Dear Nerds,
I’m trying to design a rubber band harp on a 3D printing website. I work at a library and I think it’d be a great thing to show people, demonstrating some part of the breadth of useful and fun things that can be printed with the contraptions (doesn’t always have to be bloody Pokéballs)…if only I could get the dang intervals right!
I printed someone else’s design of the same concept. It was a hollow square, with a second piece with soundhole as a lid, and then little knobs to tie the rubber bands to on either side, after wrapping the bands around (underneath) the whole thing. Despite the author’s assertion that the harp was “even tunable,” it plainly was not – each rubber band, when plucked, produced a note, but completely out of order…unless it’s some avant-garde Harry Partch micro-tonal thing.
My own first design incorporated what I thought would be a bloody obvious improvement, which is slanting the knobs so that each rubber band will produce a distinct note. This
sort of worked, but certain bands were simply too close together to produce a different tone – one particular section was like four C#s in a row or something like that. And it still suffered (although less so) from the bonkers Martian scale problem, notes all out of order. I’m willing to accept that such may be the result of trying to make a musical instrument out of, y’know, rubber bands…but just in case there’s a way to do this properly, here is my question:
Is there a set formula one can use, or some way of calculating the math correctly, for how far apart to set the knobs for rubber bands? All I can think of is to make as many as I can that can possibly fit and then recording which ones actually worked; a trial-and-error test run. I’m doing them 1mm apart in height, with a row of them 5mm from each other in length. But for all I know it’s actually a multiple of 4mm that would eventually produce a whole note. Or, 3.76mm or something. Have I made my problem adequately clear? It has so far frustrated my attempts to Google it, despite how this is something that luthiers have figured out, like, thousands of years ago. Any assistance you nerds can render will by highly appreciated.
P.S. I mean, I’m a nerd too, but I can’t math; I am the softest of scientists.
P.P.S. The forum robot knows neither the word "tunable" nor "luthier," in a fascinating bit of trivia gleaned from watching the spellcheck underline them.
P.P.P.S Here is my working model of what in the nine hells I am talking about
:
https://image.ibb.co/k3cVwb/Rubber_Band_Harp.png