The single plane theory part two- plus levers

(note that this had originally been the "two planes" theory- had you read part i, before I added slight corrections. Thanks to those who pointed out the careless error in distinguishing between the two dimensional nature of a "plane" and the one dimensional nature of an "axis". This has now been fully corrected, although I can assure you that this careless error in terminology does not affect any of the practical issues)

In this post, I will be looking at the results of the pencil experiment and exploring the nature of levers- all the way from the finger to the shoulder. In particular, at the end I'll be introducing an idea about how to balance the whole arm and finger as one unified mechanism- with low effort and very little inherent complexity. The specific aspect that I'll be describing this is not something that I have ever encountered in a book on piano technique or heard spoken of by any other teacher. However, I am absolutely convinced that I am looking at one of the single most important things that just about all great pianists have had in common- no matter how diverse their techniques might appear to be on the surface. In short, it's a way of relating the finger to the arm- within a sustainable quality of balance. In this balance it is possible to absorb the forces that the keys respond with despite scarcely any change in state- yet the finger does not have to support excessive levels of weight at the keybed.

Anyway, first it's back to the pencil experiment, for the results and analysis. Hopefully you will have found that the most efficient means of moving was to get the pencil to exert a kind of "pull" upon the key, in which the direction of the force was constantly changing- rather than a push that involved driving the pencil in a single straight path. If you didn't, that's nothing to worry about, however. I'll try to illustrate how this action can be acquired, right now. Note that, although we're sticking with the pencil for now, this gives a prior illustration of many of the concepts which we'll be applying directly to the finger, within future posts.

One thing that we can write off at once is the worth of adding a third axis of forces and movement. Mechanically, anything sideways contributes nothing of any benefit to the context of playing an individual note. This illustrates the value in generally striving to line up properly behind each finger, in order to keep the activity almost solely within a single plane (that consists of both the backwards/forwards axis and the up/down axis). Basically, it serves no purpose to direct any movement or forces sideways, and neither is there any reason to align the pencil anything other than parallel to the length of the key surface.

More about how the arm must be involved in the considerations later in this post, but the finger itself can make direct transfer of energy, when aligned to act within this plane. In fact, the closer it is to this alignment, the easier it is to integrate its action with the arm. This provides a very strong argument for judging the hand's alignment as a whole from the weaker fifth finger. It's a common fault to find pianists who put their strongest and most agile fingers in a perfect line to play- yet leave their weaker fourth and fifth fingers in a far less suitable position. Why would you want disadvantage your weakest fingers of all, by putting them in a position where their natural path of action is not even close to the plane of the key? Nowhere is it more important to fit the finger's path to the key's path than when it comes to the fifth finger. Slanting can easily lead to a vicious circle of inactivity that perpetuates the belief that perfectly capable muscles are weak- by preventing them from carrying out their natural purpose. Without adequate alignment in this plane, comfortable finger staccato from the fifth can become little short of an impossibility. Of course, you may not have the option of aligning right behind the fifth, at all times, however- especially if you have smaller hands. Keep the single plane action in mind as an ideal to strive towards whenever possible. However, in future I will talk in detail about the best way to set about activating the fingers effectively along less direct paths- which sometimes becomes nothing short of a necessity.

Here are two views of a rather lazy fifth, at an angle where it is collapsing flaccidly onto its side:

and here are two of a supportive fifth finger, the activity of which acts almost perfectly within a single plane:

I think it's pretty clear which one looks like a real pianist's hand and which one looks like that of an amateur! However, if you tend towards a lazier fifth finger- please don't suddenly go pulling the hell out of the key just yet! It's important to be gradual and patient about making such adjustments- especially if the muscles have scarcely done anything before. Bear this principle in mind, certainly, but I'd advise you to wait until I've covered the nature of what makes for healthy finger action, before you go for any drastic adjustments.

Anyway, within the plane of activity, the pencil basically rotates around the point of contact against the key. Although I don't want to get too carried away with analogies, notice the very obvious relation to a see-saw. The more you feel the end that you are holding onto is going upwards and forwards, the more the other end is felt to pull down and backwards at the point where it meets the key. This introduces a danger of slipping, of course- so you have to be careful to feel that the point at which the pencil meets the key remains stable. Initially, it's not a bad idea to rest the pencil lightly against one spot and simply rotate it around that single point, without moving the key at all. Feel the circular path around the point of contact:

If you do find it hard to avoid skids, this is a very good way of sensing how to keep the contact stable, as you begin to apply bigger forces. When the end stays in one spot, you should find that the pull on the key is extremely productive and that there is very little thud, no matter how strongly you pull. If you feel a thud, are you sure you didn't start aiming the force right down and only switch to levering AFTER the key landed? Note how there is no feel of changing the movement either during the moment at which the key lands or immediately after. The follow through is not felt differently to the act of pulling the key down to the bed. You just want to keep smoothly drifting through and beyond the time when the key has landed, before you even think of stopping. If the circular motion around the end of pencil has to progress as smoothly as possible, you cannot 'dig in' with any impact. Sometime, just concentrate on the smooth path of the pencil above all and see if you can deliberately take all focus away from the idea of the moving the key down. Strange as it may sound, this may improve the action. Forget the idea of "down" altogether and just let that part happen. Notice the circle that is initiated as a forward and up movement. As described in the last post, however, practise changing your perspective back and forth. Sometimes return to thinking about the down and back action at the other end of the pencil. See if you can gradually combine both perspectives into a single, consistent motion.

Notice how this is NOT perceived as a "tension and then release" style of movement! Basically, if you feel you have endured enough of an effort that you need to willfully release something afterwards, the movement really wasn't anywhere near good enough. It should have felt effortless all the way. So, relax by all means. BUT THEN GO BACK AND IMPROVE IT!!!! You have to be patient but, in the long run, no other intent will do- assuming that you hope to progress. Virtually all healthy base movements are felt to be continuous and all good pianists are certainly capable of doing them whenever required- even if they don't use them for every single thing. If you can't get something continuous, go more slowly until you feel that it is slow enough to be executed entirely without any bumps. This literally applies to even a single note, whether it be sounded with a finger or a pencil. Comfort must be maintained at all times- not habitually lost and then reinstated! If you think that's fine as your fundamental basis for moving a key, you might as well say its fine to routinely walk headfirst into a wall when you meant to pass through a door- as long as you wipe up all the blood from your nose and take an aspirin straight after. It's not fine at all to repeat errors. If you want to learn anything from mistakes, you have to understand that you have indeed made them. "And then relax" is far too forgiving of excess effort- even if it seems to promote relaxation on the surface. It can lead to a perpetual cycle of error- correction -error etc. rather than error- correction- correct movement.


