Réti and Bach: four-piece counterpoint

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.

Reti endgame study
White to move and draw

Here is a puzzle composed by Johann Sebastian Bach in 1747. It also looks impossible.

Musical Offering Canon 4 autograph
Canon per augmentationem, contrario motu

What is the connection between these two puzzles? What makes them puzzles, and what are their solutions?

Réti’s puzzle

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”.


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

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):


The Royal Theme.png
The Royal Theme

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.

Federick the Great & CPE Bach (Adolph Menzel 1852)
Frederick the Great shown playing his flute, accompanied by Bach’s son, CPE Bach, at the harpsichord. Perhaps they are performing the canon Per Augmentationem, Contrario Motu.

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.

Musical Offering Canon 4 Bach edn
The score of the canon from the Bach Gesellschaft edition. The top stave shows a decorated version of the “Royal Theme”; the upside-down clef at the start of the lower stave indicates that the second voice (not shown) must play upside-down in relation to the first, in notes of twice the time-value (in augmentation). Bach inscribed the canon, “As the notes increase, so may the King’s honour”.

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:

Reti endgame study move 1
The first move

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:


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:

Reti endgame study final dilemma 2
The Royal Piece harmonises with His pawn

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:


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.

Réti the Modernist

The title could refer to either brother.

The Reti brothers stand out as one of the most remarkable stories there is to tell about chess and music. Not just because one was a professional musician and the other a professional chess player, but because they are both celebrated, in their respective fields, as founders of Modernism. The phrase used by chess writers since the 1920s is “hypermodern chess”, which reflects the fact that “Modernism” as a term in the history of the arts took quite a while to become established: in fact, I believe that the use of “Postmodernism” to describe an artistic movement predates the use of “Modernism” in that sense.

Whatever the history of the word, what we understand today by Modernism is what unites the Réti brothers. An artistic movement that flourished in the early twentieth century, Modernism is distinguished broadly speaking by a constellation of ideas: the rejection, often violent, of nineteenth-century assumptions; the search for new techniques; the belief that art must always inevitably progress to its next phase of expression.

In music, the quintessential modernist has to be the Viennese composer Arnold Schoenberg and his pupils Alban Berg and Anton Webern.

Schoenberg 3 Klavierstuke Op 11 opening page
The opening page of Schoenberg’s “Three Piano Pieces” Op. 11 (1909). The first performance of this work was given by Rudolph Réti.

In visual art, probably one thinks first of Pablo Picasso and other cubists.

Willi Baumeister Chess Players III (1924)
“Chess Players III” by Willi Baumeister (1924). A cubist work by an artist who spent part of the First World War in Vienna.

Modernism, chess, music: a Viennese story

Rudolph Réti was born in Serbia, Richard in Hungary. But both grew up in Vienna, where their father, a doctor, moved in 1890 when his sons were aged four and one. Vienna in 1890 was the capital of the Austro-Hungarian empire, and a centre of activity for both music and chess. In the years that the Réti brothers grew up there, it was also the birthplace of Modernism, along with many other currents of twentieth-century thought: the Rétis grew up in the city of Freud and Wittgenstein, Kokoschka and Schoenberg. The best guide to the character of the place is Wittgenstein’s Vienna by Allan Janik and Stephen Toulmin (Simon & Schuster 1973).

The world of chess owes Rudolph a great deal, since it was he who in 1903 took his younger brother to meet the best-known chess master in Vienna, Carl Schlechter. Richard lost their first game in a matter of minutes; in their second game he resisted the grandmaster for more than an hour, and was taken along to the Viennese Chess Club as a result. The club, patronised by Baron Rothschild, had not previously admitted a junior player to membership. Twenty years later, Richard was to take second place in the Vienna chess tournament held as a memorial to Schlechter, who died in the Spanish Flu epidemic of 1918.

Music also owes much to Rudolph.  He gave the first performances of Schoenberg’s seminal modernist pieces Three Piano Pieces Op. 11 of 1909 and Six Little Piano Pieces Op. 19 of 1911 (see his Tonality–Atonality–Pantonality, 1958, p. 42n). From the musical score pictured above, Schoenberg’s abandonment of tonality (writing in a musical key) is evident; so is his exploration of new techniques: the long. held chord in the right hand of the piano in the last line of the page is to be held down silently, to create resonance effects when the left-hand melody is played.

Rudolph ended up in America in the 1930s, and his theoretical writing on music is dedicated, as Schoenberg himself was, to showing the continuity between Modernism in music and its past, especially the music of another foreign-born Viennese resident, Beethoven. Rudolph’s insight was that music theory had not previously focussed on melody and theme, over centuries developing instead an intricate theory of harmony. Rudolph sought instead to theorise what he terms “The Thematic Process”. Modernist music may have abandoned traditional harmony, but it retains the expressive potential of musical theme and melodic expression. This links together the music of the past and the music of the modernists, and also explores how music communicates.  I have relied on and tried to expand Réti’s work in my own professional career as a scholar.

Modernism and the twentieth century

One thing that unites the Réti brothers is their belief that what they were doing was part of the new discoveries of the early twentieth century: Einstein’s theory of relativity, Freud and Jung’s theories of the unconscious, Wittgenstein’s philosophy. Like other modernists, Rudolph felt that his ideas were part of his age:

Around the turn of the century the physical sciences, as is generally known, underwent an extraordinary change. […] However, even if the actual force of the old laws seemed to have vanished, their usefulness and validity within their own realm did not by any means disappear entirely. In fact, one main goal of modern physics seems to be centred on the endeavour to comprise and unify the old and new principles in one all-comprehensive law or formula.

The whole process, which is especially conspicuous in physics due to the paramount importance physical discoveries have assumed with regard to our material way of life, can also be observed in many other spheres, for instance in the psychological, the social and the political domain, and even in the arts, and particularly in music.

(Rudolph Réti, Tonality–Atonality–Pantonality, London: Rockliff, 1958, p. 1)

The list of areas showing a similar process to the new physics could have included chess. Rudolph wrote of his brother’s area of expertise in identical terms:

Even for me, poor as was my understanding of chess, it was fascinating to watch Richard try to demonstrate [his] ideas through concrete examples. […] For my brother did not fail to emphasize – and this, of course, interested me particularly and was discussed at length between us – that, after all, this same trend is visible in our time in almost any artistic field, in literature and the fine arts no less than in music, and even in science, where the rational Newtonian physics has to yield to the almost mystic theory of relativity.

(Rudolph Réti’s memoir of Richard published by Edward Winter, ‘The Réti Brothers’, Chess Notes http://www.chesshistory.com/winter/extra/reti.html)

The brothers are in agreement: Modernism in art is an aspect of the new thought of the early twentieth century, its ideas overturning previous assumptions just as relativity overturns Newtonian mechanics; and chess is one of the modernist arts.

Modernism in Chess

Richard Réti echoes his brother when he describes modern chess as a modern art:

Poster advertising Secession Exhibition of Austrian Artists, 1898 (coloured litho) (b/w photo)

In his booklet “The Tree of Chess Knowledge” [Der Baum der Schacherkenntnis, Berlin: Kagan 1921] Dr Tartakower describes the style of the “Hypermoderns.” […] This lucid sketch contains the following: “Chess can also show its cubism. Its chief representatives […] attracted the attention of the whole chess world to the most modern school. The tenets of the latter school had, till then [1920] indicated a state of secession. […]”

(Richard Réti, Modern Ideas in Chess, trans. John Hart, London: Bell & Sons, 1923, p. 140)

The title of his book, Modern Ideas in Chess, allies his thought to Modernism as a movement. For Réti, chess in 1920 is an example of cubism; its foremost artists resemble the Viennese Secessionists led by Gustav Klimt.

