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Zalgo's paradox

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These are basically Shepard tones; each one is a fundamental in the bass range with harmonics at all octaves (2, 4, 8, 16, and so on times the fundamental frequency) rolling off 3dB per octave. The result is that each one is associated with a pitch class - a note within the octave - but not with any specific octave. A well-known illusion is to sweep one up or down, with appropriate amplitude scaling; it sounds like it's going up or down *forever*.

Here, I'm playing each note roughly 249 cents lower than the last. I'm also reducing the spacing (time between starts of notes) exponentially: each note is played after 29/30 as much delay as the previous one. That leads to the paradox, because on the one hand, there is in theory no "last" note. After any note, another one will be played strictly later. But on the other hand, the piece has an end. There is a time after which no more notes will be played, under these rules. How can this be?

It's very much like Zeno's paradox about Achilles and the Tortoise, hence the name. The 3dB/octave roll-off means that at the end, when there are an infinite number of notes playing simultaneously, what we're left with is pink noise: energy spread indiscriminately across the audio spectrum with a 3dB/octave rolloff. There is no randomization here, just simple deterministic rules for playing pure tones. No other sounds are added at the end to make it sound different from the beginning. The boundary between order and chaos is all in your head.

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