The fact that Bach ended the fugue right when the relationship between the three themes is established tells me that this fugue was intentionally left unfinished by Bach. Having have the relationship established, it is left to us to fill in its development, which is doable by following fugal compositional strategies and creativity, and introduce the original Art of Fugue theme at the end. This would be Bach the teacher's final and ultimate challenge to all of us music lovers, who are eternal students of his.
He was blind after an unsuccessful eye operation and stopped all writing except a couple of works he dictated to his sons. I totally disagree with your supposition. The fact that all four subjects work together at all (not particularly well in this completion in my opinion) and in fact all four inverted subjects work as well!, as first noted by Sir Donald Francis Tovey, tells me that it was in his plan all along.
@@FertChervu This dating is simply incorrect. Much was written by 1742, but changes and additions were written in the following years, with an autograph from 1746, NOT including this fugue. In the first published edition, in 1751,CPE Bach has stated clearly after the 239th bar: "Ueber dieser Fuge, wo der Nahme BACH im Contrasubject angebracht worden, ist der Verfasser gestorben." ("At the point where the composer introduces the name BACH in the countersubject to this fugue, the composer died.")
I agree. I just lisened to two reconstructions by some other guys but it did´nt sound like Bach at all. Would be interesting to hear an AI reconstruction of this fuge though. I read John Hsu made one but I can´t find it here on TH-cam.
Definitely, this is the final solution to the subject. This completion MUST be as canonical and widely known as Süssmayer's completion of Mozart's Requiem, or Ravel's orchestration of Mussorgsky's Pictures at an Exhibition.
The way the fugue is left unfinished seems very deliberate to me, after hearing the art of fugue so many times I think I can confidently say that the last part can be completed very briefly using the three subjects, and it will sound like Bach if you follow the rules, like a puzzle that he left for us, in my mind it's a quick but powerful ending. I'm impressed with how people expand on it so much and leave their own marks on it, puts the brain to work.
Seeing/hearing this for the first time, and I love it. That permutation business is fascinating; it seems there's always more to learn about Bach. Good on Mr. Göncz for making use of it, and also staying pretty much true to the style (IMHO), even reusing episodic material and maybe even countersubjects.
One of the most perfect completions, tho finishing what Bach left unfinished certainly beyonds the capability of anyone, but still, hearing the motives (main motif from the AOF plus the three motives in Contrapunctus XIV) meant to be together after 3 centuries is touching.
I would love if someone did a Bach-esque completion of the first movement of the Pastorale, BWV 590. I have one that floats around in my head sometimes, never written down, but it is only a reprise of the same themes already heard earlier in the movement, and then repeating the opening theme in the subdominant before ending in C major. I'm sure it's quite amateurish compared to what an actual Bach scholar could do.
How can there be two dislikes? Utter ignorance, even if you disagree with the completion or, worse, your hear cannot go past EDM's bassdrum-kick-on-every-beat you must carry all the possible respect for this. I also own the score, I felt it was a given necessity to complete the edition I own of both the "Musikalische Opfer" and "Kunst der Fuge", and it's my favourite piece to play of both Works.
I have heard of contrapunctus, but never been curious of what it is. Now I think I get it (up to 7.1 % of expert knowledge🙂). It's a bit like English bells ringing/campanology, isn't it? Does anyone know if Bach composed like this intuitively, or are there some evidence that he draw up the patterns first?
