But what does that have to do with a Mobius strip? "Two players starting at the same place on the strip and travelling in opposite directions" would play the same thing if it were just a normal loop of paper. I see no reason to add the twist to make it a Mobius strip. What is that supposed to represent? Also, why is it so hard to write counterpoint that works when played both directions simultaneously? I would have expected it to be quite easy to do that, since many tunes naturally sound nice when played backwards. Separate such a tune into its two voices and place them one after another and you have one of these.
No, that's not what I meant. I wasn't saying take any song that sounds good and play it backward and forward simultaneously. I was saying if you take a song that *already* has counterpoint and sounds nice backwards (and there are a number of those), then all you have to do is separate the two voices and put those two voices back-to-back. Now when you play *that* backwards and forwards at the same time, you get the original song and then the original song backwards, which should sound fine. And it should also sound nice by itself since good counterpoint generally involves making each voice sound good in its own right.
Xezlec I assume you've never written counterpoint before if you think it is easy to write a piece that adheres to contrapuntal methodology and accomplishes a pleasing melody in both directions and while played simultaneously in opposite directions.
Well it's a given that it has to be on a mobius strip to play the whole piece. If it were a simple ring which you describe, it would play half the piece forwards and backwards simultaneously which probably doesn't harmonize correctly. I get it's not what your talking about but I'm saying it's the only way for it to make sense, the math behind it means everything perectly fits into a mobius strip, in ANY order. If you try and do something else, you'll have to figure out something else for it...
@@magicmulder if you read the background of "the musical offering" (that this is part of) it was response to a challenge to demonstrate his technical skill. His most captivating stuff to me are the cantatas which you can hear by searching BWV 1 through 200
It's stuff like this that always makes it hard to pick Beethoven over Bach as my favorite composer. Th genius displayed in this composition is otherworldly.
My highschool history teacher was lecturing about Bach last week and showed us this video. So, for those of you who didn't know, this actually began as a musical puzzle. Frederick the Great challenged Bach with a musical canon that in theory was impossible to solve, or finish. This was the answer to that challenge.
As I say above, this genius by Bach almost totally convinces me that Bach, perhaps along with Beethoven and other geniuses who seem to defy what we consider to be 'modern realities', were in fact advanced human life forms visiting us from the future. The work of Steven Greer, Bob Lazar, and Professor Michael P Masters, along with Robert Temple's 2022 book 'A New Science Of Heaven' (about plasma energies and higher intelligence, etc, and much more - actually infinitely more) correlates; as do the teachings in the Bible and other religious scriptures. Ball Lightning = the 'burning bush' for example. Supernatural phenomena, hypnotism, remote viewing... Join the dots. Thanks and love, Alan Chapman (Live Wild Live Free, etc) - incidentally that's followed by a period then the abbreviation for organisation. Also my name and the period and most common global extension. I write it like this because otherwise the algorithms on this somewhat selectively oriented platform refuse to allow my comments :)
fish and banana Bach was merely a creation of God, and if I daresay, one the very best creations, for he has given humanity such gifts that endure to this day! And I'm quite sure his music is played in heaven.
We did this piece in our Music advanced course in school back in the day because our teacher was a real big fan and after understanding the whole thing we all sat there with our mouths open.
What amazes me about J. S. Bach is how consistently good All his music is. Of course I like some of his works more than others but each one is a logical gem and perfect in its own way. He exhausts whatever is to be had from each theme.
No, no, no, if it is chicken by the sea it still a chicken, but the can says: Chicken of the Sea; therefore tuna. Which now a days is probably tuna flavored pollock the real chicken of the sea.....is Jessica Simpson worthy of being quoted wouldn't Lisa Simpson be better? Just Kidding..................lol
Depends how you define success. Fame is one thing but composing over a thousand pieces which are musically perfect another thing. I don't have the knowledge to explain Bach's perfection but just listen to his music, every bar is different and sounds unique.
Bach was a well established musician, well known and respected among his pairs (even if was less popoular than Thelemann or Haendel)... his music went out of fashion very soon after his death, but his work was well (not in all its aspects! of course) known among musicians (Mozart, Haydn, Beethoven knew his work, the well temperate clavier was well known and largely used at least as a didactic work and so on) also thank to his sons Johann Cristian and Carl Philip Emanuel (fine and usccesful musicians) and some work of his were performed witha certain regularity after his death (think that a great Bach biography was published in 1802 - "only" 52 years after his death... this couldn't happen to a forgotten or unknown composer) Usually In the past musicians were forgotten after their death and this fact begin to change at the end of XVIII century - think to such musicians as Monteverdi or Vivaldi or Zelenka (just to name a few): they were completely forgotten. "Forgotten and neglected Bach" is largely a sort of romantic myth...
Bach might be laughing merrily at us, marveling at something he could have created over a cup of tea. Or a pint of beer. How in the world he could have come up with something so deceptively simple, yet so profoundly complex? In a single line? Brahms was right to remark on the other enigmatic piece (Chaconne, Partita No.2) that the experience in creating it alone would "have driven me out of my mind". This drove me speechless!
