Hohf Article

[Richard Brekne]

Hi folks

Got done with a couple reads of Bobs article and thought I'd post some 
thoughts.  I dunno if its of interest to the present crowd on either 
list but here goes anyways. Bobs experiment as it is presented in the 
first article concentrates on the first case scenario from Birkett's  
article "Static and Dynamic Balancing of a Piano Key"  2003 and the 
experimental results Bob gets compare very nicely indeed with the 
theoretical predictions from Dr. Birkett.  Essentially what Dr. Birkett 
refers to as the dynamic breakpoint between soft and hard zones is 
exactly what Bob finds experimentally.

Note, Dr Birketts "soft zone" is the degree of acceleration that can be 
shown to be aided by key leading, and the "hard zone" is the degree of 
acceleration where keyleading can be shown to be an impediment. The 
dynamic breakpoint is where the key mass (leading) either aids or 
impedes acceleration.

Bob mentions that his measured data results in somewhat curved lines and 
seems to find this significant as compared to the straight lines in the 
theoretical model.  I would think that Bobs results are to be expected 
in any system, either his pulley system or the real piano. Dr. Birketts 
model is straightforward and is meant to simply demonstrate the basic 
principles and results from a theoretical standpoint.  What is of import 
here is the dynamic breakpoint itself more then whether there is a 
slightly non linear behavior (or not) to graphed accelerations for 
keymass and input force values.

What at this point Bob seems to have missed is that the dynamic 
breakpoint is movable. Much of the rest of Dr. Birkett's paper goes on 
to show that if the key is balanced (counterweighted) at points closer 
to the fulcrum, then the dynamic breakpoint moves upwards on the graph.  
Essentially the placement of the breakpoint is not a simple function of 
the mass added to key... but how much mass is added where. Dr. Birkett 
provides a formula for accurately calculating all these relevant 
moments.. i.e. breakpoint location, slope of change in acceleration for 
change in force, etc. for any combination of both amount and location of 
what is essentially Stanwoods FW component.

Using Bobs device, if one was to take his 5 added weights and measure 
them in terms of Front Weights, and then transpose this amount of FW to 
a point in between the key front and the balance pin hole (fulcrum) 
repeating the rest of his experiement then one would find the breakpoint 
moved so that the area of acceleration that is aided by the key mass is 
significantly enlarged. This basically confirms the idea behind the 
accelerated action. Indeed,  Dr. Birkett states at one point:

    "Adding lead to the key closer to the fulcrum enlarges the soft
    zone. Moreover, there is less difference between the dynamic slopes
    for various static balanced conditions, i.e. the key behaves more
    like the unleaded key"

I'll be interested to see what the follow up to this first article from 
Bob concludes. And I'd also like to see  him expand his experiment in 
the fashion mentioned briefly above to see what comes out of that.

Cheers
RicB




    The other thing was an interesting article by Bob Hohf which touches on
    some core points of one of the best discussions through the 10 plus
    years I've been on CAUT/Pianotech... namely the dynamic touch weight
    discussions surrounding Dr. Birketts paper on same available on the
    internet. I'll do a couple good reads before commenting on it... but I
    can already see its highly recommendable to one and all.

    Cheers
    RicB