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Example:

0.762 mm string thickness with 6.35029 kg of tension to get A=440 Hz @ 647.7 mm string length

where a force Z provides 5 mm of string movement @ point 161.925 mm from one end of the string length and vertical movement Y occurs.

X = string length

Y = movement I am interested in

Z = initial force stroke

I need to solve for the initial force required to move the string under tension at the specific place, 1/4 of the length, and then I think I can use sinusoidal formulas? It is actually circular, since the lateral movement Z causes a vertical movement Y. What formulas should I use?

I plan to post the results I calculate for all strings of a 6 - 8 string guitars at different intervals and different initial conditions(IE frequencies, thicknesses, scale lengths, etc.) on my blog.

http://dejablueguitar.blogspot.com

Scroll down to see my balanced string tension article and calculations. I wish to do something similar for string travel at the crest for many strings etc.

Thank you in advance for any help.