"One can function freely and totally only if he is 'beyond system'.
The man who is really serious, with the urge to find out what truth is,
has no style at all.  He lives only in what is."

"Set Patterns, incapable of adaptibility, of pliability offer only
a better cage.  Truth is outside of all patterns."

"Absence of stereotyped technique as substance means to be total
and free.  All lines and movements are the function."

             -- Bruce Lee, from
                Tao of Jeet Kune Do

To anyone who gets here: this project has been hanging fire almost since its inception and outline. It has been taking forever, for various reasons. My apologies for the delay and very slow progress. I will try to keep the last modification date at the bottom correct.

Now November 5, 1998, I consider the following to be a first draft of the essay.

I started thinking about the nature of piano technique over 25 years ago, and have had numerous conversations with pianists on the subject, trying to get at their internal experiences as well as how they work and practice, what they think of as difficult and what they think of as easy. I make no attempt here to distill or review what was said and considered. Some of these conversations were more interesting, informative and useful than others. There were two pianists whose conversations are still memorable and I can't help but think that those conversations have, in some way forgotten in detail, an influence in what I am writing here. Whether they would agree to all that I am writing is not at all certain, but I would like to thank two truly fine pianists for their time and effort by name. They are Susan Starr and John Covelli.

I would also like to thank Kenneth Chong both for his interest in this essay, and his searching questions, both of which were galvanizing forces to continue beyond the initial meager paragraphs and outline.

Piano Methods are like religions. Someone suddenly has a flash of insight into the nature of things and is so overwhelmed by the new found knowledge that he decides to share it with other people. We have no true vocabulary for such insights or the mental events that need to be described, so the enlightened one speaks in metaphors connected to other people's experience so that someone else might be able to understand or get an image of the appropriate mental process. Some of the listeners realize that the man has something important to say, but they are not really very bright. They listen dutifully to every word and begin telling others what they have heard. These are called disciples. Unfortunately they have understood nothing of the meaning. of the words as metaphor and latch onto the words themselves or repeat what they think they have heard embellishing to the point of dogmatism and therefore complete falsity. They are stuck in the metaphors and take them literally. Thus in first generation, the insights have been completely misunderstood, perverted to mean something completely different and utterly trivialized to the level of the disciples' inadequate understanding. What they promulgate is a kind of magic or mystery, that accentuate trappings, not essences.

Piano methods usually are described by silly things about how to curl the fingers, hold the wrist, cant the wrist, move the thumb, cross over the thumb, etc. etc... This is the trivialization, the magic, like all magic, is useless and has nothing to do specifically with anything. The implication of the magic is that by blind and mindless repetition of the magical incantations one achieves nirvana, mind you, with no other effort exerted.

Occasionally, there is some intimation that one might have to pay attention while the physical repetition is going on, but somehow exactly how one is to pay attention, much less why, never gets clarified.

This act of paying attention, the why and how of it, is the subject of this essay, which is neither easy to write nor easy to read because, culturally, we rarely speak of internal functions of mind unless it is with a therapist. A pity this, since human languages have, as a consequence, not built up a vocabulary for the area. Many of my descriptions will resort to psychology, neurology as well as analogies to mundane existence.

I studied piano as a young man. At college, while maintaining studies in musical composition, for various reasons I fell away from the piano and pursued studies in mathematics and physics. After completing a Ph.D. in physics, I worked on musical composition and returned to the piano, resolving to become a "good" pianist, putting in many hours of practice a day. For a while, the technical progress was satisfactory, advancing by an understanding of technique that turns out to be at the foundations of what is presented here. After a time, however, the progress leveled off. Eventually, despite redoubled efforts, my technique began to deteriorate. The right hand's inaccuracy increased; the hand seemed to develop a random mind of its own. My response without even thinking about it was to increase the tension in the hand to prevent the unwanted movements that it began to display. I became hesitant and then reluctant to play for anyone. At first, I thought the problem might be a psychological one akin to a hysterical paralysis but eventually decided, as it turns out rightly, that emotionally I would not be disposed to that. Since it was clear that my practice was not working, I left off practicing for a number of years, returning to the keyboard sporadically just to see if the problem had abated. It did not.

After a few more years of this, I suffered an apparently minor fall that I cushioned with my right hand. After the pain subsided I discovered that even the playing of a simple triad was impossible. A singer friend had a relative who was a pianist that had a hand problem and who had had successful surgery to remedy the difficulty. I was given his name and went to see him. After some preliminary investigation, he believed he understood the nature of my difficulty and that surgical intervention was appropriate, though not a sure thing. Since my right hand was useless at the piano and could certainly be made no worse, I agreed and the surgery followed. The junctura connecting the extensor tendon of the fourth finger with extensor digiti minimi as well as that connecting the third and fourth fingers were found to have grown massive, restricting independence and motion of the third, fourth and fifth fingers. In addition an entrapped tendon involving the third finger was discovered and freed. Postsurgical behavior of the hand was as spasmodic as before though it did seem that the hand was somehow freer and that certain physical configurations were possible that were not previously. The surgery required as side effects that the mechanical, and neurological structure regarding proprioception had to be altered, making the hand seem like it belonged to someone else. As soon as was practicable, I began practicing again to stretch the shortened tendons and muscles and in doing this managed to regain some control over the hand. The progress became so miniscule compared to the effort that I despaired of ever being able to play again and so would go months without going near the piano. This went on for almost twelve years, until something prompted me to attempt practicing the piano seriously one more time. I do not remember exactly what it was that started me to practice again, but somehow there was no longer any emotional attachment to the task. I looked at the retraining of the right hand as a cold mental and physical discipline that had nothing to do with music. There was no precedent that I could find for my particular problem and so I had only my own mind to rely on. I studied anatomy, particularly of the hand as well as relevant neurology to help develop a concept of what needed to happen physically. Any and all advice except the completely obvious was useless, and a first step was to throw out all preconceptions. At some point, I simply knew it would work and the question popped up, how long? With the conviction of success, the only answer I could give myself was, as long it takes. What if I set a goal, and missed it? Actually, I did give myself one simple goal: if there was no significant progress at then end of 6 years, I would admit defeat. Eventually this became changed to: so long as there was discernible progress, however small. over a week, I was satisfied. When, eventually, I saw progress in a single day on a regular basis, I was satisfied enough not to be bothered by a seemingly fruitless day, was truly convinced that my reasoning and general method was correct. When I ran into the inevitable brick wall, cease and desist for a day or two always worked to advantage. Generally though, I got in at least a two hour practice session every day. I accepted the plateau times as well known by psychologists in the learning process and understood them as periods of shut down for purposes of integration. At the level of concentration that I was becoming accustomed to, two hours was a saturation point. As things progressed, the level of concentration and mental exertion required became less (or easier), so I could work longer or slip in a second practice session. But, an upper level of concentration was set, and that level could be returned to whenever it was necessary. More stabilized at about the four year mark, it seemed to me that the upper level could be mental sustained for about four hours; beyond that, for me, a principle of diminishing returns sets in. This is a limit that I had to learn to recognize by monitoring my mental abilities and knowing when it was time to back off.

