One of Maurits Cornelis Escher’s most famous drawings is the staircase which seems to lead higher and higher and higher (or lower and lower and lower … depending on your frame of mind). I very recently learned (by reading in my favorite book) that a similar illusion exists in music under the name of Shepard scale. The effect is best experienced by listening to it (this is an .ogg file, but you can play it directly on the Wikipedia page if you have Java installed). The pitch of the tone seems to descend further and further and further … though ultimately it doesn’t get anywhere. I wonder if anybody can actually create this illusion on a piano. (This would require being able to differentiate between very fine nuances of volume.)

This video gives a related optical experience of zooming in closer and closer and closer, without really getting any closer.

Here’s another audio example where a rhythm appears to get faster and faster and faster (… but actually doesn’t).

Now I wonder: which senses does this work for? Could one construct a set of tastes so that each one appears to be sweeter than the last, although the set is actually periodic? Can one give a tactile sensation of more and more weight though, again, things keep getting back to where they started?

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