In 8th grade, I memorized Bach's Invention #4 over the Christmas break. My piano teacher was blown away that I MEMORIZED it. As in played it without the sheet music. People who can sit down at a keyboard and instantly play anything (no matter how complicated) as long as it's all written out and in their face amazes me. Too much visual shit going on, which is why I memorize it; it takes hours, but I get it done. ADHD has its drawbacks...
No, not exactly. He just wanted to grab atention to his music not in the same ofl hum diddle dee dumb dumb melody line plus thumpity thump bas. once you start fiddling around with this technique, it becomes fun. So not a genius. Just a good notemaker. haha!
What this proves is, without MUSIC, there would be NO MATHEMATICS!!! This is also a proof that the Creator of the universe is a being of ORDER, not chaos. God SPOKE (organized vibration) the universe into existence. By God setting everything into motion in an organized manner, sound/music could only be a medium which would require organized, orderly thinking to unlock its construction. Humans developed "tools" (a way of thinking) to "dis"-cover/uncover the perfect system that created not only music, but the order of creation itself.
Just found my french edition copy in a card box full of books I got back from stuff left at my deceased little sister's house. She left us at age 37. I'm still happy to have my book back but hope you won't have to go through such a loss to find yours. Friendship and much love.
Yes, it is obvious that Bach is directly hooked in with the infinite, and is ingenious, mathematical and technically brilliant; but do you also hear how BEAUTIFUL this piece is musically, and even emotionally??? Even if you weren't aware of the technical genius, symmetry and loopiness ( to quote Douglas Hofstadter), you can't help but appreciate the musical beauty of this piece. To me that is what is so remarkable about Bach.
J.S. Bach - Crab Canon on a Möbius Strip 0212am 17.11.23 i like this - one piece of music added to a Mobius strip... played forward and played back in one fell swoop then the opposing sides play at the same time... then you can slow the mirrored piece down as you speed the original score up... ahaha...
Da Vinci is especially rememberd for revolutionizing medicine. In the early 16th century it was forbidden from the church to harm anyones dead body, meaning it was impossible to make an autopsy and see why the person actually died (also nobody knew how the inside of a human looked). Da Vinci did not care and became the first to do a forensical autopsy and created what we today call human anatomy.
Crab canons have the special property of sounding amazing played forwards and backwards simultaneously, but that has little to do with the geometry of a mobius strip. A song with a true "mobius strip" geometry would play both sides at once: the back side is upside down, so it would play a pitch-inverted second half at the same time as the first half, followed by vice versa. (Edit: This is called a Table Canon, and Bach's Quaerendo Invenietis is an example, with true Mobius Strip geometry). You can hypothetically create a new "song" with a crab canon property out of any song, by removing half the notes (roughly evenly distributed), taking the removed notes as a single object, reversing that object, and appending it to the end, thus making two "half songs" with the second being backwards. This results in a new song, which when played forwards and backwards at the same time gives you the original song back. Of course, it would be difficult to make one that sounded any good.
Well, two things. First, I'm not aware of any Bach contemporary who did something like this to a composition of theirs. Second, in order to do this, it was suggested in your post that a song could be cut in half, inverted, glued, and looped in the same way and it would work. I've considered this, and it's probably true. But Bach didn't do that. It went straight to music composition paper. And he already knew what the result was going to be. For 1747, that wasn't too shabby. Today, I seriously doubt the masses who write music even remotely consider composing such a canon which made it a once in a lifetime endeavor. Those in the industry might think about it for a moment, then clang their glasses in toast to "Hail Herr Bach" for a job well done!
Oh, I don't deny Bach's talent...he was able to compose things in his head, as you say. Ah, it's hard to put into words what I'm trying to say. All I really meant to say was, the depiction of a mobius strip is just the animator's choice, it's not a reflection of Bach's special property. The animator could have used a regular circle or a figure 8 or anything else and it would have worked for this song. The song is not innately _like_ a mobius strip in any particular way. When I say, take a song, cut it in half, flip it etc., I'm not giving instructions on how to make a song like Bach's. Rather, I'm giving instructions on how to make this animation. And you could do this animation with a Miley Cyrus pop song (just leave out the backwards-moving bit) but that doesn't mean Miley Cyrus writes songs with a special "mobius strip" like property. There are two bars playing at once, in reverse directions along the loop. _That_ was Bach's property, that the song is played forwards and backwards at once, and that couldn't be done with another song without some special preparation and skill. The animator could have, after cutting it in half, flipped the second half _left for right_ instead of up for down, and then glued. Then he could just play both sides at once, in a single direction. That would visually demonstrate the property. But I'm just nitpicking. I actually do like this animation for what it is. The reason I commented was because I noticed that it suggests the possibility of actual mobius-like songs, with pitch inversions like I said...
