Imagine this
scene.
The controller is weary. The buildup of nervous
energy is palpable. A massive responsibility is in the controller's
hands for the overlapping trajectories of objects so distant that the
only evidence that they even still exist is a pile of data relayed from a
great distance. The controller is used to operating ''blind,'' i.e.,
only on instruments, but must now rely not only on making the right
decisions for critical adjustments, but also on the coherent
communication of those course corrections across tenuous systems. Any
mistake along the tightly-linked chain of measurement, transmission, and
decision-making could cause an unfortunate accident. A series of errors
could spell disaster. Somehow, despite lack of sleep and a poor supper,
the controller manages the task--another successful and safe arrival.
This scene unfolds not in front of a computer or radar screen,
but in the mind of the singer. The breath, vocal folds, and articulation
function and coordinate smoothly, and the tenor successfully arrives at
the end of has aria.
CONTROL THEORY The science of control
theory was first established during World War II to model and help
develop a whole new series of high performance weapon systems.
1.
Today it has evolved to include an extremely wide range of
applications from missile flight to stock market manipulations to body
temperature regulation to artificial intelligence. It also can be
applied to the human voice. ''I Could Control Myself If I Could Only Let
Go So I Could Control Myself'' is a basic paradox of the individual
singer. Paraphrased, it could be interpreted as saying that the singer
will have confidence to perform only if she attains such great mastery
that she can achieve the illusive state of free and natural tone
production. Inherent in this paradox is the self-referential, even
seemingly contradictory nature of guidance, control, and learning.
Control theory typically applies to systems that rely on separate
feedback, control, and production systems. It attempts to shed light on
how those systems interact and when they are stable. Contemporary
control theory also examines when the control system is most effective,
and how and when these systems are adaptable. All of these approaches
rely on mathematical modeling.
Great effort is spent
creating models of how the voice works. The models are, of course,
always simplifications. As computing techniques improve and the
sophistication of the methods grows, the models improve. As commercial
demand grows for them, the models improve because increased resources
are focused upon the problem. Rather than being concerned with knowledge
of the voice simply to provide greater insight into opera singing, we
now want an ATM to recognize our voice to withdraw money for dinner.
From inexact, even false and misleading models of the voice, we have
moved to elegant simplifications (Ishizaka and Flanagan
2.
) to greater detail and application to singing (Titze
3.
) to models that emphasize different facets of the problem (e.g.,
Navier-Stokes graphic visualizations
4.
and synthetic voice
5.
). There has always been an effective, accurate, and relevant model
of the voice that is, however, frustratingly
1. Ollie
Elgerd, Control Systems Theory (New York: McGraw Hill, 1967),
3-6.
2.
K. Ishizaka and J. Flanagan, ''Synthesis of Voiced Sounds from a
Two-mass Model of the Vocal Cords,'' Bell System Technical Journal
51 (1972): 1233-68.
3. I. Titze, ''The Human Vocal Folds: A
Mathematical Model. Part 1 and 2,'' Phonetica 29 (1973,
1974):1-21.
4.
J. Flanagan et al., ''Speech Synthesis from Fluid Dynamic
Principles,'' www.caip.rutgers.edu/[sim ]sinder/cfd.html.
5. C. Dodge and T
Jerse, Computer Music (New York: Schirmer, 1985), 195-222.
p.305
limited in
its accessability. The obstacle to the model is not a lack of computing
power, but a barrier of language and spirit. That model is the mind's
own model of the voice. Not only does the mind control the
voice, but in a formal sense, it also models the behavior of the voice.
With considerable reliability and flexibility, the mind of the singer is
able to prepare the voice to produce a wide range of tones of variable
pitch, timbre, and duration, and to maintain and change those tones. It
can describe and predict the behavior of the voice very well, if
imperfectly. The model itself can change as we sing, and as we learn and
grow. In control theory parlance, singing is an adaptive control
system. Unlike most man-made models, this is a model we do not have to
create, but one that we have to uncover. If we could understand more
about the way the mind models the voice, we could add to our ability to
model the voice synthetically, improve our understanding and application
of the voice itself, and, even further, gain very direct and useful
insight into how to think about singing and how to teach it.
