There will never be another like him, and there never was the likes of him before. And if you were surrounded by people who barely held their knuckles from their gait, with this in your mind all day and all night, you would also be short tempered.
This 'afterthought' by Bach on the last page of the printed Goldberg Variations leaves one completely speechless. Gerubach, your presentation is simply outstanding - worthy of the sublime subject.
Walter Bushell "The Fourteen Canons (BWV 1087): Foundation or Culmination? A re-evaluation of their position among Bach‟s late works" by Elise Crean bachnetwork.org/ub5/crean.pdf
As a Data Scientist, Bach continues to blow my mind. To see parallel structure between his music and the mathematics or transformation of data is so amazing. The inversion can be any form of a mathematical transformation - pick whatever you want. The lag or delay in the start of the inverted canon is precisely a dynamic feature used in time series machine learning. Lag features of t minus n that are used in our models.
This video is truly a work of art, a masterpiece! A real treasure, especially for musicians. Thank you very much, with the utmost respect and admiration. ✨🙏✨👍
14 is also the number you get when you add the numerical values of the surname 'Bach' (A=1, B=2, C=3, D=4, E=5, F=6, G=7 and H=8). Therefore, 2+1+3+8= *14* Some study finds that Bach knew this, so it might not be a coincidence that he stopped number of canons at 14.
He did it for fun, like doing crossword puzzles. He wrote all sorts of musical riddles for Anna Magdalena and his sons to solve. In fact Bach is holding an actual riddle (a canon triplex) in his hand on his famous painting. You can unpack the hidden 3 voices from it.
Many think that such inversions can only be found in these riddles and musical games. But in the Sonata in C major for Solo Violin, the fugue contains the most beautiful inversions, including a hidden melody in a part for single voice before a 3 voice culmination of string crossings. Then, there is an al riverso, and the string crossings repeat, with an al stretto afterwards.
What's equally amazing is that Bach wrote and actually PLAYED these canons on a simple clavichord most likely. How a human mind created #14 is pretty much a wonder of the world.
World is a better place with video makers like you. I watched this one when I was in senior high, and at that moment, I was astonished how devoted one can be in putting efforts into visualizing Bach's music. This is priceless, I can't imagine how many who genuinely love music would be enlightened by your videos.
SapereAude1490 A quote from the Art of Fugue! Just another one of Bach's genius. As if the Goldberg Variations were not already genius, he goes and writes 14 canons on the bass line!
Not clear at all. In fact, he only wrote quite a few of them. So, if he had developed an "automatic" method for doing that, he would do it everyday, casually, and we would have a ton of them rn, in my opinion. I think it is likely that he did have some kind of method of thinking and counting, but, still worked a lot inside his head and didn't write those masterpieces effortlessly.
He most probably did! A marvelous book has been written upon this very subject by the italian composer Giancarlo Bizzi - it is called "Specchi invisibili dei suoni", and I really do not know whether it has been translated in other languages (if that's actually the case, it's a true shame) - where he analyzed a number of canons from both the Musical Offering and the Goldberg Variations, either coming up with new methods of composing a canon or researching such methods in old treatises. By doing this, he demonstrated in the second part of the book that the theme of the Goldberg Variations was composed according to the principles of Athanasius Kircher's "Tabula mirifica omnia contrapuntisticae artis arcana revelans" (Astonishing table showing every secret of counterpoint), a number square that shows every moment at which an imitation should enter in order for a melody to be canonizable to itself at every interval... Really marvelous stuff. He also utilizes latin squares at length as construction device: given the extremely important presence of both canon and latin squares in the music making of Luigi Nono and Bruno Maderna, one might wonder how one could renew musical paedagogics by relying more on seemingly antiquated resources, which, although objectively out of date for some elements, can still show essential tools for developing a fluent and sound musical thought... Nonetheless, I want to present a last, fundamental point: these methods are mere tools, not magic wand. They can help realize something, but they still need to be used - wisely, I might add. Knowing how to use Kircher's square won't make you magically write the Goldberg Variations; yet, it is certainly an important tool in order to research with more ease and conciousness the right expression of one's musical thought.
Let's add a few 14th ;) - he became the 14th memeber of the Mizlersche Societät (maybe he planned that) - he added some notes to particular chorale melodies so that they contains 14 notes - 14 contrapuctus in the art of the fugue (Contrapunctus 14 might be doughtfully, but it the theme on the notes Bb-A-C-B which in German transcribes to B-A-C-H) - the manuscript of the musical offering was handed to Friefrich on the 14th of Juli ...
@@steffen5121 There is a wonderful unison between Mathematics and Music, just as there is between Mathematics and Art. Have you heard "The Musical Offering"?
Molto ben fatta la descrizione di tutti i canoni. Bach rimarrà per sempre un mistero. All'interno delle sua composizioni c'è sempre un'alchimia. E' inutile dirlo ma è il padre di tutti i musucisti!
"Wow! Thanks to you, I was able to catch a glimpse of the minds of musical geniuses for a short while. I learned a bit about the music structure and theory that I was curious about. Thank you for the great video!"
