More on Knuckles

[Michael Wathen 556-9565]

The following is an addendum to my post to the Piano list of yesterday,
September 14th.


Towards the end of my post I had asked the question about the generality of my
formula.  The answer is that it is by no means an equation which can be applied
to all pianos.  It is a unique solution for the piano in question.  What is
general is the process which I will outline below.

I have a kit for Steinway pianos which I use for the procedure.  It consist of
four samples of Steinway hammer shank assemblies, each with different knuckle
configurations.  A fifth sample is from the piano in question.  Also in this kit
is a number 40 Steinway hammer which I can slip on any of these shanks.  Each of
the hammer shanks are marked and the action arm distance that goes with them is
noted. Each shank configuration measures between two and three grams for flange
resistance.

The next step is to take Downweight and Upweight measurements for a certain
number of samples, compute the average for these measurements.  I usually
measure all te Cs and Fs in a piano.  What we are trying to determine at this
point is whether a sample from which we will record the data of Downweight to
action arm distance has a Downweight that is close to the average we compute
above.  We will also need to weigh the shank with the hammer attached to it on a
balance scale and check to see that the samples from the kit with the hammer
attached has close to the same weight.


I note the Downweight for the existing configuration them replace this with one
of the samples and the hammer from the kit and note the Downweight for this
configuration. I do the same for each of the samples from the kit.  I now will
have five action arm distances coupled with a Downweight for each one.  Armed
with this information I can perform a linear regression to get a unique equation
that will tell me what I can expect for a given knuckle configuration.  Suppose
I have ordered one of those sets of shanks from Steinway labeled "Genuine".  I
can measure the action arm distance plug it into the equation and get a
predicted Downweight.  From this I can decide whether using these "vale la Pena"
(is worth the effort).

I have on hand a Mathematical Spreadsheet program which can perform the linear
regression quite easily.  The are gobs of shareware programs which you can
obtain from Electronic BBSs which can do the same.  If you really can't find any
of these you can E-mail me and I can provide you with either a program in Basic
or I can tell you how to do the linear regression by hand..