So, did you find a comfortable movement that produces a sizable sound without impact yet? If not, I wouldn't be too put off, but hopefully that should have led to at least an improved understanding and feel for the gradual nature of high quality movements? We don't want any stops, starts or prods in the foundation level of movement. Incidentally, the exact angle may not be the same for everybody- although it should most certainly involve levering the pencil in the general manner described. If not, keep working at it! The point was not to find a single absolute angle- so you might tell all your friends that the "correct" angle at which to aim the finger into a piano key is precisely 10.2453 degrees off the vertical, or whatever else. Far from it. In fact, the exact angle of force should slowly and smoothly be changing, as you move around the circle and depress the key. Even with the pencil, it may well be dependent on such issues as the mass of your arm, the height of your stool and many other variables. This is why advanced mechanics is futile- it's just too precise to translate. Looking at things from more basic principles can actually be a lot more revealing.

If you were expecting geeky calculations or simplistic, hard and fast answers, you've misunderstood the purpose of what I'm doing here. The idea was firstly to challenge the tendency towards downward assumptions about the movement- but above all to help you to FEEL your way to a more productive path. As, I've said, this is not about cold exploration of theory but rather the practical applications that derive from it. Theory does not provide absolute answers, but a basis upon which to have a clearer idea of what you are trying to SENSE within your own feedback loop! I really do advise being thorough with these exercises and taking care to follow the detail in my descriptions. There is really very little to learned from the theoretical description if you do not use it as basis from which to improve your perceptions, so please don't waste your time reading this without doing the exercises! 

One reader told me that he felt the exercise was "worthless" because I didn't state the conclusions straight after and because I didn't explain why you should avoid what is "obviously (...) the easiest way". Well- if you don't even follow the description of the exercise thoroughly enough to realise the fact that aiming the pencil straight down is NOT the easiest way of moving the key, it certainly is "worthless"!!! Try it for yourself now. Just how stiffly do you have to hold the end of the pencil when aiming it straight down, without the end that contacts the key being greatly repelled? It is far more valuable to discover things through experience, than be told them. I cannot provide anything useful to anyone who doesn't put a great deal of effort into bringing their own perceptions to the practical elements.

Anyway, let's look more at the nature of levers, with reference to the arm as a whole. Imagine a series of hinges that connect  a series of levers. Let's say that one free hinge is fixed to an immovable point on a wall but that the others are all entirely free. Of course, everything collapses downwards:

Let's say we need them all outstretched. what if we fix the first hinge in place? The rest still collapses:

Very little benefit came. We can now add an extra internal force to stop the next hinge next from collapsing:

But the rest still collapses etc. Eventually if EVERY joint is fixed into place it all balances- as a single fixed structure, with very limited movability:

Now let's say that we start from the far end now. You pick the end up and walks away from the wall. It can momentarily 'hang' between the fixed point and the supported point. Walk far enough and you get to a point where it is fully supported in every joint without any internal forces having to be generated to stabilise the hinges. The hinges are tightened solely by the pull from the far end, coupled with the stable point of attachment at the wall. Alternately, you could leave just a slight trace of slack and EVERY joint would still be freely moveable, rather than tightened stiff. In this state, everything is "hanging" freely between two points- not being stiffly held together with internal restrictions.

(From another perspective, you could also imagine taking a long heavy sword and holding it horizontally, without any support beyond your grip. It is far easier if you rest the end even very lightly on something- giving support via two points.)

Let's now translate this idea of spreading support into a two-sided balance into the rather similar situation of an arm at a piano.

It really is quite similar. If we only supported at one end here, the elbow could only be stabilised in space via muscular effort, to prevent the gravity pulling it through the marked circular path. But then if the elbow joint were to release the forearm, the wrist would still plummet. It's a similar case, where if we start only from the shoulder end, EVERY successive joint must become be supported by an additional internally created effort, one after the other. Joint after joint is held up by effort, unless the finger is able to create a point of support. However, the moment the finger starts supporting something, the elbow and wrist can become truly free hinges- with zero internal effort! It's like a chain that hangs between two points of contact. The moment the finger plays- the arm can theoretically become wholly supported without internal efforts to fix the joints. ( although, we're likely going to want to reduce the workload upon the finger by taking some extra support at the shoulder) If the finger sets up a point of stable contact between itself and the key, it can pull in a way that would draw a loose arm forwards. This means that the upper arm can release a little more. If we take the component of force that pulls the elbow backwards and match it to the one from the finger that pulls forwards- the whole mechanism is supported. It's also VERY simple as we only have two inherent variables to balance- how much the finger is acting and how much the shoulder is supporting/releasing to balance that via the elbow.

To put that in the simplest way, basically the finger tries to pull them arm lightly forwards and upwards (via the same kind of path we see from the pencil experiment) and the elbow is released enough to pull lightly backwards in response, via gravity's action. Rather than cause the arm to actually move,  this 'tightens' up all the other joints, so they can remain still despite hanging freely (rather than be held immovably via muscular efforts). If this sounds like hard work, let me stress a few things- firstly, it really isn't! The shoulder can still support plenty of the arm's weight. We don't have to rely solely on the fact that the arm will not detach at the shoulder and let it hang completely. It can take on as much or  as little support as you like. Also, this is totally different from the manner in which traditional arm weight technique is based on downward thinking. The down forces supported by the finger are actually rather slight. The finger really doesn't have to bear that much weight for this to balance. It just has to match to the feeling for how gravity is pulling lightly backwards upon the elbow. With regard to this backwards and forwards element of the matching forces- it's really not equivalent to the whole cast of "The Expendables" getting together and having a tug-of-war using a  steel rope. The amount of pull required from the finger (in order to keep the wrist absolutely free of internal tensions) is very slight. It's not so much tightening the free joints, but ALMOST tightening them- so there's a feeling of "hanging" with a touch of remaining slack. Despite no muscular holding, the wrist cannot sag into a collapse. It is held up by forces elsewhere which are just enough for it to be supported. I'll be giving a practical exercise to show exactly to perceive this free state in my next post.  

