[CAUT] fulcrum of a key

[Fred Sturm]

	I've been thinking quite a bit lately about just exactly where the  
fulcrum of a key is. One thing that got me thinking about the question  
was David Stanwood's adjustable ratio design. It uses a fairly sharp  
and precise fulcrum, that slides from behind the balance pin to in  
front of the pin, a total of 8 mm, and changes the action ratio in the  
range of from about 5:1 to 6:1. This is from about 2 mm behind the pin  
to 2 mm in front.
	I have just been working on an action where I made use of sliced  
punchings: felt balance punchings trimmed a bit (I bought them from  
Pianoforte Supply, Crescendo punchings "accelerated"). They are sliced  
about 1.5 to 2 mm from one side, so that there is a straight line,  
which is put to the front of the key. That reduced touch weight a bit  
(by changing the ratio), but not nearly enough, so I added half card  
punchings glued to the bottom of the key (glued to the behind side of  
the balance hole). Those two things put together got me a reduction of  
about 10 grams. (It was an action that I would normally have switched  
from 15.5 knuckles to 17.5, but all the parts were near new, so I  
thought I'd try something else).
	Now I figure that my half cardboard punchings are, actually, putting  
the fulcrum pretty darned near the center of the balance pin. So it  
gets me wondering where, exactly, the effective fulcrum of a standard  
set up is. Obviously it must be somewhere in front of the pin. Since  
using felt punchings with about 1.5 mm trimmed from the front changes  
the touchweight measurably, it seems like the effective point might  
actually be near the front of the felt punching.
	As an aside, but somewhat relevant, the Steinway accelerated half  
dowel bearings actually have a moving fulcrum (as the key bottom rolls  
along the bearing), which "accelerates": it changes the ratio as you  
depress the key.
	This question has some relevance to issues like what kind of material  
is used for the balance punching (relatively spongy felt versus  
crescendo, for instance), how high paper and cardboard punchings are  
stacked, and maybe some other things as well. It may explain why  
geometrical measurements of kay ratios and action parts don't predict  
the actual action ratio (since we typically use the center of the  
balance hole as the key fulcrum).
	Has anyone out there given this much thought and come up with some  
conclusions?
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu