The 2018 chess World Championship finished this week with Magnus Carlsen retaining his title, and with it his reputation as one of the greatest chess players of all time.
Before the match began, expanding on a throw-away remark by the challenger Fabiano Caruana at the pre-match press conference, I compared Caruana’s style of play with hip hop music. Caruana was responding to a journalist who repeated a well-worn comparison of Carlsen with Mozart. So, was the 2018 title match indeed a victory for Mozart over Kendrick Lamar?
When did Magnus play like Mozart?
The match will probably be most remembered for two individual moments, both of them in endgames, and both undoubtedly destined to feature in future manuals of endgame technique. One was the extraordinary ‘fortress’ that Magnus Carlsen constructed in Game 9, when he deftly arranged his weaker forces so that the challenger could extract no more than a draw from a position in which he had two pieces and one pawn against Carlsen’s one piece and two pawns.
The other moment is truly Mozartian in its elegance and brilliance, though. It is the single move that effectively won the match and confirmed Magnus Carlsen as World Champion. All twelve of the standard length match games were drawn — a feat unprecedented in the history of the chess World Championship — which meant that the match was to be decided in a series of four ‘rapid’ games, in which each player had only twenty-five minutes on their clock, with an extra ten seconds added after each move. In the first game, Carlsen had the white pieces, and he brought about an endgame with one rook remaining on each side, and an advantage of one extra pawn for White — a definite advantage, but not enough necessarily to win. Carlsen allowed Caruana to capture the extra pawn, in order to bring about the following position at move 37. The analysis that follows owes a lot to the excellent coverage of the match by Grandmaster Daniel King (@DanielKingChess).
In this position, Carlsen did not do what I (and probably more than 99% of all chess players) would have done, and take the pawn on g7 with his rook [R x KKt7]. If he had done so, Caruana could have obtained a draw by giving check to Carlsen’s king with Ra2+ [R-QR7 check], and after the king retreats to h3 [K-KR3], the black king comes to f3 [K-KB6] and draws because of the threat of checkmate (White must prevent Ra1 followed by Rh1 [R-QR8 and R-KR8]).
Instead, and with almost no time to pause and think, Carlsen played a move of stunning, truly Mozartian elegance.
For me, this is not only the move that effectively won the match, but it is truly the move of a World Champion. Black is forced to take the pawn on f5 [K x KB4] before White takes the pawn on g7, with the result that the white king can no longer be trapped. Carlsen did indeed go on to win. Caruana must have been devastated; forced to press for victory at any cost, he lost both the next two games and Carlsen took the tie-break match 3-0.
This moment shows just how complex and difficult endgames can be, despite their apparent and deceptive simplicity. Magnus Carlsen’s ability to spot the only winning move, and the fact that it is what looks like a harmless and inessential move, shows why the comparison with Mozart is fully justified.
When did Mozart play like Magnus?
Perhaps the most appropriate comparison should be of Carlsen’s play with a piece written by Mozart at exactly the same age (Carlsen retained his title two days before his twenty-eighth birthday). Even better, Mozart’s piece is also an example of ‘rapid’ play, since it is a symphony he wrote in just four days.
In 1783, the twenty-seven year old Mozart and his wife Constanze were returning to Vienna from Salzburg where they had been visiting Mozart’s father. Leopold Mozart had disapproved of the marriage, but had been partially assuaged by the fact that they had named their newly-born first child after him. On the way home, they stopped at Linz, to stay at the castle of Count Thun, the local aristocrat, whose wife was a patron of Mozart’s in Vienna. To Mozart’s surprise, the Count had already advertised a concert to be given by his court orchestra on the following Saturday (four days after their arrival), to be conducted by Mozart and featuring a new work by him. Mozart wrote back to his father, “I have no music with me, and so am having to write a symphony at top speed”.
Whether Mozart was able to remember and reconstruct a symphony he had been working on in Vienna, or whether he really did compose Symphony 36 (the ‘Linz’) entirely from scratch in those four days, we cannot be sure; but he did indeed conduct the new work on the Saturday, and it is a masterpiece.
Magnus Carlsen’s moment of brilliance came towards the end of his game, so I shall choose a moment of brilliance from the last movement of the symphony.
The moment in question is the following sequence of little three-note motifs:
These are so simple, so unassuming. But they are also extremely memorable. Whether it is the slightly off-beat nature of the rhythm, or the subtle difference between the second group, which alternates two notes, and the others, which go in step, I cannot be sure. But these four bars, which are not important in the sense of being a main theme in the movement, are nevertheless the moment that sticks in my mind after I hear the work, and the moment I look forward to before it begins. As Roland Barthes might say, this is the moment in which I as a listener do not just take pleasure [plaisir], but find bliss [jouissance] (read Le plaisir du texteif you want to know more on that score).
These little groups of three notes grow out of motifs in the first subject:
And also the second subject:
And by the end of the movement, you hear ghosts of these three-note groups everywhere:
Perhaps the most delightful thing about them, though, is the way that Mozart deploys them when they occur. While many composers might use little motifs of this sort, it takes a Mozart — a World Champion of classical composition — to recognise how ideally they work in counterpoint. With a sureness of touch very like Magnus Carlsen’s incredible ability to think in several divergent lines simultaneously — I compared chess logic to counterpoint in Reti and Bach: four-piece counterpoint — Mozart passes these motifs in turn from the top of the orchestra to the bottom:
This looks simple enough on the page. But the effect is astonishing, and the judgment it displays is truly brilliant. When you listen to it in a moment, you can hear how Mozart follows this passage with further wonderful contrapuntal work for these three-note motifs as they accompany the main themes of the movement.
So, why does this little bit of Mozart remind me of Magnus Carlsen’s endgame brilliancy? Like Carlsen’s move, these little motifs seem inessential; they are almost a passing detail. But in fact, they are so embedded in the texture of the movement that they seem to grow naturally from its main themes, and infect every part of what follows. Similarly, the opportunity for Carlsen’s brilliancy was created by his superb judgment earlier in the game — he used nine of his twenty-five available minutes considering just one move (the twenty-seventh), after which he steered the game into this endgame — and it is the one moment that makes sense of every other move he played.
Here is a performance of the last movement of the Linz Symphony, with the sort of graphics that appeal to me. You get to hear the motifs I have been talking about three times, at 0′ 57″, 3′ 00″, and 6′ 00″. Sit back and enjoy brilliance such as we are seldom privileged to witness.
At the press conference that served as the opening ceremony for the World Chess Championship match between Magnus Carlsen and Fabiano Caruana, being held in London at the time of writing, the American challenger was reminded by a chess journalist that Carlsen had been described as “the Mozart of chess”. He was asked what similar comparison he would make of himself. His reply was:
My musical tastes lie more outside classical music, so I would probably pick someone either in the hip hop or the rock genre. This comparison to Magnus was made a long time ago, when he was a very talented up-and-coming player, and I think it was very fitting because of his great talent in chess.