The notion that the fingers should not contribute to support (but might be better off 'relaxing') after having struck a key is often expressed. But lose that support and you lose the two-sided balance! Even if relax means 'and then be comfortable' why were you ever uncomfortable??? Too much weight to support? Too much willful arm pressure? Whatever it was, none of these things should ever get in the way, if the goals are clear. Once more, what use is a poor quality of motion followed by a vaguely focused attempt at general release supposed to be? The real question is- why did the intention of both starting and finishing with a low effort balance go wrong? To explore that is the simplest and most likely solution. To look at it in terms of generally hoping to relax without even paying attention to the means of low-effort balance seems truly ridiculous, when viewed in this light. Why not focus on creating a comfortable two-sided balance between the a smooth low-effort finger action and a feeling for how gravity pulls the elbow backwards to balance? It's vastly simpler than just thinking "relax" without any specific positive intention. Relax carelessly enough to remove the most useful forces and you simply direct a need for effort into something altogether less constructive. That can actually cause MORE tension than if you start from a natural low effort movement with a clear goal in mind.

Also, note that I have yet to introduce the reaction forces that are generated by movement of the keys.When these are introduced, I'll go on to illustrate why the one-ended model requires rapid and complex changes in state, if it is to avoid heavy impacts. Conversely the two-ended support system is able to absorb reaction forces with minimal changes of state. 

Anyway, that is the basis for this model. In my next post, I'll be giving a series of extremely specific practical exercises to prepare key elements of the arm's role- so as to permit the a very low effort means of perceiving and controlling the release/witholding of  weight.

Improving movement by understanding duality of forces, plus issues of momentum

Before I come on to the second part of the post about feeling movements within one plane, in this post I'm going to illustrate how qualities of movement can be informed and better understood with regard to some very basic scientific principles. Firstly, I'd like to talk about the idea of equal and opposite reactions- with regard to acquiring a dual perspective from which to better perceive movement, rather than the one-sided view that typically evolves. I believe that this concept can be a tremendous aid to building efficiency and comfort in movement in general. Although this post will read more as an introduction to a global concept of movement (rather than contain anything immediately specific to piano playing), bear in mind that the principle will recur in a number of especially specific descriptions of the end product.  

"Every action has an equal and opposite reaction", is the slightly simplified version of Newton's law that is usually quoted. As an example, by jumping in the air a person displaces not only themself, but also the planet. There's no need to be alarmed, however. Being rather substantial in mass, the planet is affected really rather slightly (its acceleration being equal to the small force divided by the planet's huge mass). So there's no immediate need to fear that the earth might begin spiraling rapidly into the sun, should too many people take up aerobics. In fact, it's also true that when falling back down, a person's gravity draws the earth faintly towards them- basically cancelling out the effect of the jump. Anyway, forces occur in opposite pairs- which is why a gun recoils backwards upon firing, when a bullet is propelled forwards. While, in everyday life, we think of opposites as being incompatible and mutually exclusive, in mechanics opposites are part of a single logical reality. The sheer significance of this (where opposites are actually perfectly compatible, as viewed within a whole) should hopefully become increasingly clear as I continue. But basically:

Opposite explanations are not necessarily contradictory!

In virtually all movements, our natural instinct is to focus on only one side of the picture. In many cases some people might choose one of the possible perspectives and some may choose the other. However, there are countless cases where virtually everybody is guaranteed to look at one particular side of the equation, while completely overlooking the other. I'll talk more in future about how moving a finger into a key really ought to be felt equally in terms of the finger pulling at the arm (otherwise we end up stiffening, in a futile bid to stop the inevitable fact that the arm as a whole receives a force, not just the key). For now I want to show how the attempt to appreciate both "action" and "reaction" can make general movement a lot more efficient and free. 

Let's start with something as basic as walking or running. With each push off, you need to ask yourself- am I focussing on trying to use my foot to pull my body forwards across the ground, or am I trying to propel the ground backwards and behind me? Do I focus on the action or the reaction? This image shows the angle of the force, at the end of a stride. 

The force can be analysed in two components within different axes, as described in my previous post (strictly speaking a small element of force runs into a third axis- but this should be of very low significance, compared to the very large components within the backward/forward axis and the upwards/downwards axis). The action is backward from the runner's perspective (to the left from ours) and downwards. The reaction is forward from the runner's perspective (to the right from ours) and upwards. When thinking about these, we might usefully concentrate solely on the forwards/backwards aspects or the upwards/downwards aspects for a time. If we look at each axis separately for a while, it can make it easier to develop that particular element. Then we can start thinking more about the action or reaction as a whole, once again.

Let's start with the backwards/forwards forces first. It really does not matter whether you typically perceive it more from the backward action or the forward reaction. The goal is simply to acquire a balanced perception- so now try the one you are not used to. If that feels like it's a bigger effort, that's fine at first. Switch back to your normal one for a time, but then switch again. Keep switching over between the backward and forward perspectives- trying to notice as acutely as possible what feels different between the two. Both versions ought to become progressively informed by something about the quality of the other. It should feel more and more effortless until you get to the point where, upon switching, there is scarcely any difference to be found in the quality of either. After all, they are supposed to be viewpoints of the same thing- not two different things! Action and reaction BOTH occur, regardless of which you focus on! Hopefully you are now left with a product that is based on a more integrated dual understanding of forces rather than single-sided thinking. However, that might perhaps be a little ambitious, after having only just started to think this way! Most likely, there will already have been improvement to the ease, but it can be a gradual process of development. 

Now let's try it for the up and down, as you walk. Most people will probably think more of the down here. Obviously, your foot naturally exerts a pressure down into the ground. But what if you walk by looking more at the upward nature of the reaction, rather than the action? If you feel how your whole body is lifted over the top (rather than dwell on the downward action at the foot), the whole thing may feel like less effort at once. But again, switch back and forth between the up and down feels. There's not a right way and a wrong way. We want to integrate both elements for a single understanding. Sometimes feel how your foot has to press down into the ground. This will likely feel like more effort. So simply switch to the upward feel for a while. It likely tends to make you feel less digging in, even though that upward force occurs because of the down force. See if you can capture more of that ease when you return to the active perception of the down element. Again, keep alternating until the two (previously conflicting) mindsets converge to the point of causing almost no differences at all.