Ƹ̵̡Ӝ̵̨Ʒ Ha! I see what you were saying! I've had known this piece for years and found this animation intriguing but beautiful. As you said, I did find the animation somewhat redundant. It still work if the music was played along the cross section of the Mobius strip, front to back, endlessly. It would work because the piece is symmetrical and when you cut it in half no matter which way you are playing, the counterpoints from each half would seamlessly match. So I think the Crab Canon does have the property of Mobius Strip, to some extent.
The remarkable thing isn't the mobius strip visualization, but the the crab canon is played both forward and backward at the same time. This is certainly almost unique to this piece.
Hey thanks for this. This is a really useful visualization for understanding how these lines work. Eventually I hope to generate more media like this for different Bach compositions to shed light on their complexities.
Thank you for this Jos. It appeared as a UA-cam prompt a few weeks back now. Since then I have been reading up on the Bach Musical Offering, and listening to it. It served to increase my already high opinion of the man. :-)
Thank you so much for creating this video - as many times as I watch it through the years, I rediscover the way Bach literally heard how the Universe is built.
Another masterpiece by Bach, the inimitable. And very nice work from a master of graphic explication, Jos Leys. I'm not surprised. Groeten uit zonnig Wenen, Scott
Bach actually did this sort of thing in many of his canons. In one suite, he actually did something called a "Canon al Rovescio" or "Canon in Reverse". He had a subject (derived from an earlier theme, of course), but was consistently played in canonic motion with the retrograde of the subject. Bach was a true genius.
Absolutely brilliant presentation... of course, JSB was the REALLY inventor of the Möbius Strip, even if he didn't know what it was called!! Thank you for this presentation.
Mozart probably heard this by the time he was six years old and understood it and could probably play it back for you after hearing it once. That's why Mozart and J. S. Bach are among the great masters of music. Untouchable brilliance!!!
***** I'm assuming this is a joke, and I'm calling you out on it because I KNOW someone, soon or later, will take this comment seriously, and it will make me sad.
+Eorzat Actually it's not far from the truth. It has been reported that Mozart asked for the music sheet of a mass he heard in church once but saw his request refused so he went home and wrote it all down by ear. Every single note. He was 6 years old. Don't underestimate the musical abilities of an autistic brain, you could find yourself astonished.
All composers are musicians, but not all musicians are composers. So, saying that he is the best musician of all times is much more than just saying he is the best composer of all times.
+alphaknave you clearly haven't heard the right pieces then :P done well, serialism can be as delightful as some of bach's work (though I must admit that this canon in particular is one of my favourites)
I am a very visual and tactile person. I don't know anything about musical technique. So when I started reading the description I felt my attention begin to wander. But I perservered because it sounded like something worth watching. And Bach...well I felt I owed it to..somebody to at least try and follow! And I was so pleased watching the video I GOT IT! Thanks!
Eunoia's explanation is perfect. Actually, given a (musical, or of other kind) line X, let X^r be the reversed line (for instance, with characters, (abcc)^r = ccba). Now, let P and Q be staves, and suppose that the scheme of your song is "the stave P over the stave Q", that is P
At first I was amazed but I didn't understand this film at all, so I learned the piece on the piano. Now I must say I hear no difference between 1:15 (without Möbius strip) and 2:04 (with Möbius strip). The image on the film is different, but the audio is exactly the same. Even though the Möbius strip idea is genius, I believe that it is not Bach's idea. Anyway, thanks for the film !
You are absolutely right. The Möbius strip visual presentation has nothing to do with the music; rather, it may mislead the audience into believing that the composition would be more than what it is.
If there's any example to put to rest why JSB is the greatest composer of all time, this is it. An exercise in technical prowess whereby he demonstrates that not only can he compose a melodic line that is beautiful when played in the forward and reverse direction - but it sounds even more beautiful when both parts are played simultaneously! If that's not genius and a result of divine intervention, I don't know what else would qualify as such.
@@historicwine1283 If you ever diligently listened to entire Mozart catalog, most of Beethoven themes are straight rips from Mozart. Sure he expanded on them but IMO he borrowed the most of ideas out of all the greats. So who is the prophet?
I had to listen to this for my Bach class in college. Too bad the rulers of the Germanic provinces didn't realize just how insanely genius Bach was, or they would have bowed to HIM.
people like Bach were the living " computers " of their time, using their mind in a highly specialized way with practical real time enjoyable results :Just imagining the "education" or training involved into translating it all into a correct live performance is a trip in itself... As the story about the canon goes Bach would improvise on the theme up to four voices harmonization and backward too.... the moebius strip is the perfect nest for this... tnx
I could give my opinion about this on a Moebius strip but it would be a bit one sided.
That was good 😂
you are a terrible person
Joseph Peddie We’re making paper-thin jokes here. I’m pretty sure you meant “tearable”.
And it might put you on edge too.