(Fabiano Caruana, 8 November 2018)
The second part of Caruana’s answer shows that he may not fully appreciate the reasons for comparing Carlsen with Mozart, which have as much to do with the elegance and apparent simplicity of his play as with the fact that he was a child prodigy. Carlsen as a player reminds many of his great predecessor as World Champion, José Raul Capablanca, whom I compared to Mozart in my post Mozart and Capablanca: playing jokes on the amateur.
It is true that Caruana was less of a child prodigy than Carlsen: in his first chess tournament, he lost every game. On the other hand, he developed fast, earning the grandmaster title a few days before his fifteenth birthday (Carlsen became a grandmaster aged thirteen). But his suggestion that his play might be better compared to hip hop or rock is suggestive. For a start, it recalls the player he is most regularly compared with, the only American chess World Champion, Bobby Fischer. Fischer, an unpredictable genius over the board, considered himself a great rock singer, as I pointed out in Bobby Fischer: lost rock god?.
In part, Caruana’s answer simply refers to his musical tastes, which he also described in a pre-match interview for The Guardian:
He [Caruana] grew up on classic rock and spent many tournaments listening to Metallica and Led Zeppelin during his downtime, but has taken a shine to hip-hop in the last few years. “I’ve been listening to a lot of Kendrick Lamar and a lot of Killah Priest,” he says. “But it changes all the time. When I’m bored and I have nothing to do, I’ll just listen to random pop music.”
Nevertheless, I see no reason not to ask: what would “hip hop” chess look like?
Hip hop chess
Before going further, I must point out that there indeed exists a Hip Hop Chess Federation (HHCF). It is a California-based charity which uses chess and other disciplines to help children’s academic and social development in some of the most deprived urban areas of America and elsewhere. Its work is clearly brilliant, and I urge you to read about HHCF here.
However, to stay with hip hop as a music genre and the playing style of Caruana: in hip hop, an essential effect of the music is its non-stop urgency: a rapper has to obey the rules of rhyme and metre, impress the audience with verbal dexterity, and create the impression of unstoppable force, often with a shocking or sudden punchline as the end-point. Here’s an example from Kendrick Lamar, the artsit mentioned by Caruana above. It’s the end of “King’s Dead” (an appropriate title for a chess rap), from the soundtrack to the 2018 film Black Panther:
Who am I? Not your father, not your brother
Not your reason, not your future
Not your comfort, not your reverence, not your glory
Not your heaven and not your angel, not your spirit
Not your message, not your freedom
Not your people, not your neighbor
Not your baby, not your equal
Not the title y’all want me under
All hail King Killmonger
Red light, green light, red light, green light
Red light, green light, they like, we like
Now here is one of Caruana’s great wins. It was played in Dortmund in 2014, against the Ukrainian grandmaster Ruslan Ponomariov. The devotee of hip hop in this game cultivates on the chessboard a “rapping”, non-stop urgency in his play, with threats maintained on both sides of the board simultaneously. Ponomariov, having to rush his defensive pieces from one side to the other, ended up with the following position:
Black’s bishop and rook have been decoyed to the far side of the board from the black king. But Caruana’s next move, which of course he had foreseen several moves in advance, comes like a Led Zeppelin power chord:
To Ponomariov’s credit, he did not resign immediately, but allowed the combination to unfold on the chess board (Fischer once described his opponent’s resignation in similar circumstances as “a bitter disappointment”). Like a non-stop rap, Caruana has given up his rook only to have the chance to give up his bishop:
The ending is a wonderful checkmate:
“King Killmonger”, indeed!
So, who will win? Mozart or hip hop?
Of course, I cannot predict the outcome of the current title match: World Championship matches can take surprising turns; I covered one of the most surprising of all time in my post Music in Glavinic’s chess novel. As I write, the first four games have all been drawn, although in my judgment the World Champion has had the edge whenever there has been an edge to have. All of us who follow the game hope to see a genuine clash of styles: the classical, cool calm of Carlsen (who has already tested Caruana through an endgame that lengthened the first game to 115 moves played over seven uninterrupted hours) against the unpredictable “hip hop” of Caruana. The match is not unlike the 1927 World Title match when the Mercurial Alexander Alekhine defeated the first “Mozart of chess”, Capablanca, to the astonishment of most onlookers. Notoriously, Alekhine avoided ever giving Capablanca a rematch.
Perhaps Caruana should remember, though, that the title that denotes a rapper of distinction – the one at the top of the game – is made up of a significant two-letter acronym: MC.
There have been any number of chess giants who were also musicians, of course; the greater their standing in the world of chess, the more intriguing their musical achievements. Some could have been professionals in either sphere, the concert pianist Mark Taimanov and the operatic bass Vasily Smyslov being examples. There are many more in Richard James’s chess and music posts.
Here, however, is a case of a chess giant who could also have been a singer to rival John Lennon, or at least so it would seem from this intriguing 1961 interview with the great American champion Bobby Fischer:
D. ANDRIC: Some other participants of the tournament [in Bled, Slovenia] persuaded Fischer to sing when at a Bled night club one evening, hoping to have some fun at his expense. They were hushed to awe however, when he sang a series of rock and roll songs attractively and well.
FISCHER: “My main talent lies not in chess but in music: I’ve written this somewhere in my diary. Grandmaster Smyslov who could be an opera singer anywhere admitted I had a suitable voice, and I’ve got rhythm, too.”
As far as I know, this is the only recorded instance of Fischer’s claim that in becoming the only chess player ever to achieve truly global celebrity, he robbed the world of a potential rock god. I owe this fascinating quotation to the chess writer and researcher Jeremy Silman, who unearthed it in the March 1962 edition of the American magazine Chess Life, a journal whose early issues are particularly hard to obtain: no library in the UK, not even the British Library, keeps copies. Silman’s article on these treasures of chess journalism (Part Two of a three-part series) can be found here.
The 1961 tournament in Bled was a good one for Fischer: at the age of eighteen, up against many of the world’s best players, he was the only player to remain unbeaten throughout, and he finished a very narrow second to Mikhail Tal, who had been World Champion until a few months previously:
Even better, Fischer defeated Tal in their individual game, the only one that Tal lost in the tournament:
Bobby Fischer was born in the same year as Mick Jagger, George Harrison and Roger Waters. His teenage claim that his musical talent was even greater than his chess-playing ability obviously tells us more about his incredible self-confidence and self-belief than anything else. But it is a reminder that he was of the same generation as the Stones, the Beatles, Pink Floyd, and the other greats of 1960s and 1970s rock and roll. Perhaps the rock legends who played chess will be a future post in this blog. Here are four:
When is chess rock ‘n’ roll?
Bobby Fischer came closest of anyone to playing chess like rock ‘n’ roll. First of all, there were the tantrums: forfeiting a match when the start time of a game was rescheduled; accusing the Soviet chess establishment of cheating by fixing results to prevent him from winning a tournament (he then refused to play at all for nearly two years); insisting on playing some of the world title match against Boris Spassky in the tiny room at the back of the hall reserved for table-tennis instead of on the main stage (which he claimed to be too noisy). Fischer was as much a nightmare for officials and organisers as any rock diva demanding, say, a particular brand of white socks be supplied to their dressing room (Status Quo once refused to play on those grounds). You can read more about such things here.