Arguably this is at least of much an issue of psychology as one of mechanics- although the relation to the nature of forces means that it has foundations in something that is very much real. Psychological as the process of improvement may be, it is constructed around a clear-cut  rational foundation. I believe that this is a lot stronger and a lot more conducive to sustainable improvements than purer psychological strategies such as a mere "remember to relax more" etc. The psychological aspects are focused around a verifiable mechanical factor that can serve to guide the process. It is very different from wishful thinking that exists in a complete vacuum (not that I wish to write off the power of positive thinking outright, by any means).

This kind of dualistic thinking is something that I will come back to in various situations. I believe that one of the big problems in piano teaching has always been polarisation i.e. forcing it to A or B rather than a combination of A and B. Some teachers boldly proclaim the absolute truth of one side whereas others shout as loudly about the other one. However, it's very much down to the student's individual needs as to which side they might draw the most benefit from, with regard to the two-sided reality. What aids one student, might provide an active hindrance to another. In theory, if a lot more movements could be understood from dual perspectives, teachers might be in a position to solve problems with far greater consistency- regardless of which side the student might have strayed on. Although it runs a little deeper than the nature of action and reaction, in a future post I'll be going on to illustrate why the arm-weight approach and the finger based approach are basically polarisations of something that ought to be understood from a similarly dualistic perspective.

Anyway, I also need to introduce the idea of momentum, with regard to to movement. It's well established in the field of resistance training that it tends to be better if you are careful to move relatively slowly. This trains the muscles in a much more rounded way and makes errors in technique far less likely. There can be benefits from more explosive movements, but these are to be done with caution- especially if you are hoping to build sensitivity as well as strength. Anyone who's ever been to a gym will doubtless have seen the type of young, enthusiastic would-be Hercules who likes to illustrate his masculinity by attempting stacks that are far heavier than he is comfortable with. Rather than controlled movements, you see explosive actions that rely on a big initial force- rather than a consistent interaction between the muscles and the resistance. Often, much of the impetus doesn't even come from the muscles that the action is intended to train.

Scientifically speaking, this type of movement relates to the concept of momentum. I'm certainly not seeking to specifically compare piano playing to bench pressing 100kg, say. However, I'd like to illustrate how the difference between such qualities of movement has considerable relevance to both understanding the best ways to achieve control over a piano and to be able to move healthily whilst doing so. According to Newton, an object that is in motion continues to move at constant velocity, unless a resultant force acts upon it. So, if you apply enough force to something, it continues to move for a time, whether you continue pushing it or not. However, if you move something very gradually, you have to exert a more continuous force, in order to keep it moving.  When an object does not already have a large momentum, its motion is dependent upon ongoing forces- for such forces as friction would otherwise have caused a rapid stop. Conversely, a briefly large force might allow something to travel a similar overall distance, without further input of any driving force at all, necessarily. Basically think of the difference between moving around a supermarket trolley, while constantly feeling a small push- compared to if you give it a good old kick and then let it continue on its own steam, until it drops into the canal (don't really do that, obviously). 

(At this point, pure physicists may want to complain that all hammer motions are dependent on momentum- after the hammer is let free from the key. However, regardless of that, the difference between the qualities of movement is very much an issue regarding the fine detail of what happens when the key hits the key bed- in terms of how impact is absorbed and in terms of the balance that follows. When rolling out as many as 16 notes per second, the quality of balance that goes on before, during and after each note is far from a trivial issue. I believe that there is extremely good cause to understand the difference between an initially rapid impetus followed by coasting, compared with a more consistently applied force. The belief that such qualities of movement are a mere psychological illusion is tremendously open to dispute- although I do wish to acknowledge that such beliefs exists, for the sake of accuracy)

To introduce the difference between momentum based movements and more steadily controlled ones, I'd like to refer to a very useful exercise that can be performed away from the piano. In addition to providing a first hand feel for the sheer difference between such qualities of motion, it also happens to be a very good way of better sensing the upper body. Awareness will automatically be raised of many muscles that contribute greatly to the ability to balance at the shoulder (which, when trained to become more sensitive, are less likely to become heavily fixed).

Anyway, this is a very standard exercise- basically that of the press-up. However, we're going to do a very low effort version against the wall and with a very particular type of focus. It doesn't demand any great strength, but rather attention to balance. Standard press-ups against the floor are frequently done with a lot of initial momentum that serves to quickly 'bounce' the body upwards. The return to the ground often follows on as a near free-fall collapse back down- often without so much as a pause at the top. The problem with this is that it works certain muscles rather heavily and others scarcely at all. There is very little room for discrimination as to what goes into it. Severely lopsided training can easily ensue, where one half of the body operates extremely differently to the other. Even if you have the strength to do a large number of repetitions in the bouncing manner, there is reasonable question as to whether some of the relevant muscles are necessarily getting ANY training or contributing anything to the action whatsoever. If you simply move slower (looking out for any jerks, collapses or jolts), many muscles must get involved with the continuation of motion and contribute to balance. However, this can be surprisingly demanding. A standard press up is very difficult to do both slowly and with perfect form. That's why we're just going use the wall for this.

To do the "press-up", stand a couple of feet away from the wall and lean against it, with the hands at shoulder width. Obviously be careful not to strain yourself and stop if you feel any pain or excess stretching (although, seeing as it's nothing more than an enormously easier version of something so standard as a press-up, this barely seems to call for much of a legal disclaimer). Anyway, lean your body in and then control it back and forth in similar form to a regular press-up- trying to keep a single straight line from the toes right up the whole of the body. Try not to bend your back at all. So, how does that feel? Easy to do it ultra slow, with no holes in the movement?

You may well find that, while it's easy to do it fairly quickly or with the odd stop/start in the movement, it's really rather hard to do it slowly and consistently.  If so, this is where the idea of dual perception makes a reappearance. However, if you didn't end up in a position where you were clearly doing it too quickly and with too much momentum, I'd advise you not to try anything in the next paragraph before you've checked the one after. 

In this case, I believe that most people will typically have thought of the away movement in terms of the "reaction" force that generates the motion away from the wall, not the inward "action" that continues towards the wall (notice how this is actually the reverse compared to walking- where I believe that most people will tend to dig down too much into the "action", rather than concentrate on lifting themselves up via the "reaction"). So, as you go away from the wall, in order to improve you're going to want to focus on how you are still leaning into it, rather than too much on the away movement. As you go inwards, you're also going to want to feel how the wall is pushing you away still. This reversal of perspective helps to cure the excessive reliance on momentum, and enables far clearer perception of the stabilising muscles that enable a slow movement to be executed smoothly.