I did pick a small set of Chopin etudes that were to be my work horses. These pieces presented exactly the difficulties that I saw as essential for me in particular to be overcome, so in one sense, I made life as difficult as possible. For the record, they were the C major (extended articulation), A minor (fingers 3,4, 5), C# minor (articulation in both extended and contracted hand formations) from the Op. 10, and the G# minor (thirds), Db major (sixths), B minor (octaves) from the Op. 25. These, together with major and minor scales, Hungarian minor and Persian modes, chords and eventually arpeggios, have been, with few divergences, my steady practice diet for about 8 years, except for the past two or so years, where a spinal cord injury has curtailed much activity, and introduced new difficulties with both hands. The particulars are difficult to describe and I do not think it anything but a a needless digression to do so.

I do not recommend for anyone else the particular discipline or choice of work materials that I have selected for myself. These choices are peculiar to me and my special problems and are undoubtedly not appropriate for others.

I approached the problem of piano technique using the tools of analysis and logic that were part of my scientific training together with some knowledge of anatomy, neurology and brain function ultimately arriving at what seem to be the absolutes of method. The results are not like anything that I've been exposed to that purport to inculcate proper technique, which is why I thought it of interest to write them down. There is no interminable set of etudes and exercises a la Czerny; exercises come from music which do, however, include the etudes of Chopin and Liszt, and also from the standard elements: scales, arpeggios, chords in all of their standard variations. There are no rules about how the wrist should be held or the angle that fingers should make with the keyboard. There are some ideas presented for exercises. The most important thing presented, to my thinking is what should be going on mentally and physically in the execution of these exercises. This sort of thing is precisely what I find missing or confused to the point of mysticism in other discussions of piano method. The physical advice given here is inextricably coupled to the mental, and it is this rather simple advice that I believe to be the only physical advice of any general import; everything else is figuring out problems of execution that depend on individual persons with individual hands.

Without pretending to write a treatise on the history of piano technique, a few observations may be pertinent, the point of which is that while what I am writing may not have been written before, it most probably has been thought and known.

The great pianists (e.g., Liszt, Chopin, Busoni, Rachmaninoff, Horowitz, Gould) all mostly learned their technical skill at an early age and presumably forgot how it was acquired, if they ever really knew to begin with. Children (5-14 years old) are rarely interested in how they accomplish tasks or learn; that it can be done is delight enough.

Liszt did not record his method in detail, nor did Chopin. (Although, there supposedly was a manual of piano technique written around 1835 by Liszt for the Geneva Conservatoire, it has either been lost or was never actually written.) Yet, both revolutionized and generalized the possibilities in piano technique as much as Bach did in his exploitation of the thumb as a playing finger. To equal extent, Beethoven also extended greatly the notion of what was considered possible. It was Liszt who finally put to rest the notion that the Hammerklavier sonata was unplayable. It is perfectly conceivable that Beethoven didn't much care about writing piano music in his later years and simply wrote music; how you managed to play it was your problem. Hence late Beethoven is not easy to play. What is particularly interesting about Liszt playing the Hammerklavier is that the technique required to play it, especially the fugue, is not one that comes from simple mastering of the elements of scales, chords, arpeggios, etc.; the technique requires a complete freedom of the hands at the keyboard that is not locked into any conventional of pianism. Technically, one might as well be playing the Sonata #2 of Boulez or the Klavierstuecke of Stockhausen.

Liszt learned the Hammerklavier while still a teenager, and this, together with the formidable challenges of its fugue, I believe had an influence on the conscious development of his own technique. This was before he first heard Paganini and resolved to do for the piano what Paganini had done for the violin. I think that Liszt would understand very well what I am trying to write and probably be one step ahead of me.

There is some second hand information in what the students of Liszt and Chopin said he said, but substantive detail is lacking. The disciples rarely understand the master. Chopin apparently inveighed against the method of practice whereby one could read a book at the same time. Assuming that he did indeed say such a thing means to me that he clearly understood that acquiring piano technique is as much a mental as process as it is a physical one. In playing scales Chopin also apparently favored a "quiet hand" and an evenness of sidewise motion of the hand, a "souplesse" or minimally tensioned state of maximal flexibility. His beginner's scale of choice was B major, since he thought this scale configuration was the one that most naturally fit the human hand and therefore was the best scale to illustrate souplesse. I've found no particular indication of what went on in Chopin's mind regarding technique. Generally, there seems to be reluctance on the part of pianists to describe what goes on in their minds in practice and performance. One can only conjecture reasons for this.

Liszt apparently took the position of piano practice with book reading seriously for a brief period, and then abandoned it utterly. This tells two things: first, in later life even Liszt was consciously unsure about how he actually learned his own transcendental technique; second, eventually he did figure something out. That he did figure it out is demonstrated by he his technical studies. These are practically unknown in the pedagogical scene and have only been recently published in their entirety by the Liszt Society. They have as central conceptual point that of full integration of fingers and specifically of both hands. His idea was the simple one that the human piano playing tools were not just two hands, but two integrated hands thought of as a single structure. One might take this idea to its ultimate ideal as full body mind and mind integration.

