<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> Hi Mark Just a quick note on the <<competing formulas bit>>. They are not really competing at all. They are simply different perspectives, looking at the problem from a completely different angle. I've been working through this side pin displacement bit a bit more and find what looks to be a big hole in the reasoning concerning the effect of increase in the length of the string segment on the bridge surface due to strings being forced up the pins and hence having their offset angle increased. The problem is that this increase in length primarilly affects the segment on the bridge itself. The speaking length is only changed by the actual vertical rise component. And this is lengthened mind you, which in itself contributes to a lowering of pitch.  The resulting total tension increase however compensates for this but must be figured over the entire length of the string... including front lengths, lengths up to the bridge pins, back lengths and bridgesurface lengths in addition to the speaking length. This tension increase must be then applied to the very slight increase in speaking length within the standard formula for frequency. All this assumes no friction for simplicity. The net increase in frequency then for long strings at lower tensions is not nearly so dramatic after all,  tho the impact from an increased offset angle does dominate the picture. The formula sheet  provided by Dr Galembo looks a lot more comlicated then it is. Its really simple triangle trig for figureing the lengths, and Hooks law for finding the resulting increase in tension.  The formula used for calculating frequency once these two are done is the same, taken from the Calculating tension. For a given a wire of 1390 mm speaking, 100 mm backlength, 1.1 mm Ø with a 20 mm wide bridge and 10 ¤ offset and 10 ¤ pin angle all at 127,5 lbs starting tension and 0 vertical deflection, a 1 mm rise in soundboard results in a 1,029 cent rise in pitch.  Add a 0.2 mm rise in the bridge surface with all that implies for lengthening the bridge surface segement and a very slight increase in speaking length.. you get an additional 2.82 cent rise... or a grand total of a 3.85 cents rise in pitch.  Not so dramatic after all. Brings me back again to what I started off saying... the affect on long strings is minimal... and next to nothing if the starting tension is reasonbly high.  On shorter strings however... the change for bridge surface rise gets dramatic None of this includes the length from the front termination to the pin... which further reduces the net change in tension and hence pitch due to the fact that tension disperses over the entire string. Cheers RicB <blockquote> I think this has been a great discussion. There have been many aspects effecting the pitch change of strings that I had never considered and are very relevant to my work. Now those last few jabs concerning the competing formulas may not have been necessary. I didn't sit down and try to understand either formula so I'll never know who was at fault. The fact that there are formulas out there designed to clarify these things is all I need to know right now. I say go ahead and hash it out. But change the subject line so I can hit the delete button if things get too obstinate. Mitch Staples</blockquote> </body> </html>