@@jaromtoy7128 That just doesn't cut it.
so i guess the piece just go BACH and FORTH
Stop. Please.
Funny.
well done
I..I honestly laughed out loud.
Actually it goes round and round.
This is mathematically brilliant.
i'm a complete idiot when it comes to music AND math, mind explaining how it's brilliant?
But what does that have to do with a Mobius strip? "Two players starting at the same place on the strip and travelling in opposite directions" would play the same thing if it were just a normal loop of paper. I see no reason to add the twist to make it a Mobius strip. What is that supposed to represent?
Also, why is it so hard to write counterpoint that works when played both directions simultaneously? I would have expected it to be quite easy to do that, since many tunes naturally sound nice when played backwards. Separate such a tune into its two voices and place them one after another and you have one of these.
No, that's not what I meant. I wasn't saying take any song that sounds good and play it backward and forward simultaneously. I was saying if you take a song that *already* has counterpoint and sounds nice backwards (and there are a number of those), then all you have to do is separate the two voices and put those two voices back-to-back. Now when you play *that* backwards and forwards at the same time, you get the original song and then the original song backwards, which should sound fine. And it should also sound nice by itself since good counterpoint generally involves making each voice sound good in its own right.
Xezlec I assume you've never written counterpoint before if you think it is easy to write a piece that adheres to contrapuntal methodology and accomplishes a pleasing melody in both directions and while played simultaneously in opposite directions.
Well it's a given that it has to be on a mobius strip to play the whole piece. If it were a simple ring which you describe, it would play half the piece forwards and backwards simultaneously which probably doesn't harmonize correctly. I get it's not what your talking about but I'm saying it's the only way for it to make sense, the math behind it means everything perectly fits into a mobius strip, in ANY order. If you try and do something else, you'll have to figure out something else for it...
ARE YOU FEELING IT NOW MISTER CRABS
comment of the year
No its Patrick
Art thou feeling it now Mr. Krabs?
I love you for this comment
im feeling it spongebob
PATRICK THAT'S NOT A RIDE
At first I was like "yeah, it's alright, not a very exciting piece" but then I realized the true beauty of what Bach has done.
TheJaredtheJaredlong // I can admire the “twist” (pun intended) but just listening to it - not that captivating.
@@magicmulder I actually think it's really beautiful, not just about how brilliantly he composed it. It sounds so beautiful and captivating to me.
@@magicmulder if you read the background of "the musical offering" (that this is part of) it was response to a challenge to demonstrate his technical skill. His most captivating stuff to me are the cantatas which you can hear by searching BWV 1 through 200
Reminder that JS Bach did this one afternoon just to get his son a job.
he had a son?
@@Spades7009 he had 20 sons.
7 with his first wife and 13 with his second wife.
@@user-fx6xd5pm3q they were all boys?
Is this true?
@@Spades7009 sorry, 20 children not 20 sons.
I never get tired of hearing this masterpiece...
Bach was a genius
Aah, come on, you are making me blush :D
It's stuff like this that always makes it hard to pick Beethoven over Bach as my favorite composer. Th genius displayed in this composition is otherworldly.
lol
Luciano AquiNo I know
MY BOI YOU LIVIN????
My highschool history teacher was lecturing about Bach last week and showed us this video. So, for those of you who didn't know, this actually began as a musical puzzle. Frederick the Great challenged Bach with a musical canon that in theory was impossible to solve, or finish. This was the answer to that challenge.
This is hyperdimensional musical topology. Bach literally processed his music in his mind, in multiple hyperspatial dimensions.
As I say above, this genius by Bach almost totally convinces me that Bach, perhaps along with Beethoven and other geniuses who seem to defy what we consider to be 'modern realities', were in fact advanced human life forms visiting us from the future. The work of Steven Greer, Bob Lazar, and Professor Michael P Masters, along with Robert Temple's 2022 book 'A New Science Of Heaven' (about plasma energies and higher intelligence, etc, and much more - actually infinitely more) correlates; as do the teachings in the Bible and other religious scriptures. Ball Lightning = the 'burning bush' for example. Supernatural phenomena, hypnotism, remote viewing... Join the dots. Thanks and love, Alan Chapman (Live Wild Live Free, etc) - incidentally that's followed by a period then the abbreviation for organisation. Also my name and the period and most common global extension. I write it like this because otherwise the algorithms on this somewhat selectively oriented platform refuse to allow my comments :)
The mobius strip can literally be embedded in 3 dimensions lmfao
You must be a Redditor LMAO @@HilbertXVI
That could be a simple explanation
@@Mr.Oblivian And you must be a child LMAO
Bach was in a league of his own. Far above the rest of the classical composers. It not only is intelligent, it also sounds so beautiful.
Beethoven is a close second in my opinion
As i suspected, JSB is not from planet earth.