Liszt paid more attention to the idea of strengthening the hands and arm in his practice than did Chopin; but, one has to consider they played very different pianos. Chopin was a Pleyel player, while Liszt whenever possible, played an Erard. The French Pleyel had a much lighter action and a shallow dip to the keys enabling rapid passage work with greater ease (less force) than the Erard. It also had a thinner sound and a more restricted dynamic range. The Erard of Liszt's virtuosic days was much more like our modern concert grands. Relatively speaking, to play them required more physical strength than did a Pleyel. The modern grand requires slightly more strength yet. In this physical difference of pianos one can see a possible origin of Liszt's emphasis.

Though the music of Liszt is more associated with muscularity of technique, pieces of Chopin, say the Polonaises, F minor Fantasie, Scherzi, Etudes and the Sonatas, require every bit as much muscularity, as any pianist would recognize, for example, in the LH octave ostinato of the Ab major Polonaise, which happens to have an apparently independent analog in the Funerailles of Liszt.

I am approaching the problem of technique in essay as I have personally, not regarding the artistic ends to which the technique will be put. Therefore, the problem is considered as a problem of mental and physical discipline to gain a specific kind of conscious control over the muscles of hand and associated muscles. There are constraints imposed by the very nature of the hand that will be discussed and there are guides, not prescriptions, to the solution of the fundamental problem of integration based on known facts of neurology and brain function.

Ordinary gross body movement, say walking, is actually a very complicated thing involving very many muscles, agonist/antagonist muscle tension balance, balance of the body, with neuronal information flying in several directions and yet we don't think about it. It is a cascade reaction that was learned before we could even speak, with a nervous system that behaved (learned) in a very different way from how the conscious adult nervous system learns. The nervous system has not truly matured until about age 20, and is consequently up to that time still very much in a state of flux. There are milestones in the maturation process, one notable such being the bilateral specialization that takes place around the age of 5 or 6 years of age. On a gross level this has been called the "Age of Reason"; a provable connection between the neurophysiology and the gross observation would not be unexpected. A place for language and linear, analytic thinking has been neurologically established in the bilateralization.

                       Some Metaphors and Examples

There is a built in flexibility in the learned walking system that allows for new variations in terrain on which we walk, and new variations invented as a matter of volition. Much of the corrective and balancing variations come directly from the spinal cord as monosynaptic (very fast) impulses.

This is the kind of system we would like to have as a piano technique, but mostly we must develop such a technique with the adult nervous system.

I'm going to ignore the details of the physiological difference between a child's nervous system and a adult's nervous system, except to say that in a child, the neurons have not yet finished making their genetically appointed, axonal growth and connections. and environmentally modified synaptic connections. It is interesting, but I can't see anything relevant and practical being derived from knowing the difference. The point of view here is the learning by the adult nervous system. If the techniques of learning appropriate to the adult nervous system could be taught to children, it could raise the intelligence of the species enough to prevent its annihilation - a guesstimate. It's just not going to happen.

The simple surface difference between how a child learns and how an adult learns is that the child learns almost by sheer stimulation and sorting with little conscious effort, while the adult has to remember and and to create consciously, new conceptual and physiological pathways with deliberate and one might say more effort and practice.

The older we get, starting at about age 20, neurons of the brain die off and the more crafty we have to become in techniques of memory and learning. We are learning how to do something that is impossible for a child and that is how to manipulate and change our own minds/brains in a deliberate and conscious way. The more complicated the activity, the more sophisticated we have to be in using our minds. I've played with techniques for doing this almost since childhood, and found them very difficult to express in words, and also found very few people who were interested anyhow. But there are two "simple", yet connected mental activities that are involved: attention and internal visualization.

Before making something more of these two terms, I'll add one additional activity that is essential for mastering any complicated motor task, that requires speed and accuracy, and that goes along with attention and visualization; the activity is preparation. This is further separated into mental preparation and physical preparation.

A simple assertion without proof or argument: the methods of learning piano technique are exactly the same as the methods for mastering the physical and mental techniques of the martial arts, though, at the moment I cannot connect the metaphorical concept of 'chi' or 'ki' to piano technique in any clear way simply because I cannot see where it is or can be used, possibly due to experiential lack.

Now I will try to explain the practical meanings of the activities of attention, visualization, mental preparation and physical preparation.

Attention:
This very simple word is used in a fuzzy way to cover I would think many thousands of distinct states of mind that might be described by parameters such as mode (active/passive) or perhaps better (selective/nonselective) and size of the area of focus (pointed to diffuse) and of course, that to which "attention is being paid". Some states of attention can actually be recognized in the patterns of an EEG, by an enhancement of the classified waves of certain frequencies, i.e., alpha, theta or even delta waves, the later usually being associated with state of deep sleep. Alpha waves are enhanced in the Zen practice of zazen; theta waves are enhanced in shamanistic trance. In a mundane state of consciousness, the mind becomes habituated to a repeated auditory stimulus: the response seen in an EEG becomes less and less with future repetition. The mind tunes the stimulus out as not being important. The mind of a Zen master in zazen does not tune the stimulus out and his EEG response remains with every repetition the same as it was the very first time. The mind of Zen master in zazen is tuned to the moment in a receptive state. His mind is not wandering in memory of the past or meditation on possibilities of an unknown future; it is rooted in an ever renewing present, remaining physically aware of all stimuli. The "attention" is narrowed or selective in time, but diffused over all sensory awareness.

The kind of attention that you want to cultivate as a pianist is not unlike that of Zen master. The difference is that the object of attention is selective, and involves the piano keyboard, auditory awareness, and both hands as a unit together with finger substructures and physical state. That sounds like a lot to keep track of; it is. But, the human mind can do some pretty remarkable things.

Have you ever been "day dreaming" when someone who recognized the state by observing physical symptoms said "pay attention"? The fact is that you were paying attention, in way that didn't suit the psychological needs of someone else. The translation of such a demand is to pay at least simulated attention to a person, the words spoken and the vocal inflections of intimidation and implied threat. Obviously this is not a useful or productive kind of attention.

In the terms that I've use above, try to describe the attentive state of day dreaming allowing for all the variations that might be present.