Figure
1 typifies basic control theory. An interactive system has three
main parts--the ''plant,'' the ''controller,'' and the pathways of
information. A command center delineates a desired output and the
controller signals the plant to commence production. The output of
production is monitored through a feedback pathway that travels back to
the controller.
In singing, the ''plant'' is the physical
system. The pathways are the signalers and receptors. The ''controller''
is what this writer calls the mind's model of the voice. Each of these
three units can be further subdivided. The physical system includes the
breath, the oscillatory apparatus (which we will abbreviate as
''folds''), and the components of articulation (''articulators''). The
pathways can be differentiated according to each individual route and
direction of information. The mind's model can be divided into the
''predictor'' (the mind's initial source of input for a tone), the
mind's ''error measurer,'' and the ''corrector'' (the mind's error
adapter). Every one of these systems significantly influences the final
product (see
Figure
2 ).
Voice teachers are quite familiar with ''the
plant.'' After all, this is anatomy. We, or at least a physician, should
be able to locate and describe the breath, the folds, and the
articulatory structures. In practice, however, these three systems are
complex, evasive, and deeply interconnected and protected. As the arrows
in
Figure
2 indicate, each of the three systems influences and can be
influenced by each of the others.
6.
Direct and unencumbered manipulation of any one of these systems in
a live singer is elusive.
7.
Singers regularly attest to
figure 1. basic control feedback
loop. 
figure 2. voice control loop.
6.
Lawrence 
HitIndik , ''Consonant Feedback in
Singing.'' Journal of Singing 57, no. 4 (March/April
2001):15-21.
7.
Ann-Maria Laukkanen and Erkki Vilkman, ''Tremor in the Light of Sound
Production With Excised Human Larynges,'' in Vibrato, ed. P. H.
Dejonckere, M. Hirano, and J. Sundberg (San Diego: Singular Publishing
Group, 1995), 93-110.
p.306
the fact that perceived small changes in the characteristics
of any one of these systems can dramatically affect the sound. Though
we do not talk to our singing as we do to a friend or to a waiter at a
restaurant, we do communicate through established pathways. The physical
systems are constantly monitored by the nervous system that feeds the
information to the brain. The brain processes information and sends
directions elsewhere. Much like observing the United Nations without a
translator, we may not know what exactly is being said or the language
being spoken, but we can say who is speaking to whom and the setting in
which it is being said. From this information we can deduce something
about the ''fluency'' of each member and figure out how to make a
primitive greeting to the appropriate member and establish some sort of
rapport. Choosing an optimal language is the goal of diplomat,
interpreter, and teacher.
Each of the directed arrows in
Figure
2 represents a pathway in the vocal control loop. A language
directs the physical system to prepare and commence to sing. A language
carries information back to the brain from the physical system, either
through the ear or as other feedback. Finally, a language is used by the
brain to adjust the physical system. Although each of these languages
is conveyed by nervous signals, there is no reason to expect they are
the same. The appropriate information along the appropriate pathways
engenders coherence and coordination. On the other hand, a ''crossed
wire'' or the wrong language (e.g., feeding the physical system of
singing the unprocessed nervous signal that the brain receives from the
ear or a recipe for donuts) would be at best confusing.
table 1. control model types
In order to control the voice, the singer and teacher
communicate through the command center to the mind's model of the voice.
Each of that model's three components, the ''predictor,'' the ''error
measurer,'' and the ''corrector,'' may have different characteristics.
There are several candidates for the type of control model or models the
mind uses. Three are presented here (see
Table
1 ).
