Bach, Canons and the Möbius Strip


A great post from my friend and valued colleague, Espen Andersen.  I love this for several reasons:

  1. I’ve always loved J.S. Bach‘s music – there is a mathematical and emotional beauty to his work that shows how structure and order can be emotionally rich and innovative. (Refuting nicely the belief by some that structure and order are inherently dry and lifeless!)
  2. It shows how creative use of video can be a great teaching aid – with this particular piece you can learn about the canon form and the Mobius Strip.
  3. It reinforces what a rich source of useful and inspirational material YouTube has become!

Going to YouTube to get the link pointed me to lots of other fascinating stuff about Bach, Palindromes, Mobius transformations, et al.  Check out this piece, for example, on my favorite Bach work – his Toccata and Fugue in D Minor.  The video animates the piece with a “piano roll” graphic (familiar to anyone who uses Midi editing software).  For those wanting to learn the music, understand its form and structure, or just have an interesting image to follow while listening to this splendid work, it’s another great example of all the wonderful stuff out there on YouTube and available for free!

Image courtesy of JSBach.net/bass ©2007 (unpronounceable) Productions

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2 thoughts on “Bach, Canons and the Möbius Strip

  1. Hi Vaughan! I really liked the crab cannon video and shared it with young Brad – here is his fascinating response (I hope no one ever pits my son against me in this way!!!):
    This canon is truly genius. The piece that this canon is from is one of Bach’s last and most mature works. What’s really impressive about it is that the melody of the cannon, i.e. the part before the eighth notes, is a melody most likely composed by his son C.P.E. Bach for Ferdinand the Great (some give credit to Ferdinand himself). The melody was composed as a challenge to Bach’s skill because his music had long been out of favor in the German court due to the rise of an opposing style from France called “galant” which better exemplified the Enlightenment ideals that Ferdinand was so famous for. So, C.P.E. Bach wrote this melody not only to be a challenge to his father but he wrote the melody so that it was “counterpoint-proof.” In other words, he was ordered by the Emperor to write a melody that would force the older Bach to fail and admit the eminence of the new Enlightened style. When Bach arrived he was instructed to improvise a three part Fuge on the impossible theme. He did it flawlessly. Determined to make Bach fail, Ferdinand then demanded a five part Fuge. (Bach had only written like 10 of them ever) Bach respectfully admitted defeat but three weeks or so later Ferdinand recieved a completed work based on the theme complete with 9 canons, a sonata, and four fugues in 3, 4, 6, and 6 parts. The Emperor probably never heard any of it. If you can find of the first Fuge of the piece (also called a ricercar) you can hear something very close to what he improvised for Ferdinand. Then you’ll really think that he is a genius. Another fun fact, The title of the complete work, Musicalisches Opfer, is sort of a play on words. “Opfer” means “offering.” So, Musical Offering, simple enough. However, Opfer also means sacrifice. So, a little sneer at Ferdinand as well.

    Reply
    • Well, what an interesting comment from Brad Jr.! I guess he was just into his teens when I last saw him – obviously he’s learned a great deal since then! I did not know these facts, even though I’ve been a huge J.S Bach fan since childhood.

      I ran Brad Jrs. comment by Gillian, who is far more educated on classical music than am I, and she verified his facts. She added:

      “It was Mendelssohn who was responsible for reviving interest in Bach’s works. Bach’s contemporaries didn’t appreciate the genius of the composer. Mendelssohn’s family were converts to Protestantism and he was very interested in ecclesiastical music and Bach certainly had quite a canon of that (groan).”

      Please pass on my warmest wishes to Brad Jr. and my thanks for his taking the time to illuminate us!

      Reply

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