Music on a Clear Möbius Strip - Numberphile

"I wrote this piece on a Möbius strip." "What's Möbius strip?" "I don't know. He hasn't been born yet."

Time to put it on a Klein bottle, so we can have more of Cliff Stoll

Bringing back memories of vihart’s old video on this topic.

Correction at 4:30 and 4:38: as the video is still referring to the Crab Canon ("Canon Cancrizans") in The Musical Offering, it's actually not "turning the tune upside down" ("inversion" in counterpoint terminology), but rather "playing the tune backwards" (i.e. "retrograde motion"). The Musical Offering does contain a canon that involves "turning the tune upside down", which is the first of the two "Quaerendo invenietis" ("seek and you shall find") canons (the one for two voices), and this one actually has at least four possible solutions—"seek and you shall find", so Bach deliberately left this as a mystery.

I absolutely love the fact that "there are exactly Du Sautoy crossing points among the diagonals of a regular nonagon" is something that has now been stored in my brain, and I wanna thank you for that

My father had a master's degree in physics and a doctorate in music. He would have loved to see this.

As a classical and baroque music enjoyer, and an amateur mathematician, this is really one of the best videos I've ever seen.

Really super animations for this one! Great work Pete!

I'm a mediocre musician, and certainly no sort of mathematician. But this presentation somehow supports something a concert pianist once said to me: "Bach is the sound of the universe in motion." I've always thought this was true subjectively, but perhaps this is why it felt so right. Thank you as always!

🎶 This is the song that never ends. It goes on and on, my friends...🎵

One thing that was at first unclear it that the reverse playing is still right side up. I initially thought that you turned the page over. So in my imagination you would not be not playing the same notes backwards, but rather their counterparts on an inverted staff. EITHER OF THOSE WAYS, that he figured it out without recording devices or software is mind blowing. Actually, it seems that doing it as he did without inverting, using the same notes, would seem to be more difficult!!

Whenever I see a piece by Bach, I'm always like, "Yup, here's someone who didn't play a wind instrument."

I love seeing mathematicians analyze music.

I have a bit of a correction here, Bach did not invent the puzzle canon, those were an established tradition in polyphony from the Late Medieval/early Renaissance at least.

The book "Gödel, Escher, Bach" by Dr Hofstadter is a must read to really appreciate the level of intelligence needed to compose something like this.

As a person who loves Mathematics my favorite composer is also Johann Sébastien Bach particularly his Brandenburg concerto 3,4,5 and Minuet & Bardinerie.

I've never understood why we'd send music into space, after all, it's just a collection of notes. But now i do. Because it's probably the most objectively complex piece of audio/visual data we can send. It's beautiful.

There is a type of music called table music where you place the music on the table and the 2 musicians play on opposite sides of the table. One is playing it normal and the other backwards and upside down.

I think Bach's Fugue in E minor (Well-Tempered Clavier book I) can also be visualized on a Möbius strip. Also, one of the many neat things of his Musical Offering is that the music is printed such that the music can be placed on a table, musicians can stand on either side of the table, pretend that their side is right-side-up, and the same melody makes counterpoint. So not only is it mathematically interesting, but it's also creative in how musicians occupy their space.

Going back to the 60s, the BBC drama Z-Cars had a very distinctive theme tune. The spin off series "Softly Softly" was the same piece of music simply turned upside down.