But more to the point, Bobby Fischer was someone who could play chess like rock and roll. Here’s what I mean:
When this game was played, Fischer was fifteen. He was also the defending US Champion. Reshevsky, playing Black, was one of the strongest grandmasters in the world, who had previously won the US Championship seven times, and would win it again one last time in 1969.
In this position, Fischer played the chess equivalent of a rock power chord:
Astonishing! After ten moves, Reshevsky is lost. He gamely took the marauding bishop with his king, and Fischer played:
Another power chord! In the resulting position, either Reshevsky is going to take the knight with the king, in which case it is checkmate in a maximum of six moves (Fischer had worked that out); or Fischer is going to win the black queen (which is what actually happened — Reshevsky took the knight with the pawn, allowing Fischer to take the black queen with his queen). Reshevsky eventually resigned on move 42.
That’s chess rock ‘n’ roll.
Here’s another chess rock moment, from Fischer’s game against Robert Byrne (another American grandmaster) in the US Championship of 1963:
Time for another power chord:
Fischer’s opponent did not realise until several moves later why Fischer had given up a whole piece. After move 21, Byrne resigned. The two grandmasters explaining games to the public in the commentary room thought, when the game ended, that Byrne must have won since Fischer was so far behind in material. Fischer later described his opponent’s resignation as “a bitter disappointment” — it had prevented the following position actually appearing on the board:
Here, Fischer had foreseen another two-piece sacrifice leading to mate:
Checkmate on move 25, as a result of a piece sacrifice on move 15. That is chess rock ‘n’ roll.
Rock and roll in performance is very loud; chess is usually very quiet. But the display, bravado and technical brilliance of Bobby Fischer was the same as that of the greatest rock performers. The brilliant moves above did not come out of nowhere; they rely on absolute technical mastery, as much as a Brian May guitar solo.
Perhaps the best moment to end on is the turning point of Fischer’s greatest match, when he won the world championship by defeating Boris Spassky in 1972. In the first five games of the match, Fischer had lost two (one of them by not turning up), and won two. In the sixth game, Fischer played an opening he had almost never played before. He proceeded to win with such style that Spassky, on resigning, stood and applauded him.
The number of novels that centre on the game of chess is small, but it does include works by some significant authors. I have already traced the role of music in Nabokov’s chess novel, The Luzhin Defense. Perhaps the most-discussed chess novel is Stefan Zweig’s Schachnovelle, translated as The Royal Game and, more simply, Chess. Zweig’s novella does not allot a large role to music, which is perhaps surprising, since Zweig grew up and lived in Vienna from the 1880s until his exile in the 1930s. Zweig was a librettist for the composer Richard Strauss, and possessed a large collection of music manuscripts, including Mozart’s handwritten catalogue of his own works. It is clear from Zweig’s autobiography The World of Yesterday, however, that for him, the music of Vienna was equated with the culture destroyed by the advance of National Socialism. His Schachnovelle, written in 1941, is among other things a protest against the philistinism of modern Europe in which music can no longer sound. Shortly after completing it, Zweig and his wife committed suicide.
So once again my exploration of music, chess and their common themes leads me back to the Vienna of the fin-de-siècle. And this is also the setting of the novel on which this post focuses, Carl Haffner’s Love of the Draw, published in 1998 by the contemporary Austrian author Thomas Glavinic. It is a short novel, and well worth reading. I advise you to get a copy if you have read this far into this blog post. It is also a straightforwardly historical novel, based on one of the most notable matches ever played for the chess world championship.
The match in question was between Carl Schlechter (1874-1918), one of the the strongest players of his day, and Emanuel Lasker (1868-1941), the second World Chess Champion. The match took place in 1910. It was a ten-game match, with the first five games played in Vienna, where Schlechter was born and lived, and the second five in Berlin, Lasker’s home city.
The match was tied, and according to the rules agreed before its start, Lasker retained the title. Lasker was extremely fortunate: Schlechter led 1-0 at the half-way point of the match, and Lasker only managed to achieve the tie by winning the last game, in which Schlechter first had the advantage, and then mis-played a drawn position. Few would doubt that Schlechter was the one player who seriously rivalled Lasker’s status as World Champion in the twenty-seven years that he held the title between defeating Wilhelm Steinitz in 1894 and losing to José Raul Capablanca in 1921.
Schlechter had only one weakness as a player, which was his tendency to accept offers of a draw. From that stems the title of Glavinic’s novel.
Music in the names
One might wonder why Glavinic decided to rename the protagonist of the novel “Carl Haffner” rather than “Carl Schlechter”. “Schlechter”, after all, could be a motivated name, since it means “worse” in German. Nearly all the characters based on historical people appear in propria persona: Emanuel Lasker, of course, along with famous players of the day such as Janowski, Marshall and Tarrasch; but in the first chapter we meet Carl Haffner’s clubmates, the lesser-known chess masters Max Weiss and Hugo Fähndrich, and all the members of the Vienna Chess Club seem to appear under their own names.
There are just two characters based on real people whose names have been changed. One is Haffner himself, of course, and the other is the first person we meet in the book, Georg Hummel, the chess correspondent of the Neue Freie Presse, editor of the Wiener Schachzeitung and a notable chess player in his own right. Hummel is based on Georg Marco (1863-1923), who was indeed one of the strongest players in the world in the 1890s, and whose match with Carl Schlechter in 1893 marked the beginning of Schlechter’s international recognition. The ten-game match finished with every game drawn.
Glavinic, then, has chosen to rename two characters, presumably because his fictionalised versions of them depart from what is known of their historical counterparts (although as far as I can discover, we know remarkably little about either Schlechter or Marco). What is notable, though, is that both the names he uses have musical resonances. The name Haffner suggests two works by Mozart: the “Haffner Serenade” and the “Haffner Symphony”. Both were written for Mozart’s friend and contemporary, the Salzburg aristocrat Sigmund Haffner. And the name Hummel suggests Johann Hummel (1778-1837) the composer and virtuoso pianist of much the same period as Mozart. Mozart lived in Vienna; the Haffner Symphony was premiered there. Hummel worked in Vienna, as Director of the Imperial Military Music School.
Music, then, is in the background of the novel – in what literary critics might call its intertext. Or perhaps Glavinic’s choice of fictional names is pure coincidence, plucked out of his Viennese subconscious.
The suggestion of a musical as well as a Viennese background to the novel becomes stronger, however, when the role of music in the narrative is considered.
Music in the background
It would be an exaggeration to say that music plays a central role in Glavinic’s novel. However, the role it does play is significant. Glavinic renames his protagonist so that Carl Haffner can have a fictional family background and fictional formative experiences. Chapters narrating his Bildung alternate with those narrating the chess world championship, which are simply an imaginative re-telling of the Schlechter / Lasker match.
