TonyGonzales84 -> RE: Manufactures choice of strings on a guitar (Jun. 25 2020 0:25:44)
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My apologies for the while it’s taken me to do this. I dug around a bit suspecting strongly that in the end I’d end up where I am, namely, the classical expression for the fundamental frequency of a stretched string is as good as I’ll be able to estimate the difference in required tensions at different scale lengths. Konstantin correctly stated this as 3.7% for a 662 mm scale vs a 650 scale guitar. I am including my results here, and not starting a new thread, because I do not wish to over-sell null results, often the yield of “research.” This originally started with my comment on the relative perceived hardness of EJ-46 strings on a 662 mm scale guitar vs that on a different luthier’s 650 mm scale guitar. I believe it’s given that 1) Tom Blackshear is correct in stating that, the top’s torque response to the strings’ applied loads is the biggest driver in the perceived hardness (the important apples to apples requirement), and that 2) Konstantin correctly states the 3.7 % numerical value for the string tension difference resulting from the classically derived result for a stretched string’s fundamental frequency, and finally, 3) orsonw is correct that the vibrating system has to include the entire guitar. I also believe orsonw’s science philosophy comment, that guitars are secretive where revealing themselves to “reductionist measurement,” is probably currently true, for the method of attack I tried on the problem. I am including a two page summary, scanned as pdf, of the results I obtained, that I would view as a sidebar or appendix, to be read only if it interests you, and with my apologies for my handwriting! My hope had been that I could find some quantification of the guitar’s effective mass and stiffness, that I could then incorporate in my glorified back-of-the-envelope analysis, but I found nothing like that (probably because no one’s needed to set up a test lab to measure said quantities!). I did find a (surprisingly to me) large number of finite element modeling of various types of guitars – classical, steel-string, carbon construction, etc, performed at various universities, world wide. These tend to focus on frequency response analyses, showing mode shapes and deformations. I did not know there is so much work being done here! Echi, I would be very interested in seeing design guide formulae used by various luthiers, especially if they are of similar form at the different shops. I do understand that these are the types of guidelines that would be closely held and guarded.
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