Dear Jon,
> On the lute and guitar, and other instruments of fixed string lengths that > are "stopped" to change notes the problem is a bit different than on the > harp, psaltery and other such - where the string is not stopped, each string > is its own pitch. But the calculation of strings remains the same. The same formulas can be used to determine the string tension. However, on instruments with stopped strings the tension sligthly increases when the string is pressed against the fingerboard. But that has to taken into account when finding the proper fret positions. > Breaking point (tensile strength) > Mass (density) > Acceleration (a constant that has been variously described to me, it happens > to match the 32 feet per second per second of gravity, but I think that is > likely a coincidence and the constant has to do with the normal pull by the > finger). It is not a coincidence and it has nothing to do with the pull of the finger. It simply has to do with the units you use. Since force = mass times acceleration it is possible to define a force unit via the acceleration it produces on a mass unit. earth's gravitational acceleration is used for that purpose because it is more or less constant and is present anywhere on earth. I don't know US-units very well, but this is surely the reason why earth's acceleration appears in your equation. > As one who has played guitar for well over fifty years I found the formulas, > and the empirical comments, to be ridiculous, until I tested them. Whatever > the guage of a monofiliment string (the wound strings are different, their > mass increases but the tensile strength doesn't - the core guage is the > tensile strength) the pitch at which it will break is almost constant, with > regard to length. Although this is not what one would assume, it is quite logical: Let's say you have a thin and thick string of the same material. The thick string could be x times stronger than the thin one. However, to obtain the same frequency you also need a x times higher stretching force. Therefore both strings break at the same frequency (but different stretching forces). I think this is one reason why the old lutenist's rule to tune the highest course as high as possible without breakage is not so arbritrary as it seems. At least it is independent of the string diameter. It mainly depends on what the player considers to be "as high as possible". Greetings, Stefan
