Creating patterns

Patterns analysed by the Réti brothers in music and in chess

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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:

Approach to PC(1) V--I

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:

Approach to PC(2) IV--V--I

Approach to PC(4) complete

And here is one from a real piece of music that you might recognise:

6-4 cadence analysed

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):

 

 

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

Rudolph_Reti_125
Rudolph…

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.

RichardReti
…and Richard

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).

Robert Schumann 1839
Robert Schumann in 1839

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).

Clara Schumann in 1840
Clara Schumann in 1840

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.

Kinderszenen main theme variants

 

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’]:

Kinderszenen basic shape with no.2

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:

Kinderszenen basic shape with no.7

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:

Kinderszenen basic shape in bb 22-3 of no.7 notes circled

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.

Tartakower (New York 1925)
Tartakower in 1925

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:

Reti vs Tartakower 1910 move 8
Réti vs Tartakower, Vienna 1910. Can you spot White’s winning move?

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!!]:

Reti vs Tartakower 1910 move 9

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 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 vs Duke Karl & Count Isouard 1858 move 15
Morphy vs The Duke of Brunswick & Le Comte de Vauvenargues, Paris 1858. Can you spot White’s winning move?

Morphy’s stunning win was, like Réti’s, a queen sacrifice leading to that same rook-and-bishop mating pattern:

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:

Maczuski vs von Kolisch 1864 move 13
Maczuski vs von Kolisch, Paris 1864. Can you spot White’s winning move?

Once again, a queen sacrifice leads to checkmate, this one even more like that in Réti’s game:

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:

Koltanowski vs Dunkelblum 1923 move 12
Koltanowski vs Dunkelblum, Antwerp 1923: can you spot White’s winning move?

By now, the winning combination should be familiar:

Finally, a more recent game between two strong amateurs:

Amini vs Gralla 2010 move 15
Amini vs Gralla, Hamburg 2010. Can you spot Black’s winning move?

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’:

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:

Reti vs Fischer 1923 move 10
Réti vs F. Fischer, Vienna 1923, after 10 moves. How should White proceed?

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:

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:

Reti vs Fischer 1923 move 12 annotated

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:

Reti vs Rubinstein 1923 move 14
Réti vs Rubinstein, Karlsbad 1923, after move 14. How should White proceed?

Réti reproduced his idea from the Vienna tournament, this time creating two lines of attack into the enemy camp:

Reti vs Rubinstein 1923 move 15 annotated
Réti vs Rubinstein, move 15

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”.

Bundesarchiv_Bild_102-00457,_Emanuel_Lasker (1929)
Emanuel Lasker

The following year, Réti again played in the strongest tournament organised, this time in New York. He faced the former World Champion, Emanuel Lasker:

Reti vs Lasker 1924 move 11
Réti vs Lasker, New York 1924, after move 10. How should White proceed?

Once again, Réti manoeuvred his pieces to create a new line of attack into the enemy camp:

Reti vs Lasker 1924 move 14 annotated
Réti vs Lasker, move 14

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:

Reti vs Lasker 1924 move 24
Réti vs Lasker, after move 24

With typical inventiveness, Réti tried playing the motif from the other corner:

Reti vs Lasker 1924 move 25 annotated
Réti vs Lasker, move 25

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:

 

Capa vs Lilenthal 1936 move 11
Capablanca vs Lilienthal, Moscow 1936, after move 11. How should White proceed?

By now, it should come as no surprise to see the pattern created by Capablanca’s next two moves:

 

Capa vs Lilenthal 1936 move 13 annotated
Capablanca vs Lilienthal, move 13

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.

José Raúl Capablanca (1931)
Capablanca in 1931

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).

Andor Lilienthal (1936)
Andor Lilienthal in 1936

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.

 

 

 

 

 

 

 

Author: Robert Samuels

I teach music for The Open University and play chess for Cowley Chess Club in the Oxfordshire Chess League.

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