Key Leads and Inertia

[David M. Porritt]

Stephen:

Thanks for the material on key leads and inertia.  I've downloaded
and saved it for reference material.  

dave

*********** REPLY SEPARATOR  ***********

On 5/30/2003 at 1:52 AM Stephen Birkett wrote:

>Yo - action dudes:
>
>Well it's about time I earned those oatmeal chocolate chip cookies 
>which Bill very kindly sent  mmmm. Thanks much Bill for the treat.
>
>I have revised the slides (on my website), converting into a very 
>brief article about inertia/leads, adding some discussion about the 
>general case of a real piano [as opposed to ye massless beam etc.], 
>and clarified the concept of breakpoint. I also included a page with

>the simple derivation of the relevant formulas on which the graphs 
>are based, in case anyone wants to go through those - nothing more 
>than simple high school physics here. 
>http://real.uwaterloo.ca/~sbirkett/key_balance.pdf
>
>Someone commented:
>>At one point it is said:  "moving the location of the lead moves
the 
>>breakpoint (along the
>>red line)"  thoough there is no relationship (formula) given. I am 
>>wondering just
>>what this might be.
>>I imagine that it wouldn't be too difficult to come up with a 
>>formula to relate break point to lead location, but it probably 
>>would be for a specific key configuration (a specific location of 
>>finger force and a specific location of action mass).
>
>The added stuff gives the relevant formulas for the general case of 
>adding lead(s) to a real piano key (with all action junk). The 
>breakpoint acceleration can be identified according to the location 
>of the lead in relation to the point of application of the finger 
>force - nothing else is required. Only when you want to find the 
>corresponding breakpoint force do you need to examine the 
>distribution of mass in the key and action components.
>
>In general the force/acceleration graph for a given key/lead 
>configuration has 2 parameters: the intercept (static balance
force), 
>and the slope (dynamic sensitivity). These are both affected 
>simultaneously by lead location and mass, so you can't say mass 
>controls one and location the other. The graphs I described are 
>actually based on the formulas which are easily derived, but I
hadn't 
>included those in the article to keep it simple.
>
>>As the lead is moved closer to the balance point the slope of the 
>>balanced line becomes closer to the unbalanced line, so that the 
>>response of the key must become more like an unbalanced key.
>
>Yes.
>
>>  >Its interesting that the use (or not) of leads changes
absolutely
>>  >nothing relative to the division between hard/soft play.
>>I don't understand what you mean here.  The charts show that the 
>>location of the leads affects the break point, or the level of
force 
>>required to go from soft play to hard play.  At a given lead 
>>location, the break point is independent of the amount of lead - 
>>perhaps that's what you mean.
>
>Yes. That's what I mean.
>
>>One thing that I question about the charts is the meaning of the 
>>break point between soft and hard play.  Stephen's conjecture is 
>>that in the soft play area the action is 'harder to control'. 
>>You'll notice that the break point for the unbalanced key moves
with 
>>the lead location under discussion, and yet the unbalanced 
>>configuration hasn't physically changed at all.  Why should the 
>>location of the breakpoint, or transition from the hard to control 
>>zone to the easier to control zone be changing for the unbalanced 
>>key?
>
>Because it's related to the force for which any lead added at a
given 
>location gives the same acceleration, i.e. a comparative concept. 
>It's not an attribute of the unleaded key per se. It's only defined 
>when you pick a location to put a lead in that key.
>
>>greater for the non balanced line. This seems at odds with the idea

>>that the key would be more difficult to control in the soft zones 
>>for the balanced key then the non balanced key.
>>It would seem (intuitively) to me that one would have better
control 
>>when the slope of the acceleration is slight. And this regardless
of 
>>which zone we are in. ....
>
>another someone commented on this:
>>This is an interesting point.  I have to agree with you that 
>>intuitively it would seem to me that the action setup with the most

>>shallow slope would be easiest to control.  Less change in 
>>acceleration per change in force.  The action would be less 
>>'touchy', so to speak.
>
>Yes. This is one certainly possible interpretation - I added some 
>comments on the subject of control in the article version. I did say

>in the original slides that the question of "more or less difficult"

>control was "arguable" ["some might believe" etc.] It really depends

>on whether it's easier to control smaller absolute forces over a 
>shallower slope vs larger forces over a steeper slope [this in the 
>soft zone]. The answer is not unequivocal and needs investigation.
>
>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
>_______________________________________________
>pianotech list info: https://www.moypiano.com/resources/#archives

**************** END MESSAGE FROM  Stephen Birkett
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_____________________________
David M. Porritt
dporritt@mail.smu.edu
Meadows School of the Arts
Southern Methodist University
Dallas, TX 75275
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