There are three family members who together define Carl’s personality, and music plays a significant part in all three relationships.
The successful grandfather
Carl’s grandfather Rudolph is a comic playwright whose greatest opportunity was being invited to write the libretto for Johann Strauss II’s operetta Die Fledermaus. He flunks the chance: “Failing to grasp the importance of his task, he supplied Strauss with a poor, half-hearted piece of work.” Glavinic is adapting history here: the libretto for Die Fledermaus, to this day the most popular operetta of all time, was in fact written by a real Carl (not Rudolph) Haffner, who was indeed a well-known comic playwright. And the writer credited as the lesser co-author of the libretto, Richard Genée, later claimed that he had to completely rewrite the original text and that he had never even met Haffner.
The Rudolph Haffner of Glavinic’s novel, although successful, fails to understand the significance of music, as the incident with Die Fledermaus demonstrates. He forces his son Adalbert to learn the violin, which Adalbert detests. Adalbert (the fictional Carl’s father) becomes completely alienated by his father, and leaves home on his twenty-first birthday with the words “I’m off to play some music”. He then earns his living by playing the violin in Viennese wine gardens. He marries, without telling his father, and Carl is born.
The drunken father
Adalbert is a violent drunk who does not love his wife and hardly provides for his family. Eventually, he elopes with a barmaid, produces a half-sister for Carl and dies in poverty. His abandonment of his wife and child, the most significant and traumatic event of Carl’s childhood, is narrated as the meeting-point of (reader, you guessed it) music and chess:
On the evening after that eventful night [when he decided to leave his family], Adalbert took out his fiddle and played it in one of the wine gardens where he was still welcome. Although completely out of practice, he soon got into his stride because he wanted to play. Not the cloying taproom melodies he detested so heartily, but classical music of a wild and passionate nature. He played as if possessed by the devil. No one in the establishment had ever heard the like.
The next day, with Carl’s hand in his and the money he had earned in his pocket, he called on Samuel Gold, who ran a bookshop not far from the Gasthaus zum Hirschen. He put some coins on the counter and told the bookseller, without more ado, that the money was all he had. It would have to suffice to equip Carl with a chessboard, a set of chessmen to go with it, and the principal textbooks on playing the game.
(Carl Haffner’s Love of the Draw, p. 70)
Samuel Gold, incidentally, is a real historical personage: he was a composer of chess problems who in 1887 became the thirteen-year-old Carl Schlechter’s first (and only) chess tutor.
The loving half-sister
Finally, there is Lina Bauer, Carl’s half-sister (the product of Adalbert’s elopement) and the person Carl seems to care about more than any other. He spends the evening before the match with Lasker with her, when “She played his favourite piece on the piano before he left.” And when the match moves to Berlin for its second half, he again spends the evening before his departure with Lina:
After they had a snack lunch together, she sat down at the piano. […] He didn’t know why, but he felt nothing for any woman, apart from the one who was playing his favourite tune at that moment.
(Carl Haffner’s Love of the Draw, p. 88)
The piano that Lina plays is itself an emblem of Carl’s love for her:
Carl watched Lina grow up with warm-hearted affection. When he asked her what she wanted most of all, she confessed that she dreamed of playing the piano. Carl paid for her piano lessons. Meantime, he scrimped and saved until he had amassed enough money for a second-hand concert grand. He did not mind limiting himself to one meal a day and wearing a thin, threadbare jacket in winter. The day on which the piano was delivered meant more to him than any victory ceremony.
(Carl Haffner’s Love of the Draw, p. 138)
Music runs, then, as a background to the story of three generations of the Haffner family. It is also just about the only activity that interests Carl other than chess. The evening before the final game of the match, which Carl has only to draw to become World Champion, he spends in the smoking-room of his hotel:
Carl’s attention was focused on a figure in a black tailcoat. A lean, angular man of melancholy mien, he went over to the piano and bowed. Carl, who knew the cheerful piece he proceeded to play, listened spellbound. […] Carl’s excited reflections on the world championship were challenged, and eventually defeated, by the music.
(Carl Haffner’s Love of the Draw, pp. 146-47)
What is the music doing?
I do not know whether Thomas Glavinic is a musician. He is certainly a good chess player, as his entry in the FIDE international database of chess players proves.
He does not describe the games between Haffner and Lasker, as they are played, by using musical metaphors (unlike Nabokov). However, music is the inescapable subtext of the entire book. There is a kind of counterpoint between chess and music which sets in relief questions such as playing for love or playing for money; performing because others require it or because you are driven to perform; dedicating your life, with significant personal sacrifice, to an activity that is not ultimately productive of anything except beauty. These questions define the life of Carl Haffner, as they apply to chess; they also define the lives of his father, and to some extent his grandfather and half-sister, as they apply to music. Perhaps Schlechter’s unsuccessful bid to become World Champion was the most musical moment of chess history.
I want to answer the question, “Did Beethoven play chess?” because several people claim that he did. I remarked on this fact in my Book review: Music and Chess (Achilleas Zographos), where Beethoven is listed as one of the many chess-playing musicians of history.
Now, I am not an expert on Beethoven’s biography; I learned my lesson there when I speculated on the genesis of one of his works in a research paper, and discovered that a pre-eminent Beethoven scholar was in the audience. And I would love it if Beethoven turned out to have been a devotee of the Royal Game; Viennese classical music is under-represented on that score. Mozart’s favoured game was billiards; Haydn was not (as far as I know) among the ranks of chess-playing composers. Any excitement at finding the chess games of F. Schubert in book indexes is dispelled by learning that František Schubert was a Czech chess master who once beat Richard Réti, but was no relation of Franz Schubert.
There is no reason why Beethoven might not have played chess, after all: the first chess book in German was published in 1795 by a Viennese contemporary of his; the chess-playing automaton known as “The Turk” was one of the wonders of the age; Napoleon himself (whom Beethoven admired for a long time, although he lost faith in him when Napoleon became a dictator as self-declared Emperor) certainly was a keen chess player.
Tracing the evidence
I had, however, never come across any evidence that Beethoven even knew the moves of the game, let alone took a serious interest in it. And so I was fascinated to see him in the list of names in Achilleas Zographos’s recent book. When I expressed some dismay in my review at the lack of evidence presented to support his inclusion, the author himself paid me the courtesy of a reply, and made two helpful suggestions: one was to consult a book I should have thought of myself, The Even More Complete Chess Addict by Mike Fox and Richard James (which I have mentioned many a time in earlier posts), and other was to take a closer look at footnote 18 on page 26 of Music and Chess: Apollo meets Caïssa.
