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 Flanagan2. ) to greater detail and application to singing (Titze3. ) to models that emphasize different facets of the problem (e.g., Navier-Stokes graphic visualizations4. and synthetic voice5. ). 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.
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.
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
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.
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 (C4) 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.
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.
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
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.
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). 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.