Probalistic causal model The mind may rely on a
probabilistic causal model of how the voice works, sometimes called
''muscle memory.'' From massive amounts of data it has compiled through
its own measured experience, it links the desired output with the
parameter inputs whose most probable output is closest to the one
desired. The mind forms in effect a weighted database of pairings of
inputs and outputs. Inputs
p.307
that were deemed successful would be weighted more heavily.
Consistent with our experience of memory, the probabilistic model also
would count more recent experience, emotional events, or episodes that
are in any way remarkable as individually more weighty. When it comes
time to choose the input for a desired tone, the mind performs
calculations and comparisons. For example, if ninety per cent of the
time opening the mouth more on a high note is effective, then that
strategy becomes built into the automatic model. This kind of method
produces results that are consistent with experience and avoids the
complications that arise from trying to model with functional equations
too many complicated systems with too many variables doing too many
nonlinear behaviors. On the other hand, it requires a lot of computing
power and a lot of memory. It also may build ineffective or inefficient
behavior into the system. Using the probabilistic model, if the
optimal strategy for producing a note has never or rarely been
experienced, the mind will probably program another less efficient input
extrapolated from all previous behavior. With this kind of model, in
order to create a new behavior, the accumulation of previous experience
must be overcome by the new strategy. The mind would have to weigh the
new strategy more heavily than the past behavior. This could occur with
repetition and special emphasis.
Functional model The mind
may rely on a functional model of how the voice works. Based on internal
''hard wiring'' and perhaps also on primitive learned behavior, the
mind has a logical construct of a formal functional relationship between
chosen parameters and output. This functional relationship could be
modeled externally as a system of differential equations. For example,
when the mind orders signals to be sent that increase a particular
parameter of vocal fold tension a small amount, it may expect the pitch
to rise a small amount based on an internal program that could be
represented externally by just a few relatively simple equations. This
information may be programmed from birth and be part of the basic
physical system. For example, excitement causes faster respiration and
higher pitch as a basic physical response. Inflection of speech would be
an example of a combination of learned and physical behavior.
Analog feedback system The mind may rely on an analog feedback
system that adjusts the sound. After measurement of an error in output,
it would adjust selected input parameters based on a simplified model
that limits the dimension of the input domain. Because of this
simplification, it both gains in applicability and loses in generality.
Depending on the quality of the model and measurement, it could approach
the desired result through a feedback loop.
The actual
control model used by the mind is most likely a combination of the above
three types. The general character of the overall model and the
specific precision of each component type would vary with talent and
training.
A SPECIFIC CONTROL MODEL FOR THE VOICE Based on
observations of the process of singing and the various time frames under
which it operates and regulates itself, it becomes possible to consider
the following generalized conglomerate model. The ''predictor'' would
be a combination of a probabilistic causal model and a functional
extrapolator. The ''corrector'' would work as an analog feedback system
based on a simple, linear functional model. An experienced, talented
singer would have a strong ''predictor'' that consistently would place
the voice near the intended target and also would have a ''corrector''
that was able to make the necessary small changes. On the other hand, a
novice singer would have a weaker probabilistic model due to
inexperience and would consistently need to make greater adjustments.
These adjustments would take longer to achieve, more likely be
inefficiently realized, and even be outside the corrective scope of the
limited linear functional model.
8.
Without the ''error measurer,'' the second component of
the mind's model, none of the adjustments to the initial settings of
the voice could occur. The mind receives the feedback and processes it.
It compares the output sound with what it expects to hear and what it
wants to hear. As the mind reacts directly to the sound, it also
measures against expectation and judges against the imagined ideal.
Expectation and imagination are both parts of the mind's model of the
voice. Without them there is no comparison and hence no chance for
adjustment and correction.
