The soundbox of this harp is a long thin wooden torus, formed into a figure 8 and folded back on itself.
Then a series of strings can be stretched between adjacent sections of the box, so that their plane forms a Möbius strip.
Classified as a harp not a zither because the strings are perpendicular to the wooden surface they attach to, not parallel. And because attaching both ends of a string to the same soundboard on a zither is trivial.
You could reinforce this thing with struts and braces but I would prefer the soundbox to be self-supporting.
Not sure where the tuning keys would fit...-- pocmloc, Apr 02 2011 (?) Möbius planetary gears http://robotics.eec...hoover/Moebius.htmlJust found this - if you replace the blue and white gears with strings, this kind of shows the geometry of my instrument. [pocmloc, Apr 02 2011, last modified Apr 03 2011] Drawing https://picasaweb.g...vtA?feat=directlinkTop view, side view, front view. [pocmloc, Apr 04 2011] Chorus or Sambuca http://books.google...epage&q=sam&f=falseA Renaissance fantasy biblical wind instrument, could be the basis of a Klein bottle horn? [pocmloc, Apr 05 2011] Love it! I wonder whether the standing wave in a Möbius shaped soundbox would form a deeper resonance than one in an equally sized non-Möbius shaped volume?-- zen_tom, Apr 02 2011 Well, [zt], unless I am misremembering youthful experiments with paper, tape and scissors, the soundbox of this device would not be a Möbius strip, it would be a double length strip / rod with two twists. i.e. if in cross section we make it D section, with the flat part of the D the soundbox and the curved part the laminated back, then it would just twist twice as it curled around?-- pocmloc, Apr 02 2011 If we can figure out how to turn a Klein Bottle into some kind of wind intsrument, we'll have the makings of a pretty decent quantum band...-- Alterother, Apr 04 2011 sphericon harp-- JesusHChrist, Apr 04 2011 The Klein bottle could be an ocarina, but only if the ‘mouthpiece’ were constricted enough to blow into - taking away some of its Kleininess.
The sphericon could be made of sheet metal and with a small pebble inside, as a kind of rattling bell.-- pocmloc, Apr 04 2011 Love the sketch. Klein-Kazoo [Alterother]?-- 2 fries shy of a happy meal, Apr 06 2011 random, halfbakery