Vi Hart has a clever video where she actually folds “space time”. You might imagine that folding our 3(4)D space-time would be hard (unless she happens to be extremely heavy! :-), so instead of working in our 3(4)D real space-time, she works in musical space-time by folding tone space! One of the most eye-catching things she does in that video is to make a mobius strip out of a music box sheet, thereby inverting the melody. (This particular stunt, although eye-catching, is actually not all that clever because all it does is to invert the melody. All you really need to do is to put the tape in the other way, and it’ll have the same effect in a less eye-catching manner. There are some other manipulations she does that are much more clever.)
One problem with Vi Hart’s video is that although she plays around with the formal (tonal) space-time, she doesn’t really do anything musical. So Leo and I decided to play around with actual melodies and see how they come out if you fold them in various ways. We tried a bunch of manipulations, and they mostly sounded like noise. I think that this is because the tonal space inversion in the particular strip width that we have on hand inverts into keys that are in some weird key. Probably we could have played around with transposition and got some of those manipulations to work better.
But one came out really beautifully. So here we present to you, a new tonal invention: Poe or Peel.
(Challenge for the reader: Why the weird name, esp. where does the “or” come from? 🙂
Incidentally, although there are many awesome math videos on YouTube, we find that NumberPhile has some of the best. Here’s an especially awesome mobius strip video from them. (This is part one of two — definitely watch both parts!)