I would like to calculate the maximum distance, crest, a guitar string will travel at it's center when plucked in order to determine how high the string needs to be on the fretboard to avoid striking parallel frets and thus avoiding "fret buzz". 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.