Long S's, F-Holes, Stringed Instruments, and Calculus

That's right. All of those things are actually related. Let me tell you a little story.

Last night, I was sitting at the Garnet Valley Jazz Festival, watching one of the bands play. While letting my mind wander, my gaze fell on one of the guitars onstage. This wasn't one of your typical acoustic, or even one of your typical electric guitars. It looked more or less like the one to left. Very, well, violin-like.

While looking at the guitar, I thought, 'Well, huh, isn't it weird that the openings on the guitar look an awful lot like an integral sign in calculus?' I shared this with some people and got a less than enthusiastic response (though I do still love your sense of humor :) ). I decided to shelve the thought for then and look it up when I got home.

And so here I was sitting, looking up the integral sign to find out of it had some relation to the openings on stringed instruments. First I was led to this article on Wikipedia about the Long S. If you've ever seen one of the original Constitutions of the USA, this is the symbol in Congress that makes it look like "Congrefs." No, it's not that the founding fathers didn't know how to spell, just that back then, the long s sound (like in the word paradiSe, loSt or CongreSs) was written as, well, a long s. It looks a lot like an F without the middle bar. Interesting.

I continued to read in the article and found out that Leibniz (the other founder of Calculus, with Newton being the first) used the long s as a shorthand for the Latin word "summa" (sum), which would be written "fuma," when writing integrals. This makes perfect sense, considering that the integral is the infinite sum of the function times dx. Wow, that makes a lot more sense than when I thought the integral sign was a f.

Still, I hadn't found the answer to my original question of "Why stringed instruments have an integral sign on them?" Though, now I could rephrase the question replacing integral sign with long s. It turns out those holes in stringed instruments are called f-holes because of their resemblence to the cursive f. But really, they're long s's. It's just that in modern typography, the long s isn't really used at all, so it's confused for f. The f-holes do serve as sound amplifiers, but at the same time they're mainly aesthetic. So, there's really no shape that they have to take, they've just taken taken the shape of the long s by tradition.

So, there you have it. A careful web we weave. Isn't it interesting how seemingly disparate objects could be so carefully intertwined? If not, I'm happy I learned a few new bits of trivia.

Namaste.