For anyone who drives an automobile properly, there arises a state of attention that is quite different from the mundane state of attention, which is mostly just distracted. In driving, distraction can be lethal. The knowledge of that can induce the driver to adopt a diffused but still focused attention on the road ahead, and vehicles behind and on the side as well as potential movement of vehicles entering and leaving the stream of traffic, not to mention road feel, feedback from the driven vehicle and host of other aspects of surroundings, and all pretty much simultaneously. Here is a mundane example of a diffuse and yet focused attention or awareness that is very much unlike the requirement in the admonition or command "pay attention", and yet very much like the sort of attention appropriate to piano practice. The following is a continuation and expansion of the attention concept into the notion of thinking.

               Thinking and Hemispheric Specialization:

What is normally considered thinking, as opposed to the noise of internal rumination, is analytic problem solving. The problem is well posed and there presumably exists at least one given method of solution. This thinking is primarily logical and deductive. No all problems are amenable to, nor solved by deductive reasoning alone. Some inductive reasoning is always necessary since knowledge and information regarding the problem at hand is never complete in real life even though it may be in a textbook problem.

In most righthanded people, the analytic, linear, deductive, form of thinking seems to be located in the left hemisphere of the brain which would then contain Broca's area which functions as a formulator of linear language and Wernicke's area which functions as a decoder of spoken language.

The right hemisphere which is connected to the left hemisphere by a thick neuronal "cable" called the corpus collosum, seems to operate on possibly different principles of organization and has functions that include: the recognition of faces and forms, the creation of graphical images, and in some illusive way, the apprehension and creation of abstract forms in general the apprehension and creation of the local forms of music and sound.

There is an interesting and probably important difference, statistically, in the hemispheric distribution of activity that has been found between those who have been trained in music and those who have not. In people not trained in music, musical activity is generally restricted to the right hemisphere, while in those who have been trained in music, musical activity is distributed over both hemispheres. To what extent and how are the two hemispheric activities correlated through the corpus collosum? That is just a question, to which I have have no answer. The answer to this compound question must be rather complicated. It seems unlikely that the two activities are uncorrelated.

I suspect strongly that one would find in creative mathematicians, that mathematics is then also bihemispheric in nature, and that people like Ramanujan might even have a slight right hemispheric dominance in creative mathematical activity. Acts of invention appear to involve critical or analytic thinking as an act of selection against arising intuitive forms. It is not completely silly to expect that the manufacturing by the brain in the the right hemisphere may have a a certain amount of randomization in it just as there is randomization in the body's production of immune system antibodies.

The right hemisphere is often said to be the seat of the transcendental leaps that are completely necessary for the creation of the mechanisms that others use as deductive systems; I think there is probably some truth to this, but also think that this right hemisphere with a language of forms cannot function alone in a creative activity, but requires the left hemisphere to give expression to form, and that this is the "explanation" for music in musicians being a bilateral activity: there is a bidirectional communication between the hemispheres so that each modulates the other's activity. There is necessarily an analytic component of music to a musician or a musically cognizant person.

That the human brain or even the cerebral cortex is not just one ganglion but has areas of specialty goes, of course, further than lateralization as the existence Broca's area and Wernicke's areas indicate. A high degree of specialization can probably also be found in any mammal.

Vision:
Visual patterns are supposedly formed in occipital lobes which are directly connected to the optic nerves, in a crossed and complicated way. Evolutionarily, the occipital lobes are not new structures, and it is usually assumed that they play no important bidirectional role in the activities of the cerebral cortex. Neurologically, how is one to conceptualize the phenomenon of internal visualization? Close your eyes and conjure up the image of a loved one. Is this purely or mostly a right hemispheric activity? Does it also involve activity in the occipital lobes? Again, I don't know the answer to this question; what I do know suggests the answer to the second queation to be no. But perhaps someone more neurologically knowledgeable could cite appropriate research that gives an answer. It would be interesting to know, but the answer is not necessary for the following.

Visualization:
It is a common experience that people can close there eyes (as just an aid to minimize interference) and conjure internal images. Graphical artists use this ability and with them it would probably be found by virtue of practice and stretching of the ability and reinforcement to be more detailed and precise that in others. Is graphical art also a bihemispheric activity for graphical artists? "Look at the stone, and merely cut away what doesn't belong."

Thinking in pictures:
Thinking in pictures and thinking in abstract forms is still thinking, though it does not follow the patterns of linear deductive analysis of the left hemisphere, and the type of thinking that allows creators to make the leap of arriving mentally where, perhaps no one has been before. Things are seen to fall into place by form, not by logic, and understood to be "true" or in just proportion; the problem remains of convincing one's self and others of that truth by expressing its necessity.

Composers speak of solving compositional problems, performers of performance problems. Such problems are very difficult to explain to someone who has not experienced them just as a problem of mathematics (or the aesthetics of mathematics) is difficult to explain to someone not experienced in mathematics. Though the problem is difficult to explain in arts and sciences, the expression of the solution is available to anyone who sees, hears or reads the appropriate language. How difficult it would be let someone experience the beauty of a poem by Goethe when they don't know German, of Lermentov when they don't know Russian.

It is actually only through the solution that one can infer and thereby understand just what the original problem was, and this is an indecisive method of getting at the problem at best. So, the problem as seen by the solver is not necessarily the problem as later defined and explicated by history and folklore.

A right hemispheric process must be read by the left hemisphere in order to communicate the discovery and it must be done in an analytic and linear way. Translating between these two modes of thought is almost never easy. How often does one "have a thought" and then have difficulty in "putting it into words"? Understanding the truth or "justness" of a proposition or solution and providing the unassailable proof of it are two vastly different things. The very providing of the proof is yet another act of creation and requires the form sense of the right hemisphere as well as the syntax of expression. Similarly, the left hemisphere must be read by the right hemisphere else the right has no coordinated direction in its own brand of thinking.

