How a Bach Canon Works. Brilliant.

Bril­liant. This mov­ing man­u­script depicts a sin­gle musi­cal sequence played front to back and then back to front. Give the video a lit­tle time to unfold.

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Comments (41)
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  • test­ing new com­ment sys­tem… =0

  • Open Culture says:

    Hi all,

    Does this new com­ment sys­tem seem ok? Any thoughts?

    Thanks for the hand,
    Dan

  • Greg says:

    Twit­ter and FB con­nect both were tak­ing for­ev­er to con­nect so used Open Id which worked fine/quickly. To be fair, twit­ter has seemed to be hav­ing issues today so prob­a­bly some­thing on their serv­er end.

    I like the con­cept of being able to use any id to log in though!

  • RaphaelleH says:

    That is incred­i­ble. Love the infi­nite loop visu­al. And DISQUS is fan­tas­tic. Just need to get it for myself already.

  • Open Culture says:

    Hope­ful­ly the Twit­ter and FB logins will work. That’s part of what I was hop­ing to accom­plish here.

    Thanks again,
    Dan

  • gary says:

    as always Open Cul­ture is #1 in my book, thank you!

  • Nicolas Buff says:

    Great, infor­ma­tive ani­ma­tion. I recent­ly learned that once upon a time musi­cians would mail their canons to one anoth­er as puz­zles. The task was to unrav­el how the canon worked from the sin­gle giv­en line. What­ev­er hap­pened to great pas­times like these?

    • Beta Cummins says:

      Nev­er, ever knew that. Worth repeat­ing: what­ev­er hap­pened to pas­times like these?

      Cheers!

  • gor­geous­ly genius.

  • Beta Cummins says:

    I love Bach, but can’t recall hav­ing lis­tened to this piece before. What is it called?

  • IridiumDinosaurs says:

    The rela­tion­ship between music, art, life and math­e­mat­ics. The notion of ‘unde­cid­able propo­si­tions’. such as the geom­e­try in some­thing you see in the esch­er tri­an­gle, which does­n’t seem wrong but does­n’t work either, in your sys­tem. struc­tured music which you hear and the pat­terns or puz­zles of the can­non, how is that pos­si­ble?. The exis­tence or nature of God as an axiom, The notion of genius, athe­ism, a uni­verse,.. with or with­out a god, or to believe.…

    AN INTERESTINGLY POWERFUL FORMAL SYSTEM (any­thing) which is seem­ing­ly incom­plete, or inconsistent,..The impli­ca­tion, in philo­soph­i­cal terms, is that we must always choose between know­ing that there are truth’s that can­not be proven (incom­plete­ness) or know­ing that there are state­ments that are both true and false, at the same time (incon­sis­ten­cy). with­in a (your) giv­en frame­work SUCH AS LIFE. .… The whole GEB idea and con­cepts about mean­ing, loops and val­ue with­in the infi­nite real­ly forces me to think of the way we live… need to get pri­or­i­ties right methinks.

    This is a book which cov­ers every­thing! (Gödel Esch­er Bach, an Eter­nal Gold­en Braid by Dou­glasHof­s­tadter.)

    this a book which explains every­thing with meaning!(Critical Path by Buck­min­ster Fuller)..

  • Lori says:

    Absolute­ly bril­liant!!!

  • What does the twist in the Möbius loop rep­re­sent? The tune does not seem to swap high for low (so far as I could tell).

  • Victoria says:

    Of course! Har­mo­ny, Coun­ter­point and Com­po­si­tion are pure Math­e­mat­ics — and the rea­son I was allowed an alter­nate cred­it to the Math cours­es on offer in my last year of High School! The real beau­ty of this for me was the plea­sure of the har­mon­ic expres­sion of Math­e­mat­ics. How­ev­er, I would always encour­age pur­su­ing the Cal­cu­lus and Geom­e­try cred­its even if you are intend­ing to be a musi­cian! Math­e­mat­ics pro­vides a won­der­ful and nec­es­sary entry to so many oth­er sub­jects.

  • mary o'connor says:

    math­e­mat­ics and music are of the world and our expe­ri­ence. they are not so much man made as man-found and dis­cov­ered.

  • ketler says:

    Won­der­ful!

  • aya yuson says:

    music is math & math is music… ‘cept music sounds good.

  • Luca says:

    Infi­nite jest. Ear­ly morn­ing Bach is the men­tal equiv­a­lent of brush­ing my teeth. Even 5 min­utes seems enough to defrag what remains of my hard-dri­ve.

    A pre­cious site, is this. Thank you.

  • fuse says:

    Here’s my rock music crab canon — it’s the song and its ret­ro­grade mixed togeth­er — same for­wards or back­wards! Also please read the pro­gram notes — it is a palidrome — the first word is the last, the sec­ond word is the sec­ond last, etc. All hail the arch!
    http://tindeck.com/listen/lpvc
    Also, I;ve writ­ten a good fugue in clas­si­cal style (last variation)for all you coun­ter­point junkies! Enjoy!
    http://tindeck.com/listen/jbbb

  • Amaz­ing­ly done!!! Bra­vo!!!

  • Elly Smith says:

    I did love hear­ing Bach. Don’t hear music like that these days. I have some of Bach’s CD’s.Will have too lis­ten to them again to com­pare.

    d

  • This is amaz­ing, I’m SO going to use it in my teach­ing!