So what does “cubist” chess look like? Here is the opening which is named after Richard Réti:

Reti opening
The Réti Opening

And here is another, a gambit against the French Defence:

Ret gambit (French)
The Réti Gambit

Both these openings demonstrate an essential principle of “hypermodern” or Modernist chess: to control the centre of the board from the sides, instead of trying to occupy it with pawns. This is what White’s knight and c-pawn are doing in the first diagram, and White’s dark-squared bishop in the second. Richard Réti’s signature move, 1.Nf3, is now the third most-played opening move. His opening is frequently seen at the very highest levels of chess: for instance, the world no. 3 player, Fabiano Caruana, used the Réti Opening in 2016 against the world no. 1, Magnus Carlsen. In the film of Nabokov’s novel The Luzhin Defence (2000), we see the climactic game open, of course, with the Réti Opening (see Music in Nabokov’s chess novel).

This style of play disrupts the perspectives of chess theory developed in the nineteenth century; it forces the players to look at what makes a “good” position from a different angle; in fact, from more than one angle at once. This disruption of “normal” or “natural” perspective is why Réti describes his thinking as “cubist”. He explicitly links the new ideas in chess with the Modernist swerve away from naturalism in visual art:

New ideas rule the game and have considerable similarities with the ideas of modern art. As art has turned aside from naturalism, so the ideal of the modern chess master is no longer what was called “sound play” or development in accordance with nature.

(Richard Réti, Modern Ideas in Chess, p. v)

Next time I am disorientated at the chessboard by an opponent’s devastating attack on the centre launched from the very corner of the board, I shall at least know I am participating in the history of modern art. I shall have Schoenberg’s music ringing in my ears.

Picasso 'Chess' (1911)
Pablo Picasso, “Chess” (1911) New York: Metropolitan Museum of Modern Art

Music in Nabokov’s chess novel

Music’s role in Nabokov’s 1930 Novel “The Luzhin Defense”

Luzhin defense book coverThe Luzhin Defense, described by Mike Fox and Richard James as the best novel about chess ever written, is an early (1930) work by Vladimir Nabokov (1899-1977). The central character is the Luzhin of the title (we never discover his first name), one of the strongest chess players in the world. The “Luzhin Defense” is the chess opening he prepares to combat his chief rival for the world title, the Italian grandmaster Turati. Ironically, although the encounter between Luzhin and Turati forms a crucial passage of the book, the defense is never played, since Turati avoids his own trademark opening when they finally meet over the board.

Nabokov himself was a chess enthusiast. Like the Luzhin of the novel, he was born and raised in St Petersburg; also like Luzhin, he left Russia after the 1917 Revolution to live abroad. Nabokov is better known as a composer of chess problems than as a player. In his autobiography, Speak, Memory (New York: 1960) he compares the intellectual challenge that the composer of a chess problem sets the solver to the challenge that the author of a book sets his reader. The fact that Nabokov felt this comparison to be apt explains at least two aspects of his work: firstly, his liking for unreliable narrators or other narrative devices that make following his novels a problem-solving challenge for his readers; and secondly, the frequent appearance of chess within his books, always with metaphorical significance. In his most famous work, Lolita (1955), there is an early scene in which Humbert Humbert (an extremely unreliable narrator) plays a game of chess; in the game, he freely sacrifices material to achieve his goal: to turn a small, white pawn into a queen, and using her to mate. Indeed a metaphorical prefiguring of the action of the novel. The role of chess in Nabokov’s fiction generally is explored in ‘Solus Rex: Nabokov and the Chess Novel’ by Strother B. Purdy (Modern Fiction Studies 14:4, 1968).