I really don't know why I haven't been curious🤔, it's very interesting. I've always described Bach's music as going in a pine forest up north here: tree, another similar tree, another almost similar tree (and so on). Here I see it graphically👍
@@christinae30 I'm sure Bach works mathematically with his fugues notice that Contrapunctus XI is all the same as the main subject of the first contrapunctus with a few rhythmic changes and some notes which belong to the same tonality tho which makes it unique (descending from A to F and from F to D), his final Contrapunctus having some kind of symmetry its theme notes are the same even if you play it backwards. If you look carefully at the score you will find a mathematical perfection at different points of the music :)
Contrapunctus=Counterpoint. Counterpoint is the basis of the art of combining melodies (as opposed to, say, one singer plus oompah oompah backing group). Most composers have used this, but Bach is the expert - nobody has rivaled him. It's what makes "rich" music "rich". Like a layered fudge cheesecake. Bach learned this early, but by the time he wrote this piece, it was second nature. He extemporarized a 3-part fugue as a party trick on a theme the emperor fluted for him. Musical Offering, Ricercare a 3. But then he went home and wrote a bunch more. Routinely, he composed, wrote out the parts, copied or got them copied, and trained the singer at a rate of one cantata a week, in addition to his regular duties. It's like a painter; once you train for 20 years, you can knock a painting out in minutes without much thought. Bach wrote more music in his life than you would be hard-pressed to copy by hand in yours.
You can find all information in the description, it is explained in the article: wesley.hu/_files/the_ultimate_fugue_malina_j_hungarian_quarterly_2007_4.pdf
Basically, Goncz discovered that Bach was using a type of mathematical set theory to guide how the various themes and voices evolved from beginning to end. Goncz then extended Bach's method to finish the piece. The four rows in each box represent the four "singing" ranges of soprano, tenor, alto, and bass. The numbers represent the 4 different themes of the piece. Upside down numbers mean the theme is played inverted (upside down) at that point. Empty cells represent either silence for that voice at that point, or non-theme notes used to provide additional harmonic structure. Besides providing an amazing finish to this incomplete work, it also shows the incredible brilliance of Bach. The only other major artists in history to have achieved such an amazing fusion of science and art are probably DaVinci and Jackson Pollock (it was discovered after his death, that he somehow instinctively incorporated fractal math theory in his paintings, that grew increasingly complex math wise as he grew older. Amazingly, computer scans of his paintings can detect the fractal content, and tell real Pollock paintings from virtually identical fakes ).
PointyTailofSatan, sorry for my inadequate English. Zoltan Goncz' completion is one of the best, but we don't find any quadruple development in inversion. And there is no real development in any major key. That's pity because the quadruple sounds so wonderful in major keys. He also add voices long time before the final developments. If we do that, the challenge loose some of the glance. It's more easy to write a completion if we add voices. On the other hand, he successfully present all four subjects in all four parts! For those who don't do that, they haven't write any completion. Do you know the completion written by Yngve Jan Trede? In my opinion it's a good one, also on TH-cam.
The AOF isn't a piece for the average listener. It's a dying Bach's noble and desperate last attempt to pass at least some of his musical skill to future generations. It's very doubtful he would have left it hanging in the middle of a bar so others could complete it. Sadly, his sons moved on to mostly lighter forms, like style galant. The only real Bach disciple of later Baroque period counterpoint was probably Krebs, also said to be Bach's favorite student. But if Bach's music was considered old fashioned later in his life, Krebs was considered ancient, and is very rarely heard, even today, except by period performances by organists.
Dort wo Bach seine Fuge unvollendet lässt, endet auch Musik und die Tonsetzung beginnt. Manchmal ist es besser wenn Genies nicht alles sagen wollen und Mittelmaß sollte es akzeptieren. Where Bach leaves his fugue unfinished, music ends and the tonesetting begins. Sometimes it's better when geniuses don't want to say everything and mediocrity should accept it.
The first fifth is augmented, not perfect, so it's only a fifth on paper, not to the ear, and four-fifths of the way through the piece would hardly be the "first hurdle" anyway.
@@DanielSilva-gc4xzUnequal 5ths where the second 5th is perfect are expressly forbidden in several treteases contemporary with Bach which, of course, were based on compositional practices of the day. Why on earth would Bach want the permutation matrix, the pinnacle of the entire AoF, to contain such a voice-leading error? Jeez, it's worse than I remembered. When the 4th subject is in the bass, at 12:31, there is an unprepared 2nd-position chord. I'm not saying I could do it perfectly. It's incredibly difficult, and it might not have a solution within rules of counterpoint at the time. But this realisation definitely breaks those rules.
