<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <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 bgcolor=white lang=EN-US link=blue vlink=purple> <div class=Section1> I believe you are the one confused.  Did you do the problem as I outlined?  For BPP to change between two notes targeting the same frequency, the speaking lengths must be different.  To see whether a change in frequency between two strings will be different with a change in length as a function of BPP you must start with two strings that have a different BPP.  If the strings are equal speaking length then no matter how you change the string diameter altering the tension and hold the frequency constant, the BPPs will change together.  A change in length will not result in a difference in the change in frequency between the two.  However, if you start with two strings of unequal speaking length with the same starting frequency, the tension (a in the first example) will be different, but the BPP’s will not be equal.  Now when you impose a similar change in length there will be a difference in the change in frequency between the two.   The more complicated calculation comes because we comparing just two different notes on the same piano.  You then must do the calculations and convert the change on each note to cents deviation so that you can see whether as the percentage of a semitone, one changes more than the other.  In other words, does the high bass go “out of tune” more or less than the low tenor.  The relative BPPs of the respective notes will give an indication of which will go out of tune more and it is the one with the lower BPP that will go out of tune more.  Namely, the BPP of the low tenor on a Steinway B, for example is around 22%.  The first note of the high bass is around 60%.   I have my own spreadsheet, thank you, perhaps yours needs a bit more work.   That’s the best I can do with the explanation for now—I gotta go to woik.  <div> David Love davidlovepianos@comcast.net www.davidlovepianos.com </div> -----Original Message----- From: caut-bounces@ptg.org [mailto:caut-bounces@ptg.org] On Behalf Of Richard Brekne Sent: Monday, June 11, 2007 11:15 AM To: caut@ptg.org Subject: [CAUT] pre-stretching new string?   David I'n not being antagonistic at all. I am just trying to help you understand something you seem clearly confused about. The two unknown formula link you offered for example.... there is no way you can use that in the context you have suggested.  Its a completely different problem type. The Tension formula is T = f^2*L^2*d^2* K  where K = the string density * PI / 981 You cant fit that into solving for an  aX+bY=c problem.  There is no way around it. You can calculate the change in length and measure the pitch change to get tension... or you can calculate change in length and change in tension to get pitch.... but you have to get two of these in order to get the third. As far as the diameter is concerned.  Use the spreadsheet I supplied with accompanying justifying formulas.  You can easily enough juggle the input tension for different wire diameters for same wire lengths to get the same starting frequencies. Then change the deflection input for both strings.  As long as they are the same length... any same deflection will cause the same frequency change. Cheers RicB See my other post but of course diameter plays a role.  It is a factor in determining break point percentage.  A thicker string will have a higher break point percentage and a thicker string will need to be at a higher tension to achieve a certain frequency at a given length than will a thinner string.  Simple stuff.  The claim about BPP as a factor in determining which string will go out of tune more goes way back.  You don't need to use BPP in the formula, you can simply calculate it for the two strings in question and observe the relationship-see my other (corrected post).  Please don't be so antagonistic.  I'm really trying to help you here.    </div> </body> </html>