Luzhin defense DVD box
Nabokov’s novel was made into a film in 2000 and is available on DVD (note the different spelling of ‘Defence’ in the title)

The Luzhin Defense, however, is the only one of Nabokov’s novels in which chess is, as it were, the main subject of the narrative. Luzhin is taught the game by an aunt, when a boy of 12 or 13, after being fascinated by the sight of a chess set in his father’s study. His phenomenal powers in the game are quickly evident, and innate (in this, his story is not unlike that of Bobby Fischer much later, who was taught the game at the age of six by his sister, from the instructions in a set she had happened to find in a local candy store).

What Nabokov’s novel captures, entirely successfully, is the obsessive compulsion of the game, which occupies Luzhin entirely and to the exclusion of all other interests, skills or social relations. He meets and marries another Russian emigré, and settles in Berlin. There he reaches the pinnacle of his career, playing chess of an unbelieveable standard in a major tournament which culminates in his confrontation with Turati. During this long-anticipated game, he suffers a kind of mental collapse and is hospitalised. He gives up the game in order to preserve his sanity, and is nursed to health by his new bride. At the denouement of the novel, he is lured back to the game by his former manager, with catastrophic consequences.

The character of Luzhin is a literary creation, but is also to some extent an amalgam of real people: some of the events recounted of his childhood are those of Nabokov’s own; the end of the story was suggested by the fate of a real Berlin chess master, Curt von Bardeleben (1861-1924); as a Russian escapee from the Bolsheviks who reached the very heights of the game, he recalls Alexander Alekhine (1892-1946), the fourth chess World Champion. His arch rival Turati is hardly developed at all as an independent character in the novel; but his name recalls that of Richard Réti, as does Nabokov’s description of Turati’s playing style, which corresponds exactly to the “hypermodern” style of play developed by Réti and others in the 1920s:

This player, a representative of the latest fashions in chess, opened the game by moving up on the flanks, leaving the middle of the board unoccupied by Pawns but exercising a most dangerous influence on the centre from the sides.

(Vladimir Nabokov, The Luzhin Defense, trans. Martin Scammell [1930, translation 1964], Penguin Classics 2000, p. 61)

Music in the novel

Why, then, write at length about this novel in a blog devoted to the connections between chess and music? The answer is that, throughout the novel, Nabokov himself makes analogies between the two. Sometimes the connection is overt, sometimes hidden or symbolic. But it is a theme that runs through the whole book, as the following quotations demonstrate.

The first time that Luzhin sees a chess set is during a party given by his father in their St Petersburg home. The boy is hiding in his father’s study, trying to avoid attention, when a violinist, who has just performed for the guests, enters to take a call on the telephone. He opens a box of chess pieces on Luzhin’s father’s desk, and on seeing the boy (who has never seen the set before), he asks him if he knows how to play:

‘What a game, what a game,’ said the violinist, tenderly closing the box. ‘Combinations like melodies. You know, I can simply hear the moves.’


Luzhin steals the chess set, and asks his aunt to teach him the game. When his extraordinary talent is discovered, his first chess teacher is an elderly doctor friend of the family:

He spoke about the grand masters he had had the occasion to see, about a recent tournament, and also about the past of chess, about a somewhat doubtful rajah and about the great Philidor, who was also an accomplished musician.


Music is already a Leitmotif of the narrative.

Later on, once Luzhin is celebrated as one of the great players of his day, his father, a writer, imagines writing a novella about his son. He remembers watching him giving a simultaneous chess display as a child:

The writer Luzhin did not himself notice the stylized nature of his recollection. Nor did he notice that he had endowed his son with the features of a musical rather than a chess-playing prodigy, the results being both sickly and angelic […].

