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
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