Whether or not this hemispheric division of labor happens to be a strictly true picture of neurophysiological reality is practically irrelevant. The exact truth would leave one engulfed in its details and leave precious little power left for using the metaphor. What, of all our so called knowledge is not metaphor and model? We call it knowledge because it is useful to our purposes. The purpose may be to create more metaphor. The purpose may be to create art, build a bridge, increase our pleasure, communicate some useful thing to another human being, receive a useful thing, or send a man to the moon. There is always some form of utility and purpose to knowledge. The metaphors I speak of here have been useful to me personally and I see that they may be useful to someone else.

A Linguistic Digression:
The verbs "to know" and "to say" in English are remarkably sloppy and imprecise given its overly large vocabulary. Many other languages make fine distinctions as to the origin or state of knowledge that is purported to be known or communicated. Romance languages make the distinction between knowledge of fact and knowledge that is acquaintance; almost similarly in German "wissen" and "kennen". Such distinctions made in Cherokee are far more subtle and demanding, so much so that it has been said that it is almost impossible to lie in Cherokee; the very structure of the language demands specificity. Perhaps making Cherokee the official language of the US Congress or government in general wouldn't be a bad idea.
End Digression.

As a general rule, any real life situation there is necessarily an interaction of form or synthetic thinking and analytic thinking. Regarding music, for a musician, music is a definite part of real life; possibly, that has bearing on the bihemispheric activity involving music that appears in musicians; and with fair probability, similarly regarding creative theoretical scientists and creative artists in general. Scientists are much like artists, their constraints are, however, more severe.

A musician whether composer or performer has problems to solve: for a composer, what notes or events follow what notes or events, how does a local event terminate, and generally the very nonlinear problem of how all events somehow fit together to make an integral whole that is the architecture of the piece; for a performer, there are the questions arising from that which is unwritten by the composer concerning dynamics, articulation, tempo and phrasing. These choices are not arbitrary and follow a kind of nonlinear logic that is perceived by the artist through an understanding of form that is anything but deductive. It is more like solving a knotty puzzle: finding a piece with certain properties that fits in a specific environment. By examining the logic of a composition, I've seen errors of pitch in scholarly editions of Bach that have been in print for over a hundred years. The error is an error simply because the composition taken as a whole declares it to be so. Art, particularly music, is about as arbitrary as mathematics.

A Note on Deductive versus Inductive logic:
Deductive logic, by definition, reasons from the general to the particular. Guessing that a particular must follow from a general axiomatic system is a matter of logical art. When the particular is proved as a theorem, the matter is in essence dead, excepting other creative proofs of the same particular. One might claim that the particular is already contained in the general, in principle, and so in one sense deductive logic is a dead thing. This is true but for some mitigation:

Proof is act of creation:
Generalities given as axiomatic systems, of "sufficient complexity" are incomplete, which is to say, given the axioms and accepted methods of deduction, there will be "true" propositions that cannot be proved. This actually describes Gödel's first incompleteness theorem. When propositions can be proved and can then be called theorems, a sequence of logical steps getting to the theorem must be invented; I say invented, and not discovered because the sequence is never unique.

A Note on Making Hemispheric Connections:
How the hemispheres are bilaterally involved in a specific activities or task seems to be a matter of training as well as a probable genetic component, and in general, since any acculturation being also a training, be also a matter of culture. Jaynes, in his "The Origins of Consciousness in the Breakdown of the Bicameral Mind", argues that modern consciousness actually arises from just such a connection being made and then transmitted as a matter of culture.

Most "methods" of piano training take a very physical view, consistent with the notion that playing the piano is some simple motor task that can be drilled into the nervous system by mere repetition and that some correct ritual form must be followed concerning the wrist position or attitude, finger curl, and other purely physical matters. If one were simply to look at the videotaped performances by Rubenstein, Horowitz, Gould, etc., it becomes apparent that all of these correct hand and motion forms are all being utterly violated, and would have most conservatory teachers into a paroxysm. The classic response from many teachers of piano when confronted with this contradiction is: oh - well, that's X, he was a genius and ..... The rest is inconsequential, and you, whoever you may be cannot be one of these legends, so you must conform to the rules which govern mere mortals. Such an answer is neither satisfying nor constructive, and still leaves the essential questions unanswered. Musicianship is neurologically speaking a bihemispherical activity as is any creative process. Composing, performing and listening are all creative processes. Musicianship involves an understanding of all three. The "problem" of musicianship is then to figure out how to make what must be a bihemispheric process into a coordinated bihemispheric process, which is to say to make coordinated connections between the hemispheres of the brain. This problem also seems to be the problem of "being a mathematician". In both cases, the standard education takes the easy and fruitless road of addressing the analytic left hemisphere only. There is a difference between knowing music/mathematics/art and creating music/mathematics/art.

Suppose one wanted to make some guesses as to what, neurologically, is involved in a piano technique. If some idea is had of that, then there is some hope that something sensible might actually be said concerning acquisition of the skill. At very least, some ruleouts may be possible.

There are a few things that are clear from history and experience without much learned searching: piano technique is not innate, is not acquired by magic, and does indeed require practice and repetition; it is not generally easy and requires work. The real question is what kind of work? What are the signs or criteria for good, which is say, effective, practice?

I don't seriously think that I know all that will be physically good for any given student of piano, since that depends on too many factors. I don't and can't give a method, in the sense of a recipe; I don't believe that such a recipe exists. Putting experience, neurology, psychology and little logic together does seem to give a clue as to what is involved and what criteria a dedicated student might consider as a metamethod or system of criteria for determining what to do and how to do it, or perhaps more simply put, how to recognize and solve the technical problems that arise during the process of learning.

The metamethod, in distinction from most piano methods, will focus not on physical processes, but on mental processes which are much harder to communicate: to say "hold your hand so" is much clearer, but useless, with example that to say "think so", "perform the following mental operation", or "put yourself in the mental state X". Clear examples cannot be given for things mental. Nevertheless, I will try using analogy and metaphor, and see what comes of it.

   Observations:

   First let's collect some facts of life by history and observation.

   1) Technique, as well as musical maturity are acquired hierarchically.
      An initiate not only could not start by playing Beethoven's
      Hammerklavier Sonata or Liszt's B minor Sonata, but would probably
      not be able to make any sense of it anyhow.
      It takes experience and practice in listening to hear all the voices
      of a four voiced fugue; it is not something humans are born with.
      If you can't hear them, can you play them properly?