@@jamesrockybullin5250 As everybody said before, Bach did this all the time, no matter if it were "expresively forbidden in [treatises] contemporary with him". Bach never was a scholar, and musical treatises were not academic research products on that time. Considering his despite against his "mainstream" contemporaries on the opera, and how he acquired his knowledge and skills by tradition and experience, it's not so hard to imagine Bach may had despite against "scholar" musicians too. Besides, most of the knowledge put on paper by conservatories --which were not in Bach's days the cultural hegemony they are now, is due to outsiders like Bach or Beethoven. Same treatises say that, in counterpoint, some harmonic rules are flexible enough to make music idiomatic, because these outsiders made the rules flexible. In the very same Art of Fugue --as such as in every other fugue by Bach, we find hidden eighths, diminished fifths parallel with natural fifths, third grade duplications, second position unprepared chords, seventh leaps, crossing voices, distances between bass and alto greater than a tenth, and so on. Having these "hurdles" here when every other feature is consistent with Bach's style, is irrelevant.
The fact that Bach ended the fugue right when the relationship between the three themes is established tells me that this fugue was intentionally left unfinished by Bach. Having have the relationship established, it is left to us to fill in its development, which is doable by following fugal compositional strategies and creativity, and introduce the original Art of Fugue theme at the end. This would be Bach the teacher's final and ultimate challenge to all of us music lovers, who are eternal students of his.
The Matrix Coding of Bach
Or he died. lol
He was blind after an unsuccessful eye operation and stopped all writing except a couple of works he dictated to his sons. I totally disagree with your supposition. The fact that all four subjects work together at all (not particularly well in this completion in my opinion) and in fact all four inverted subjects work as well!, as first noted by Sir Donald Francis Tovey, tells me that it was in his plan all along.
@@2024Warren Bach came blind in 1750. The Art of Fugue were written in 1741. Letting that unfinished because of his blindness is just a myth.
@@FertChervu This dating is simply incorrect. Much was written by 1742, but changes and additions were written in the following years, with an autograph from 1746, NOT including this fugue. In the first published edition, in 1751,CPE Bach has stated clearly after the 239th bar: "Ueber dieser Fuge, wo der Nahme BACH im Contrasubject angebracht worden, ist der Verfasser gestorben." ("At the point where the composer introduces the name BACH in the countersubject to this fugue, the composer died.")
Probably the best completion out there.
This is more logical, elegant and inevitable. It is mathematical in its vision.
th-cam.com/video/S3x_sqrSCus/w-d-xo.html
I agree. I just lisened to two reconstructions by some other guys but it did´nt sound like Bach at all. Would be interesting to hear an AI reconstruction of this fuge though. I read John Hsu made one but I can´t find it here on TH-cam.
100%
Low bar to cross
Definitely, this is the final solution to the subject. This completion MUST be as canonical and widely known as Süssmayer's completion of Mozart's Requiem, or Ravel's orchestration of Mussorgsky's Pictures at an Exhibition.
The way the fugue is left unfinished seems very deliberate to me, after hearing the art of fugue so many times I think I can confidently say that the last part can be completed very briefly using the three subjects, and it will sound like Bach if you follow the rules, like a puzzle that he left for us, in my mind it's a quick but powerful ending. I'm impressed with how people expand on it so much and leave their own marks on it, puts the brain to work.
The algorithm brought me back here. For the first time in many years. Such a happy reunion!
This is the absolute ultimate in contrapuntle and fugal study.
10:33 Bach ends, and Goncz begins
Thanks.
Seeing/hearing this for the first time, and I love it. That permutation business is fascinating; it seems there's always more to learn about Bach. Good on Mr. Göncz for making use of it, and also staying pretty much true to the style (IMHO), even reusing episodic material and maybe even countersubjects.