Turning to Fox & James first, they too ascribe a love of chess to Beethoven. But they are quite circumspect about it:
Jostling for a place among the reserves [of a fantasy musicians’ chess team] would be Schumann […] Mendelssohn […] Richard Strauss [… twenty other musicians are listed]. And, according to The Polish History of Chess, Chopin and Beethoven.(Fox & James, p. 33)
So they give a single source, which is another book rather than any primary evidence from Beethoven’s letters and so forth. After some further exploration, I identified “The Polish History of Chess” as Z Szachami Przez Wieki I Kraje (Jerzy Gizycki, Warszawa 1984). Courtesy of the Bodleian Library, I summoned it up and discovered that Fox & James were quite right: Beethoven and Chopin are both mentioned. But they are only mentioned once. Here is the paragraph, together with what I, Google Translate, and my good friend Geoff Chew (a musician who really does speak Polish) made of it:
Wielu szachistów można snaleźć pośród muzyków. Kompozytorem był słynny szachista francuski Philidor. Królewską grę znał Beethoven i Chopin. W posiadaniu doktora Jerzego Goreckiego, prawnuka Mickiewicza, znajdował się zabytkowy okrąkły stolik drewniany w naturalnym czerwonym kolorze, na którym, według jego oświadwicz i Fryderyk Chopin (od 1978 roku w zbiorach Museum Literatury w Warszawie).
Many chess players can be found among musicians. The famous French chess player Philidor was a composer. The royal game was known by Beethoven and Chopin. Dr. Jerzy Gorecki, great-grandson of Mickiewicz, possessed an old, round, wooden chess table in a natural red colour, on which Mickiewicz was said to have played Fryderyk Chopin (since 1978 in the collection of the Museum of Literature in Warsaw).
(Gizycki, p. 228)
This doesn’t get us much further. There is real anecdotal evidence given that Chopin played chess at least once with the poet Mickiewicz (whose lyrics he set to music), but nothing more than another bald assertion that Beethoven was a chess enthusiast.
So that left me with Achilleas Zographos’s footnote. Here it is:
The main sources for this list are the articles by Wall, Bill; Musicians and Chess; 8/8/2013, chessmaniac.com, and by Silver, Albert; Musical giants and chess; 3/7/2015, Chessbase.
Consulting these two online articles (both well worth reading, by the way) yielded less in the way of historiographical evidence than I had hoped. The second of them doesn’t mention Beethoven at all, although it does have a photo of David Bowie playing chess with Catherine Deneuve.
Bill Wall’s article, though, does mention Beethoven. Here is what it says:
Ludwig van Beethoven (1770-1827), the German composer and pianist, was a chess player. He was a good friend of Johann Maelzel, the builder of one of the first chess automatons.
That’s all. No mention of a source, but there is some detail. Beethoven’s “good friend” Johann Maelzel seems to be the link.
Maelzel’s mechanical marvels
Johann Nepomuk Maelzel (1772-1838) is one of the more colourful characters of music history. He was an inventor who settled in Vienna in 1792 (the same year as Beethoven), and soon afterwards began to display his “panharmonicon”, a kind of mechanical organ which played orchestral music. Maelzel was aiming to profit out of the popularity of automata of all kinds, especially automata which could play musical instruments. Maelzel and Beethoven met in 1812 or 1813, and the inventor persuaded the famous composer to write a “Battle Symphony” for his panharmonicon. Beethoven did so, and then expanded and arranged it for a regular orchestra (it was written in between the Seventh and Eighth symphonies). The “Battle Symphony”, or Wellington’s Victory at Vittoria as the orchestral version is called, was premiered, along with the Seventh Symphony, in two charity concerts organised by Maelzel in 1814 to raise funds for Austrian soldiers wounded and maimed in conflict. At this time, Maelzel also invented several ear trumpets in an attempt to help Beethoven’s progressive deafness.
To describe Maelzel as Beethoven’s “good friend”, though, is sadly not quite accurate. There was a violent quarrel following the concerts arranged by Maelzel, over the rights to Beethoven’s “Battle Symphony”, which Maelzel wanted to play on his tour to the rest of Europe with his panharmonicon. Beethoven describes him thus:
[…] his low and disloyal character is displayed in expressions such as the following: “I shit on Vienna and I’ll see to it that people in London are told that here in Vienna one is paid 10 gulden” […] Maelzel is an ill-bred fellow, quite uneducated and without refinement.
(Letter to Dr Carl, Edler von Adlersburg, July 1814: The Letters of Beethoven, trans. Emily Anderson, London: Macmillan, 1961, Vol. I, letter 485, p. 461)
Beethoven also describes Maelzel’s ear trumpets as “not of any real use” and accuses Maelzel of stealing his work.
There seems to have been some sort of reconciliation, however, since Beethoven was very impressed by the one of Maelzel’s inventions which you may own yourself: the musical metronome. From 1817, Beethoven started to put metronome indications on his works to indicate the speed he wanted. How accurate Maelzel’s metronome was, and how realistic Beethoven’s expectations were of performers as his deafness became complete, are things still vigorously debated to this day.
So, if “good friend” doesn’t really fit the bill as far as Beethoven’s relationship with Maelzel goes, what about the other claim by Bill Wall, that Maelzel was “the builder of one of the first chess automatons”? This too, unfortunately, isn’t quite true. The automaton in question was in fact the most famous of all chess-playing machines before Deep Blue, known as “The Turk”.
The automaton could move the pieces on a chess board, and appeared to be able to beat any human opponent. It was a marvel of its age, and exhibited all over Europe.
It was not, however, built by Maelzel. Its inventor was in fact a Hungarian called Wolfgang von Kempelen, who first demonstrated it to Empress Maria Theresa in 1770. Maelzel bought it from Kempelen in 1804, a good few years before he met Beethoven. Maelzel repaired it, and exhibited it to Napoleon in Vienna in 1809. He then took it to Milan, where he sold it for a huge profit to Napoleon’s stepson, Eugène de Beauharnais. A few years later he managed to buy it back, and took it to Paris and then London on the European tour over which he and Beethoven fell out so badly.
The Turk was a remarkable machine, but it was a fake as far as playing a game of chess was concerned. You can see in the photograph the compartment on the right where a small grandmaster had to be concealed to control the machine’s moves. This subterfuge meant that Maelzel had to hire short, impoverished chess masters (of which, then as now, there was a ready supply) wherever he exhibited the machine. Napoleon was actually defeated by Johann Allgaier, the strongest player in Vienna in Beethoven’s day, whom I mentioned earlier as the author of the first chess tutor in German.
So, did Beethoven play chess?
It has been an interesting search through published books on chess, and a fascinating encounter with that entrepreneur, inventor and showman Johann Maelzel. But there is, I am afraid, no evidence at all that Beethoven did have an enthusiasm for chess.
The English translation of Beethoven’s letters runs to three thick volumes (I quoted Beethoven’s view on Maelzel’s character from them earlier). I have looked through them all, and there are no mentions of chess, or The Turk, in any of the letters involving Maelzel, and no mention anywhere of Allgaier (who was known in the city as well as being the inhabitant of The Turk). No mention either of François-André Philidor, a contemporary of Beethoven and by far the best-known chess-playing musician of that or any other time.
Sadly, I have to conclude that the assertions with which I began, that the composer of The Eroica symphony, Fidelio, and Wellington’s Victory had a particular interest in the battle of the wooden soldiers over the sixty-four squares, are without evidential basis. The search has emphasised to me the pitfalls of wishful thinking, which can undo your attacks over the chessboard as easily as your search for historical truth.