8. Johann Sundberg,
''Maximum Speed of Pitch Changes in Singers and Untrained Subjects,'' Journal
of Phonetics 7 (1979):71-9.
p.308
APPLICATIONS OF CONTROL THEORY TO SINGING Aside from
the illumination of the categories, organization, and connections of the
singing process provided by control theory, are there other advantages
to viewing singing from that perspective? Control theory does offer at
least three additional kinds of help. First, it offers general
mathematical results that apply to voice. Second, from the specific
voice control model described above we can derive explanations of
several physical and behavioral observations. Finally, the approach
utilizing control theory should suggest preferred strategies and
language for improved singing and teaching of singing.
Control
theory puts issues such as controllability, optimization, and
adaptability in mathematical terms. Because singing is an evolved
organic process, we might expect it to be controllable, optimal, and
adaptable.
To paraphrase the mathematics, a system is said
to be completely controllable if for any initial state and any given
final state, there exists a control function such that the final state
can be achieved.
9.
We might interpret the mathematical notion of controllability to
translate to the context of singing as follows: to be a completely
controllable system, the mind must be able to direct the voice smoothly
and accurately from one singable tone to any other singable tone.
Singers and teachers know that this capacity is one of the most highly
desired ideals, and quite difficult to achieve in practice.
A
theorem of control theory states that if the system and the control
strategy are linked so that the system responds with sufficiently
''responsive local flexibility,'' then the whole system is completely
controllable.
10.
We can apply this notion of ''responsive local flexibility'' to
singing to mean that, given any initial tone the voice is producing, the
mind can direct it smoothly all around the immediate area of that tone.
For example, a singer who sings the note middle C (C
4) in a
soft tone with a particular timbre, can adjust smoothly to slightly
different pitches, volumes, and timbres.
This mathematical
result applies to all qualified systems of control theory. See how it
applies to singing. A singer needs only to develop the ability to make
relatively small adjustments in the various characteristics of each
tone. Then, it follows from mathematics that he will be able to make
smooth adjustments to any (even distant) singable tones. If this theory
seems untrue, an example follows presently that will demonstrate how it
is consistent with a favored vocal technique. If it seems obvious, then
it is interesting to reflect on the underlying generality of the
situation.
Along with naturalness and freedom, flexibility
is always valued among singers. Perhaps the most classic bel canto
vocalise is the
messa di voce (a gradual crescendo and
decrescendo of an otherwise unchanged tone). Practice of this exercise
is in effect an attempt to achieve one of the mathematical causes of
complete controllability.
Focusing on local, small effects
influences and can even determine global behavior. This statement can
apply equally to politics, pollution, and the polished voice. The
''local'' behavior is the behavior in the immediate vicinity. The
''global'' behavior is the behavior and health of the whole system. This
one result of the mathematics on controllability also suggests that to
achieve the desired mastery of complete controllability, we may benefit
not only from practice of the
messa di voce, but additionally
from a whole range of similar exercises based on other characteristics
of tone. Gradual raising and lowering of pitch and gradual manipulation
of all the constituents of timbre (including vowel color and so-called
placement) would help develop the sufficient ''local'' flexibility and
responsiveness that predicts and enables complete controllability.
If there were grand designers for the system of singing, they not
only would want to control the voice with stability but also would like
to find the best control system. There are different ways to
characterize the optimal goals of a control system. The optimal goal may
be:
- 1. To minimize the time to
achieve the target goal; or,
- 2. To
achieve ''terminal control,'' i.e., to achieve a final state as near as
possible to the desired state; or,
- 3. To
achieve the target with the minimum effort.11.
Each of these kinds of optimization
is valued in singing, but each does not necessarily demand the same or
even a complementary strategy. As the alternative title of this article
indicates (''I Could Control Myself If I Could Only Let Go So I Could
Control Myself''), singers constantly cope with issues of over- and
under-control. On the one hand, singers need to control their voices
sufficiently to produce complex and difficult organization of sounds. On
the other hand, both the physical facts and the aesthetics of singing
prefer a
9. S. Barnett and R. G. Cameron, Introduction
to Mathematical Control Theory (New York: Oxford University Press,
1985), 97.
10.
Ibid., 99-101.
