---------------------- multipart/alternative attachment :) found a typo that needed correcting. Changed word in red below. Richard Brekne wrote: > Hi folks > > I keep getting amazed in conversations I have with different folks > about how to correctly measure the arms of the key (or any other lever > for that matter) to arrive at the correct key ratio (lever ratio). So > heres a little overstated example. I hear the following three > procedures, and some folks are quite adamant about the correctness of > the one they adhere to. > > 1 ) Measure straight across the top (makes most sense for our purposes > to me btw). > > 2 ) Measure down to the point where the key contacts its support > identifying this point as the fulcrum. > > 3 ) Still others say it is this second but each length is multiplied > by the cosine of the angle formed from the horizontal and the line > taken down to this fulcrum. (in the below example < A and < B ) which > really is so close to the first method its not worth noting the > difference. > > It seems customary in our work to divide the short arm by the long arm > so in each case thats what I'll do using the exagerated example below. > > The first method yeilds a ratio of 0.5, the second, 0.79, and the > third 0.5 > > Now I constructed this exact lever at the shop, and hung it on a > swivel for minumum frictions to check out what weights would balance > the lever horizontally. Using 10 grams lead on the short side I > needed 5 grams on the long side. Speaks for a 0.5 ratio eh ?? If it > was anything like the second method I would have needed more like 7.9 > grams to balance 10... and this wasnt even close. > > Then I did some measuring of movement distances and found as close as > I could measure that from the exact horizontal position shown below, > a vertical drop of 20 mm on the long end resulted in a 9 mm rise on > the short end. This works out to 0.45 ratio. Again.. if the second > method of measureing the arms of the key is correct this 20 mm of > vertical drop on the long end should have resulted in something much > closer to 15,8 mm rise on the short end. > > As it turns out, I believe I could extend those arms down that same > dotted line forever and not essentially change the ratio relative to > weight. Movement wise things are a bit different as the point that > lies on the normal to the horizontal intersecting the fulcrum also > moves more the lower the fulcrum is. But it still conforms closer by > far to the 0.5 figure then the 0.79 figure. > > The only real difference in a real piano key is that we are not > dealing with anywhere near so extreme angles as in the example below. > > So... I ask you... why we are supposed to measure down to the balance > rail, and up to the capstan and at the same time not take into > consideration the horizontal deflection of their angles before > figuring their ratio ? > > [Image] > Cheers > RicB > > -- > Richard Brekne > RPT, N.P.T.F. > UiB, Bergen, Norway > mailto:rbrekne@broadpark.no > http://home.broadpark.no/~rbrekne/ricmain.html > http://www.hf.uib.no/grieg/personer/cv_RB.html > -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html http://www.hf.uib.no/grieg/personer/cv_RB.html ---------------------- multipart/alternative attachment --------------7E570D91DE6BC45875DC9A38 An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/3c/14/d6/69/attachment.htm --------------7E570D91DE6BC45875DC9A38 A non-text attachment was scrubbed... Name: C:\\DOCUME~1\\RICHAR~1\\LOCALS~1\\Temp\\nsmail7P.jpeg Type: image/jpeg Size: 14717 bytes Desc: not available Url : https://www.moypiano.com/ptg/pianotech.php/attachments/6d/0d/0d/b8/nsmail7P.jpeg --------------7E570D91DE6BC45875DC9A38-- ---------------------- multipart/alternative attachment--
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