What: Okay you got me! Yes, this is not an optical toy, but an auditory one… the Shepard tone was named by/after scientist (and optical illusion lover) Roger Shepard in 1964, in this paper [1], Circularity in Judgments of Relative Pitch. Honestly worth checking out, as the paper instantly references the Penrose stairs [2], as a source of inspiration.

So what are we experiencing here? Well essentially a tone, or sound that feels like it is perpetually rising, or falling depending on the setting you have.

How To: Well, initially click to play (with sound on), and you should hear the sound/tone/hum, whatever you call it. For the default settings it should sound like the tone is getting higher and higher and higher… pretty much infinitely, like you’re always on the cusp of tipping over to the top, forever.

You can play with the different notes, and an endless “sinking” mode as well. I put a few little bits in here that at times made me feel like I was experiencing the effect more or less, so everyone could be a little bit different. In my cases, I was just listening to the tone over and over for a long time, so perhaps the option to slightly de-sync the octaves helped as my ear tried to hone in on the different frequencies starting.

Explain it: A fun thing about the auditory illusion, is I was able to add in a “how it works” toggle into the page, since we really have a full visual space available, so click that over and keep reading!

Essentially we have multiple tones at different octave levels that all glide upward together, and then at the higher ends and lower ends, we slowly phase in the volume. Your brain can’t really pick apart what is fading out, coming in, and so you’re stuck in a little bit of a stasis of “rising” or “sinking”

Wait, have I been subject to this before? You bet! Honestly it’s worth checking out the Wikipedia [3] for this since it’s been around for so long, and has appeared in so many places, but a couple of the fun ones I had run into.

• In the Dark Knight Batman series, the Bat-Pod (the motorbike thing), the bike does a kind of “constant” acceleration, with no gear shifts etc, when you look back at the videos [4] after learning about this effect, you’ll definitely recognize the tone.
• In Super Mario 64, the endless staircase [5], is a very similar version of the same effect, over a longer period with individual notes.

Cites and Extras:

• [1] https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf Shepard’s 1964 paper “Circularity in Judgments of Relative Pitch” - Journal of the Acoustical Society of America
• [2] Penrose Stairs … I’ve not really found a fun way to make this illusion interactive, or in any way with code outside of how it currently exists, so it’s not appeared on this site, but something for me to look into!
• [3] The wikipedia for this effect I try not to source it, but the list of places this effect is used is really good! The spectogram of the effect is very good too.
• [4] The Bat-Pod utilizing the Shepard tone, as it endlessly accelerates. Nothing can stop Batman.
• [5] Super Mario 64 Shepard Staircase truly, this effect has been hiding around all over the place, now that you notice it once, you likely will a lot more.
• If you enjoy this auditory illusion, check out the Risset Rhythm, which applies the same trick to tempo instead of pitch, an endlessly accelerating beat!

I've researched these optical illusions in my spare time but am clearly not any kind of expert and my explainations are pretty smooth brained, if you find something mis-cited, earlier examples, or general mistakes please new let me know via toymaker@toms.toys, be kind!