11. Ibid., 245-47.
p.309
sound that is
least encumbered by control. Hence the phrase ''Let go!'' is proffered
far more often than ''Hold on!'' in the context of a voice lesson. We
value sound production with the minimum effort (goal 3). We also value
accurate singing (goal 2). Modern classical singing especially values
less slurring and sluggishness moving to a note (goal 1). To satisfy all
three of these goals simultaneously requires a compromise and very well
could be the cause of some of the quirky behavior of the voice (and of
the singers themselves). We have already referred to the
adaptive nature of the model of the voice. We can observe it in
children, in our students, and in ourselves. The model can clearly
change for the better or the worse with the experience of feedback and
other intervention.
The specific control model proposed
earlier can also shed certain light on some voice behaviors. One of the
difficult issues in singing is real or perceived holes or ''breaks'' in
the voice. These may occur at the overlapping of registers, or simply be
a poorly produced, weak, or tenuous part of the voice. According to the
previous discussion of the concept of complete controllability, if the
singer demonstrates complete flexibility in the vicinity of each note,
there should not be any breaks. If a break is apparent, then there must
be some note or region of notes where the necessary flexibility is
lacking.
The behavior of ''breaks'' may be described in
greater detail with the specific control model. When the singer prepares
to sing a pitch at a ''break,'' the ''predictor'' feeds the input
parameters to the physical structure. In the case of a ''break,'' the
singer does not have the resource of a memory of efficient or free
production. Instead, the inputs of the ''predictor'' are a combination
of the best of an unhelpful lot and some extrapolation calculated to
improve the output. This extrapolation will probably not be particularly
helpful because it is derived from the previous inputs. The illusive
optimal, ideal inputs are more than likely a very different set of
parameters. As the brain receives feedback from the voice through the
ear and other channels, it will be interpreted by the ''error measurer''
as short, even far short of the desired output. The ''error measurer''
then orders the ''corrector'' to make a correction.
Because
the ''corrector'' is based on a simple functional model, it is a
relatively blunt tool. When the ''corrector'' makes an adjustment at a
break, it probably also is confronted with a lack of flexibility. Its
small, simple change of input likely will fail to improve the situation.
It even may begin a worsening loop until time, fatigue, stress, and
breath finally end the unpleasantness. The ''corrector'' may usually be
well suited to tweaking a tone slightly (perhaps simply by raising or
lowering the tension in a small group of muscle fibers), but it is not
capable of making the necessary complex adjustments of many parameters.
The control model of the voice explains both the power of
bad habits and fears to inhibit improvement, and, on the other side of
the coin, of technique and confidence to enhance singing. As we
discussed earlier in the context of probabilistic models, if a singer
always has sung a note poorly, he likely will continue to do so. Coupled
with a bad output, there could also grow a negative association, a
fear, that could lead to inhibiting and further ineffective control
input--self-predicting failure. Because the initial source of inputs is
based largely upon the weight of experience, a wholly new, better
behavior needs special reinforcement. Such reinforcement may occur
through repetition or through greater conscious attention--two factors
that may be scarce when confronting a new technical challenge in
uncomfortable surroundings. Similarly, for a singer with good technique,
who has the experience of many optimal productions of a desired output,
the control model would naturally return to the associated successful
inputs.
The omnipresent and essential feedback that the
mind's ''error measurer'' interprets and weighs against expectation and
imagination also can contribute to both negative and positive loops of
fear and confidence. Some of these behaviors could be based on the basic
physiology and psychology of the singer. Confronted with the feedback
of the sound of his own voice singing a loud high note, the tenor may
recoil or rejoice and/or attach associations of excitement, pleasure, or
anger. These associations could cause reactions in the singer that then
could affect the input to the physical system that in turn affects the
sound. What may seem like small effects can be magnified by both vicious
and virtuous loops.
