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If you want an interesting animation on top of that, here is a Shepard-Risset glissando with an animation based on work from M.C. Escher:

https://www.youtube.com/watch?v=u9VMfdG873E

The animation is actually more engaging than the sound, but they do work amazingly well together.
This YouTube video is the best example of a Shepard Tone I've heard: https://www.youtube.com/watch?v=OsBanpBQj0k

In a dystopian way it's the ever rising desire of intensity and panic for the economy to eternally grow.

Similar to the visuals of this eagle's wing and lion's fur: https://i.pinimg.com/originals/e5/34/b3/e534b3beef8e2e2d5765... continually flowing outward, but the overall look staying the same. Together they have become how I think of human generations ; forever birth, aging, death of individual people outflowing to the isolated edges of old age, but the overall structure holding. Differnt to a river made of individual water drops or history repeating like a spiral.

Vox did a great video on how Hans Zimmmer used this in the Dunkirk soundtrack to create growing suspense and anxiety.

https://www.youtube.com/watch?v=LVWTQcZbLgY

This was the first thing I thought of. I love that the technique relates to the tone and themes of the movie instead of just being a cool effect.
Huh. Whereas my first thought is always the noise of the bat-cycle from The Dark Knight - which is also directed by Nolan and scored by Zimmer.
That's where I came across the article, from reading about Zimmer. Dunkirk had a very loud, but great soundtrack!
I have always seen Tom Jobim’s “Águas de Março” as a beautifully-conceived usage of Shepard’s Tone in a song:

https://youtu.be/wBEesrdaRog

I have been in love with this song for decades. There is definitely a feeling of circularity going on. Here are a couple of my favorite versions, if anyone wants to go down the rabbit hole.

SF Jazz Collective (heavy modern jazz arrangement):

https://www.youtube.com/watch?v=z-F_1OvPdqA

Cassandra Wilson (earthy, lyrics in English):

https://www.youtube.com/watch?v=cIehPcFebHo

Trio Mocoto (melody played on Cuica, which is nuts):

https://www.youtube.com/watch?v=tqTlFa3Fnlk

These are fantastic. Thank you! I can't imagine how in the world that person in Trio Mocoto played the melody on that instrument. Mind-blowing.

As an aside, I recently heard on the radio a cover of this by Art Garfunkel, which may be one of the worst things I've heard. As you may expect, he mananged to strip all of the life out of the song, which made me sad.

I always heard it the other way... constantly descending (like rain)
Same. Shepard's Tone can refer to either perceptually-rising or falling tones.
I've always thought a shepard tone is basically an audio version of a barber's pole. When it spins, it looks like its endlessly rising.
In both, the illusion can be broken by focusing on the top or the bottom. This is pretty easy for me with discrete scales, but a bit harder in the glissando at the bottom of the article. I've got nothing on the perpetual melody, though.
that's exactly right. psychophysics is fascinating!

my favorite example of a shepard tone appears in an old wilco track that appears to be missing from the list.

notably shepard wrapping forms the basis of octave invariant chroma scales used in handcrafted features for old school automatic music transcription algorithms. (probably supplanted by nn stuff today)

Watch CNN/FOX for 1 month and you'll become very familiar with the mechanism. Somehow things can always be getting worse.
Sometimes the bass notes (left hand) on an accordion are blended in this way. The stradella bass only lets you play a single octave of bass notes. But if each note plays octaves, and as you go up the scale, the top octave fades out and the bottom octave fades in, it's not very easy to tell which octave you're in.
I sometimes compare this to the seemingly ever rising absurdity of life/business/politics etc.

"The Shepard tone of insanity"

Things seem to perpetually get worse in some way, or so it seems. But often it just appears that way due to similar mechanisms of newly introduced stupidity. Or something like that.

I learned recently, via a Tolkien biography, that this is the Medieval view of the world - that things are always getting worse.
Yeah, I call that the fallen world fallacy. Once you recognize the basic concept, you start to see it everywhere. Atlantis was some amazing civilization that did everything right, but then some corrupt stinker spread his corrupt ideas it and it fell. The Garden of Eden was perfect, and some schmuck ruined it, and things immediately started to suck, and continued to suck more the further we got from it. Etc etc. These are the underpinnings to so many independent world cultures. It's fascinating.

I wonder if it's just inherent to human minds? Or if it's a natural consequence of how we start off as infants having everything taken care of for us, in a world where everyone we know has a defined role and mostly sticks to it, and then as we grow, we find more and more responsibility, and opportunity to make mistakes, and we learn that adults are just fallible humans like us...

In my personal view, I think the reason this mindset exists is that humanity never solves all problems at once. We're constantly playing a game of marco-polo crossed with whack-a-mole. Sure we may never solve all of our problems, but that's the fun of being a human.
I want to figure out how to specify a Shepard tone in `sox`. (Open invitation to draft with me on thread.)
Usually this is done in a `kilt` as well. The key is to use a bagpipes.
Old school version:

https://youtu.be/tg50ozbZcqM?t=216

In the stepwise descent Bach uses the complementary interval of a seventh to leap up before he runs out of pedal notes (i.e., a seventh is just a step with the lower note moved up an octave). But organ pedals typically have some turbocharged partials grooving along, so the leap up a seventh can easily be confused with change of tone color or even volume change on a descending step. Paired with the sustained chromatic harmony changes in the right hand, the pedal's bassline seems to be eternally descending. (Plus Bach extends this unadorned circle of fifths passage much longer than he normally would in any other piece-- if the purpose isn't to imply a potentially eternal descent I don't know what he's doing here...)

Try listening without watching the scrolling score and see if you can pick out where those pedal leaps are.

Also-- ascending new school version, now with "carriage returns":

https://www.youtube.com/watch?v=Q6LmG9myHxA

You also get a nice simulated "Nyquist frequency" when the piano runs out of keys. :)

Edit: clarification