JSB is not human!!! He's a divine archangel!!!!!!!!!!!!!!!!!!!!!!
fish and banana Bach was merely a creation of God, and if I daresay, one the very best creations, for he has given humanity such gifts that endure to this day! And I'm quite sure his music is played in heaven.
just middle of Germany :D
We did this piece in our Music advanced course in school back in the day because our teacher was a real big fan and after understanding the whole thing we all sat there with our mouths open.
@@quondamchoir6615 Heaven is perfect and changeless, therefore timeless, therefore without music. I think I'll go to Hell for preference.
Bach's genius remains incomprehensible. Out of this world.
What amazes me about J. S. Bach is how consistently good All his music is. Of course I like some of his works more than others but each one is a logical gem and perfect in its own way. He exhausts whatever is to be had from each theme.
"I was obliged to be industrious. Whoever is equally industrious will succeed equally well."
Bach
"Is this chicken, what I have, or is this fish? I know it's tuna, but it says 'Chicken by the Sea.'" - Jessica Simpson
No, no, no, if it is chicken by the sea it still a chicken, but the can says: Chicken of the Sea; therefore tuna. Which now a days is probably tuna flavored pollock the real chicken of the sea.....is Jessica Simpson worthy of being quoted wouldn't Lisa Simpson be better? Just Kidding..................lol
Bach wasn't very successful at his time. People didn't begin to see Bach's compositions as art before the 19th century: long time after his death.
Depends how you define success. Fame is one thing but composing over a thousand pieces which are musically perfect another thing. I don't have the knowledge to explain Bach's perfection but just listen to his music, every bar is different and sounds unique.
Bach was a well established musician, well known and respected among his pairs (even if was less popoular than Thelemann or Haendel)... his music went out of fashion very soon after his death, but his work was well (not in all its aspects! of course) known among musicians (Mozart, Haydn, Beethoven knew his work, the well temperate clavier was well known and largely used at least as a didactic work and so on) also thank to his sons Johann Cristian and Carl Philip Emanuel (fine and usccesful musicians) and some work of his were performed witha certain regularity after his death (think that a great Bach biography was published in 1802 - "only" 52 years after his death... this couldn't happen to a forgotten or unknown composer)
Usually In the past musicians were forgotten after their death and this fact begin to change at the end of XVIII century - think to such musicians as Monteverdi or Vivaldi or Zelenka (just to name a few): they were completely forgotten.
"Forgotten and neglected Bach" is largely a sort of romantic myth...
Bach might be laughing merrily at us, marveling at something he could have created over a cup of tea. Or a pint of beer. How in the world he could have come up with something so deceptively simple, yet so profoundly complex? In a single line? Brahms was right to remark on the other enigmatic piece (Chaconne, Partita No.2) that the experience in creating it alone would "have driven me out of my mind". This drove me speechless!
J. S. Bach (1685-1750)
Möbius Strip: 1858
:O
To be fair the graphic in the video is kinda unnecessary and more like "oo look how cool it looks", but still very :o indeed
Further proof Bach was not human
Do you mean ö
This guy is ahead of his time
Mobius put a name a previous idea!
In 8th grade, I memorized Bach's Invention #4 over the Christmas break. My piano teacher was blown away that I MEMORIZED it. As in played it without the sheet music.
People who can sit down at a keyboard and instantly play anything (no matter how complicated) as long as it's all written out and in their face amazes me. Too much visual shit going on, which is why I memorize it; it takes hours, but I get it done. ADHD has its drawbacks...
I got goosebumps just watching this video. How did he make this piece? This blows my mind.
A true genius.
No, not exactly. He just wanted to grab atention to his music not in the same ofl hum diddle dee dumb dumb melody line plus thumpity thump bas. once you start fiddling around with this technique, it becomes fun. So not a genius. Just a good notemaker. haha!
STOP
Nope. Genius.
Daniele Martinelli . Pure genius
"I was obliged to be industrious. Whoever is equally industrious will succeed equally well." - Bach
Bach is the great master who came to earth to teach us composition
I think this proves that Bach was a mathematician.
PS1897 there is no doubt in that.
PS1897 His mirror fugue from the Art of Fugue prove it better; they are astonishingly well done
What this proves is, without MUSIC, there would be NO MATHEMATICS!!! This is also a proof that the Creator of the universe is a being of ORDER, not chaos. God SPOKE (organized vibration) the universe into existence. By God setting everything into motion in an organized manner, sound/music could only be a medium which would require organized, orderly thinking to unlock its construction. Humans developed "tools" (a way of thinking) to "dis"-cover/uncover the perfect system that created not only music, but the order of creation itself.
@@deliseovpstudio2978 big brain time
@@deliseovpstudio2978 pretty sure mathematical laws were in place before music was a thing. Otherwise the sound waves would be pretty wack.
Okay, after half a bottle of wine this utterly fried my brain. I read Godel, Escher, Bach decadse ago, but I need to find a copy again.
Half a Klein bottle?
Just found my french edition copy in a card box full of books I got back from stuff left at my deceased little sister's house. She left us at age 37.