We can speculate on not only the smooth
''connectability'' of two tones, but also on how the mind's model
actually moves from one tone to the other. As diagrammed in
Figure
2 , the command center orders the voice to sing the initial tone
and then shift to the next. The control model achieves the first tone
and monitors it through feedback until it is time to shift. At that
point, the ''predictor'' is responsible for the major
p.310
change to the next desired tone. The ''predictor'' finds the desired
input from a combination of the probabilistic model and a functional
extrapolation. As the desired note is approached, the ''corrector'' also
brings the output closer to the desired tone. This behavior is
consistent with observed results.
12.
Because there is already a tone sounding, however, the weighted
database for the probabilistic model and the extrapolation would be
different from that of a tone in isolation. The mind automatically would
weigh recent experience more heavily than distant ones. The
extrapolation would also more likely be based on the current inputs for
the first tone. Hence, the next note would more likely be produced in a
manner similar to that of the first note. This behavior is also
consistent with observations of both the benefits of legato singing and
the difficulties of register adjustments. While it is aesthetically
pleasing for two contiguous notes to be smoothly connected--partially
because of many common qualities--if two notes from significantly
different ranges share too many characteristics, one of them may be
awkwardly produced--either too heavily or too hollowly.
Time
scales The viewpoint of control theory highlights behaviors that may
occur as a result of the different time scales involved in the
production and regulation of sound. Singing takes place at many speeds.
The fastest, if we do not include the imagination and its impossible
behaviors and false expectations, is the speed of the sound itself. This
contrasts with the comparably tortoise-like acquisition of new habits
and skills. Consider how the time scale and the control model relate.
The predictor is entirely responsible for the first attempt at a note
the singer sings after a rest. When a singer has the time to prepare a
phrase, he can assert more selective, conscious control over the input
parameters. When there is less time, as notes are flying by and the
singer is moving from note to note, the singer is constrained by the
inertia of the previous moment and lack of time to intervene
consciously.
At an even smaller time scale, during the
moment-to-moment production of sound, limited adjustments still can be
made. They are influenced and limited by the length and response time of
the feedback loop. The ''predictor'' likely will not submit changing
inputs, because it has already submitted its best inputs for an output
target that has not changed. If there is an error, the only hope for
directed improvement is with the ''corrector.'' The mind's
''corrector,'' however, can respond to the sound of the voice no more
quickly than the total time it takes for the sound output to travel to
the ear, be processed first by the ear and then by the ''error
measurer,'' and subsesquently the time it takes for the corrector to
process an adjustment, the time it takes for the nervous signal to
travel back to the physical system, and the time it takes for the
physical system to respond. The quantity of time, the ''total error
correction response time,'' is a crucial value in the feedback process
of singing and figures strongly in any mathematical modeling of the
control system. Based on the measured values of specific thresholds and
minimum response recognition times that range from 20-50 msec up to
200-300 msec, we can speculate that the total error correction response
time is between 40 and 200 msec. This duration can be compared to that
of other relevant, similarly scaled speech events. It may be greater
than the time it takes the voice to produce many transient sounds,
13.
which would predict that voiced stop consonants and short staccato
bursts should be difficult to tune. (This is consistent with the
writer's own experience as a teacher, that singers need to devote
greater conscious attention in order to be accurate on the pitches of
these vocally challenging short sounds.) It may even relate to the time
of 300 to 600 msec that it takes for the onset of vibrato after a rest,
14.
and the time it takes (approximately 125-170 msec) for one cycle of
normal vibrato or abnormal vibrato (as long as 250 msec or as short as
83 msec).
15.
At a faster time scale, beyond even the intervention of the
''corrector,'' the behavior of the system could be influenced only by
more direct neural pathways or other independent fast-acting physical
conditions.