(p. 47)

Finally, the crucial episode of the novel arrives, when Luzhin is to encounter Turati at last. Nabokov turns again to music; not this time using the craft of a musician as an alternative or parallel occupation to that of a chess player, but using music as the metaphorical backdrop to the game itself. Just as the violinist at the St Petersburg party could “hear the moves”, the grandmasters seem to find music within the board:

At first it went softly, softly, like muted violins. […] Then, without the least warning, a chord sang out tenderly. This was one of Turati’s forces occupying a diagonal line. But forthwith a trace of melody very softly manifested itself on Luzhin’s side also. […] Turati finally decided on this combination – and immediately a kind of musical tempest overwhelmed the board and Luzhin searched stubbornly in it for the tiny, clear note that he needed in order in his turn to swell it out into a thunderous harmony. […] But the chessmen were pitiless, they held and absorbed him. There was horror in this, but in this also was the sole harmony, for what else exists in the world besides chess?

(pp. 91-92)

This game is never finished. Luzhin’s mental crisis intervenes, and the remainder of the novel charts his attempted recovery, which depends on his avoiding the game of chess at all costs. It is his wife who superintends this, and at a party that mirrors the one at the start of the novel, she regrets that Luzhin is no longer recognised, as she overhears another confusion of the careers of chess master and musician:

A rather pretty but boring young lady. And that strange marriage to an unsuccessful musician, or something of that sort. ‘What did you say – a former socialist? A what? A player? A card player? […]’

(p. 135)

As the end of the novel approaches, representations or artificial reproductions of both chess and music become prominent. Luzhin is tracked down by his former manager, a man called Valentinov, who wants him to return to the game; not to play competitively, though, but to take part in a film about the game. This is enough, however, to provide a fatal and musical recapitulation of Luzhin’s past:

To the sound of this voice, to the music of the chessboard’s evil lure, Luzhin recalled, with the exquisite, moist melancholy peculiar to recollections of love, a thousand games that he had played in the past. […] There were combinations, pure and harmonious, where thought ascended marble stairs to victory; there were tender stirrings in one corner of the board, and a passionate explosion, and the fanfare of the Queen going to its sacrificial doom.

(pp. 171-72)

And the final denouement of the novel comes when Luzhin gives up trying to avoid what seems to him an inevitable chess combination played against him by fate:

And suddenly Luzhin stopped. It was as if the whole world had stopped. It happened in the drawing room, by the phonograph.

(p. 175)

The appearance of the phonograph here is significant: it reproduces music mechanically, just as Valentinov’s film reproduces the life of a chess master artificially. In the early part of the novel, the music was real, and the chess was Luzhin’s real life too; at the end, he is trapped in an unreal world of mechanical reproduction: on a pocket chess set, he repeatedly sets up the pieces as they had stood in his game with Turati at the point that they had adjourned play. He distracts himself by listening to music with his wife, but as reproduced on the phonograph. Chess and music still mirror or echo each other, but no longer sustain lived experience.

Why chess and music?

Nabokov, it seems to me, understands intimately and at first hand the power and seductive attraction of the game of chess. It is small wonder that he turns to music as the central metaphor to articulate his novel. Great technical skill, unremitting devotion to practice, a reliance on inspiration, and the appreciation of great aesthetic beauty by connoisseurs: all these are shared by both music and chess. The two arts are also, of course, bound up with Russian cultural and political identity in the early twentieth century.

If you have read this, I urge you to go and read (or re-read) the novel. Try and read it as if you were listening to a recital.

Mozart and Capablanca: playing jokes on the amateur

I am not the first person to compare José Raúl Capablanca (1888-1942), the third chess World Champion, with Wolfgang Amadeus Mozart (1756-1791), the Classical composer. They were both child prodigies; they are both thought by many to be the greatest exponents of all time in their fields. Emanuel Lasker, the second World Champion, and Alexander Alekhine, the fourth World Champion, both rated Capablanca higher than any other chess player. Beethoven and Haydn both rated Mozart similarly as a composer.

The comparison between Capablanca and Mozart is most seductive, though, as a comparison of style. Capablanca’s style of play seemed effortlessly simple: he had a liking for simplifying positions, exchanging pieces until there seemed to be too few left for either side to win. Capablanca would then, time and again, proceed to win the apparently drawn game. His play was so precise that there was a period of over a decade (1914 to 1925) when he lost only two games (one of them to Richard Réti, of whom perhaps more in another post). In one tournament, in New York in 1916 against thirteen other top players, he won his first twelve games in a row.

