Does practice make perfect?

The value of five-finger exercises and pawn endings

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One of the things I disliked most in my childhood was piano practice. Not that I disliked playing the piano; in fact, I spent quite a lot of time sitting at the piano and playing things through. But I did very little practising. Playing scales, or other keyboard exercises, were things I almost never did. Partly, this was because my piano teacher (whom I liked very much and to whom I owe a great deal) did not teach me how to practise, nor explained to me why practising is important, and how it differs from playing pieces through and hoping that by repetition you will play them better.

Much the same was true of my early experiences of playing chess. I learned the moves from my father; I played at a club at school and later for a club in the local league; but all I ever did was play games. I did try to memorise some common opening moves (which I found very difficult to do beyond the second or third move), but no-one ever suggested to me that playing chess might be a skill that required practising.

The proverb, “Practice makes perfect” therefore intrigues me. What exactly is practice? Is it just playing a piece on the piano again and again, or playing games of chess as often as possible, with the hope in both cases that  improvement will be the inevitable result? Or is there more to it than that? Equally, what does it mean to play music, or to play chess, “perfectly”? Is that even possible? And will it result from proper practice?

My attitude to piano practice changed abruptly and forever when I was sent to a new teacher as part of starting my music studies at university. That teacher was Phyllis Palmer, who is something of a legend amongst those who ever studied with her. At my first lesson, she told me that the piece I played to demonstrate my standard was badly chosen, my posture was dreadful, and my technique was poor. She also introduced me to a book of piano exercises, recommending I try the easiest two. “These,” she remarked, “are what a professional would use for the whole of their career.”

What do you do when you practise?

Here is one of those piano exercises by Dohnányi to which the redoubtable Phyllis Palmer introduced me:

Finger exercise (Dohnanyi) transparent

When I first saw this, it looked trivially easy. You put your five fingers on the five white notes C, D, E, F and G, and only use one hand (to begin with; you add the other hand, an octave lower, later). You keep one note depressed while you play the others. The pattern changes by one note in each bar until it repeats itself. Easy.

Then I tried playing it. I couldn’t.

Nowadays, I often start a practice session with this exercise, which trains your fingers to move independently, and makes them stronger. It is an exercise that shows the value of practising.

Now here is a chess position to which, a year or two earlier, an older member of my chess club introduced me:

pawn ending exercise 4 (Black to move and lose)
A pawn ending. Black to move.

“What do you think of this position?” He asked me. “It’s Black to move.”

“It looks like a dead draw,” I replied.

“Quite right. Try and play it out.”

Since Black’s king  can’t go forwards, I moved it one square backwards. “Ah!” said the older player who then, in a few more moves, forced my king into the corner, took all Black’s pawns, and won.

The position should indeed be a draw. But of Black’s five legal moves, four lose. It is a position which shows the value of practising.

Five-finger exercises and pawn endings

There is an affinity between five-finger exercises and pawn endings like the ones above. They enable you to develop the kind of ability which underlies much more complex tasks, which however cannot be attempted unless the “practice” task is completely mastered.

The piano exercise by Dohnányi is not a great piece of music, but if you can play it perfectly, then your fingers will be able to attempt the counterpoint of a Bach fugue or the figuration of a Chopin Étude. Equally, the pawn ending is not a great game of chess; but if you know how to draw and not lose the ending, you will be able to tread a path through real, tricky endgames.

Both kinds of exercise look deceptively simple. The first bar of the Dohnanyi exercise is fairly easy, in fact; the second bar is a lot harder, and the third bar really takes practising. Pawn endings share this deceptive quality. Here is an apparently symmetrical, equal position; White is to move. It is a win for White.

pawn ending exercise (White to win)
White to play and win

On the other hand, if the kings are anywhere except in the corners, the result is different:

And here is a similar position where, if White is to move then White will win, while if Black is to move then Black can draw:

pawn ending exercise 3 (White move win Black move draw)
White to move and win; Black to move and draw

How do you practise?

Now that I am no longer a child, and thanks to Phyllis Palmer’s accurate assessment of my weaknesses, I enjoy practising the piano. A regime of Dohnányi’s A Legfontosabb Ujjgyakorlatok [Essential Finger Exercises] and Bach’s immensely beautiful, immensely tricky 48 Preludes and Fugues (Book 1 in odd-numbered years, Book 2 in even-numbered years) will keep me happy for the rest of my life, I should think.

Practising chess technique used to be more laborious, requiring books of puzzles, endgame studies, and the like, as well as a board and pieces (unless you could play blindfold, which I cannot). That, however, has been entirely changed by the internet. Nowadays, a regime of practising using an internet chess site is a direct parallel to practising a musical instrument. The examples above were endgame puzzles; here is an example from Chess.com’s training website, where you need to remember basic pawn technique to win an ending that looks as if it comes from a real-life chess game:

pawn ending exercise (Chess.com tactic 175366)
Chess.com tactic 175366. White to move and win. Click to try it yourself!