Ottimo completamento. Molto bello.
Magnificent, well done!
Bravo, Maestro Gömcz.
Merci, j'attendais ce moment depuis longtemps. Pendant un instant, j'ai cru que c'était Bach qui l'avait fait.
This is music!
Absolutly amazing!
One of the most perfect completions, tho finishing what Bach left unfinished certainly beyonds the capability of anyone, but still, hearing the motives (main motif from the AOF plus the three motives in Contrapunctus XIV) meant to be together after 3 centuries is touching.
A series of Stories with Silence and Melody is finally about to ending..
Great.
The state of the universe before the big bang.
:,) ♥
Nice analysis, but exposition can have more than 4 themes, as long as they are in main or dominant key
I would love if someone did a Bach-esque completion of the first movement of the Pastorale, BWV 590. I have one that floats around in my head sometimes, never written down, but it is only a reprise of the same themes already heard earlier in the movement, and then repeating the opening theme in the subdominant before ending in C major. I'm sure it's quite amateurish compared to what an actual Bach scholar could do.
How can there be two dislikes? Utter ignorance, even if you disagree with the completion or, worse, your hear cannot go past EDM's bassdrum-kick-on-every-beat you must carry all the possible respect for this.
I also own the score, I felt it was a given necessity to complete the edition I own of both the "Musikalische Opfer" and "Kunst der Fuge", and it's my favourite piece to play of both Works.
I have heard of contrapunctus, but never been curious of what it is. Now I think I get it (up to 7.1 % of expert knowledge🙂).
It's a bit like English bells ringing/campanology, isn't it?
Does anyone know if Bach composed like this intuitively, or are there some evidence that he draw up the patterns first?
I really don't know why I haven't been curious🤔, it's very interesting.
I've always described Bach's music as going in a pine forest up north here: tree, another similar tree, another almost similar tree (and so on). Here I see it graphically👍
@@christinae30 I'm sure Bach works mathematically with his fugues notice that Contrapunctus XI is all the same as the main subject of the first contrapunctus with a few rhythmic changes and some notes which belong to the same tonality tho which makes it unique (descending from A to F and from F to D), his final Contrapunctus having some kind of symmetry its theme notes are the same even if you play it backwards. If you look carefully at the score you will find a mathematical perfection at different points of the music :)
Contrapunctus=Counterpoint. Counterpoint is the basis of the art of combining melodies (as opposed to, say, one singer plus oompah oompah backing group). Most composers have used this, but Bach is the expert - nobody has rivaled him. It's what makes "rich" music "rich". Like a layered fudge cheesecake. Bach learned this early, but by the time he wrote this piece, it was second nature. He extemporarized a 3-part fugue as a party trick on a theme the emperor fluted for him. Musical Offering, Ricercare a 3. But then he went home and wrote a bunch more. Routinely, he composed, wrote out the parts, copied or got them copied, and trained the singer at a rate of one cantata a week, in addition to his regular duties. It's like a painter; once you train for 20 years, you can knock a painting out in minutes without much thought. Bach wrote more music in his life than you would be hard-pressed to copy by hand in yours.
epic
That's a summ matrix
what does the little box on the left hand side mean?
You can find all information in the description, it is explained in the article: wesley.hu/_files/the_ultimate_fugue_malina_j_hungarian_quarterly_2007_4.pdf
Basically, Goncz discovered that Bach was using a type of mathematical set theory to guide how the various themes and voices evolved from beginning to end. Goncz then extended Bach's method to finish the piece.
The four rows in each box represent the four "singing" ranges of soprano, tenor, alto, and bass. The numbers represent the 4 different themes of the piece. Upside down numbers mean the theme is played inverted (upside down) at that point. Empty cells represent either silence for that voice at that point, or non-theme notes used to provide additional harmonic structure.
