<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-tab-span" style="white-space:pre"> </span>I thought I'd do some calculations to see how much difference a 1mm change in knuckle height would make to regulation. Bottom line, about .010" in dip, or about 1.3 mm in capstan/hammerline adjustment, significant but well within what I would consider normal regulation variance.<div><span class="Apple-tab-span" style="white-space:pre"> </span>For those interested, here's how I did the calculations. I used Ron Over's spreadsheet (I call it Ron Over's because I got it from a handout in a class he gave a few years back). This spreadsheet is set up to do a fairly simple calculation of the three intersecting lever pairs in a piano action: Key ratio, wippen ratio, and shank ratio. Key ratio is key front segment to key back segment (balance hole to keytop, balance hole to capstan top). WIpp ratio is center to cushion/capstan, center to jack top. Shank ratio is center to knuckle/jack top, center to hammer crown. Pretty basic Archimedes lever mechanics. Multiply the three ratios and you get a compound ratio for the whole system. This doesn't give precise practical results, and I think the reason has to do with the difference between measuring arcs and straight lines, and the fact that the wipp/shank intersection is pretty far from the convergence line. That said, it comes reasonably close and is a pretty good predictor in a proportional way.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>The change in knuckle height will create a change in the shank ratio, by changing the center/knuckle distance. There is a right triangle involving the centerpin and the knuckle. The hypotenuse is the actual lever arm, the distance from the centerpin to the middle of the knuckle top (knuckle/jack top meeting point). The other sides are from the center of the centerpin down the middle of the shank to the middle of the knuckle core; and from the middle of the knuckle core at the middle of the shank to the top point of the knuckle. GIven two sides, the Pythagorean theorem can be used to calculate the other.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>I took an average 17 mm as the centerpin/knuckle core measurement, and an average 12 mm as the knuckle top to center of shank measurement. 20.8 mm is the calculated lever arm from centerpin to knuckle top. Changing the 12 mm knuckle height to 13 mm, the lever arm calculates at 21.4 mm, a significant difference of 0.6 mm. (Moving the knuckle core 1 mm out to 18 mm makes a slightly bigger difference, changing the lever arm to 21.6).</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>I then plugged these numbers into the spreadsheet, using average vanilla figures from a Yamaha C-7 for key and wipp ratios, and came up with a compound action ratio of 5.17 for the 12 mm height, and 5.02 for the 13 mm height. This is a significant difference of about 3%.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>What does this mean in practical terms? One way of looking at the ratio, is that for every 1 mm of keydip you get (1 times the ratio) mm of hammer rise. Taking 10 mm of keydip, you have a 51.7 mm hammer rise for the 12 mm knuckle, and 50.2 mm of hammer rise for the 13 mm. Now in fact something on the order of 8.5 to 9.0 mm of keydip actually propels the hammer to the string, the remainder being taken up in letting off and aftertouch. 8.8 mm will raise the 5.17 ratio hammer 45.5 mm, and will raise the 5.02 ratio hammer 44.2 mm. To raise the 5.02 ratio hammer the same 45.5 mm requires 9.06 mm of dip, or .26 mm more. That is approximately .010", a blue punching. Or you get just about the same effect by raising or lowering the hammer via the capstan by 1.3 mm, a turn of probably less than 45 degrees.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Bottom line, a change of 1 mm in knuckle height is definitely significant, and something to keep an eye on. I think it makes sense to sort shanks if this can be done fairly rapidly, and I'd probably put the high ones in the bass, where thicker strings and farther letoff might actually make this a good thing in terms of consistency. But I don't think it is something to lose a lot of sleep over on a day to day basis <G>.<br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Regards,</div><div>Fred Sturm</div><div>University of New Mexico</div><div><a href="mailto:fssturm@unm.edu">fssturm@unm.edu</a></div><div><br class="webkit-block-placeholder"></div></div></span><br class="Apple-interchange-newline"> </div><br><div><div>On Mar 3, 2008, at 10:36 AM, Jon Page wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div><blockquote type="cite" cite="" style="padding-top: 0px; padding-bottom: 0px; "><font face="Arial" color="#000000">I'm not sure I follow your logic here...</font></blockquote><blockquote type="cite" cite="" style="padding-top: 0px; padding-bottom: 0px; "><font face="Arial" color="#000000"><br></font></blockquote><blockquote type="cite" cite="" style="padding-top: 0px; padding-bottom: 0px; "><font face="Arial" color="#000000">Isn't the letoff button going to be custom regulated to that wippen/</font></blockquote><blockquote type="cite" cite="" style="padding-top: 0px; padding-bottom: 0px; "><font face="Arial" color="#000000">jack? Hence, won't the distance the wipp travels before the jack </font></blockquote><blockquote type="cite" cite="" style="padding-top: 0px; padding-bottom: 0px; "><font face="Arial" color="#000000">tender touches the button be essentially the same? And isn't </font></blockquote><blockquote type="cite" cite="" style="padding-top: 0px; padding-bottom: 0px; "><font face="Arial" color="#000000">aftertouch then custom set relative to letoff?</font></blockquote><div><br></div><div>OK, perhaps my conceptual model isn't fully functioning, I'll have to</div><div>do a side-by-side comparison tomorrow morning.</div><div><br></div><div>But I do get good results from paying attention to the knuckle height.</div><x-sigsep><pre>-- </pre></x-sigsep><div><br>Regards,<br><br>Jon Page</div></div></span></blockquote></div><br></div></body></html>