I try to practise every day. Like Schumann, I try to make Bach my “daily bread”. In chess, I am still very poor at endgames, partly because I prefer to practise tactical puzzles which reinforce the kind of pattern recognition I waxed lyrical about in Creating patterns.

I certainly don’t manage to practise the piano every day, but I do usually manage to practise chess tactics (which takes a lot less time). And in both realms, there is no doubt that my technique has become a lot more secure.

So, does practice make perfect?

No, of course it doesn’t. At least, not in the sense that I will ever become a pianist to rival András Schiff or a chess player to rival Magnus Carlsen. However, what practice can perfect is that underlying technique that can allow you to aspire at least to competence. Ninety-nine times out of a hundred I can play that Dohnányi exercise as well as anyone; and ninety-nine times out of a hundred I can draw a drawn pawn endgame, or win a won pawn endgame. It is practice that enables me to stop worrying about the routine business of playing the right notes or choosing reasonable moves, and get on with the rewarding business of interpreting great music or formulating chess strategy. But in both contexts, that is true only if I keep practising, daily if possible.

Even a professional pianist or a professional chess player has to practise – in fact, professionals practise an awful lot more than I do or could. It was Phyllis Palmer herself who first gave me that well-worn adage: “An amateur practises until they can get it right. A professional practises until they can’t get it wrong.”

The chess and music blog: one year on

Chess and Music Blog stats after one year
My readers come from every continent except Antarctica.

It is now a year since I began this blog, so I thought it was time that I thanked everyone who has taken the time to read any of the posts which have been appearing at the rate of about one per month (this is in fact the fourteenth).

I was asked recently whom I thought I was writing for. It was (and is) a very difficult question to answer. The truth is that I write these posts for myself, of course. I remain fascinated by the connections between the human activities of chess and music, and I am sure I shall remain so.

What has been gratifying, though, has been the discovery that others share my fascination – enough to read this blog, at least. In the twelve months that I have been posting, more than 500 visitors have paid this site a visit. More surprisingly to me, the site has been viewed from a total of 55 different countries across the world. Most of you come from the UK or the USA, of course; but this is my opportunity to hail whoever you are from Estonia, Honduras, Kenya, Palau and elsewhere who have stumbled across this blog at least once.

I do know some of my readers, who are club-mates from Cowley Chess Club, colleagues from The Open University (which has had an extremely eventful year since this blog started, although I would not claim any causation either way), and friends prepared to indulge me. But I have also made friends through writing here: I suspect that Greece features high up in the list of countries where the blog has been read mainly because I have come to know Achilles Zographos since his excellent book was recommended to me. If you haven’t read his book, at least read my book review: Music and Chess (Achilleas Zographos). And I have become at least a Facebook friend of Richard James, whose book with Mike Fox, The Even More Complete Chess Addict, and whose own chess and music posts remain constant sources of inspiration.

Finally, as I begin a second year of these blog posts, I do want to reassure my readers that I haven’t exhausted my topic. I am rather well aware that it has been quite some time since I last posted (when I answered the question Did Beethoven play chess?). Partly this has been due to the demands of earning a living during troubled times for my employer; partly it has been because the post on which I have been working for some time, a return to the Vienna of the early twentieth century and Arnold Schoenberg, has led me down paths I did not suspect and which have taken time to pursue (including attempting to translate a lengthy academic article written in German). But rest assured that my thoughts on Schoenberg will appear before long, and that I have plenty more musico-caissic topics to write up.

 

Book review: Music and Chess (Achilleas Zographos)

A recent book on my favourite subject

music_chess_frontcoverMusic and Chess: Apollo meets Caissa. Achilleas Zographos. Milford, CT: Russell Enterprises, 2017. ISBN: 978-1-941270-72-1 (print); 978-1-941270-73-8 (ebook)

Books on chess are a curious genre. There are an awful lot of them, they are very hard to find in libraries. They nearly all fall into one of a few categories. Books on openings. Books on improving your chess technique. Collections of games (by an individual, or from a world title match, or from a significant tournament).

And that is about it. What all these books share as a quality is that they are absolutely incomprehensible to anyone who is not a keen chess player. I have many of them, and if I leave them lying around, members of my family ask me when I am going to read a “proper” book.

There are just two kinds of exceptions to this rule, and these exceptions contain my favourite kinds of chess book. The first is chess biography or autobiography: Korchnoi’s Chess is my life is worth reading as much for its picture of the privations of  the siege of Leningrad as for its depiction of one of the most obdurate personalities ever to have graced the game.  Emanuel Lasker: The life of a chess master (J. Hannak) is a riveting account of an extraordinary personality. But the second kind of exception to the normal run of chess literature is my favourite: books which take chess into other realms, such as literature or film (see my earlier post on Nabokov’s The Luzhin Defence), or the anecdotal and eccentric (by far my favourite is The Complete Chess Addict by Mike Fox and Richard James, and its enlarged version The Even More Complete Chess Addict). And now – joy of joys! – the chess publisher Russell Enterprises has presented a book on exactly the topic of this blog.

