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String Stretching, Frequency Modulation, and Banjo Clang

Posted by davidppp on Wednesday, April 16, 2014

I fulfilled my promise to my friend Rick to make him a 5 5/8" deep pot Goodtime for his very own.  When I tried it out, side by side with the original 5 5/8", the two had lots in common.  However, I was afraid that Rick would declare the new one in need of a sock under the head, while part of the charm of the original (at least to my mind) was that it was already sufficiently mellow without.  The only obvious mechanical difference was the tailpiece.  The original had a No-Knot to match the cut-down 2" rim banjo, while the new one had a stock Goodtime tailpiece.  Switching to a No-Knot on the new one produced a much better match.

I figured that this tailpiece effect was so dramatic that I should be able to understand it, at least vaguely, from first principles.

Physics descriptions of vibrating strings almost always assume that tiny variations in tension as the string moves can be ignored.  And that analysis actually works very well.  But I finally had to admit that, as the strings go over the bridge and the bridge moves up and down (a LOT on a banjo compared to other instruments), the strings have to stretch.  Trying to figure out what that stretching might sound like, I stumbled on the work of early pioneers in electronic music synthesis.  They long ago discovered a relation between frequency modulation (what you'd get from bridge motion and string stretching) and metallic and bell-like timbre.

In the end, I'm convinced that this stretching, which is a necessary mechanical consequence of the drumhead and floating bridge, is a key part of banjo sound.

You can find my write-up at http://www/its.caltech.edu/~politzer .   Or, even better, if you want to support my banjo research, do a Google search for:  banjo physics .  It should come up near the top -- and will continue to do so the more people click there.

Comments, suggestions, criticism are all welcome.



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