David and friends have done all the hard leg work in this
system.
One of the problems was determining what hammer weights made
sense. After weighing thousands of hammer David came up
with a chart list hammer weights as "loud, Medium and Quiet"
based upon experience, piano size and hammer weights. So if
you have a heavy set of hammers you will get a louder tone,
a lighter set of hammers will produce a quieter wounding
tone. Basic physics.
Them how much front weight should be in a key. Inertia is a
major problem with actions designed for light hammers that
get heavy replacements. As is an optimum key weight that
does not challenge the health of the hands of the long time
players. And working backwards, what should the hammer
weight be, the front weight, the over all leverage, and all
the rest of the details.
So, David has done all the calculations and produced a wall
chart that will provide all the information you need to do
the work.
What I have done is to use hammer weights and notes numbers
and David's hammer weight chart and determined that to solve
the problem of hammer weights and note numbers I needed a
quadratic equation to solve for the line the represents the
best fit possible give the weights I have. The program will
show the slop of the line (curve actually) and solve for the
exponent representing the line point for the give note, the
deviation from one note to the other and the deviation for
the note number. Taking these three values and plugging
them into an already set up spread sheet the sheet will
calculate the optimum weight for each hammer in the set.
You weigh and it tells you what the weight should be.
A 14.81651 12.39978 10.30361 8.004135
B -0.03489 -0.02605 -0.02378 -0.01774
C -0.00062 -0.00055 -0.00046 -0.00037
Y=A+B*X+C*X^2
W=A+B*K+C*K^2
14.78099
Key Heavy/loud Medium Light/soft
1 14.8 12.4 10.3 8
22 13.7 11.5 9.5 7.4
44 12.1 10.2 8.4 6.5
66 9.8 8.3 6.7 5.2
88 6.9 5.8 4.6 3.5
The top part are the values for the four lines of the three
weight ranges, below that are the equations then the ranges
defined by David.
I am not real strong in math by I did work this out over a
period of time.
There is a fairly narrow range of hammer weights you will
have to work with for a given set of hammers. I have to
pick your set and your targets before hand. If you allow
the hammers to rule your beginning point you could be in
trouble. You do not want to put a set of S&S D hammers on a
little 4'6 Worthlesser or you will be in deep stuff quickly.
One of the problems David solved for us was what are over
weight hammers and what are under weight hammers. Before we
took what we got and tried to make them work but without
knowing what we were doing. Some people were intuitive
about making it work and other just followed the cook book
list. David defined, in understandable numbers, what should
be and what you can actually accomplish.
No rocket science and given a basic understanding of the
mechanics involved any reasonably intelligent person should
be able to understand and apply the simple physics involved.
David is a very gifted man but he has brought the science
involved down to a level we all can understand, although I
must admit, there will be some head scratching involved.
Just follow the wavering lines and you will find all the
data you need. If the numbers don't work out then you may
need helper springs or to relocate the capstans or use
different shanks or as Richard Brekne, REALLY change the
action geometry. Most of us never encounter an action of
such poor design and execution as has he.
Jeesch, stuck my nose in it again.
Newton
This PTG archive page provided courtesy of Moy Piano Service, LLC