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Monday, 15 November 2010

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:


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.


  1. Very interesting indeed.The obvious answer regarding the pen would be the shortest way beteween two points is a line.But here the goal is to optimize effort so I'd say the least effort is obtained when going forward up like Kemal Gekic and others. I'm sure we all do that to a certain extent unconciously or not.

    On the other hand the context doesn't allow the least effort way of striking the key so in a way ALL possible options to get the key down should be managed.Even "down from side to side" which is the way you get the key down in rotation.

    But I'm waiting for the next chapter is it possible to develop a technique totally based on least effort?

    As I said a very interesting approach this a century and a half debate on armweight finally gets enlightened by some scientific facts.

    Best regards

  2. Cheers for the comment.

    I'm looking at a foundation of base level movements that are based on the least effort possible and as widely applicable as possible- rather than seeking to impose limitations upon anything. I'll go through other types of movement in future, I hope, but want to cover the most widely applicable base level first.

    Also,I suppose it's not necessarily about the least effort overall- but simply ensuring that you are capable of doing things without effort that is perceived as unnecessary or strenuous.

    "Effort" is a slightly problematic term though- as is "efficiency". Strictly speaking, a lever action is actually less efficient and takes more input energy to do a job than a direct movement. However, in terms of perceived "effort", taking out the heavy landing of a very direct movement actually makes the effort seem less. I'll be looking at "efficiency" more in terms of "ease" and simplicity, I suppose, more than in terms of the strictest mechanical definition of "efficiency" with regard to energy conservation.

    However, from either perspective, I do find it very inefficient to have to rotate the whole arm on every note. I don't personally regard willful rotation as part of the base level- as it is vastly less transferable compared to simple finger actions. I think you just need to find adequate freedom in the arm.

  3. As fas as the W-axis is concerned, it is just the matehmatical way to express the 4th dimension of an infinite number of possible spatial dimensions. As far as reality is concerned however, this dimension is of great importance (atleast in this essay).

  4. meant to say not of great importanc*

  5. importance** I shouldn't be typing this at 2 am...

  6. this blog is phenomenal. i have read in texts how the hand and arm operate as a system of levers but no where have i seen these concepts illustrated or demonstrated. so grateful to have found your blog posts!!!