Basically, in order to change your perception you're probably going to want to think of the forces in terms of the opposite direction to that in which you are moving in. However, at this point it would be all too easy to slip into careless polarisation! So, I have to emphasise that not everyone will necessarily be the same. Was excessive momentum actually the problem? If not, you might have looking at totally the wrong solution! Remember that we have to look at both sides- not merely one or the other. If you found that you were actually digging in too heavily (which some may have done), we need to reverse the whole thing! Anyone going with a feeling that resembles ancient machinery grinding together needs to lighten the action.As they go away from the wall, they need to stop thinking of leaning inwards and think away from the wall. As they go into the wall, they need to feel gravity is allowed to ease them inwards- rather than be in a position of resisting it quite so much. Remember though, regardless of the initial fault you still need to switch back and forth from time to time though. Otherwise, the individual cure might just leave you doing it wrong on the other side- instead of converging on what you actually want. Both perspectives are valuable. Neither is inherently more correct or incorrect- except with regard to the current nature of the issue (note that 'current' is a key word).

I hope that this helps to establish some issues of movement with some clarity as well as the danger of polarised one-size-fits-all thinking. Although none of this post is specific to the piano whatsoever, I hope that people will have considered taking the time to think about it. I believe that this is a major issue in terms of what we ought to be understanding, when trying to make corrections to movements. By understanding that superficially opposed mindsets can be one-sided descriptions of a single whole, you can converge on (the seeming contradiction of ) being able to view it from BOTH sides at once! One-sided thinking may be important in the short term, in order to progress closer to the correction. However, two-way understanding is always the end goal. Do we want the person who went too quick to start digging in? Do we want the person who was digging in to start bouncing up and then collapsing in? After a certain point, sometimes you basically have to go back to WHAT HAD BEEN THE PROBLEM!!! If I'd started with that, if might well have sounded pretty ridiculous. But I hope that what I've written will have established the sheer danger that lies within sticking to just one view of a two-sided whole. Looking at just half of the picture without ever referencing it back to the other is rarely wise.

The "Single Plane" Theory part i (plus issues of understanding gravity)

(Sorry, if you were hoping for the latest 9/11 conspiracy theory- I'm afraid you've just landed in rather the wrong place.) 

In this first specifically aimed post, I'm going to begin to introduce both the concept and relevance of axes (plural of the singular axis) or planes of movement. An axis is basically a line of motion- similar to the concept of dimensions, of which there are of course three (well, according to wikipedia we seem to have managed to extend that to one extra these days, but I couldn't personally tell you where the fourth one might be. Rest assured that I'll be omitting the mysterious "w" axis and sticking to the more traditional three). Obviously we are all aware of the upward/downward axis in which keys (basically) move- although it's worth remembering that a key is technically the end of a very long lever, so even this is not strictly a perfect description. We also know that gravity acts along this path. However, here I'll be illustrating some of the benefit to movement and efficiency, that comes from adding greater focus to what also occurs within the forward/backward axis (i.e. directly forwards towards the piano or backwards and away from the piano, from a regular seated position). Obviously there is also the third axis of motion- the sideways line that runs from left to right (or vice versa). This too will prove to be of major importance- although it will not be brought so much into the picture until I have fully established the role of the first two.

Anyway, "That's all very boring" I hear you saying. "What's this got to do with playing the piano- Steven bloody Hawking? I suppose you'll be harping on about black holes and parallel universes next?" Well, as I'll show you how to feel for yourself, the widely held intention to move the key in a perfectly downward path of motion can be HUGELY problematic- causing physical tensions, low efficiency of energy transfer, potentially damaging shock waves through sensitive joints and rather lumpy tone (the last two notably due to the thud that comes with landing the key so directly into the path of the key bed). At this point, to be entirely clear, let me stress that I'm NOT advocating slipping across the surface of the key. Quite the opposite. However, if you grab yourself a pencil (ready for a little experiment), later on I'll show you how to discover what level of significance actually lies within the backwards/forwards axis. If you can totally free yourself from the seemingly obvious assumption that you necessarily ought to aim a key straight down, that change to the rationale alone may very well cause you to experience improvements in the comfort of your playing and help to increment the depth of your tone (even though this is very much a preliminary element).

Anyway, before we get to any of the practical experiments, I'd like to establish a little more of the explanation as to why this is so important. Of course, the key itself goes (almost) directly downward. The problem lies in the fact that the body, the arm and rarely so much as the finger will ever be aligned anywhere near to being straight over the top of the keyboard! With optimal alignment, the sideways axis can virtually cease to be much of a practical issue (incidentally in the future I will go more into the precise nature of what actually defines the often mysterious nature of good alignment- for when you fail to find good alignment, forces within the sideways axis DO tend to arise as major cause of compensatory muscular tensions or unpredictable movements). Anyway, conventional seated postures demand that we use forces that exist very significantly in the backwards/forwards axis. However,  Mitchell Zeidwig (when not too busy balancing a double bass on his chin whilst playing Liszt) found a rather interesting way to partially resolve this problem, if not necessarily the most practical one: 

See the actual performance here on youtube. Pretty remarkable stuff.

Anyway, we cannot afford to simplify to the point of supposing that moving the key is only about up/down forces and actions (be this specifically in the forefront of the conscious, or an underlying assumption that stems merely from casual observation). It just isn't possible to restrict everything to up/down forces alone. If you pretend it is, then the brain's mechanism of trying to simulate such a scenario is liable to turn free joints into fixed points in space- by using muscular efforts to FORCE them to stay still, as if locked in a vice. Without getting to the heart of this flawed mindset, some pianists cannot even tell that they are holding anything still! Rather than fix joints in place, we need to find a more sophisticated way to free them up- i.e. we need to embrace the reality of the backwards/forwards axis and cultivate better understanding of it. This is far more productive than willing yourself to relax, if you persist with a model for movements that mechanically NEEDS fixations to operate. Until you deal with it, the underlying mindset is inherently at odds with the possibility of achieving relaxation- in a contradiction that the subconscious is simply not likely to be up to resolving. Those who are sensitive to movement may (very rarely) be lucky enough to acquire the feel for the backward/forward axis entirely unconsciously- but it's far easier to make improvements when you can consciously steer away from erroneous simplifications in the very foundations of the intent.  

