<html> <head> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"> <meta name=Generator content="Microsoft Word 10 (filtered)"> <style>  </style> </head> <body lang=EN-US link=blue vlink=purple style='word-wrap: break-word; -webkit-nbsp-mode: space;-webkit-line-break: after-white-space'> <div class=Section1> <p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size: 10.0pt;font-family:Arial;color:navy'>Yes, Ron Nossaman pointed that out already.  I stand corrected (again).  </span></font></p> <p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size: 10.0pt;font-family:Arial;color:navy'> </span></font></p> <div> <p><font size=2 color=navy face="Times New Roman"><span style='font-size:10.0pt; color:navy'>David Love<br> davidlovepianos@comcast.net<br> www.davidlovepianos.com</span></font><font color=navy><span style='color:navy'> </span></font></p> </div> <p class=MsoNormal style='margin-left:.5in'><font size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>-----Original Message-----<br> <b><span style='font-weight:bold'>From:</span></b> pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] <b><span style='font-weight:bold'>On Behalf Of </span></b>Joe DeFazio<br> <b><span style='font-weight:bold'>Sent:</span></b> Tuesday, July 15, 2008 9:39 AM<br> <b><span style='font-weight:bold'>To:</span></b> pianotech@ptg.org<br> <b><span style='font-weight:bold'>Subject:</span></b> RE: summer sharpness in low tenor</span></font></p> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>on July 15, 2008, David Love wrote:</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'><br> <br> <br> </span></font></p> <span style='orphans: 2;text-align:auto;widows: 2;-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;word-spacing:0px'><span style='-webkit-text-stroke-width: -1'> <div bgcolor=white link=blue vlink=purple style='word-wrap: break-word; -webkit-nbsp-mode: space;-webkit-line-break: after-white-space'> <div> <p class=MsoNormal style='margin-left:.5in'><span class=apple-style-span><font size=1 color="#144fae" face=Helvetica><span style='font-size:9.0pt;font-family: Helvetica;color:#144FAE'>An examination of the formula for frequency of a string as a function of tension (or BP%), diameter, length (BP%) and looking at the differences in the rate of change depending on tension levels should yield more clarity.   </span></span></font></span></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;color:navy'> </span></font></p> <div> <p class=MsoNormal style='margin-left:.5in'><font size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;color:navy'>For example, take two strings of equal length producing equal frequency (the dependent variable) but with different diameters (gauges—they will have different amounts of tension and they will also have different BP%) and then change the length equal amounts and you should see a difference in the change in frequency between the two.  </span></font></p> </div> </div> </div> </div> </span> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Although I am far from an expert in rescaling or the physics of piano strings, I don't believe that the part of this about BP% is accurate.  My understanding is that two strings of equal length producing equal frequency will both be at exactly the same percentage of their respective breaking points.  For instance:</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Note 40 (C4), speaking length, 715mm , diameter of 0.040",  tension 199.957lbs, %breakpoint <b><span style='font-weight: bold'>49.436</span></b>%</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Note 40 (C4), speaking length, 715mm , diameter of 0.038",  tension 180.461lbs, %breakpoint <b><span style='font-weight: bold'>49.436</span></b>%</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>(figures from Pscale)</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>In other words, though the second string is smaller in diameter, and will be at a lower tension when producing the note "middle C," since its diameter is in fact smaller, its breaking point will be lower, and it will be at exactly the same <b><span style='font-weight:bold'>percentage</span></b> of its breaking point.  As I understand it, this is because, as its diameter changes, its breaking point changes proportionally.  See pages 33-35 in John Travis' "A Guide to Restringing" (in the section by James Hayes) for a simple experiment you can do to demonstrate this empirically.</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>The aspect of the string's behavior that does change in the example above is <b><span style='font-weight:bold'>inharmonicity</span></b>:</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Example above with 0.040 diameter, inharmonicity = 0.192</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Example above with 0.037 diameter, inharmonicity = 0.173</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>If I am wrong in my conceptual understanding, someone please correct me.  I want to be sure that I understand this correctly.</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>I will also point out that, from my archive reading and past posts, there are at least two formulae out there for calculating breakpoint and breakpoint percentage, so some of you might plug my numbers into your formula and get a different value for %breakpoint. However, that value should be identical for the two wire diameters given above.</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Joe DeFazio</span></font></p> </div> <div> <p class=MsoNormal style='margin-left:.5in'><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Pittsburgh</span></font></p> </div> </div> </body> </html>