I'm still happy to have my book back but hope you won't have to go through such a loss to find yours.
Friendship and much love.
i can’t explain how much my brain loves this
I don't know how to react to this incredible genius...
Same. I'm assuming a genius wouldn't react to it. They'd just start playing.
Douglas Hofstadter was fascinated and spent so much time describing it, but you have done even more to make it a visual, as well as a musical, delight
I’m waiting for the Klein bottle version.
*lol*
Underrated comment
What a great math joke!
Lmfaoooo ahahhahaha hehehe
He did a Klein bottle version too. I know it inside out.
I've been listening to Bach for well over fifty years and I can still be surprised. . . brilliant.
Yes, it is obvious that Bach is directly hooked in with the infinite, and is ingenious, mathematical and technically brilliant; but do you also hear how BEAUTIFUL this piece is musically, and even emotionally??? Even if you weren't aware of the technical genius, symmetry and loopiness ( to quote Douglas Hofstadter), you can't help but appreciate the musical beauty of this piece. To me that is what is so remarkable about Bach.
J.S. Bach - Crab Canon on a Möbius Strip 0212am 17.11.23 i like this - one piece of music added to a Mobius strip... played forward and played back in one fell swoop then the opposing sides play at the same time... then you can slow the mirrored piece down as you speed the original score up... ahaha...
Bach was the da Vinci of music.
RawRiffRock But he's not really remembered for it, like he's remembered for his paintings and other visual art.
Bach to music as Newton to phisycs
Da Vinci is especially rememberd for revolutionizing medicine. In the early 16th century it was forbidden from the church to harm anyones dead body, meaning it was impossible to make an autopsy and see why the person actually died (also nobody knew how the inside of a human looked). Da Vinci did not care and became the first to do a forensical autopsy and created what we today call human anatomy.
@@RobespierreThePoof Da Vinci lived before vesalius.
???
Bach is the bach of music...
The are some composers that have many sublime moments, but only Bach's tend to infinity
왜 바흐가 음악의 아버지인가 싶어 찾다 보게 된 영상인데 13년 전이라니 미쳤다... 대단하셔
Bach is called 'the father of music' in Korea. This video is also great. Thanks
As a fan of classical music and mathematics, this I should adore my entire life.
Crab canons have the special property of sounding amazing played forwards and backwards simultaneously, but that has little to do with the geometry of a mobius strip. A song with a true "mobius strip" geometry would play both sides at once: the back side is upside down, so it would play a pitch-inverted second half at the same time as the first half, followed by vice versa. (Edit: This is called a Table Canon, and Bach's Quaerendo Invenietis is an example, with true Mobius Strip geometry).
You can hypothetically create a new "song" with a crab canon property out of any song, by removing half the notes (roughly evenly distributed), taking the removed notes as a single object, reversing that object, and appending it to the end, thus making two "half songs" with the second being backwards. This results in a new song, which when played forwards and backwards at the same time gives you the original song back. Of course, it would be difficult to make one that sounded any good.
Well, two things. First, I'm not aware of any Bach contemporary who did something like this to a composition of theirs. Second, in order to do this, it was suggested in your post that a song could be cut in half, inverted, glued, and looped in the same way and it would work. I've considered this, and it's probably true. But Bach didn't do that. It went straight to music composition paper. And he already knew what the result was going to be. For 1747, that wasn't too shabby. Today, I seriously doubt the masses who write music even remotely consider composing such a canon which made it a once in a lifetime endeavor. Those in the industry might think about it for a moment, then clang their glasses in toast to "Hail Herr Bach" for a job well done!
Oh, I don't deny Bach's talent...he was able to compose things in his head, as you say. Ah, it's hard to put into words what I'm trying to say.
All I really meant to say was, the depiction of a mobius strip is just the animator's choice, it's not a reflection of Bach's special property. The animator could have used a regular circle or a figure 8 or anything else and it would have worked for this song. The song is not innately _like_ a mobius strip in any particular way.
When I say, take a song, cut it in half, flip it etc., I'm not giving instructions on how to make a song like Bach's. Rather, I'm giving instructions on how to make this animation. And you could do this animation with a Miley Cyrus pop song (just leave out the backwards-moving bit) but that doesn't mean Miley Cyrus writes songs with a special "mobius strip" like property.
There are two bars playing at once, in reverse directions along the loop. _That_ was Bach's property, that the song is played forwards and backwards at once, and that couldn't be done with another song without some special preparation and skill.
The animator could have, after cutting it in half, flipped the second half _left for right_ instead of up for down, and then glued. Then he could just play both sides at once, in a single direction. That would visually demonstrate the property.
But I'm just nitpicking. I actually do like this animation for what it is. The reason I commented was because I noticed that it suggests the possibility of actual mobius-like songs, with pitch inversions like I said...
Ƹ̵̡Ӝ̵̨Ʒ Ha! I see what you were saying! I've had known this piece for years and found this animation intriguing but beautiful. As you said, I did find the animation somewhat redundant.