      Here, I confess a bias in taste: "properly" is with the independence
      clarity and distinction of contrapuntal voices together with the
      musical cohesion as Gould achieves.  Playing music is all about
      expressing or projecting the form inherent in the score.

   2) Playing any given piece does not mean being able to play any other,
      both musically and technically.

   3) Sightreading is a distinct task and must be cultivated and learned
      separately.  However, a good sightreader, can play any score within
      technical limitations.

   4) To a master pianist, the act of performing is often not a completely
      and complete conscious activity.  I've known musicians who are playing
      wonderfully on stage, but whose mind is also considering what to get
      for food after the concert, weighing whether pizza would be a good
      idea.  I somehow doubt that this was the case with Gould, who was
      so completely engrossed in what he was doing that he was even oblivious
      to the fact that he was conducting and singing at the same time.
      By direct observation, Rubenstein was either absorbed in what he
      was doing or paying attention to the audience as much as they were
      paying attention to him.  Each has a unique mental pattern; but,
      the interesting point is that neither full consciousness of music 
      nor of physical execution is apparently necessary.

      I am using inferential logic here based on observations, and
      my assertions must looked at circumspectly and questioningly.

   5) A chamber player or concerto playing soloist is paying attention
      not only to what he is playing but to what others are playing,
      balancing, weighing, adjusting, sorting, anticipating as the
      cooperation continues within the form of the piece.

   6) There is a story, apparently with corroborating witnesses, about
      Liszt sightreading the Grieg concerto while making a running commentary
      on the score which he had never seen before.
      It is normal for people to walk, talk and think at the same time;
      however, note the impairment of thinking and even talking if the
      walking is done on a crowded street where one has constantly to avoid
      collisions.  The act of walking has acquired a complication that
      some people adjust to by exposure and practice.

      Activities and thoughts can superpose, but there is an individual
      and circumstantial limit to the degree to which such superposition
      is successful.

Neurology:

Proprioception:
To the present point: how does a person "know" where his hands and fingers are? Position sense in the hand is redundantly give. There are sensors in the joints and there are also sensors (Golgi tendon organs) in the tendons of the hands. The Golgi organs as well as the joint sensors fire or respond to changes, which is to say movement. With stillness, regardless of conformation, the sensors will stop firing and stop feeding back information on position to cognitive faculties. This situation is not unique to the hand. This information of position is constantly being fed back to the brain or spinal cord during motion, and yet, we use very much our visual cues to accomplish proprioception. A pianist does things that are of such complexity and rapidity, that normal ocular visual cues are not enough.

What must be refined in practice in a pianist is the brains decoding of the sensory cues as well as an internal visualization that can operate with greater rapidity and complexity that a vision that uses the bulky ocular vision. This is metaphorically using the speed of a CPU of a computer rather than processing in some slower peripheral device. Ocular vision is necessarily stuck in the present moment while an internal vision is not only not stuck in the present moment, it is not even stuck in a single moment, but can be spread over an anticipated time. Entire passages, pages or even movements and pieces can be grasped and anticipated with internal vision. The trained ability to do this is clearly also a form of memorization.

Superposition:
Does the brain actually superpose cognitive tasks or activities? From the above examples, the answer is yes.

Are tasks categorized so that different categories can be superposed but, two tasks in the same category cannot? Or, is this just harder and another task to master: think of a translator between two languages - a good one can listen in one language while speaking in another. This is a special a task as sightreading or transposing while sightreading. Even people who are genuinely bilingual or multilingual have difficulty doing this unless they have trained themselves to do it, so as to act as translators in informal situations where the speaker whose words are being translated is oblivious to the ongoing translation, e.g., U. N. translators.

Alternatively, does the mind act line a computer's CPU in a time sharing system, which actually only does performs one task at a time but which switches between tasks do a little bit of all required tasks in such a scheduled way so it appears that all tasks are being served simultaneously? Nature is filled, and human minds are filled with illusions of perception. Computer software continues the trend.

The brain has a division of labor that goes beyond division by hemispheres, so that many primitive activities that are highly localized can be coordinated to form complex activities that are also servomechanistic. Some long term memories are actually encoded at the molecular level; you can't much more local. These localities and the divisions of labor easily provide for the independent/coordinated superposition of activities of the brain.

Superposition of neurological activities is not the same thing as superposition of cognitive activities, and yet there is also indication of of just such superposition. From the localization of neurological activities one can infer their superposition in time. From experience and observation one can infer similar superposition of cognitive activities.

What seems to be the case in cognitive functions is that while the can be superposed, there is a necessary prioritization that goes with that superposition, which is to say they are also coordinated. One and only one cognitive activity is dominant at any given time. One and only one cognitive state is dominant at any given time. Here the concept of time sharing comes into play. The important thing for a pianist is develop a wide repetoir of cognitive activities and states which involve bihemispheric connections and activities.

If every act of a pianist were indeed sequentially volitional, in a simple sense, piano playing would be quite impossible: from perceived volition to action requires about 0.20 seconds, which would leave an maximal theoretical limit of 300 sequential notes played per minute. Any professional pianist can do better than this since it means playing 16th notes at mm quarter note=75. That each note is a separate and independent volition is an untenable hypothesis. I have not even taken into account the complexity required in the performance of complex counterpoint.

There are two ways to alter this hypothesis: one is by invoking an intervention by quicker response that would be provided by the monosynaptic reflexes of the spinal cord; the second is by allowing that volitional actions need not be sequential, and that there is no prohibition on the superposition of volitions, though there may be a limitation. Reality always involves limitations, which is why thoughts of magic, however unrealistic, are often emotionally preferred, and unfortunately believed.