Patterns analysed by the Réti brothers in music and in chess
It is hardly controversial to say that both chess and music rely on the recognition of recurrent patterns. Is this a trivial observation? Or is there a deeper connection in terms of the kinds of patterns that structure and make meaningful the experience of playing the game of chess or listening to a work of music? Does the observation that both activities rely on pattern recognition actually indicate a cognitive similarity between the two arts?
This post explores these questions. In this I am once again guided by the Réti brothers whom I introduced in Réti the Modernist: Rudolph, the pioneer of music analysis, and Richard, the visionary chess grandmaster.
It is one thing to say that chess and music both require pattern recognition; quite another to define what constitutes a “pattern” in this context. To begin with, I am going to work with two different kinds of pattern: firstly, general patterns that are found everywhere and without which the piece of music or game of chess doesn’t make sense; and secondly, individual patterns that define specific examples in either field. The first category comprises patterns that define well-formed pieces of music or legitimately played games of chess; the second category comprises patterns that are memorable enough to act as “signatures” for their author (whether a composer or a chess player).
I am in fact much more interested in the second kind of pattern than in the first; but please bear with me while I start with a comparison of generic, universal patterns in chess and in music.
Checkmates and cadences
Beginning students of music, and beginning chess players, are alike taught certain basic patterns as the essential first step towards understanding how the respective arts of composing and chess-playing work. Every game of chess aims towards a checkmate; every piece of music aims towards a final cadence. Admittedly, here I am talking about tonal music in the Western tradition; but that is going to be my focus for this post. Other posts have considered atonal music, such as that of Réti’s friend (and chess player) Arnold Schoenberg (see Réti the Modernist).
Sticking with tonal music, here is a cadence:
To repeat the point that this is the place where students of composition begin, this example (with the analysis underneath the staves) is taken from my own Open University module. I suggest you sign up for it now: it’s called Inside Music.
There are many different ways of approaching a cadence. Here are two:
And here is one from a real piece of music that you might recognise:
Just as there are many ways of approaching a cadence, there are many ways of approaching a checkmate. Here are four, which all aspiring chess players have to learn (hover your mouse over each to see its caption):
The back rank mate
The knight with bishop mate
The rook with bishop mate
The rook with knight mate
These are all patterns which recur again and again, in many different forms (whether you are thinking of pieces of music or of chess games). They are meaningful: the meaning of the patterns in music is to signify the end of a phrase, or the end of the whole piece; the meaning of the chess patterns is to signify the end of the game. In both cases, these patterns accord with Wolfgang Köhler’s definition of a pattern in Gestalt psychology, which is that their meaning is different from that of the components of the pattern: the individual notes forming harmonies in accordance with the rules of tonal composition, or the individual pieces moving in accordance with the rules of chess. It is the pattern itself that signifies ‘cadence’ or ‘checkmate’, and this makes it a Gestalt.
The Réti brothers and pattern recognition
The patterns just identified are generic: they are learned by students because they have a level of generality that makes them recognisable in innumerable contexts. What fascinated both the Réti brothers was the recurrence of patterns which have a quite different level of individuality, so that instead of signifying something general, they identify something unique.
In both cases (music and chess) the relevant Réti identifies these patterns as the signature of the creator of the artwork in question. These patterns personalise the musical work or the game of chess, and in each case this was a significant innovation in the understanding of the field. Rudolph Réti was one of the first thinkers (along with Schoenberg and a few others) to develop a theory of how patterns in melody shape a work of music; a topic strangely absent from the centuries of theory of harmony, tonality and form. And Richard Réti was one of the first thinkers (along with Nimzowitsch and a few others) to develop a theory of manoeuvring pieces not in order to win material or deliver checkmate, but in order to create a better pattern to their disposition.
Rudolph Réti and patterns in Schumann
Let’s start with the older brother, Rudolph, and his analysis of a wonderful work by another chess-fanatical musician, Robert Schumann (1810-56).
The work in question is Kinderszenen [Scenes of Childhood], a multi-piece consisting of thirteen short individual pieces written in 1838 while Schumann was engaged to be married to Clara Wieck (her father was opposing the match). Rudolph Réti devotes a whole chapter of one of his books to this work (Rudolph Réti, ‘Schumann’s Kinderszenen: A “Theme with Variations”’ in The Thematic Process in Music (Macmillan: New York 1951) pp. 31–55).
With a work like Kinderszenen, it is always worth asking whether the pieces are entirely separate from each other, linked just by a general mood summed up in the title of the whole collection; or whether there is some musical connection between them that links them together. Rudolph Réti sets about demonstrating that a single “musical idea”, an individual pattern of notes, links together all the pieces. This pattern is found in the melody that begins the first of the pieces, which is called “Von fremden Ländern und Menschen” [“Of Distant Lands and Peoples”]. Réti doesn’t actually think that the opening melody of the work is the “basic pattern” that unites the whole. It is the first individualised example of a “basic pattern” that is ideal, abstract: it underlies all its individual occurrences in the work, but isn’t identical to any of them. Réti infers the “basic pattern” from the opening melody and its slightly altered repeat at bars 14-15.
You can hear the great pianist Vladimir Horowitz (1903–89) perform the piece here: his sensitive playing of these pieces depicting the carefree days of childhood, as an old man (the concert was recorded in 1987), is suitably elegiac.
Having identified this “basic pattern”, Réti sets about discovering it in every single one of the pieces that make up the Kinderzszenen. Here it is in the melody of No. 2, ‘Curiose Geschichte’ [‘Curious Story’]:
As Réti points out, the basic pattern here uses exactly the same notes as in the first piece, even though the key has changed from G major to D major.
Horowitz’s performance of this piece is well worth hearing, although the link here lacks video:
And here is the same basic pattern in possibly the best-known of the Kinderszenen, No. 7, ‘Träumerei’ [‘Daydreaming’], where Réti finds it in the middle of the theme, transposed down from G major to F major:
Horowitz’s performance is spellbinding:
Réti also thinks he can detect the basic pattern at its original pitch, in the middle of the texture rather than in the melody, at the climax near the end of the piece. Personally, I think this is pushing things a bit; but it shows Réti’s deep belief that the basic shape recurs everywhere:
I’ve circled in red the notes that Réti thinks make the basic shape; the first two are both in the first chord, but played one after the other according to the arpeggiation marking included by Réti; presumably it was in the edition he owned, since it isn’t in Schumann’s original edition. Horowitz plays the chord as Schumann wrote it, without arpeggiation; but he did have huge hands.
Richard Réti’s brilliant checkmate pattern
One thing that certainly does make playing chess a different kind of thing from writing music is that no-one who uses an idea from one of the great players of the past is going to be accused of plagiarism. If I were to write a piece that started with the “basic pattern” used by Schumann in the Kinderszenen, I would at the very best be credited with a conscious hommage to the nineteenth-century master. If I ever manage to reproduce Richard Réti’s most famous mating pattern, I would not only be delighted, but my chess-playing friends would congratulate me.
