Measuring center pin resistance

[Phillip Ford]

> >>   Every measurement you do in a piano should be accompanied by a relative
> >> error of measurement discussion (which should be easy)
> >
> > I'm not sure what you mean by this.
> >
> > Phil Ford
>
>Sorry for my English, Phil.  By relative error of measurement, I mean just
>this :
>
>when you measure, say, the length of a string, you use, say, a ribon meter
>graduated every 1 mm ; so when you take the measure of a string and find
>that it is say 1000 mm long, you should rather say that it's length is for
>sure somewhere between 999.5 mm and 1000.5 mm.  1 mm is here the absolute
>error of measurement that you make (the largest difference possible between
>your reading and the actual length of the string).  Reported to a length of
>1000 mm this means a relative error (the absolute error divided by the
>nominal length) of 0.1 % ; when reported to a length of 50 mm, the same
>system of measurement induces a relative error of 2 % , which is 20 times
>more.  When using those nominal data (1000 mm or 50 mm) in a formula
>multiplicating those values, the relative error of the results is also
>multiplicated.  We should keep an eye on the time where the results have
>such large relative errors that they don't mean anything of use anymore.
>In French it is called "erreur relative".  What is the word for that in
>English ?
>
>Best regards,
>
>St�phane Collin.

Sorry for the slow response.  Your English is correct.  It is relative 
error.  I didn't understand what you meant by every measurement having a 
discussion about it and why it would be easy.  Also, here you mention that 
we should keep an eye on 'large relative errors'.

To take as example the hammer center resistance, which started this thread, 
I suppose to establish the relative error you would need to know the 
accuracy of the gage being used to measure the force and the accuracy of 
the scale measuring the location of the force to determine the relative 
error.  That doesn't seem too hard.  The hard part seems to be deciding how 
much relative error is significant, or in other words, how much is a large 
relative error.  I think you could only determine this with tests to see 
how sensitive the pianist is to the particular parameter that is being 
measured.  If the pianist can't tell the difference between a resistance of 
20 g-mm at the hammer center and 200 g-mm at the hammer center, then your 
relative error could be large and it wouldn't significantly affect the 
outcome.  So you could use a very crude gage or see that the hammer swings 
somewhere between 1 and 20 times and be OK.  On the other hand if the 
pianist can tell the difference between 20 g-mm and 30 g-mm of resistance 
at the hammer center for certain kinds of playing, then it becomes 
important to have a means of measuring that gives a relative error that is 
small with repect to these values.  Establishing how sensitive pianists are 
to various parameters in the action doesn't seem so easy.

Phil Ford