No matter how useful volitional or reflex acts are parsed neurologically, the resulting model is overwhelmingly complicated and it is obvious that the act is not expressed in an act that controls the maze of complication in detail. There is instead a neurological cascade effect where something triggers a chain reaction or cascade of neurological firing that ends in the desired complex effect. The intermediaries of the cascade are established through practice and training. But, there must be that initial neurological event that is the trigger. Reflex is relatively speaking, easier to understand than a volitional act, which may or may not have a physically discernible result: the result may be a "mere" thought. There are physical and mental reflexes that have as trigger some fairly simple physical or mental trigger. Some reflexes are essential hardwiring of the nervous system and others are learned. Many mental and physical activities have at the end of their neurological cascade, reflexes, which when physical are mostly monosynaptic (therefore fast) reflexes that involve the spinal cord directly and not the brain.

What is missing in this picture is the trigger for a complex task. My assertion on this is that mind uses a simple, but carefully nurtured metaphor with which it can deal effectively and usefully, often that metaphor is an internal image. Some voice teachers teach their students to visual their voice. Students of meditation are often taught to center or balance themselves. Concepts of center, balance, focus and rootedness are involved in the proper teaching of martial arts. Yoga students visualize the power of the kundalini shakti rising to excite the chakras. Mandalas and their cognates exist as explicitly geometric metaphors used in meditative forms. Images and sound appear in all human cultures where a change of consciousness or of mental state is involved. I have difficulty seeing this over and again and thinking that it is an accident. Images, our most powerful metaphors of knowledge, are so powerful that we internalize them as the trigger metaphors for complex thought and physical action. These are the internal things that we can deal with, and do deal with, even in such seemingly simple acts as picking up a fork or a glass.

The idea of explicitly using internal visualization in the practice of acquiring piano technique should, at this point, seem completely obvious, as if I have said nothing new or interesting, but merely excited an old memory. There is, however, a little more to the story that just saying visualize internally.

The existence, in music, of vertical events in the senses of confluent contrapuntal lines or chords suggests strongly that the notion of "instantaneous" pattern plays an important part in playing, therefore in technique and therefore in the practice that is to produce the technique.

Patterns of music are multidimensional and not merely vertical but involve dynamics, relative relationships to precedent and antecedent patterns, etc., and then presumably must at least involve the right hemisphere for both their perception and manipulations or transformations.

The Prepotential EEG in Volitional Movement:
It appears that for simple volitional body part movments, there is discernable potential rise in EEG as long as a half second before any actual movement. [See Emperor's New Mind] It also appears that volitional movements and the simple volition without movement, just thinking about executing a movement evoke very similar neoronal patterns.

Training the prepotential and facilitating neuronal pathways: - through the mental preparation process -

Standard Psychology:
There are plateaus in learning in general and there are plateaus is learning to be a pianist. If the plateau turns into a block, there is some problem to solve which will involve defining or understanding what the problem is and then finding a way through proper vivualization, and practice of mental and physical preparation to solve it.

Standard Epistemology:
Like most knowledge, pianism and musicianship is quasihierarchical, and builds expands from some fundamental foundation, sometimes altering extending and replacing the foundation itself.

                                 PRACTICE

The General Routine:

Mental Preparation: use of the prepotential without action. training in sensitivity to the prepotential and honing of that is the "secret" of a piano technique. There is, of course, no secret to the existence of the seemingly impossible: it exists. The secret is a general understanding of a metamethod by which the seemingly impossible is achieved; and, this is the subject at hand which I am trying to make as scientifically reasonable as I can. There is a long way to go for a "proof".

The question and answer that I'm trying to get at here is just how this training and honing can be accomplished

Physical Preparation: Occurs after the mental preparation

To try to give bones to the theory, I'll give a series of exercises, starting with the simplest, that can be applied with suitable changes to working at any musical material.

Exercise 1. [Awareness and Imaging]
Place both hands in some in some standard "five finger" conformation on the keyboard, e.g., C-G as in a C major scale. Close your eyes and let the hands relax as much as possible. The fingers are just barely touching their keys. Visual a focused attention on each finger starting at one side and working slowly, finger by finger to the other side. Work backwards. All the while, move absolutely nothing; only your point of attention will move. If you keep this up, you should become of aware of two things, 1) As you focus your attention on one finger, your mental image of the others will fade. 2) After a while you will evenetually loose the sense of where your fingers are relative to each other and even the mental image of your hand.

If 1) does not happen, two things are possible, a) you have already learned how to expand and superpose attention states and are probably a pretty good pianist already, or b) you are fooling yourself into thinking that your attention and visual imaging is the best you can do. With such completely internal subtleties it is very easy not to see what you don't see. Try harder to see the holes, lapses, droupouts or fadeouts of you internal imaging.

If 2) does not happen, you are cheating in absolute stillness. If you move fingers or hand, even ever so slightly, you will be exciting the proprioception sensors of both joints and tendons that will send signals to the brain about where fingers and hand are in space. If you remain absolutely still, these sensors will loose excitation and not feed back the proprioceptive information; that's just neurological reality. Perform this exercise with various hand positions in scale and passage segments and chords. Although, physically, you are doing nothing observable, which is the point, you are developing a mental foundation, and becoming aware by experience of proprties of mind and body.

Discounting problems 1) and 2), this should have been relatively easy. The ease is partially associated with the cultural ease of point centered attention and left hemispheric dominance. The next exercise complicates the first, by adding an action.

Exercise 2. [Isolating Mental preparation]
Use the same starting position as in the first exercise. Only now the notes will be played. As before focus attention on each finger separately, but for each finger, after attention is focused, visualize as clearly as possible what you would do if you were to play the note under that finger. Unhurriedly, rehearse several times what you would do, each time looking to clarify the image of the independent playing of this finger. You will reach after 6 or less such mental rehearsals a point of dimishing returns where no further internal visual clarification is had. Now, play what you just rehearsed, noticing how it conformed to your final best rehearsal. Just drop the finger and retract it; slowly, we're not going for speed here but rather clarity of purpose. Does the hand otherwise remain still? Is the action of the finger smooth? Assured? Without hesitation on your volition? If not try to get it as good as you can noticing once again a point of dimished returns. When that happens, move on to the next finger. For a variation, use other sequences of fingers than simply up and down.

