"Nyiregyhazi (can we call you Andrew? - it's quicker to type!): I've had a read of your blog and you have some good points to make. I'm not sure you couldn't make them more succinctly in places, mind you, and even as a physicist (although I've earned my crust as a pianist for over a decade I'm actually qualified in physics) I had trouble following it in places."
Yeah, I'm planning on doing a concise summary of the chain idea at some point- as well as using more diagrams and videos to illustrate things. As I've been developing the ideas, I've often realised that certain things can be explained in quicker ways, without compromising the content or depth of scientific explanation.
"As far as I can see, you have overlooked the role of inertia of the hand/arm/body. The fingers weigh very little and of course the keys of a piano don't weigh very much more. When the keys are depressed and released there is a low-pass filter effect applied by the inertial mass of the heavier bits of the player, which means that the muscles in the shoulder, for instance, don't generally have to react as fast as those in the fingers. This makes the analysis rather complicated."
Not at all- this is very much part of it! When the weight of the arm causes a force to tug backward at the wrist, it makes it possible for a finger to pull very hard indeed. The lack of inertia in the hand is no longer an issue- as it is kept very stable by this pull. I'm currently working on a post that goes back to the pencil experiment for a couple more elements- that I believe will provide a very clear practical illustrations of the problem with active arm pressure. When the arm is held stiff, the finger is limited in how it can pull, but when it hangs properly (from a stabilising finger), it makes it possible for the finger to create huge forces while the arm merely hangs back. I agree that it's very much more complicated when the whole arm's inertia is involved in more direct pressure- but I'd actually dispute that this is as necessary as believed. When I get to the fingers, I want to show how the vast majority of actions are extremely wasteful of energy- and how powerful a finger is when levering in a way that ensures that nothing is lost into slack.
"In addition, there are all sorts of reasons for pushing and pulling in apparently bizarre directions. For instance, many pianists (me included) tend to 'pull the key towards them' (i.e. stroke the key from fallboard towards the player while pressing down) when playing quietly. The simple explanation of this is that it creates a diagonal trajectory for the finger of which the downward vector is a relatively small part, making it easier to control the downward velocity of the key."
Absolutely agreed. I'm using something similar to this as the basis for most finger actions- although largely without moving the finger along the key. Recently a major breakthrough came from realising the problem with old-fashioned explanation in (supposed) physics. It only recently hit me, but the idea of the knuckle as a static fulcrum is over simplified nonsense. Why is the contact between finger and key not viewed as the fulcrum? Feeling the finger moving around this point makes for a very efficient action and minimises the impact at the keybed (as additional momentum continues to act upon the finger through to the rest of the arm, in a way that redirect the movement forward and up rather than to compress downward into the bed). This has been a collossal breakthrough. You can illustrate it very easily with a pencil. Pulling the key with a levering action makes for far more sound than pressing with the arm (unless the pencil begins and descends absolutely vertically- and hits the keybed absolutely dead-on, with the arm's momentum crashing behind it). When the right quality of levering action is used, I think it's pretty easy to make a big sound from the finger. I don't think enough pianists use this style of action though- and hence perceive weakness due to a less efficient action.