Mozart’s harmony and sense of musical timing give a similar impression of effortlessness and brilliancy combined. Much of his music is constructed from phrases and chord progressions which are, quite literally, just like those found in thousands of other works from the same period; and yet Mozart’s music is unmistakably different, because it always seems just right. It often sounds simple; it never sounds amateurish.

To conclude this first attempt (there may be others to follow) at illustrating the similarities between these two epitomes of classical grace, I am going to turn to one of Capablanca’s games and one of Mozart’s works. The game by Capablanca is not one of his best by any stretch of the imagination; neither is Mozart’s piece one of his best. But they serve my purpose because they both show the encounter between the Master and the amateur.

The Capablanca game was played in a simultaneous exhibition given in 1918 in New York. His opponent’s name is not known; in this story, he stands for the spirit of amateurism. We can stand around the virtual chessboard and admire as an audience.

Capablanca started with the most popular first move in chess, moving the King’s Pawn two squares forward (1.P-K4 or 1.e4 in chess notation). His opponent did the same (1…P-K4 or 1…e5). Then each player moved a knight, and then the other knight; each castled, moved a bishop, then a pawn. The following symmetrical position had been reached.

diagram (1)
Position after move 6

This position has probably been seen thousands of times. But at this point, the true amateurism of Capablanca’s opponent showed itself. He reasoned that, if he simply repeated the Grandmaster’s every move symmetrically, then the game would remain equally balanced and end in a draw. The next moves saw the other bishops move out, then knights move to the centre, then queens move a single square each:



At this point, Capablanca took a piece (a knight), daring his opponent to stick to his plan. He did:

Capa game m7 (1)
Position after move 10

And here, Capablanca showed his classical brilliance: a check (which of course could not be copied with another check), the sacrifice of a bishop with another check, two checks from the queen, and it was checkmate:

Capa game mating attack
The mating attack

Less of a chess game than a chess joke: a lesson in the dangers of slavishly imitating a master craftsman without understanding the craft.

The piece by Mozart I want to put next to this game is his “musical joke”, Ein musikalische Spass (K.522). No-one is quite sure why Mozart wrote this piece, but it demonstrates a very similar spirit to Capablanca’s “joking” game. Imagine the scene: Capablanca sitting opposite his amateur opponent; we are standing among the onlookers, at first puzzled by the apparently amateurish play, then at the end marvelling at the grandmaster’s brilliance. And now imagine Mozart, deliberately writing a piece which conjures up the image of an amateur composer, who slavishly copies musical phrases from other pieces without understanding how they ought to fit together; we are the audience, at first puzzled, then marvelling at how the composer of genius can portray a composer of platitudes without becoming platitudinous himself.

Capablanca’s game finishes with a swift, brutal mate-in-four. Mozart’s piece ends with the instruments playing a final cadence, but in four different keys at once. Enjoy the video below.

Richard James’s chess and music posts

Even more complete chess addict coverRichard James is jointly responsible with Mike Fox for the utterly wonderful The Even More Complete Chess Addict (Faber: 1993). In that book, they comment, in their section on famous chess-playing musicians, that “If [they] could be reincarnated, they’d look pretty good in the European club championship (and even better at the post-match concert)”.

Fortunately for me, Richard has gone beyond his 1993 book in a series of blog posts about musical chess players. His posts are mainly historical and biographical, and if you are reading this, you ought to be reading them. They appeared intermittently in a blog called The Chess Improver, and are quite hard to find as a group. So here are links to all seven:

Part 1: Philidor

Part 2: Erkel and Brodsky

Part 3: Parratt and Goldenweiser

Part 4: Oistrakh plays Prokofiev

Part 5: Taimanov plays, Smyslov sings

Part 6: Other voices

Part 7: Nette sings, Daniel plays

Is writing in sonata form like playing chess?