The pattern in question comes from a game Réti played against Savielly Tartakower in 1910. Over their careers, these two grandmasters played each other many times: Réti won on fifteen occasions, Tartakower on fifteen, and a further fourteen games were drawn. But this game is the best known. Réti won in just eleven moves. The game was played in Vienna, where both chess masters lived. Réti was 21, Tartakower 23. After eight moves, the game had reached the following position:
Tartakower had just taken Réti’s knight on e4 with his own knight [8…KtxKt], apparently winning a piece, although White can regain it with the move Re1 [R-K1]. However, Réti had set a trap: White wins, with mate in three moves.
DON’T CONTINUE UNTIL YOU HAVE GUESSED THE MOVE!!
The move Réti had foreseen was Qd8+!! [Q-Q8ch!!]:
Black can take the white queen — in fact, that is the only legal move — but then a double check from bishop and rook simultaneously, Bg5+ [B-Kt5ch], leads (depending on how the king moves) to one of two very pleasing checkmates:
The mate played in the game
The alternative possible mate
The game became well known. However, one has to wonder whether Réti knew a game played sixty years earlier in a box at a Paris opera house between Paul Morphy, the world’s strongest player of the time, and two French aristocrats:
Morphy’s stunning win was, like Réti’s, a queen sacrifice leading to that same rook-and-bishop mating pattern:
The queen sacrifice
The story of this game is told in more detail here.
Or perhaps Réti knew a game of 1864, a defeat for another top player of his day, Ignaz von Kolisch:
Once again, a queen sacrifice leads to checkmate, this one even more like that in Réti’s game:
The queen sacrifice
Whether Réti knew these earlier games or not, it is as I remarked a fortunate aspect of playing chess that no-one is bothered by accusations of plagiarism. Certainly not Georges Koltanowski, who arrived at the following position on his way to becoming Belgian chess champion of 1923. Black has just played Qxh2 [QxQR2] and is threatening Qa1 [Q-QR1] checkmate:
By now, the winning combination should be familiar:
The queen sacrifice
Finally, a more recent game between two strong amateurs:
This time, it was Black (Rene Gralla, a Hamburg lawyer and rock journalist who has interviewed Mick Jagger, Ringo Starr, and others) who unleashed the ‘Réti combination’:
The queen sacrifice
So that is five games, played over a span of nearly 150 years, all as it were variations on a recognisable theme.
So far, all these chess patterns have led to checkmates. They can only happen on the rarest of occasions, and are so memorable that they are associated with Richard Réti’s name, simply because his win against Tartakower became well-known.
But these chess patterns are not really like the patterns observed by Richard’s brother in the music of Schumann. To find a kind of pattern that can properly be called a Gestalt pattern that carries the sign of its creator’s authorship, we really need to look at the most complex phase of a chess game, the ‘middlegame’: the phase between the opening (roughly the first dozen moves or so, in which generally each side tries to move each piece no more than once), and the endgame, where just a few pieces strive to hold a draw or deliver checkmate.
One would think that the middlegame in chess is unique in each game, and so it would not be possible to create patterns more complex than very general rules (“control the centre”, “find a square for a knight where it cannot be attacked by an enemy pawn”). Richard Réti, however, showed that even in the middlegame it is possible to create a recognisable pattern that recalls his authorship whenever it it seen.
Richard Réti’s middlegame pattern
Like so many memorable creations in chess and in music, the middlegame pattern that bears Réti’s name was invented in Vienna. Réti’s opponent was called Fischer (absolutely no relation to his much better-known namesake born twenty years later). Here is the position in which Réti’s genius came up with a unique manoeuvre:
This is what chess players call a “closed” position, with all the pieces and pawns still on the board. Réti has played the “Réti opening”, positioning both of his bishops at the sides of the board and leaving the centre squares free of white pieces.
In this position, Réti came up with a startling idea. He moved his rook from c1 [QB1], in order to slide his queen right into the corner of the board:
Réti vs Fischer, move 11
Réti vs Fischer, move 12
This is modernism in chess: from what appears to be the very worst square from which the most powerful piece can operate, Réti hopes to influence the long diagonal that runs from that square to the far corner of the board. In this closed position, the long diagonals are the straight lines from one side of the board to the other with the least number of obstructing pawns on them:
The pattern is more than just an inventive and unusual disposition of the pieces. It is a Gestalt, a shape with meaning: the curious position of the white queen aims to dominate the game by controlling the long diagonal leading to the enemy king.
Fischer was a local amateur player competing in the annual Vienna tournament; Réti was an acknowledged grandmaster. So it is hardly surprising that Réti won this game. However, later that same year, he was playing in the strongest tournament organised, at Karlsbad. Here, facing one of the strongest players in the world, Akiba Rubinstein, the following position arose:
Réti reproduced his idea from the Vienna tournament, this time creating two lines of attack into the enemy camp:
Once again, the pattern was the basis of a winning strategy. Like Schumann’s recognisable motif that holds together all the pieces of Kinderszenen, Réti’s motif not only had perfect meaning in the context of the games in which he played it, but was also memorable and unusual enough to carry his signature, as it were. It is “Réti’s middleground pattern”.
The following year, Réti again played in the strongest tournament organised, this time in New York. He faced the former World Champion, Emanuel Lasker:
Once again, Réti manoeuvred his pieces to create a new line of attack into the enemy camp:
Lasker, a superb defender, prevented Réti’s idea from bearing fruit. Later in the game, after Réti had sacrificed rook for knight in an attempt to break open Lasker’s fortress, the following position arose:
With typical inventiveness, Réti tried playing the motif from the other corner:
The game was a terrific struggle, which Réti eventually lost. Lasker went on to win the tournament by a clear 1½ points, ahead of the reigning World Champion, José Capablanca.
In the plagiarism-free world of chess, even motifs forever identified with their creator are free for all to use. Capablanca himself, more than a decade later, was faced with the following position against another strong grandmaster:
By now, it should come as no surprise to see the pattern created by Capablanca’s next two moves:
This may have been some sort of hommage to Réti, who had died in 1929; but it was still the basis of a winning strategy for Capablanca.
Conclusion: patterns and meaning
I have tried to point out several times that the significance of the kinds of patterns I have been exploring, in music as well as in chess, is that they have meaning. They are not just pleasing configurations of chess pieces or of musical sounds; they are what a psychologist might term a Gestalt: a pattern whose meaning is different from the meaning of the individual components which constitute it.
This appeal to psychology is not accidental. Schumann’s music evokes more than just simple pleasure at its melodic beauty: it summons forth the world of childhood experience, tempered by memory and nostalgia (particularly the way that the aged Horowitz plays it).
Equally, when Lilienthal saw Capablanca move his queen to the corner square of the board, the gesture must have had a psychological effect: Lilienthal was just too young to have played Réti, and Capablanca signalled with the “Réti manoeuvre” that he was employing against him the kind of “hypermodern” attack Capablanca was himself famous for having refuted time and again by his legendarily precise play. It was Lasker who first wrote about the importance of psychology in chess; he would select not necessarily the objectively best move in a position, but the strategy he thought best suited to his opponent. One of his dictums was “Chess is not an art, or a science, but a struggle”.