Anyway! The first exercise. I mentioned in the introduction that gravity is widely misunderstood. The misunderstanding is based upon these very same principles. Gravity is perfectly downward, yes. But we must understand that THE RESULT OF GRAVITY on a series of levers (e.g. A human arm) frequently is not! As soon as you talk about gravity causing sideways forces, some people will immediately give you a funny look. But think of the basic mechanics that go into in a gym machine such as this:

Just two pulleys translate the vertical force of gravity into an almost perfectly horizontal pull. Once the weights have been lifted, not only is the gravity trying to pull the weights back down, but it is trying to pull the handle on which the lifter has pulled back along the sideways path. So what REALLY happens when you have quite so many free joints as in a human arm? Well, let's see. Place your hand on the keys as if it to play but then collapse your palm flat onto a cluster of keys and relax your whole arm as much as possible, until it slides right off the keyboard.

"Great! Thanks for wasting my time, you frickin' schmuck!" you're probably thinking. Well, yes, this is a very standard exercise that has been used for years. I didn't claim otherwise. BUT!!!- now try again and this time seek to perceive what really goes on here. Feel your elbow this time. Which direction did gravity move it in? Straight down? Certainly not (assuming that you started with your shoulder nicely at ease). It primarily pulls your elbow backwards (yes, this is slightly simplified, before any pure physicists should protest, but the primary issue here is that the resultant PATH of the elbow is vastly more backwards than downward- the slightly more complex details being of no importance to the practical issue). Gravity seemingly acted sideways! Consider now- if you release weight in your arm, this backward pull is always present, not just the downward aspect! That is, unless you find a corresponding force to balance the backward element, by pulling you forwards.

Anyway, that's getting a little far ahead, so let's come back to the issue of  the elbow actually going backwards, without yet worrying about bringing in the notion of a force to prevent that. Without this practical observation, it is all too easy to fall into the trap of dwelling too heavily on the fact that gravity is a "downward force". Yes, it technically is, but because the resultant effects of gravity are not that simple, the association is deeply problematic. It means that the subconscious is highly liable to "correct" the movement- by using potentially unnecessary muscular contractions or fixations. If inaccurate surface assumptions are lodged in the mind (no matter how deeply in the unconscious parts) they really need to be corrected via the conscious. Then you can put yourself in a position to start feeling what truly goes on- and start to function without the underlying impediment. In order to have a chance of freeing yourself from the excess tensions that such seemingly minor misunderstandings can cause, to hope to will specific muscles into relaxation just isn't adequate. Long-term treatment begins with the source of the problem, not the immediate symptoms. First you must adjust the global overview that introduces the effort. So, the moral is thus:

Forget all preconceptions based around gravity being a downward force and start a clean slate. Downward motions and gravity are not inherently the same thing! Gravity's action is to be understood from that which you can OBSERVE and FEEL through awareness of what results from muscular release. Only by understanding gravity via acutely sensitive personal observations about its truest resultant effects (rather than via preconceived assumptions) can you even begin to truly understand its role.

It's all too easy to falsely think that the results of gravity are necessarily equatable to exact downward motions (despite the fact that it is channeled through so many joints that will greatly redirect it, unless fixations occur) . Drastically worse still, you might even end up thinking the reverse- that actively exerting a downwards force equals using gravity. This evidently occurs in the demonstration within the Taubmann octave film about supposed "free fall" into octaves. In such cases, what is supposed to result from release of effort results in added effort (frequently while simultaneously wasting some of this effort to offset the ongoing action of opposing muscles that simply needed to let go)! You have to start from releases and observe the movement that results- ideally with at least as much attention on the less obvious backwards/forwards as on the up/down. Only then can you be in any position to integrate gravitational effects with sensitivity, instead of by fighting with generic seizures. In the near future, I'll also be introducing the forces that the key sends back at you with regard to Newton's 2nd law. When you move in a directly downward path, the tensions that you are likely to be involving (simply to achieve such a path) don't make terribly good cushions against the massive force that the single axis of motion will cause you to contact head on!

Anyway, while this is all very important to consider, it's still very much preliminary. If you're thinking "that was just a big psychological dung heap- where's the meat, Pedro?" then I'd urge you to wait until I get onto the more specific applications that will rapidly start to follow on. Right now, it's about time we put this thinking into practice at an actual piano! So, have you got that pencil ready? Yep, that's right- we're still easing in at the shallow end, I'm afraid. You're going to use the pencil to play for now, not your fingers- but this should actually give a clearer illustration. Before looking at bringing in the hands and arms, I want to illustrate (or rather, prod you into figuring out for yourself) what an exceedingly direct application the forward/backward issue really has to even a single note. Anyway, here goes:

Grab yourself a long pencil and hold it horizontally across a key (just touching the key with the end of the pencil) like so:

and depress- looking for efficiency and quality of contact. Can you make a big sound with ease and comfort (after all, even here, there's a lot of "technique" to how you move)? You're looking for maximum tone and maximum feeling of "connecting" throughout the whole path- but also for an effortless sense of absorbing the spare energy, upon reaching the key bed.

So, which direction did you aim it in? What? You aimed it straight down? What the hell do think you are playing at? Did you pay attention at all- or have you been too busy picking your nose and scratching your bum? Anyway, to be serious again- it really doesn't matter too greatly what you did, the first time around. Let's try a whole variety of different ways of moving. Even deliberately include the straight down approach as one of them. You need to feel for yourself how the different paths effect different possibilities.

Did you aim the whole pencil in a single path? Or did you find it more efficient to lower/raise the end of the pencil you are holding? As in:

or:

Did you aim a single, consistently directed force, or did it change direction at all? What happens if the pencil slides along the key? Conversely can you make sure that it contacts the same spot, while applying notable levels of forward pushes, or backwards pulls? Experiment to see how just much of a backward or forward feel  you can do without slipping and glancing along the key. Then experiment with reducing it again, to see how much or how little seems to help the most. Remember though above all- no coming down straight over the top like this:

Even Zeidwig comes at the keys with a large horizontal element to his fingers. We have to look at coming from a place that involves at least some kind of horizontal element for this to be relevant to normal playing. As long as you do so, feel free to aim the force in any direction you wish.

