<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div apple-content-edited="true"> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-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: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-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: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dale Probst<br>Registered Piano Technician<br>Ward & Probst, Inc.</div><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><a href="mailto:dale@wardprobst.com">dale@wardprobst.com</a><br>940.691.3682<br><br><br></div></span></span> </div> <br><div><div>On Sep 21, 2012, at 6:10 PM, Dale Erwin wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><font color="navy" size="2" face="Comic Sans MS, sans-serif"><font color="#000080" face="Comic Sans MS, sans-serif" size="2">Hi David</font> <div><font color="#000080" face="Comic Sans MS, sans-serif" size="2">  The first step here is to </font><font color="#000080" face="Comic Sans MS, sans-serif">always</font><font color="#000080" face="Comic Sans MS, sans-serif" size="2"> check the displacement first and then see how the numbers add up after measuring. I get numbers typical to the ones you state. I think Rick Wheeler at Roseland key uses Dels Method and I could never reconcile Ricks A.R. numbers with mine....till now.</font><span style="color: navy; font-family: 'Comic Sans MS', sans-serif; font-size: 10pt; "> </span></div> <div><font color="#000080" face="Comic Sans MS, sans-serif" size="2">and logically displacement is </font><font color="#000080" face="Comic Sans MS, sans-serif">displacement</font><font color="#000080" face="Comic Sans MS, sans-serif" size="2">...it doesn't lie. Its not a microscope but its a quick magnifying glass. Usually the difference between displacment numbers and measured number is no more than 1/10. ie 5.93 to 5.83</font></div> <div style="color: navy; font-family: 'Comic Sans MS', sans-serif; font-size: 10pt; "><br> <div style="clear:both"><font size="1" color="royalblue"><b><font face="Georgia, Times New Roman, Times, Serif"><font color="black"><font color="mediumblue" face="Comic Sans MS, sans-serif">Dale Erwin R.P.T.<br> <font color="green">Erwin's Piano Restoration Inc.</font><br> </font></font></font></b></font><font color="darkgreen"><span style="font-style: italic;"><b><font size="1"><font size="1" color="black"><font color="blueviolet"><font color="black"> <font color="black" face="Comic Sans MS, sans-serif">Mason & Hamlin</font><font face="Comic Sans MS, sans-serif">/Steinway/</font><font color="black" face="Comic Sans MS, sans-serif">U.S. pianos</font><font face="Comic Sans MS, sans-serif"><br> </font></font></font></font><font size="1" color="cornflowerblue" face="Comic Sans MS, sans-serif"><a href="http://www.Erwinspiano.com">www.Erwinspiano.com</a></font><font size="1"><br> </font><font size="1" color="crimson" face="Comic Sans MS, sans-serif">Phone: 209-577-8397</font><br> <font color="darkgreen"></font></font></b></span></font><tt><tt><font color="darkgreen"></font><span style="color: rgb(31, 73, 125); font-family: arial, helvetica; font-size: 10pt; "> </span></tt></tt></div> <div style="font-family:arial,helvetica;font-size:10pt;color:black"> <div id="AOLMsgPart_1_15b45aab-5881-47cf-ba77-4683a587289e"> <div class="WordSection1"> <div> <div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in"> <div class="MsoNormal"><b><span style="font-size:10.0pt;font-family:">From:</span></b><span style="font-size:10.0pt;font-family:"> <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [<a href="mailto:pianotech-bounces@ptg.org?">mailto:pianotech-bounces@ptg.org</a>] <b>On Behalf Of </b>David Love<br> <b>Sent:</b> Friday, September 21, 2012 7:52 AM<br> <b>To:</b> <a href="mailto:pianotech@ptg.org">pianotech@ptg.org</a><br> <b>Subject:</b> Re: [pianotech] Action Ratio measuring</span></div> </div> </div> <div class="MsoNormal"> </div> <div class="MsoNormal"><span style="color:#1F497D">Using my Renner action model I made the following measurements and calculations using both methods and this is what they yield.  While the exact point of measurement on using Del’s method, especially at the knuckle jack contact point, is difficult to be precise on and can be interpreted differently, there’s no question that even with the range of possible measurement points that method yields a lower number, too low, in my opinion.  When I calculate the action ratio by displacement, key travel versus hammer travel, the result is as you see below.  It should also be noted that with the displacement method the actual travel should be measured as the length of the arc segment and not the secant line that connects the two points (low and high) in a straight line.  Thus, the ratio using that method would be slightly understated.  That agrees more closely to the method I’ve suggested and is part of the reason that I use it.  I urge those with an action model to test the findings on their own.  </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D">Del’s method</span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" width="541" style="width:406.0pt;margin-left:-.75pt;border-collapse:collapse"><tbody><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="center" style="text-align:center"><span style="font-size:10.0pt;font-family:Courier">Ea</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="center" style="text-align:center"><span style="font-size:10.0pt;font-family:Courier">Ra</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-bottom:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Ratio</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td></tr><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Key</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">265</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-left:none;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">134</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">0.51</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td></tr><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Wippen</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">66</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">94</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">1.42</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Action Ratio</span></div> </td></tr><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Shank</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">22</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">142</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">6.45</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;border:solid windowtext 1.0pt;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">4.65</span></div> </td></tr></tbody></table> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D">My