For students of music theory, the topic of “sonata form” is both central and daunting. The phrase “sonata form” is used to describe a kind of musical form that arose in the eighteenth century and is still in evidence today. Sonata form is arguably the most flexible, creative and widely-used form in the canon of Western art music of the last three hundred years.

Beginning students of composition naturally want to know what the rules of sonata form are: what is it that defines the form? How does a composer set about writing a piece in sonata form? The answers are nearly always frustrating. Sonata form, they are told, is less a form than a principle … or a style … or a theory; it doesn’t have hard-and-fast rules. And yet it must have rules: otherwise, it couldn’t be thought of as a form at all.

The most recent musicological book to attempt to define sonata form is Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata by James Hepokoski and Warren Darcy (Oxford University Press 2006). It is huge, compendious and brilliant. And, in answer to the frustrated student wanting to know what the “rules” of sonata form are, the authors wisely turn to the game of chess:

[…] the basic concerns of Sonata Theory are learned relatively quickly—like the moves of chess. These concerns may seem simple precisely because they are simple. […] Beyond the elementary principles of Sonata Theory, though, lies an elaborate network of possibility, nuance, flexibility, sophistication, and detail that takes patience to master. As with chess, again, one may learn the moves rapidly, but to play the game at a fully proficient level is more difficult.

(Hepokoski and Darcy 2006, p. 12)

I do not know whether either Robert Hepokoski or Warren Darcy is a keen chess player; neither of them appears in the current FIDE database of active players. But I strongly suspect at least one of them is, because the comparison is so apt. At every moment of writing a piece in sonata form, the composer is faced with a set of possible continuations; all of them adhere to the general conventions of the form, but some sound banal while others sound brilliant. And the grandmaster, contemplating which of the many legal moves on the chessboard he or she will select, is offered the same potential, the same oscillation between banality and brilliance.

Playing through a sonata form movement by Mozart is indeed much like playing through a game by Capablanca; we all know the rules, but  we can only wonder at how the results are brought about.

Why make this comparison with sonata form in particular, though? Surely any musical form: fugue, variation form, operatic aria, or whatever, has this same balance of rule-based convention and individual brilliance? Well, yes; but perhaps the connections between sonata form as a practice and chess playing go deeper. I suspect they do; but that is a topic for future posts.

The Chess and Music Blog

Thoughts on playing

Bob at the piano (compressed)
The author, Robert Samuels, playing Ah! Vous dirai-je, maman (Mozart’s variations)

This blog shares my thoughts on two fields which engage the obsessive-compulsive side of my personality. I am an enthusiastic and unrepentantly mediocre player, whether playing music or playing chess.

That is to say, there are many contexts in which other people think I am quite a good player. As far as music is concerned, these are of course the contexts to which I try to confine myself: playing the piano at a community fund-raising event, playing the organ (very mediocre) at church. But musically, I am always chasing after the music I can hear, and know ought to be coming from the instrument. An endless quest that leaves me in genuine awe of those who really can produce the music that remains, for me, ideal. And so I teach music, I talk about it whenever I am asked, I write about it, I research into it. Because I cannot, quite, play it as I want.

Bob Samuels playing chess
The author, Robert Samuels, playing the Nimzo-Indian Defence (Capablanca variation)

As far as the game of chess goes, my standard of play is astoundingly similar. I might seem quite a good player in a casual or friendly game; I am proud to play for the fourth-best of my local chess club’s five teams. But in every serious game, I chase after the elusive brilliance I can admire in others, but never quite recapture myself.

And so I am writing this blog in the same spirit as I write about music: to try to understand what it is that enthralls me. I am convinced that the similarity of my competence in each field is no accident. The connections are multiple.

Do not expect posts in this blog to be either regular or systematic. But they will be thoughtful.