So, which direction did you actually have to exert the force in, for the most efficient transfer of energy? Oh, and once you feel that you've found the efficient way, why not try some of the alternatives, purely for observational purposes? Actually, go ahead and start with the vertical pencil now, even, to see what a very pure single axis motion is like. Try all angles. Even introduce some sideways forces, if you wish. You can go into all three axes.

Anyway, I'm going to leave it there for now, but hopefully that will already have provided plenty to think about- if you've done some decent experimenting. If you didn't bother with the experiment, then just what the heck did you hope to learn- from plowing through all of those words but then not engaging in any kind of explorations? The idea of this is for you to teach yourself something. That can't come through the rational element alone- if you don't work at channeling the understanding directly into something that relates to the nature of movement.

In my next post, I'll continue a little more about the idea of axes and introduce planes (which are 2 dimensional versions, based on two axes), as well as the idea of levers- particularly with reference to the results of the pencil experiment. I'll also be looking more into some of the mechanical reasons as to why some types of movements will have been felt to be highly efficient, whereas some others are inherently wasteful of energy- all of which will soon start to lead into the specific implications for regular playing.

Introduction

Although countless books have been written on piano technique, what deeply puzzles me is the seeming absence of any books that specifically derive practical advice from the wide implications of the most fundamental laws of mechanics. Before I put anyone off from reading any further, I should stress a few things at once: Firstly, none of the following articles will be about learning a "mechanical" piano technique- rather the stress is always going to be on PRACTICAL piano technique (by which I mean one that results in physical ease but which also opens the door to greater extremes of sound and orchestration). The reason I am writing this is because I have found the implications of basic mechanics to be spectacularly effective at both translating into better movement and into better sound. This is not an academic exercise but an attempt to improve the understanding of what needs to actually be perceived, in order to find the easiest path towards formulating quality of movement. Frankly, the pure scientific issues themselves don't greatly interest me- UNLESS they specifically lead to a means of making improvements. Of course, sometimes thinking about something that might have seemed totally abstract can suddenly reveal an unexpectedly useful implication. However, on here I do not intend to even mention anything that I have not already drawn a very notable practical consequence from. You'll find applications supported by theory, not theory for its own sake.

Also, I will go out of my way to keep the actual physics as simple as possible. You won't find me detailing pointless calculations that involve estimated coefficients of friction, or using trigonometry to calculate the specific force in Newtons that a particular muscle might have to apply. I'm looking at broad issues with significant implications, not number-crunching. In fact, I claim no background in especially advanced mechanics myself (although I have previously studied mechanics as part of both maths and physics A levels). What I have found notable when thinking these issues through is just how overwhelmingly simple it is to put BASIC mechanical laws into the context of piano playing.

Above all, what has astonished me is just how practically beneficial the implications are, with regard to attaining ease and efficiency of movement. I've discovered that much of what I had been doing (over many prior years had been wasted on playing the piano really rather poorly indeed) is comparable to having tried to find an 'instinctive' feel for playing poker- without having actually learned all of the rules first. When it comes to movement, the laws of mechanics are (literally) the rules. Of course, you need to develop a 'feel' to play either poker or the piano to a remotely high standard. But surely we ought to START by learning the rules and their most standard consequences? After all, no mechanical rules can be broken.You can only seem to break them. Looking at certain inescapable facts has allowed me to do things which, for many years, I thought really were impossible. But clearly that's because I simply didn't properly understand the rules. It's theoretically possible for a person to push the limits of a set of rules further than anyone else and it's possible to make them work for you. But if this doesn't evolve by instinct, the best thing you can do is stop hoping to 'transcend' anything with wishful thinking and start understanding the sheer possibility that exists within the limits of the rules.

These days there are countless books on technique that are tremendously informed by research into the make-up of the human body. While this is certainly be to applauded, why have authors not put the same level of research into the most basic laws of the universe? What's the point in skipping so far ahead as to start learning the names of individual muscles and bones- if you do not yet understand the overwhelming implications of Newton's 2nd law?

Every action has an equal and opposite reaction

How can it be that this never even seems to get a mention? It cannot be overstated how much of problem this is, if not dealt with (especially at the moment when the key lands against the key bed in FFF playing). Why do so many people seem to fight against the piano with so much effort? The simple answer is because of irrefutable Newtonian physics. Above all, it is because they do not know how to deal with the forces that the piano sends back at them. Flowery metaphors are often used and relaxation is always stressed (often with little more than short term benefits), but HOW do you move in a way that will absorb this force, mechanically speaking? Many authors have floundered around the issue in overwhelmingly vague terms, but what makes it rationally POSSIBLE to do it, specifically speaking? To be able to relax away from the piano is very different to knowing how to relax in the face of the return force. Here's a film of myself playing a few years ago, before I started making any changes to my technique.

http://www.youtube.com/watch?v=I2vAsriTZE8&feature=mfu_in_order&list=UL

You'll see that, when it rises from the keys, my wrist often relaxes to the extent that my hand sags down like that of a limp-wristed drama queen. So why couldn't I relax my wrist properly in the big chords, if it was so busy relaxing (to a dysfunctional excess) elsewhere? Not because I didn't know how to relax but because the mechanical basis to my movements made it IMPOSSIBLE to both apply a large force and keep it more relaxed. I didn't want to be stuck unable to play louder than mf for life, so rather than reduce the returned force by playing lighter, I put up with uncomfortable tensions and impact. There was simply no alternative (that I knew at the time), unless I wanted to reduce the range of my intentions- which would hardly have been much better.

Technique does not come merely from good use of the body. Neither does it come from understanding mechanical laws. It comes from good use of the body in the context of mechanical laws. They cannot be separated or you can be certain that there will be gaps in the understanding and probably even areas where beliefs contain outright factual accuracies. To cure seizures (or preferably find a better way from the first time you ever play), you have to understand the force that makes you resort to them. Okay, a small number of great pianists learned this by 'feel' alone and have no idea how they do it- but they are in a real minority compared to those who succeeded in never getting anywhere by 'feel'. If it doesn't take you there, you need to stop doing and start understanding how to deal with the returned forces. It's time to forget the negative of the idea that you have to attempt to stop seizing up and start working on the positive of what leads you to a position of being ABLE to absorb forces, rather than fight them.

