The Math Behind Bach's Crab Canon

Dive into the fascinating world of Johann Sebastian Bach's Crab Canon! Explore the intricate mathematical patterns that make this piece a masterpiece. Learn about symmetry, inversions, and palindromes, and see how Bach's genius created a composition that plays forwards, backwards, and as a mirror image. Perfect for music lovers and math enthusiasts alike!

[hansgraf]

This video is amazing I can’t believe it doesn’t have more views

[scottekim]

Nicely animated and explained. The man walking forward and singing works very well as a visual explanation. And the little animated jokes are delightfully paced. No one (in video or in print) has yet analyzed how these canons work in detail, so I'll be doing that on my channel. As you point out, the standard i - iv - v - i harmonic progression does NOT reverse in classical harmony, so how did he do it? And this is the simplest of the canons! What blows my mind is when you listen to the piece you hear a musically coherent composition, not all the thought that went into it.

[ohadrip]

This is amazing !!
You sir are very under-appreciated, be very proud of the work you’re doing !

You are seen :)

[emreusername]

Great visualization and explanation. Just a little suggestion if you ever do a remake: After your enjoyable representation of two Johns singing forwards and backwards, you could've repeated it, but that time bounced two Johns at the middle to show the symmetry as well.

[RidiculouslyRandomProductions]

5:01 mah bro when I say a SINGLE word

[eloisaanascovillavicencio]

🎼🎹🎶🎵The best explanation of this master piece. Thanks sir 👏👏🎹🎶🎵🎼

[maidaiskandar]

amazing! thank u sm for ur explanation❤

[Rayenn_]

This Crab Canon is not even the most complex piece in his musical offering. There is another canon where you can play the imitation at three different timings, and it still aligns with the leading voice.

There is also a trio concerto consisting of three movements that uses Frederick's chromatic theme as the main theme. There is also another canon where Bach transposed each voice into all 12 keys.

And of course, there is the Ricercar a 6, which is a much more complex musical work in his musical offering.

On top of all, his Musical Offering is just a very small part of Bach's entire body of work. His Contrapunctus is on another level, let alone many of his vocal works, such as Confiteor (from the Mass in B Minor), where you have a double fugue (two subjects) that is entirely made up of intricate strettos from beginning to end, with double augmentation near the conclusion. Within the same work (Mass in B Minor), there is Credo, which is basically Bach's only known seven-voice fugue.

[alekseipupyshev]

The best explanation of Crab Canon magic so far 🎉

[giannottister]

Instead, it is very likely, that Bach improvised the 6-voice fugue on part of the King's theme in order to partially fulfill the royal request.

[ZukoHeirToTheThrone]

how are you hitting every one of those notes tho 😭

[Skhal]

Nah nah nahhh nananananah nah nah nah nah nanananananah 😁🤩

[yowfu]

Did you made up the part bach was failing one that contus firmus? Because he couldnt improvise 6 voices fugue? It can only be a composition and i am pretty sure bach would improvise on anything without thinking at least 3-4 voices and its been well excepted in academy as that too.

[dellasrevenge]

you painted Bach as a nervous coward... He was one of the most German dudes ever for God's sake... He was so defiant that he mocked Friedrich with his musical offering!