Control and the ''error correction response
time'' play a critical part in runs, trills, and other fast-moving
passages. Because the voice may need to move accurately between pitches
faster than the time it takes even the ''corrector'' to converge on each
intended pitch, the system must rely mainly on the ''predictor'' to
guide the voice. In fact, vocalises that emphasize velocity may
effectively force the singer to relinquish unwanted muscular
intervention based on sound feedback (''over-control'' through
listening). A control system based on sound feedback alone can not
accurately produce such fast passages. The relative slowness of the
feedback channels
12. Johan Sundberg, ''Maximum Speed of
Pitch Changes in Singers and Untrained Subjects,'' Journal of
Phonetics 7 (1979):71-9.
13. Philip Lieberman and Sheila
Blumstein, Speech Physiology, Speech Perception, and Acoustic
Phonetics (Cambridge: Cambridge University Press, 1988), 190-192.
14. Johan
Sundberg, ''Synthesis of Singing,'' Swedish Journal of Musicology
60, no. 1 (1978):107-112.
15. Richard Miller, The Structure of
Singing (New York: Schirmer, 1986), 182.
p.311
compared to the desired
speed of the note progression makes it impossible to control the note
pattern. To account for this behavior, any control model of the
voice must have a component that is independent of short-term feedback.
In our model this is the ''predictor.'' On the other hand, the
''predictor'' does not account for the way in which singers approach and
adapt to a pitch destination. The ''corrector'' predicts and explains
this and also other behavior on sustained notes.
Vibrato It
has long been suspected that vibrato is due in part to some synergism of
the muscle and nerves.
16.
Although vibrato can not be explained by the feedback pitch control
loop alone (if it were an unavoidable result of any similar regulatory
feedback loop alone, then one would expect vibrato to be a natural
result of whistling), it can be modeled with the proposed control
system. The ''corrector'' itself could be described in such a way that
it maintains the pitch through an oscillatory motion around the target.
That motion would mimic vibrato. Together with a critical damping factor
in the modeling of the folds, the control system could account for both
normal vibrato, abnormal vibrato, and straight tone. This vibrato-like
behavior, the effect of different time scales, and the numerical
simulation of the specific proposed control model for the voice are the
subjects of a current investigation by the author.
17.
APPLICATIONS OF CONTROL THEORY TO TEACHING VOICE We can
improve our singing by improving the participating players in the
multifaceted adaptive control system. For the physical system this is
achieved directly by maintaining and enhancing the health, flexibility,
and response of the various body elements, including the breath
mechanisms, the oscillatory structure, and the articulatory structures.
These goals are the aim of the general hygiene and fundamental vocal
exercises that make up much of the basic instruction from the practical
voice teacher.
We can improve the mind's probabilistic model
of the voice by gathering and inserting more data, especially pairings
of successful inputs and outputs, so that the model can fill in missing
holes and extend to uncharted areas. We can extend and improve the
database by drawing from previously excluded data from both internal and
external experience. The teacher can guide and coerce the student to
include experience from nonsinging sounds like the incredibly rich and
promising area of speech sounds and emotional sounds. These internal
sounds have the advantage of already having linked the inputs with the
output. It is also useful to expose the singer's mind to different
external examples of vocal sounds. Though these external examples do not
come linked with the necessary internal input, they could provoke
constructive and creative extrapolation. The probabilistic model could
also be improved by refining the weighting or the judgment attached to
the various input-output pairings. If the mind wrongly judges an output
to be successful, that misconception needs to be corrected before a
better behavior can be expected.
As discussed earlier, bad
vocal behavior that has evolved into a bad habit poses a great
challenge. The probabilistic model suggests that to overcome a bad
habit, the teacher should creatively link a new improved set of inputs
with particularly strong, positive feedback. This prediction is
consistent with the observation that teachers sometimes successfully
resort to theatrics to reinforce an improved vocal behavior. The
startling sound and comfort of the improved output itself may be
sufficiently memorable to the singer that it outweighs the accumulation
of past experiences on the internal model and immediately engenders
better behavior.