method</span></div> <table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" width="541" style="width:406.0pt;margin-left:-.75pt;border-collapse:collapse"><tbody><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-bottom:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="center" style="text-align:center"><span style="font-size:10.0pt;font-family:Courier">Ea</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-bottom:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="center" style="text-align:center"><span style="font-size:10.0pt;font-family:Courier">Ra</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-bottom:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Ratio</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td></tr><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Key</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">260</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">128</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">0.49</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td></tr><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Wippen</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">62</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">100</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">1.61</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Action Ratio</span></div> </td></tr><tr style="height:12.0pt"><td width="72" nowrap="" valign="bottom" style="width:.75in;border:none;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">Shank</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">17</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#92D050;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">127</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="72" nowrap="" valign="bottom" style="width:.75in;border:solid windowtext 1.0pt;border-top:none;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">7.47</span></div> </td><td width="72" nowrap="" valign="bottom" style="width:.75in;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"></td><td width="109" nowrap="" valign="bottom" style="width:82.0pt;border:solid windowtext 1.0pt;background:yellow;padding:0in 5.4pt 0in 5.4pt;height:12.0pt"> <div class="MsoNormal" align="right" style="text-align:right"><span style="font-size:10.0pt;font-family:Courier">5.93</span></div> </td></tr></tbody></table> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div class="MsoNormal"><u><span style="color:#1F497D">Measured by displacement.  6 mm of key travel yields 35 mm of vertical hammer travel 6/35 = 5.83</span></u></div> <div class="MsoNormal"><u><span style="color:#1F497D"><span style="text-decoration:none"> </span></span></u></div> <div class="MsoNormal"><u><span style="color:#1F497D"><span style="text-decoration:none"> </span></span></u></div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div> <div class="MsoNormal"><span style="color:#1F497D">David Love</span></div> <div class="MsoNormal"><span style="color:#1F497D"><a target="_blank" href="http://www.davidlovepianos.com/">www.davidlovepianos.com</a></span></div> </div> <div class="MsoNormal"><span style="color:#1F497D"> </span></div> <div> <div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in"> <div class="MsoNormal"><b><span style="font-size:10.0pt;font-family:">From:</span></b><span style="font-size:10.0pt;font-family:"> <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [<a href="mailto:pianotech-bounces@ptg.org">mailto:pianotech-bounces@ptg.org</a>] <b>On Behalf Of </b>Delwin D Fandrich<br> <b>Sent:</b> Thursday, September 20, 2012 12:10 PM<br> <b>To:</b> <a href="mailto:pianotech@ptg.org">pianotech@ptg.org</a><br> <b>Subject:</b> Re: [pianotech] Action Ratio measuring</span></div> </div> </div> <div class="MsoNormal"> </div> <div class="MsoPlainText">I use the measure points because they make the most sense to me—I've no idea how they correlate to those used by others. The most wear on a key takes place about 20 mm back from the front of the key so I assume that is where most pianists strike the keys most of the time. So that is where I start my measure. The next lever goes from the balance point to the center of the capstan. Then from there to the wippen flange center. Then to the tip of the jack where the jack contacts the knuckle. (Yes, I know the force goes first to the jack center but if you study the action model....) And then from the knuckle center to the hammershank center and from there to the tip of the hammer. Anyway, those are the points I use.</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">The longer the lever the less absolute accuracy matters. I usually try for the nearest half-mm. Sometimes I settle for the nearest mm.</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">It's easier when you are designing an action and key set—you can take it out to 14 decimals on the computer screen if you want. Not that that makes any real difference in the real world. And you don’t have to go through any contortions to get your measurements.</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">ddf</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">Delwin D Fandrich</div> <div class="MsoPlainText">Piano Design & Fabrication</div> <div class="MsoPlainText">6939 Foothill Court SW, Olympia, Washington 98512 USA</div> <div class="MsoPlainText">Phone  360.515.0119 — Cell  360.388.6525</div> <div class="MsoPlainText"><a href="mailto:del@fandrichpiano.com">del@fandrichpiano.com</a> — <a href="mailto:ddfandrich@gmail.com">ddfandrich@gmail.com</a></div> <div class="MsoPlainText"> </div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">-----Original Message-----<br> From: <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [<a href="mailto:pianotech-bounces@ptg.org">mailto:pianotech-bounces@ptg.org</a>] On Behalf Of Brown, David<br> Sent: Thursday, September 20, 2012 11:48 AM<br> To: <a href="mailto:pianotech@ptg.org">pianotech@ptg.org</a><br> Subject: [pianotech] Action Ratio measuring</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">Del, David and all-</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">Huge thanks for the completeness of these explanations and  examples. Del, the pdf was very clear. I am on a Mac, so bins  and the like come out wacky. I do notice from your example that this is yet a third way to measure key in, from balance point to front rail pin. How fussy are these in practice? Do the relationships remain constant? It would not seem so. +/- a mm? More ? Less? Thanks for all for taking daytime for this. It will take a while to digest.</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">Best-</div> <div class="MsoPlainText"> </div> <div class="MsoPlainText">David</div> </div> </div>  </div> </div> </font></blockquote></div><br></body></html>