It still work if the music was played along the cross section of the Mobius strip, front to back, endlessly. It would work because the piece is symmetrical and when you cut it in half no matter which way you are playing, the counterpoints from each half would seamlessly match. So I think the Crab Canon does have the property of Mobius Strip, to some extent.
The remarkable thing isn't the mobius strip visualization, but the the crab canon is played both forward and backward at the same time. This is certainly almost unique to this piece.
It would certainly make noise, but it wouldn't work musically. It'd be cacophony.
It is beyond my grasp of understanding but I love it.
“If only the whole world could feel the power of harmony.” W.A.Mozart
Read about this in Godel Escher Bach. Love it.
Hey thanks for this. This is a really useful visualization for understanding how these lines work.
Eventually I hope to generate more media like this for different Bach compositions to shed light on their complexities.
Derpin MacDerperonton plz do, , it is much needed.
This was the very first video I saw on UA-cam. More than a decade later it's still one of my favourites.
Quanto mais escuto Bach, mais maravilhado ficamos. Gênio, gênio.....
Wow, I mean wow. I can't believe I didn't see it coming but that was certainly incredible.
Holy crab!
Thank you for this Jos.
It appeared as a UA-cam prompt a few weeks back now. Since then I have been reading up on the Bach Musical Offering, and listening to it. It served to increase my already high opinion of the man. :-)
Thank you so much for creating this video - as many times as I watch it through the years, I rediscover the way Bach literally heard how the Universe is built.
Another masterpiece by Bach, the inimitable. And very nice work from a master of graphic explication, Jos Leys. I'm not surprised.
Groeten uit zonnig Wenen, Scott
Bach actually did this sort of thing in many of his canons. In one suite, he actually did something called a "Canon al Rovescio" or "Canon in Reverse". He had a subject (derived from an earlier theme, of course), but was consistently played in canonic motion with the retrograde of the subject. Bach was a true genius.
Really the most fantastic film i've ever watched, thank you master!
Such genius is staggering. Thank you Jos Leys, for presenting this so brilliantly.
Fabulous, Bach and the way was made this video, FANTASTIC
Thank you for sharing
Absolutely brilliant presentation... of course, JSB was the REALLY inventor of the Möbius Strip, even if he didn't know what it was called!! Thank you for this presentation.
Thank you for this very nice demonstration of its structure !
This video shows the sublime genius of Bach, which impresses me every single day of my life...
Yes, indeed, the music of the soul. And also of the brain and heart. There's Bach, and then there's everyone else.
Bach was a alien bro
I love it and I must watch it every once in a while 💙💚
Simply brilliant - the visualization as well!!
Excellent! It's J.S.Bach! Gods own musician! Thx for uploading!
Merry christmas to all of you🎄
Mozart probably heard this by the time he was six years old and understood it and could probably play it back for you after hearing it once. That's why Mozart and J. S. Bach are among the great masters of music. Untouchable brilliance!!!
Mozart was a genius, but don't let the myths influence your opinion too much. What you described is just unrealistic.
Mozart....overrated.
Probably. Twice.
UNTOUCHABLE BRILLIANCE!!!!!!!!!!!!!!
You silly
***** I'm assuming this is a joke, and I'm calling you out on it because I KNOW someone, soon or later, will take this comment seriously, and it will make me sad.
+Eorzat Actually it's not far from the truth. It has been reported that Mozart asked for the music sheet of a mass he heard in church once but saw his request refused so he went home and wrote it all down by ear. Every single note. He was 6 years old. Don't underestimate the musical abilities of an autistic brain, you could find yourself astonished.
I don't know what's going on here or why it's so impressive but this is so goddamn cool
Clever! A great little video that demonstrates the idea better than words every could!
This is a most fantastic visualization of Musikalisches Opfer. What a great teaching tool! Thanx!
How can any one ever possibly say who is the greatest musician of all time?
Utter the name Johann Sebastian Bach, do the math.
Compooooser
also musician :D
oh bullshit
John Dunstable, Josquin Desprez, Carlo Gesualdo, J.P. Sweelinck, Dietrich Buxtehude - a few names, J.S. Bach would have mentioned!
All composers are musicians, but not all musicians are composers. So, saying that he is the best musician of all times is much more than just saying he is the best composer of all times.
Amazing. Modern composers may wonder how Bach was capable of imagining this piece without a computer.
Love,
It encourages me to believe that Bach was some sort of alien/advanced human form visiting us from the future.
And these "unparalleled art/amazing intricacies" were all in a day's work...for him.
This was really very well done! Thanks, Jos Leys.
Almost makes me want to give up writing, but I'll soldier on till I drop!
Meu Deus, Bach era um gênio na música 😮
Really neat concept. The animation really helps to follow along as well.
Thank you so much for the visual. It makes so much sense, especially I'm studying Mobius strip in topology now.