Besides providing an amazing finish to this incomplete work, it also shows the incredible brilliance of Bach. The only other major artists in history to have achieved such an amazing fusion of science and art are probably DaVinci and Jackson Pollock (it was discovered after his death, that he somehow instinctively incorporated fractal math theory in his paintings, that grew increasingly complex math wise as he grew older. Amazingly, computer scans of his paintings can detect the fractal content, and tell real Pollock paintings from virtually identical fakes ).
PointyTailofSatan, sorry for my inadequate English. Zoltan Goncz' completion is one of the best, but we don't find any quadruple development in inversion. And there is no real development in any major key. That's pity because the quadruple sounds so wonderful in major keys. He also add voices long time before the final developments. If we do that, the challenge loose some of the glance. It's more easy to write a completion if we add voices. On the other hand, he successfully present all four subjects in all four parts! For those who don't do that, they haven't write any completion. Do you know the completion written by Yngve Jan Trede? In my opinion it's a good one, also on TH-cam.
Miller Charles Garcia Kevin Davis Barbara
is it supposed to be this slow
The AOF isn't a piece for the average listener. It's a dying Bach's noble and desperate last attempt to pass at least some of his musical skill to future generations. It's very doubtful he would have left it hanging in the middle of a bar so others could complete it. Sadly, his sons moved on to mostly lighter forms, like style galant. The only real Bach disciple of later Baroque period counterpoint was probably Krebs, also said to be Bach's favorite student. But if Bach's music was considered old fashioned later in his life, Krebs was considered ancient, and is very rarely heard, even today, except by period performances by organists.
Dort wo Bach seine Fuge unvollendet lässt, endet auch Musik und die Tonsetzung beginnt. Manchmal ist es besser wenn Genies nicht alles sagen wollen und Mittelmaß sollte es akzeptieren. Where Bach leaves his fugue unfinished, music ends and the tonesetting begins. Sometimes it's better when geniuses don't want to say everything and mediocrity should accept it.
Falls at the first hurdle, parallel fifths between soprano and also at 12:13.
The first fifth is augmented, not perfect, so it's only a fifth on paper, not to the ear, and four-fifths of the way through the piece would hardly be the "first hurdle" anyway.
Bach does that all the time (augmented fifth and fourth to a perfect fifth). Nothing to see here.
Bach used parallel fifths and fourths quite often actually.
@@DanielSilva-gc4xzUnequal 5ths where the second 5th is perfect are expressly forbidden in several treteases contemporary with Bach which, of course, were based on compositional practices of the day. Why on earth would Bach want the permutation matrix, the pinnacle of the entire AoF, to contain such a voice-leading error?
Jeez, it's worse than I remembered. When the 4th subject is in the bass, at 12:31, there is an unprepared 2nd-position chord.
I'm not saying I could do it perfectly. It's incredibly difficult, and it might not have a solution within rules of counterpoint at the time. But this realisation definitely breaks those rules.
@@jamesrockybullin5250 As everybody said before, Bach did this all the time, no matter if it were "expresively forbidden in [treatises] contemporary with him". Bach never was a scholar, and musical treatises were not academic research products on that time. Considering his despite against his "mainstream" contemporaries on the opera, and how he acquired his knowledge and skills by tradition and experience, it's not so hard to imagine Bach may had despite against "scholar" musicians too. Besides, most of the knowledge put on paper by conservatories --which were not in Bach's days the cultural hegemony they are now, is due to outsiders like Bach or Beethoven. Same treatises say that, in counterpoint, some harmonic rules are flexible enough to make music idiomatic, because these outsiders made the rules flexible. In the very same Art of Fugue --as such as in every other fugue by Bach, we find hidden eighths, diminished fifths parallel with natural fifths, third grade duplications, second position unprepared chords, seventh leaps, crossing voices, distances between bass and alto greater than a tenth, and so on. Having these "hurdles" here when every other feature is consistent with Bach's style, is irrelevant.