impedance and empericism -- longer

[Richard Moody]

Del, (I think) wrote.....
>- we are supposed to define a mathematical relationship
> that will accurately predict the effect on the harmonic coefficient of a
> single string lying somewhere along the string scale that results from a
> change in relative humidity from, say, 40% to 60% and if we can not
> currently provide this formula then this cause and effect relationship
>does not exist?

No data, no formula, either a relationship exists but can't be measured
accurately and consistently enough, or yes,  perhaps there is no cause and
effect  between humidity and inharmonicity.
     The varied readings of an ETD MAY indicate that a cause and effect
relationship MIGHT exist, or indicate that the measuring device itself is
failing, or being used to measure beyond its limits. Who cannot say that
perhaps the effects of humidity are on the instrument rather than on what is
being measured? Never the less, a mathematical formula to define and predict
the effects of RH on Ih will never come about wo consistant and repeated
measurements.
    A mathematical relationship between tension length and diameter for
inharmonicity was offered by R Young, after extensive experiments and lots
of data gathered.  He did not include RH. To be fair he did not measure for
it, but it never occured since inharmonicity was thought result from
properties of cast steel piano wire.
    Now tuning machines are recording differences of Ih and people are
saying it is due to RH?  That is quite a stretch, if I may, to even imagine
that  changes in humidity can affect the properties of the steel in the
wire.
If ETD readings were consistant and repeatible at various levels of RH I am
sure a formula would have come out a long time ago.  But what seems more
likely but that no one is considering is that the machines themselves are
not accurate for measuring Ih, on a scientific level at least. However
judging by their success in tuning pianos, they must be getting something
right.  The most expedient way to determine accuracy is for two different
instruments to give the same reading.  (Of course if they don't then one or
both are not accurate, and you have no idea which is which) If there is such
a thing as acoustical engineering in universities, that would be the place
to seek out instruments to compare ETDs to.
---ric