While single finger attention is not hard, the eventual object is to have full unwavering attention to and visualization of both hands together and superposed, also supposed with simultaneous clear visualization and control over each of your ten fingers. I propose to get there by entending the point attention slowly by building ever more inclusive pictures and dragging new objects of attention into successive pictures as the building progresses. So we can start with uniting two finger attention states into one while maintaining the original individual pictures. This gives three supeposed states of attention.

Exercise 3. [First expansion of attention]
Use the same hand positions as the last two exercises. Pick two adjacent fingers, and work like exercise 1, focusing attention first on one and then the other, but alternate just between the two fingers. Remember this is eyes closed and there is no movements of eyes involved; it is all internal. Slowly increase the frequency of alternation, but while one finger is being focused upon, try to increase the attention and internal visual clarity of the other finger Perform the same with all 10 posible combinations of two fingers for one hand and then expand the set of fingers to both hands with 45 combinations. It's a very simple exercise and you can make a lot of soundless work for yourself. Expand this then to actual playing as in exercise 2, with two possibilities: play the notes together or alternately in an even 1-2 pattern or in triples, or in quintuplets or ....

Exercise 4. [Expansion of attention between hands, Symmetric playing]
This is the same as exercise 3, except that the thinking and playing involves symmetric or "mirror" playing. The hands are mirror images of one another and by playing mirror-symmetrically, and new kind of refinement of attention and criterion for internal clarity arises, namely the difference between what each hand is doing. The image of each hand is automatically a clarifier for the other. This is almost a sneaky trick to work on internal clarification. A C major scale, chomatic or whole tone scale beginning on Ab or D, or Persian mode (D Eb F# G A Bb C#D) are good starting material.

Exercise 5. [Further expansion of attention]
Use the same hand position as in exercises 1-4. Work as in exercise 3, but pull a third finger into the picture so that the three fingers are pulled into a consolidated picture while attention is also simultaneously on each of thne individual fingers. Use the method of switching back and forth beteen fingers and 2-1 combinations of them fuszzing the isolated pictures until there is a smooth solid image. It is important to prepare both mentally and physically, every action. Different combinations of fingers will be more difficult than others.

Continue the prococess pulling in an additional finger until there is a complete picture of both hands together with each hand seprately and each finger seprately. This is much easier said than done. Patience, attention and time. When things start to slip in your mind, go back to something easier. Playing notes without strengthening the internal control images is a mistake and more than a waste of time.

Exercise 6. [Keyboard independence - flying passage work]
Here, understanding and fluency, not perfection, with exercise 5 is assumed. The following should be performed first slowly, by looking in order to establish references and gauges; second by looking away and stealing quick glances to restablish orientation when the internal images fail; third with eyes closed and no visial feedback at all.

Pick any scale or passage segment. Keep the hands above and away from the keyboard. Think of which finger in each hand will go to the starting note. Spread the fingers of both hands. Visualize the complete two hand picture. Think about flexing the begining fingers. Flex the begining fingers, in preparation. Now, move both hands down to the keyboard so that the two fingers come just into contact (with assurity), but without playing the notes. You will work on trying to make this motion (physical preparation) as quickly and as accurately as possible through mental preparation (rehearsal) of the movement by also varying your initial position and trajectory of approach (from above, from L from R) all combinations and everything in between. After every approach, lay the flexed finger into the note, playing it. Immediately extend and retract the finger while the hand move back to some initial [position in preparation for the next note. Procede in the same manner, note by note. Vary the initial position for any note so that it becomes arbitrary. Work toward doing all of this with eyes closed, visualizing hands, fingers and keyboard.

Exercise 7. [Hand positions in pasage work]
Use the same system as in exercise 6, but have two fingers arrive at two notes *simultaneously*. Increase the number of fingers and use various combinations of however many fingers you are working with so that the hand and its control pictures take into account the keyboard, but are not bound to it. While doing this expand and stretch the hand or close its conformation. The accuracy should not depend on any specific hand conformation. Start this very slowly so that every motion of articulation and retraction is deliberate and conscious.

Exercise 8. [Hand positions in chords]
While exercise 7 was concerned with scalelike material, execise 8 is the same, but with chordal material which will sometimes use all 5 fingers of a hand, and sometimes only a subset.

Exercise 9. [Chordal artriculation]
Pick a chord, any chord, preferably both hands Spread both hands for the chord and rest the fingers of each hand lightly in position. (personal preference is ninth chords); use the same chord in each hand or arrange mirror symetrical chords. Now divide the fingers in to sets I and II. Play the alterations in both hands of set I and II using mental preparation. Keep minimal tension and sometimes maximal temsion in playing of the sets. Use all possible combinations for sets I an II. Divide further into sets I II III and work similarly.

Perform any exercise, not as a physical rote exercise, but as an exercise for mind and body, making as much distinction and variation in touch, speed, dynamics, rhythm as can be conjured and invented. For any session, there is as in weight training a point of failure. Learn to recognize it and desist; you would be wasting your time.

Considerations of The Purpose of Scales:
The playing of scales has been part of every keyboardist's training, and there are two ways to look at scales: 1) as boring and mindless repetition, which should be avoided; or 2) as a particular kind of exercise that has a value that must be discovered.

Because of the ubiquitous nature of the exercise of scales, I would prefer the second attitude as being more valuable, no matter the ultimate conclusion one comes to.

The usual explanation for scales, chords and arpeggios as being good exercise is that musical material is made up of these as components, and the reasoning goes that if you master these elements then anything which is composed of them will come much easier ounder the fingers. That may have some truth, but I see another reason. The practice and performance mindset is not an ordinary state of consciousness.

One of the traditional methods common to many diverse cultures of inducing an altered state of consciousness, particularly that of a shamanistic type of light trance is repetitive sound that becomes familiar.

I suggest that this purpose can also be served through the attentive playing of scales. The practice can also serve simultaneously as a physical warmup and as a psychological cue.

More on Flying Scales and Passages
In this type of practice, the speed and accuracy, of positioning the fingers of each hand just touching the destination notes is point. Bring the hands as much as as a foot or two from their intended destination and again internal rehearse the motion, spreading and keeping the attention over both hands while the appropriate fingers are being singled out.

Obviously, the idea can be extended to any type of exercise or passage in any composition.