14 canons and number 14 is Bach's signature... amazing! GERUBACH excellent work with all your videos, especially with this one... Bach's last musical words!
Kok Weng Leong - One big difference is that Bach actually produced something connected to reality in a realized manner; whereas Einstein produced nothing connected to reality by fumddidling in fantasy. Another big difference is that Bach fathered multiple intelligent children and, as far as we know, remained with his wife; whereas Einstein sired multiple retarded children and abandoned them and their mother when he gained the first hint of celebrity. Another big difference is that Bach, I feel confident, loved his people; whereas Einstein expressed in vile and vulgar fashion his absolute hatred for those same people and desired that be destroyed to the uttermost. Perhaps Einstein should not be held in comparison to Bach at all or to even be mentioned at all.
Very nicely done. I did notice one mistake in the score - the inversus in the bass clef for the prolation canon at 13:30 indicates A instead of G at the dominant resolution. Though what Bach did is impressive, it is actually deceptively simple if you know the right techniques and organizational principles. I am currently writing a book that will be posted for free as a PDF online that goes into depth on how to do this, and even goes further in complexity. For those of you interested in the text, please feel free to reach out. Another great text that discusses this (and is the first to do so in English to my knowledge) is Kendall Durelle Briggs’s “Craft of Tonal Counterpoint.”
Toda esta clase de curiosidades y ejercicios intelectuales de formar los canones, las inversiones, etc. me recuerdan a lo que hacia Leonardo da Vinci con su escritura. Otro genio mas!!
Bravo, gerubach - if Johann Sebastian himself could see this, you know he would be delighted! These miniatures contain the sounds of molecules and galaxies performing their appointed rounds -
The newly discovered canons and your sequencing and presentation is now one of my favorite videos. Thank you so much! Brilliant and inspiring for my work on the Goldberg V.!
L. Sebastião A. Castro kinda true, I did a research paper on Mozart and most of his later works resembled the complexity of Bach. If only Mozart lived 20 more years...
@@Thelaretus Possibly, though I think that without Bach, Mozart could not have reached the heights that he did reach. "Singet dem Herr ein neues Lied" was a revelation for Mozart.
Normies would've said Beethoven was the greatest, simply because he was deaf and creating a lot popular tunes. I wouldn't be surprised if they aren't aware about the fact that Beethoven wrote an opera.
Robert J. Brownlow I would say however that it would be even better if the canons were displayed in treble or bass clef rather than the movable C clefs used here. Many students will be lost and not really be able to grasp the brilliance.
+Robert J. Brownlow Teach them the C clef! Show them the beauty in it! Life in music should not be a succession of "readers digest" experiences! It's easy to learn and there are many exercises (Bach Chorals for instance)
This is so cool! It reminds me of something I saw here on RU-vid presented by John Eliot Gardiner regarding the notes on the sheet music in the portrait of Bach. I thought I had heard these before. Way back in the early '80s I purchased a CD by Don Dorsey entitled "Bachbusters." I had to go to Amazon to verify it, but these were in the CD. It's taken all day to remember where I heard it. I lost the CD years ago.
I'm pretty sure Bach would have been a multiple Nobel Prize winner if he had lived in the 20th century. Or he would found the cure for cancer or invented time travel or something. His brain and imagination worked at the highest level possible for a human being.
Well, this is the best guide to understanding Bach's counterpoint that I've ever found ... and it's not close. If the definition of genius is the ability to make the complex simple(r), gerubach is a true genius. Now to watch it every day for about 5 years.
Hindsight is the best foresight, but... Notice how most ot those notes form part of a broken chord (an arpeggio); any "lagging" within the context of that arpeggio will sound alright because it's almost the same as doubling. The key then becomes how the transitions between chords are handled, because the lagging note would be playing a note from the previous chord and potentially clash with the current chord. Which means that the lagging note needs to play a note that is "shared" by both chords. Like just in between the repeat (8th/9th) note Bach uses D for the lagging/leading note, which is both shared by the previous chord (G: I, as the fifth) and the current chord (G: V(b), as root). And so forth for every chord change. This also forms part of the reason why 16ths - four notes needed to express an arpeggio for every potential chord change (each quarter). But thinking about that as he was composing it... I'm sure I couldn't have cooked up something like that.
Thanks for sharing. I was looking for Bach to write canons. Actually I was looking for inspiration for my own canon - and then I found this... Johann Sebastian Bach was a counterpoint genius and a form aesthete. As if God as Creator had personally lent a hand, Bach writes his pieces seemingly playfully, as if they were spontaneous creations and ends with "etc.", as if he could easily write 14 canons as well. Simply unbe-f...ing-leavable ! And now? What am I supposed to write another canon...
che fortuna poter vedere gratuitamente queste cose! Prima te le dicevano ai corsi di composizione e occorreva pagare corsi su corsi perchè venissero insegnate.
Amazing! Bach had maths and music sussed well before the Minimalists of the 20th century. And the amazing thing is that it doesn't sound contrived. Unless the intricacies of the maths is pointed out, you wouldn't know. Still sounds like music.