The other elements of the mind's model, the
''error measurer'' and the ''corrector,'' also may be enhanced. The
''error measurer'' benefits from more clarity of and confidence in the
expected and imagined goal fed in from the command center. The
''corrector'' takes great advantage from freedom in the parameters it
attempts to adjust. Without flexible response, the ''corrector'' will
certainly work less effectively.
We can improve the
communication channels by choosing the most effective and appropriate
language for each component. If we wish to communicate to and within the
mind's model, we need to speak a language that will be understood well.
To return to the United Nations analogy, if we speak to the French
delegate in German, he may know our general condition, but he probably
doesn't want to listen to us. We know the mind's model understands the
raw language sent by the ear, that of tone quality, and we know it
responds to the language sent by the command center, that of expectation
and imagination. We would not expect it to understand the digital
output
16. Ibid., 183-4.
17. Lawrence HitIndik , ''Numerical Simulation of a
Control Model for the Voice'' (in preparation).
p.312
of a computer or hard data conveyed to it by a scientist. It
follows that the best way to ''speak'' to the model is not necessarily
the most truthful and the most scientific. Instead, we can surely say
that the most effective language is the language that causes the best
change in sound. That language, as teachers regularly experience, is
made of sound, music, image, and inspiration. The main control
path to the voice is through the mind's model. The teacher must
communicate to the model in order to change the student's voice. As is
shown in the control diagram (
Figure
2 ), the mind's model receives input from the command center, the
mind's model itself, the ''error measurer,'' and the feedback from the
plant. These are the teacher's potential paths for persuasion. For
example, the mind's model regularly figures adjustments based on error
comparisons to the sound received through the ear. This process is, in
fact, a language the teacher could exploit to communicate to the
student's budding model of singing. The student's model is very
susceptible to the influence of this language. The teacher could produce
a cleverly chosen sound just like that the student would normally
receive as feedback, but which leads to an error measurement and then
adjustment in the student's model that would improve the sound. There
are many dangers in demonstrating to students, not the least of which
are the risks of a creating an unintended bad example and of generating
extreme fatigue in the teacher's voice; however, this outlook on the
language of the control system argues strongly for the efficacy of the
teacher providing sung instruction.
The mind receives other
feedback during singing. Any of these senses or even sounds that take
other pathways to the mind offer potential pathways to improvement.
Feedback is very powerful; but it is not the only way to the
mind's model. The command center is always connected to the mind's model
of the voice. When a singer prepares to sing, he or she forms an
expectation that is communicated to the mind's model. The language and
form of this communication are a more nebulous area than that of the
feedback loop. Besides pitch, timbre, volume, and duration, concepts and
feelings are communicated from the command center to the mind's model.
It is at this point that the art of the singing teacher assumes a
pivotal role. The teacher can inspire the singer, make the singer more
confident, and choose just the right image to shift the mind's model
toward an optimal solution. The language or image offered through the
command center is interpreted by the mind's model. Like a representative
from a distant, unknown country speaking before a temperamental
assembly, the teacher seeking improvement can not be quite sure what to
say or gesture. Formulas, equations, and numbers are not the universal
language of the mind's model. Language that is scientifically rigorous
may be translated and misinterpreted as comically as a phrase mangled by
whispering down the lane or by poor computer translating software. A
fanciful, colorful, evocative, simple, but by no means literal or
scientific image that connects with a singer's deeply felt musical past
could be much more effective.
Imagine this scene.
On
a distant mountain top, the singer says to the master, ''I need
guidance.'' The master says, ''Let go.'' The novice responds, ''I could
only let go if I could control myself.'' The master smiles and whispers,
''You could control yourself if you could only let go so you could
control yourself.''
Control theory gives us a unique
perspective on the process of singing. As good and practical science, it
models, questions, and predicts. It divides singing into recognizable
units, and reveals the connections and pathways. It raises a critical
question, How much of what we hear is from the physical process and how
much is from the control of that process? It also predicts that science
alone is not the best manager and teacher of singing.