Later on, I hope to show how a number of changes in the understanding can rather easily stop people battling against the forces that the piano returns to you- and how you can even build up to applying huge forces (if desired) in a manner that permits even the largest rreaction forces to be absorbed with really very little effort whatsoever. You won't hear me coming out with any vague nonsense along the lines of "treat the piano like you're trying to sooth a newborn puppy" or "imagine you're making tender love to a blow-up doll" or whatever such poetic nothingness is usually resorted to. I'll show you how to stop fighting against a force and how to let it simply dissipate into your whole arm. Once you know HOW to absorb the reaction force in the first place, who knows? Maybe such images will even become surprisingly useful?  

Although I will try to make the scientific aspects easy enough to understand, anyone reading can feel free to skip to the practical implications and the various exercises for movements and perceptions that will be included, if they prefer. It's technically quite possible for the how to be useful, even if you don't have the patience to follow the explanation as to why. However, I include the 'workings' for a couple of reasons. Firstly, some of the implications might sound rather counter-intuitive. I'm not going to ask anyone to put their blind faith in some random bloke on the internet- so I want to give a clear proof, say, that movement A might be a definably inefficient means of producing tone and that it leaves certain muscles with no choice but to lock up. Equally, I'm not asking for blind faith in why movement B, say, might both be more efficient at transferring energy and more conducive to comfortable shock absorption. Also- while I've put a lot of thought into all of this and feel very confident of both the purer explanations and the practical implications, I want everything to be accountable. If anyone with a background in physics should disagree with any of what I write, I'd very much like to know. I'm interested above all in trying to advance understanding, so I'd actually be deeply grateful if anyone wants to pick me up, on anything that they might dispute, or let me know if they feel I've overlooked an important factor.

Coming back to the practical side though, a lot of movements can look identical on the outside, but be drastically different in the inner workings. By understanding the underlying mechanical principles that LEAD to the possibility of efficiency, you are much more likely to succeed than if you try to copy what you see on the outside.

As an example, later on I'll illustrate the difference between two types of finger action that look almost identical to the eye. Both have uses (Horowitz certainly used extreme forms of both), but one risks landing the keys with more impact. The other uses very strong actions and easily absorbs the reaction force. While most great pianists know how to use the latter to the full, I'll explain how a simple flaw in the mindset leaves few pianists able to exploit it. Again, the ability to differentiate between these two different qualities of movement (unless already acquired by lucky instincts) comes from knowing both the rules of mechanics and the implications of them. Rational understanding is only destructive to the instincts when it is based upon inaccurate understanding or incomplete understanding. In such cases, unguided instincts may even be better than the results that stem from a misconstrued rationale. However, the problem is that all humans make observations. There are many generalised observations and commonly held beliefs that are totally inaccurate. As I'll illustrate in my first detailed post, the path in which a finger frequently needs to activate can seem very odd, compared to what you would immediately imagine. When superficial assumptions are corrected by greater understanding of context in mechanical laws, it's far easier to reprogramme your understanding of movement.

At some point I'll explain why many people still grossly misunderstand the interaction between gravity and the body- dwelling too much on the fact that, in isolation, gravity is a perfectly downward force (but forgetting how many levers it interacts with and ignoring how this totally redirects the force). Frequently pianists end up working their muscles too hard- while erroneously believing that gravity is the source of the downward force.

Look at this film from 20 seconds in onwards:

http://www.youtube.com/watch?v=qwY-pDnmSiE

Gravity!!! That's as clear a thrust as you could imagine! Certainly not 'free fall'- which is TOTAL relaxation, by definition! What exactly is going on with all of these inaccurate explanations and paradoxes? While the Taubmann approach has many positives, it tries to be scientific but then comes out with a wealth of jumbled self-contradictory premises. If it's simply a metaphor to aid the sensation, then better to declare that! If it's supposed to be scientific, then lets remove this contradiction about doing a "free fall" without relaxing- whatever that's supposed to mean. Maybe not relaxing refers to the way she visibly presses so hard into the keybed after the supposed "fall" or maybe it refers to the thrust that so clearly occurs instead of an actual fall? Who knows? Either way, the way she digs in for the example looks very unhealthy to me and the explanation is utterly ambiguous. If I'd paid the few hundred pounds they charge for those tapes, I'd have been pretty unimpressed. Despite some of the positives about the approach, there's really a lot of room for improvement, in the attempt to explain things(not to mention the demonstration of how to bang your arm so stiffly into an octave).

Anyway, later on I'll give a few exercises that make it easy to perceive for yourself the direction of the force that gravity REALLY transmits to your arm (as a clue, it's rarely anywhere near being exactly downward in its effects). Ironically, when misunderstood, aspects of gravity can be one of the biggest hindrances to transmitting a downward force through the key. I'll show how properly understanding the resultant effect of gravity on a body can improve its use, as well as how it's also possible to improve action in the hand, by exploiting gravity as a balancing counter-force (often with no visible dropping at all) rather than as a power source.

There is not merely a single correct way to move. But there is an absolute truth in the laws that determine what is possible. Some ways of moving provide seemingly limitless possibility. Others provide very few possibilities, due to inescapable physics. While there are many alternatives that function just fine with regard to mechanical law (even if sometimes unusual to look at), some things are simply at odds with it. You have to be careful to differentiate between valid individual solutions (of which there can be many) and things which are inherently flawed. Sometimes saying "this is just my own way of playing" basically amounts to putting yourself in a strait-jacket. It's important to be willing to rethink things- unless you're happy to stick with the level you are already at, of course.

PS. In many ways the approach of this is likely to be rather similar to that of Alan Fraser, author of the "Craft of piano playing". I am extremely grateful to him for forcing me to rethink so many things about piano technique and for revealing a number of specific physical issues. Many aspects of what I shall be writing will have been inspired rather directly as an off-shoot from his principles about function. I will do my best to avoid inadvertently plagiarising anything, although I should certainly acknowledge how much of the foundations are owed to his work. Some of this is likely to involve slightly different descriptions of rather closely related movements. Even when the ideas have nothing directly in common whatsoever (and even in the few areas where I actually disagree rather violently with his explanation!), I should give him all due credit for inspiring the ongoing thought processes and experiments which will have led to them. Although many of the original premises here will stem more greatly from the starting point of mechanics, the process of integrating the implications into actual body movements is greatly inspired by his approach. Although I will be aiming to be even more rigorously scientific about certain issues (and also tend to place a little less trust in the subconscious- vital as it is for many things) this is very much intended to complement and work in tandem with the Craft of Piano playing approach.