  • Anna says:

    Bril­liant
    Your site is amaz­ing
    Love you guys

  • A. Person says:

    I should­n’t be sur­prised this is nar­row, stu­pid, and just wrong- it’s titled “A Bach Canon”. A) it’s a fugue, unless you’re real­ly going to explain a Can­crizans Canon [and it’s not a sim­ple one in con­text]. B) it’s not a type only com­posed by Bach- there’s no such thing. Unless it said ‘A fugue from X piece by J.S. Bach’, it’s a mis­nomer. Stu­pid­i­ty about clas­si­cal music, and dis­miss­ing accu­ra­cy as elit­ist and unim­por­tant, is an indi­ca­tion of this coun­try’s whole atti­tude prob­lem with the arts and cul­ture. I expect­ed bet­ter from open­cul­ture.

  • A. Person says:

    I should­n’t be sur­prised this is nar­row, stu­pid, and just wrong- it’s titled “A Bach Canon”. A) it’s a fugue, unless you’re real­ly going to explain a Can­crizans Canon [and it’s not a sim­ple one in con­text]. B) it’s not a type only com­posed by Bach- there’s no such thing. Unless it said ‘A fugue from X piece by J.S. Bach’, it’s a mis­nomer. And musi­cians (includ­ing opera singers, instru­men­tal­ists, com­posers, etc) spend years learn­ing, and cre­at­ing based on, *actu­al­ly* learn­ing and watch­ing how these things “work”. And, real­ly, Stu­pid­i­ty about clas­si­cal music, and dis­miss­ing accu­ra­cy as elit­ist and unim­por­tant, is an indi­ca­tion of this coun­try’s whole atti­tude prob­lem with the arts and cul­ture. I expect­ed bet­ter from open­cul­ture.

  • Mark says:

    A. Per­son: This is actu­al mate­r­i­al from Bach’s Musi­cal Offer­ing, as it says as the book opens at the begin­ning of the video (Musikalich­es Opfer). He used that mate­r­i­al as the video shows in com­pos­ing the actu­al work. So its actu­al­ly quite cor­rect, and an inter­est­ing look into the how the work is struc­ture. It is out of con­text of the com­plete work, but regard­less, go study the actu­al piece, and you will find exact­ly what is dis­played in this video.

  • miok says:

    i like peanut but­ter.…

  • Nancy Joy Koch says:

    Bach’s mind was absolute­ly incred­i­bly bril­liant!

  • John says:

    It does sound like a crab, I feel hun­gry.

  • Frankie G. String says:

    Nice video. Would even be nicer with real music!

  • August Grillo says:

    Theme is by Fredrick The Great giv­en to Bach while vis­it­ing. Bach impro­vised on this chro­mat­ic theme for sev­er­al hours, went home and wrote an enor­mous work, the Musi­cal Offer­ing as a gift to Fredrick. Some of the puz­zle canons instruc­tions were sim­ply marked ” seek and ye shall find ” The work ends with a fugue in 8 parts that sounds very mod­ern. Great piece of music.

  • jonathan damelio says:

    This real­ly is bril­liant! Did Bach see the mobius strip in his mind while he wrote this or did he phys­i­cal­ly do this with his staff paper? Real­ly makin my math knowl­edge from the 70’s go into over­drive. You see the Mobius strip was dis­cov­ered by Ger­man math­e­mati­cians August Fer­di­nand Mobius & Johann Bene­dict List­ing in 1858. Bach died in 1750, ONE HUNDRED YEARS BEFORE the strip was dis­cov­ered!

  • MT says:

    To: A. Per­son.
    Actu­al­ly, you are wrong. This is a canon from the Musi­cal Offer­ing. Not a fugue. Your rant is real­ly mis­placed. Maybe it’s your atti­tude that’s the prob­lem.

  • outseeker says:

    His tal­ent is tru­ly beyond my com­pre­hen­sion. Thanks for the video to illus­trate why I can nev­er be such a musician/composer :)

  • paul delesdernier says:

    Why did the chick­en cross the mobius strip? To get to the same side.

  • Dia's Mom says:

    I just played the video for my 11 year old. His first com­ment was, “Wow, so it’s just as bril­lant back­wards as for­ward!” , and, “Now, that’s a music writer!”. I loved it, short, to the point ‚and well said.

  • Dorothy says:

    I love the devine ele­gance of it’s sound and struc­ture. Mag­nif­i­cent.

    (Note to A. Per­son: Not know­ing some­thing, or being incor­rect isn’t stu­pid­i­ty. Stu­pid­i­ty is the inabil­i­ty to learn, not the lack of knowl­edge. Aftr read­ing the his­to­ry of this piece, I’d say you exposed yours. Light­en up; it’s just as ele­gant, regard­less of what you call it or who used the form. I’m sad you could­n’t just enjoy it.)

  • Apolloguy says:

    A per­son just got Bach-slapped for being too sharp. Give it a rest and mea­sure your notes.

  • Victor Fleischer says:

    Exam­ple of BACH can­non was bril­liant. Superbly done!
    BRAVO…BRAVO!!! I have been in love with JOHANN all my life.
    Thanks.

  • John Carter says:

    A fuse in my mind just broke… Holy cow.

  • Mario says:

    Bril­liant but off script. The Canon is in c minor, i.e: 3 flats (b, e, a). The notes on the pen­ta­gram are off by one line, i.e: the 3 flats are wrong­ly placed on d, g, a. Sim­i­lar­ly with all the notes. No won­der I couldn’t rec­on­cile what I was hear­ing to what is writ­ten! What a pity. Worth cor­rect­ing. It is so good!

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