The first thing I want to say about this book is that you should definitely get yourself a copy, if you are reading this blog. I need to put that first, because I could hardly fail to welcome a publication such as this. Having said that, there are of course lots of things here which I would have put differently or with which I don’t quite agree. But these are the kinds of  things one should discuss over a convivial drink, not reasons for disparaging the book.

Achilleas Zographos (since I contacted him, this blog has gained Greece as a new country in its stats profile) is a much better chess player than I am (he is a FIDE trainer) and also a much better performer (he is a concert pianist). There are times when his perspective is clearly that of a performer rather than a composer. But there are a lot of things I like about his book.

Things I like about this book

The author is clearly a man after my own heart, with a taste for the quirky and occasionally bizarre which I love. Perhaps all of us who love both chess and music as arts are similar in that way. He has compiled a huge quantity of anecdotes and information of the sort I find fascinating. Quite a lot of it I knew already (unsurprisingly); Fox & James (see above) are frequently cited as a source for anecdotes. But there is plenty in the book which I didn’t know: for instance, I didn’t know the sixteenth-century Italian poem which invented the dryad Schacchia, goddess of chess, and the eighteenth-century English poem in which she acquired the name Caïssa (the poems are described here); I had never come across Guido van der Werve’s chess piano (here is his concerto in three movements); and I did not know that GM Levon Aronian, who is about to compete in the 8-player knockout to determine the next World Title Candidate, has a passion for jazz.

The book is sumptuously illustrated. At the back are links for internet sources for the illustrations and YouTube videos. Sadly, some of these links seemed to be broken when I tried them; but I loved the quality of the illustrations reproduced. Trying to download one of the illustrations led me on an interesting detour. On p. 128 is printed a lovely canvas by Kandinsky, with the title Schach-Theorie [Chess Theory], and the date 1937. I did not know that Kandinsky (one of my favourite artists and a collaborator with the composer Arnold Schoenberg) had an interest in chess. When I found that the link at the back of the book seemed to be broken, I tried an internet search for the painting, and discovered that it has two quite different attributions. The canvas is owned by the Guggenheim Museum in New York, where it has the title Graceful Ascent and the date 1934.

45.970
Vassily Kandinsky, Graceful Ascent (1934). Or is it Chess Theory (1937)?

I have to say that Graceful Ascent seems more convincing as a title, although there are some details near the top of the canvas that could conceivably be chess pieces.

45.970
Could some of these shapes be chess pieces?

So where do the probably false title and date come from? Further internet searching turned up what seems the likely source, and a wonderful anecdote. In 1937, the year that many of Kandinsky’s paintings were confiscated by the Nazis and displayed in the Exhibition of Degenerate Art, a retrospective of his work was displayed in the Swiss city of Bern. The city was home to another of the Bauhaus artists, Paul Klee, and the exhibition was to be the last time that the two artists met (Klee was seriously ill and died in 1940). According to the Bern artist Peter Matter, the two giants met in front of Kandinsky’s work Schach-Theorie, and both were seized by a sudden desire to go back to Klee’s house and play each other at chess. So perhaps the internet translation of Matter’s diary is the source of the misattribution. And perhaps it was a different canvas: both Klee and Kandinsky produced other works at that time that suggest the game of chess much more clearly to me (hover your mouse to see the titles).

So this is probably an error, as far as the content of the book goes; but I could hardly complain at that, since it sent me on a rewarding hunt which enabled me to place these two alongside Schoenberg as artists enthusiastic for the Royal Game.

 

Things I don’t like so much about this book

Most of the things I am less impressed with in the book are not the fault of its author. While the publisher should be applauded for commissioning this work, the author is not writing in his native language, and the services of a copy-editor would have improved it as a text to read. Infelicities such as “At the moment of writing” (rather than “At the time of writing”, p. 13); or grammatical lapses such as Steinitz’s “systematic, scientific approach of the game” (rather than “…approach to the game”, p. 21), are frequent and irritating. My annoyance at the blurb on the back cover engendered an earlier blog post, Prodigies: the preserve of music and chess? although I did discover on p. 39 that it was the American grandmaster Edward (not the World Champion Emanuel) Lasker who originally commented on child prodigies as a phenomenon of chess, music and mathematics.

Things that puzzle me in this book

Tarrasch quote
Wouldn’t you buy this t-shirt?

