Sorry for not following up with these emails a bit faster.... Phil phollowed up with: >I agree that from the point of view of the pianist's finger that >what is happening at the backside of the key is irrelevant. But >from the point of view of Phil Ford (or anyone else reading this >paper and trying to understand what you did) it is relevant. Not really, on both counts. It *is* relevant in a sophisticated analysis, because all the various dynamic parameters change throughout the keystroke [that is the reason for the computer model being developed]. But it is also irrelevant to understanding the approach taken in the article, which was not intended to more than a *very* simple illustration of the principles....to understand what is being done there you just make the assumption that the pianist's finger has to accelerate the key stick and some action stuff at the other end, then see how things change when you put lead(s) in the keystick. The approach breaks down if you try to go deeper into understanding a real key action, but all your various comments and objections would be true in a more sophisticated analysis. > To determine the mass and center of mass of the keystick itself >seems relatively straightforward. Not so with the action mass as I >see it. The mass of the action components is not all supported by >the key. Some of it is supported by the action rails. So, how much >of the mass of the action components is included in your reference >key? And where did you put it? Haven't put any numbers into the equations, so all the various parameters remain theoretical inventions at this point. If we are to get anywhere with the illustration we need to keep it simple. I assumed this distribution of masses in their at-rest configuration is being acclerated: masses of the hammer, shank, whippen, rep lever [balancier to those who go the other way], capstan, and damper [if you include that, and I expect it does make rather a big difference]. As you say the mass of the key is simpler, and I agree you should exclude the parts of the above which are fixed, e.g. the flanges. >The action components' weight is acting at the capstan. I doubt that >the center of mass of the action components is right over the >capstan. So where did you locate this 'mass'? What I have said >before is that what I would do for a first cut is take a scale >reading of the action components installed on the action rails with >the whippen sitting on the scale approximately at the capstan >contact point. Then treat this as a pseudo mass that would be >applied to the keystick at the capstan location. Is this what you >did? The point of action of the mass at the capstan is only really relevent to statics, a la Stanwood et al. That wouldn't give the centre of mass or moment of inertia for dynamics, at least insofar as the assumptions of my illustration, but there's no reason we can't change those assumptions if it seems to give something that is easier to visualize. After all the only real purpose to the exercise as it is laid out is to illustrate the principles. Applying all the mass (point) at the capstan would be an extension of the "simple case #2" in the article, for which the mass of the action parts is all concentrated at a point, but we also provide the key stick with some distributed mass. On reflection, it's probably just as good an approach for illustrating principles and checking sensitivity to variations in key leading, as the one I suggested, which itself is not really more realistic of what happens in a real action [action parts have their own centres of rotation about which they have moments of inertia etc]. With your suggestion you would be assuming: (i) a lead-free key stick, for which the moment of inertia might be estimated assuming a uniform distributed mass beam, or with a simple experiment; and (ii) an action mass located at the position of the capstan, for which it is easy to get the MI. >... Locating all the mass at a point and deriving the inertia from >mr^2 will give the wrong answer. But you've said that you didn't do >this. No, but my assumptions are not really any better, so let's go with the version you suggest since it is much easier to estimate the MI. >.... If we eventually want to try to use this information in the >real world we need to have a method of arriving at inertias that it >simple enough for the tech in the field to use. This either needs >to be a simple calculation method or a measurement method. I am not >aware of equipment for measuring inertias that falls within the >budget of a lowly piano technician. Perhaps you know of some >inexpensive equipment. Could you enlighten me? Not really. But let's keep it simple for now and use the point mass option + key stick. We shouldn't be thinking about practical techniques etc. - keep in mind the only purpose of the analysis is illustrative, and possibly checking sensitivity to lead variation, and examining the significance of dynamic effects. For that we can use simple estimates and ballpark figures. >Could you expand on that a little? It feels so different because >you have a different breakpoint? Not necessarily that. What I meant was that, as a pianist, I can feel a very significant difference in dynamics when playing back of the keys, and this is often utilized to create a particular type of tone. > >> A quick calc. puts the breakpoint somewhere in the mid-dynamic >>range for a mid lever lead position (~20m/s^2). >Would you mind sharing a sample calc with us? Telling us what >values you're assuming? Sure. A loud blow corresponds roughly to 5 m/s at the hammer/string impact. Assume uniform acceleration from rest over say a 10mm keydip and you can calculate an estimate of the accleration for a moderate blow. I re-iterate what I've said all along: >>This proves nothing about whether the breakpoint is actually >>important from the pianist's point of view, or about the control >>aspect, both of which need to be investigated experimentally before >>conclusions can even be hinted at. You can't beat some simple experiments to see if any of this is really important to a pianist. Too much theorizing is bad for health. That being said, I'll repeat: the only purpose for the little exercise I posted on the website was simple illustration of principles and ballpark estimates for significance of the effects. Stephen -- Dr Stephen Birkett Associate Professor Department of Systems Design Engineering University of Waterloo Waterloo, Ontario Canada N2L 3G1 Davis Building Room 2617 tel: 519-888-4567 Ext. 3792 PianoTech Lab Ext. 7115 mailto: sbirkett[at]real.uwaterloo.ca http://real.uwaterloo.ca/~sbirkett
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