Thank you so much for this.
Bach simplemente no tenía límites... ESTO ES IMPRESIONANTE!
Holy shit, this is probably the most mind-blowing piece of music I've ever heard in my life.
very special ,accomplished work of a master
This is so amazing that my computer won't even play it for me !
My choice to live in the mountains.
This is basically Serialism 400 years before it existed, and twice as genial.
Joel Carli it's not serialism, it's not 400 years before, but I do agree it's genius ;)
Not 400 years, true, I overshot it haha. And it's not explicitly the same as serialism, but it is similar, in that yes, it's genial.
Joel Carli Serialism is not aesthetically pleasing, whereas this is, despite it's logical complexity. That's why it's FAR SUPERIOR to serialism.
+alphaknave you clearly haven't heard the right pieces then :P done well, serialism can be as delightful as some of bach's work (though I must admit that this canon in particular is one of my favourites)
+Xatnu Rowan You're right: I haven't heard much serialism. I heard some of Schoenberg's, vomited all over myself, and vowed "never again!"
I am a very visual and tactile person. I don't know anything about musical technique. So when I started reading the description I felt my attention begin to wander. But I perservered because it sounded like something worth watching. And Bach...well I felt I owed it to..somebody to at least try and follow! And I was so pleased watching the video I GOT IT! Thanks!
The best musician overall to ever live.
Eunoia's explanation is perfect. Actually, given a (musical, or of other kind) line X, let X^r be the reversed line (for instance, with characters, (abcc)^r = ccba). Now, let P and Q be staves, and suppose that the scheme of your song is "the stave P over the stave Q", that is
P
bichord - I don't know. Something just doesn't add up.
At first I was amazed but I didn't understand this film at all, so I learned the piece on the piano. Now I must say I hear no difference between 1:15 (without Möbius strip) and 2:04 (with Möbius strip). The image on the film is different, but the audio is exactly the same. Even though the Möbius strip idea is genius, I believe that it is not Bach's idea. Anyway, thanks for the film !
You are absolutely right. The Möbius strip visual presentation has nothing to do with the music; rather, it may mislead the audience into believing that the composition would be more than what it is.
I think the point it was showing was that the two parts can join together seamlessly?
it's absolutely sublime, I love this piec sooo much !
If there's any example to put to rest why JSB is the greatest composer of all time, this is it. An exercise in technical prowess whereby he demonstrates that not only can he compose a melodic line that is beautiful when played in the forward and reverse direction - but it sounds even more beautiful when both parts are played simultaneously! If that's not genius and a result of divine intervention, I don't know what else would qualify as such.
알클사에서 넘어왔는데....너무충격적이다
Godel , Escher , Bach :
Good book.
Nice!
Searching for this comment
P.S.: MU
MUU
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Beautiful visualization. Thanks!
Bach is an angel.
Bach is my only misgiving regarding the nonexistence of the divine. Otherwise I'm an utter atheist.
I feel this so hard
You're not an atheist if you believe in Bach.
the holy trinity: bach, motzart and chopin.
@@tennisracket6987 Bach and Beethoven.The rest are merely prophets.
@@historicwine1283 If you ever diligently listened to entire Mozart catalog, most of Beethoven themes are straight rips from Mozart. Sure he expanded on them but IMO he borrowed the most of ideas out of all the greats. So who is the prophet?
mind blown!!!
Enigma illuminated! I'm going to share--this is coolest thing I've seen all year.
great video. blew my mind when they both played at once
I had to listen to this for my Bach class in college. Too bad the rulers of the Germanic provinces didn't realize just how insanely genius Bach was, or they would have bowed to HIM.
I'm a person
Congratulations :)
OH HI IM ALSO A PERSON< TOTALLY NOT A ROBOT HAHA AHA ERROR
[_] I am not a robot.
snap woohoo
that's a human person
wow. this is just pure greatness. Well done.
Thank you!!!!!
great production! JS Bach would really enjoy it.
The first 2 notes sounds like it's going to be the Evangelion opening
This comment is cursed
Hello fellow digenerate. Guess us weebs all notice these things.
This comment is blessed
This comment is blursed
This comment is blreapeated
Asian dad: Great. Now play it backwards.
Kid: I did that already...
people like Bach were the living " computers " of their time, using their mind in a highly specialized way with practical real time enjoyable results :Just imagining the "education" or training involved into translating it all into a correct live performance is a trip in itself... As the story about the canon goes Bach would improvise on the theme up to four voices harmonization and backward too....
the moebius strip is the perfect nest for this...
tnx
Meu Deus! Sou apaixonada por Bach. Que presente maravilhoso. Grata!🎶🎶🎶🎶🎶🎶🎶😂😂😂😂💥😂😂😂😂😂😂😂😂😂😂😂😂
vim pelo PAS
this made me feel uneasy. like having Riharda
brilliant i never expected he also makes the forward pieces
Brilliant and illuminating. Thank you!