG. 2b depicts a rising slope at the beginning. In correspondence
therewith, FIG. 2a has a pulse at this position. At the next alteration of
the signal in FIG. 2b, this signal has a negative slope, while in
correspondence therewith, there is a negative pulse in FIG. 2a, and so on.
Similar relationships can be observed in the case of a comparison of FIGS.
3a and 3b. If FIG. 3b exhibits a positive pulse having a rising and a
falling edge, then, in correspondence therewith, the signal waveform of
FIG. 3a firstly shows a positive peak and then a negative peak.
Since evaluating algorithms for the output signals of electromagnetic
transducers 11, 12 are known, and a pre-processing of a signal can be
achieved by the simple process of obtaining the derivative with respect to
time from the piezoelectric elements 7, 8 then it is also possible to
convert the output signals produced by the piezo-electric elements with
the aid of conventional processing techniques.
The processing of signals in systems of this type frequently occurs in
digital manner. Accordingly, the output signals of the corresponding
sensors i.e. the electromagnetic transducers 11, 12 or the piezo-electric
elements 7, 8, pass through an analog-digital conversion process. If
thereby the sampling rate is kept constant, at 10 kHz for example, then it
suffices for the differentiation or formation of the derivative with
respect to time if one forms the differences between individual sampling
values, these samples not necessarily having to follow one another
directly but they could also be separated from each other by a
predetermined number of samples. The derivative Y n! from a signal X n!
then results for example from the following equation:
Yn!=Xn!-X n-k!
wherein X n! constitutes the sampling value, whilst Y n! forms the
current output value of this conversion, k is a constant value.
The selection of this value k, i.e. the selection of the spacing in time
between the samples which are drawn upon for forming the derivative with
respect to time, is important to the applicability of the process. It
depends on two factors, namely, the sampling rate and the slope of the
signal. The value k should be selected such that it is equal to the number
of samples that delineate the steep climb of the signal from 10% to 90% of
its maximum value. However, since this value is also dependent, inter
alia, on the tone produced by the strings 3, 4, one can be very nearly
satisfied by employing here an average value for each string.
If the value k is smaller, then the proportion of signal peaks compared to
the high frequency interference peaks that are always present in the
signal will decrease. If the value k is too large, the derivative will
lose its similarity to the signal from the electromagnetic transducers.
As described above with regard to FIGS. 1a and 2a the effective length of
the string as well as the position of the plucking point can be determined
by measuring the time interval between the transient pulses travelling
over the string. Nevertheless, the measurement of time for determining the
interval between the pulses is occasionally subject to uncertainties. For
this reason the evaluation of the pulses is made in an arrangement as
shown in FIG. 4.
A guitar has normally six strings, however for the sake of simplicity only
the signal analysis for one string is discussed with reference to the
signal analysis device of FIG. 4. Provided for each string is a pick-up
42, which, for example, can be a piezoelectric sound pick-up. The pick-up
42 is coupled to an analog/digital-converter 43 which has one channel for
each pick-up 42. The analog/digital-converter 43 is connected to a
differentiator 411, the output of which is connected to a microprocessor
44 which provides the input and output management for a neural network 45.
A selection device 46 can also be provided between the microprocessor 44
and the neural network 45, the function of which selection device will be
described later.
Moreover the analog/digital-converter 43 is connected to a frequency meter
47. The frequency meter 47 and microprocessor 44 are connected to a
comparisons device 48. The comparison device 48 is connected to a MIDI
interface 49. The comparison device 48 is likewise connected to the neural
network 45, to be specific, to a learning input 410.
Under the management of the microprocessor 44 and, if appropiate,
conditioned by the selection device 46, the neural network 45 receives a
sequence of pulses or groups of pulses and classifies these sequences in
each case into one of a multiplicity of specific classes. Here, each class
allows a conclusion as to the pitch and, if appropiate, also as to the
position of a excitation of this string.
By using the selection device 46, individual pulses are selected from the
sequence of groups of pulses which are registered by the pick-up 42 and
said individual pulses are fed to the neural network 45. The neural
network can identify similarities between individual sequences of groups
of pulses and classify the "plucking transients", which are represented by
these sequences of pulses, in such a way that their assignment to
individual classes, which in each case reproduce a pitch and a position of
excitation, is possible with great certainty. The identification sequence
is triggered here by the occurring pulses. The successive positive and
negative pulses or groups of pulses are forwarded to the neural network,
which tries on each occasion to assign the pattern pick-up or the sequence
pick-up to a previously learned sequence. This detection sequence is
repeated until either the neural network has produced a positive result or
the frequency meter 47 has provided the corresponding information. If the
neural network is still in the learning or training phase, in many cases
the frequency meter will be quicker. However, after a certain training
phase, the neural network 45, which can itself form the rules for the
identification if it is programmed accordingly, has stored sufficient
information to be able to undertake the classification itself in a
extraordinarily effective manner. The neural network 45 also forms
specific rules for generalities, so that even patterns which have not been
learned specifically can be identified, providing these have specific
similarities to the examples already learned.
Since the frequency meter undertakes a pitch identification in parallel,
further learning is also possible during the operation of the signal
analysis device. The comparison device 48 compares the pitch determined by
the neural network 45 with one determined later by the frequency meter 47.
Here, it is possible on the one hand to follow the fine pitch changes,
which are a means of expression of the player, on the other hand, using
this procedure, errors or inaccuracies in the algorithm which is applied
by the neural network 45 can be discovered and eliminated. The comparison
device 48 specifically couples the determined error back into the neural
network 45 and triggers a new learning algorithm, so that the same error
can not occur again, as a result of the improved identification
capability. In the event that no difference occurs, the comparison device
48 forwards the signal or signals unchanged to the MIDI-interface 49.
The output results of the neural network are processed further in such a
way that the MIDI-interface 49 can make MIDI-signals available, which can
drive a MIDI-synthesizer or an expander module. The pitch encoded in the
MIDI-signal corresponds in this case to the pitch of the guitar string.
Moreover, the plucking position can also be contained in the MIDI-signal
as monitoring information, as an encoded sound quality character.
The above description of the signal analysis device includes a
differentiator 411 coupled to the output terminal of the
analog/digital-converter 43. Due to the use of this differentiator 411 a
pressure transducer such as a piezo-transducer 42 can be used and
nevertheless the signal processing in parts 44 to 48 can remain the same
as for processing output signals of an electromagnetic sensor.
A zero adjustment analysis such as is known from DE 195 00 750 A1 may then
be appended to the formation of the derivative function.
Instead of implementing the tone recognition apparatus by hardware as
described above in connection with FIG. 4 it can also be implemented by
software.
FIG. 5 shows an embodiment of the invention comprising an A/D-converter 43,
a central processing unit (CPU) 50 connected to the output of the
A/D-converter and a MIDI-interface 49 connected to the output of the CPU
50. The CPU 50 receives a program from a CD-ROM drive 51.
FIG. 6 shows the essential steps of the program which is recorded on the
CD-ROM of the CD-ROM drive 51. It consists of the steps of reading
waveform data Xn! from the A/D-converter 43, differentiating said
waveform data Xn! with respect to time to form a derivative
Yn!=Xn!-Xn-k!
exhibiting transient plucking pulses and evaluating the effective length of
the string and tone pitch on the basis of the transit time differences of
the plucking transients.
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