The Réti brothers were alike in many ways, and we know from Rudolph that they discussed the similarity of their ideas regarding chess and music. The topic of pattern recognition is probably the one in which their ideas came closest to each other. It is no accident that it was the topic that enabled both brothers to become great theoreticians in their respective fields.
A comparison of a chess puzzle by Réti and a musical puzzle by Bach
Here is a puzzle composed by Richard Réti in 1921. It looks impossible.
Here is a puzzle composed by Johann Sebastian Bach in 1747. It also looks impossible.
What is the connection between these two puzzles? What makes them puzzles, and what are their solutions?
In Richard Réti’s puzzle, there is a race between two pawns: the white pawn is racing up the board, the black pawn is racing down. If either of the pawns reaches its final square, it becomes a queen and that side wins the game; if both become queens simultaneously, the game is drawn.
The puzzle requires the White player, who moves first, to draw the game. What makes the puzzle seem impossible is that the black king is easily able to stop the white pawn from queening, whereas the white king seems to have no hope at all of stopping the black pawn. This is best shown by a concept taught to all beginning chess players, “the square of the pawn”.
The square of the white pawn
The square of the black pawn
When you have no pieces left except your king, and your opponent is racing a pawn towards its queening square, you can stop it if — and only if — your king can enter “the square of the pawn”. As you can see, the black king is already in the white pawn’s “square”, while the white king is three moves away from the black pawn’s “square”. The white king also seems hopelessly far away from protecting its own pawn if the black king approaches and captures it.
However, the puzzle does have a solution. The study consists of three elements: the square of the white pawn; its upside-down counterpart, the square of the black pawn; and the “Royal Piece”, the white king. The movement of the white king is the key: it has to move in relation to both the “squares of the pawns” simultaneously. As if the Royal Piece has the job of harmonising both other elements in a kind of counterpoint.
Now back to Bach and his impossible puzzle.
Bach’s puzzle is from one of his last pieces, the Musical Offering [Musikalisches Opfer]. The story of the piece is that Bach visited the court of Frederick the Great of Prussia in 1746. The king played Bach a theme of his own composition (the king was a keen and accomplished flute player):
At the king’s request, Bach proceeded to improvise a three-part fugue on the theme. He then apologised that he could not improvise something more worthy of such a wonderful theme, and promised to send King Frederick a finished piece once he had returned home to Leipzig. The result was the Musical Offering, which consists of three groups of pieces, all based on the “Royal Theme”. One of the groups is a collection of ten canons, which Bach presents in the manuscript as puzzles.
A canon is a piece in which a musical theme plays in one voice and is repeated by a second voice before the first one has finished: the simplest kinds of canons are rounds, such as London’s Burning or Frère Jacques. Puzzle canons, which were very popular in Bach’s day, provide just the melody of the canon, with cryptic instructions for constructing the second (and possibly third or further) voices. The solver has to work out how to create a harmonious result while obeying the instructions.
The canons of the Musical Offering all harmonise the “Royal Theme”, a meandering and chromatic melody which is hard enough to harmonise without making the accompaniment work as a canon at the same time. In the canon I am discussing here, the instructions are that it must work “Per augmentationem, contrario motu”, which means that the second part must play the melody in notes twice as long as they were originally (augmented, or “Per augmentationem”), and also upside-down (in contrary motion, or “contrario motu”). At the same time, the result of these two melodies playing together must harmonise with the notes of the “Royal Theme”. Quite a task.
By now, the similarity that I find between Bach’s puzzle canon and Réti’s chess puzzle might be clear. In Bach’s canon, the “Royal Theme” must harmonise simultaneously two other themes, which are upside-down versions of each other and proceed at different speeds. In Réti’s puzzle, the “Royal Piece” must coordinate simultaneously with two areas of the chess board, which are upside-down versions of each other, featuring pawns racing at different speeds. Réti’s puzzle is a study in counterpoint, as is Bach’s.
The solution to Réti’s puzzle
The first move in Réti’s solution is not hard to see — the white king advances in chase of the black pawn:
But the king does not just chase after the black pawn: the Royal Piece moves not to h7 (KR7) but to g7 (KN7). He moves towards the “square of the black pawn”, but also towards the “square of the white pawn”. By harmonising his move with both squares, the white king can, contrapuntally, achieve the harmonious equilibrium of a draw.
If the black pawn simply races to become a queen, the white king supports and advances his own pawn:
The black pawn races
The resulting position
In the resulting position, black has the choice of queening the pawn and allowing White to do the same, or attacking the white pawn, when the Royal Piece harmoniously supports it:
Either way, a draw is achieved. And astonishingly, Black cannot disrupt this contrapuntal harmony by first advancing the black pawn and then attacking the white one:
The pawn and king both race
The resulting position
By continuing to approach both “squares of the pawns”, the Royal Piece keeps them harmonised in counterpoint. In the position above, Black can take the white pawn, but then the Royal Piece will enter the “square of the black pawn”; or Black can race the pawn towards queening, but then the Royal Piece will save His own pawn.
The solution to Bach’s puzzle
The following realisation of Bach’s puzzle features Frederick of Prussia’s own instrument, the baroque flute, which is entirely appropriate. The cool animation shows the musical lines as blobs: you can see the Royal Theme (played twice, with orange blobs when the viola da gamba plays it, and red blobs when the flute does), accompanied in counterpoint by the canon, played by the harpsichord (green blobs) and the violin (blue blobs). You can see that the shape of the blue blobs is an upside-down version of the green blobs (contrario motu); you can hear that it is going at half the speed (per augmentationem), which is why the line of blue blobs is only half the length of the line of green blobs.
This particular solution to the puzzle was arranged by Silas Wollston, whom I happen to know: he studied with my colleagues at the Music Department of The Open University, gaining his PhD in 2009. Today he is a Fellow of Queens’ College, Cambridge. I don’t know if Silas plays chess; he certainly plays Bach as few people can.
Conclusion: chess, music, counterpoint
The intellectual pleasure to be had from solving each of these two puzzles (or, in my case, marvelling at the solutions without being able to solve them) seems to me to be of the same kind in each case. Both studies, when solved, produce a result that is elegant, sophisticated and deeply satisfying to witness. On one level, there is the technical brilliance of manipulating a restricted range of materials: just four pieces on Réti’s chessboard; the constraints of harmonising the Royal Theme in Bach’s canon. On another level, though, each study demonstrates the challenge set by all counterpoint in music, and by all games of chess as well: that of holding in the mind simultaneously several different fields of action, which behave independently of each other and yet interact and may alter each other at any moment. This, I believe, is why so many musicians are also lovers of the Royal Game, and vice versa. Certainly Richard Réti was, as I discuss in Réti the Modernist. Chess is a contrapuntal art.