There are a lot of lists in this book. That is no bad thing in itself; I like lists. The last chapter, ‘Quotations’ is in fact just a list of good quotations, which ought to delight designers of chess-related t-shirts.

Other lists are more intriguing. For instance, Beethoven appears in a long list of musicians who had a passion for chess on pp. 23–24; he is mentioned a dozen times elsewhere (the book has a good index), but always just as an emblem of “the great composer”; nowhere are we told the source for believing he had an interest in the game of chess. My scan through the several hefty volumes of his letters could find no mention of it at all; but I would love to know what evidence there is.

But lastly, the thing which puzzles me most about this book is actually the way that it compares the technical elements of chess and music. Several times, the author’s love for the quirky leads him to the most extraordinary chess compositions to illustrate the most ordinary elements of music. One is the study by Petrovic which is presented as an example of the role of rhythm and tempo in chess:

Mate in 271 (Petrovic 1969)
White to move. Mate in 271 moves.

Another is the beautiful but totally bizarre study by van Reek which illustrates the musical idea of ‘texture’:

White to win (texture study)
White to play and win

But the puzzlement I felt reading through the lengthy chapter entitled ‘Components’ which works its way through ‘Time, rhythm and tempo’, ‘Melody and movement’, ‘Harmony’, ‘Texture’, ‘Structure’, and ‘Timbre / colour’ turned from slight annoyance to perfect calm with the realisation that this most difficult of fields, making detailed and persuasive comparison of the technical aspects of the arts of chess and music, is left  open to my own blog to attempt. Keep reading my posts here to see how well I get on with trying.

 

 

 

 

 

Prodigies: the preserve of music and chess?

This short blog post is inspired by a statement I read this week in the publisher’s blurb for what looks to be an interesting book, Music and Chess: Apollo meets Caissa  (Achilleas Zographos, Milford: Russell Enterprises 2017). This is not a review of the book – you can expect one of those in due course – and, with one book to my own name, I know better than to attribute what you read in the blurb to the author of the book. It is printed on the back cover, and also on all the websites from which the book can be purchased. Here it is:

It has long been recognized that there are only three major areas of human endeavor which produce prodigies: music, chess and mathematics.

Is this true? I found myself wondering (a) whether this assertion is justified, and (b) whether it does indeed demonstrate an innate connection between these three fields in particular.

I shall have to leave to one side the question of definitions of the terms “prodigy” and “major areas of human endeavour”. After all, this is a piece of advertising copy rather than a philosophical proposition. But the more I looked at it, the odder it seemed.

Are there prodigies outside of music, chess and maths?

If “prodigy” means someone who attains mastery of a field at a very young age, it seems to me that there are other “areas of human endeavour” which produce this phenomenon. I can think of three straight away:

  • Sport in general. Even without turning to womens’ gymnastics in the 1970s, when it seemed that mastery of the sport was the province only of pre-pubescent girls, exceptional talent in many sports shows itself very early indeed. I remember reading an anecdote of John McEnroe’s father throwing a baseball for his five-year-old son to hit in Central Park, when a passer-by asked whether the talented midget worked in a circus. Wayne Rooney was the top goal-scorer in his father’s local pub football league at the age of nine.
  • Acting. The number of incredibly talented child actors is long indeed. Shirley Temple was the highest-paid actress in Hollywood before retiring at the age of 22 and becoming a diplomat (American Ambassador to Ghana and Czechoslovakia). Mark Lester, Macaulay Culkin, and more recently, Daniel Radcliffe and Emma Watson all demonstrate that exceptional talent can show itself early and stay with its owner into adulthood.
  • Romantic poets. They may not have been children, but the whole movement of Romantic poetry in the early nineteenth century was certainly the province of teenagers: Keats, Shelley, arguably Byron, Wordsworth and Coleridge, all produced their best work in their teens or perhaps early twenties.

Are the greatest musicians and chess players always child prodigies?

Capablanca aged 4, Chess Notes 6521
Capablanca aged 4 (from Edward Winter’s Chess Notes no. 6521)

It is undeniable that some of the greatest musicians, and some of the greatest chess players, were also child prodigies. In chess, the clearest example is the third World Champion, José Raul Capablanca (1888–1942), whose ability was reported in the Cuban press before his fifth birthday.

 

 

 

 

 

 

Mozart by Louis Carrogis (1763) wikimedia commons
Mozart with his father and sister. Painted by Louis Carrogis when Mozart was seven years old.

In music, the obvious candidate is of course Wolfgang Amadeus Mozart (1756–1791), who learned to play the piano at three, was touring Europe with his father as a soloist before his tenth birthday, and composed his first symphony at the age of nine. 

 

 

 

 

 

 

 

However, these two are not typical. Indeed, Richard Réti was of the opinion that Capablanca’s exceptional talent (his predecessor as World Champion, Emanuel Lasker, and his successor, Alexander Alekhine, both rated him as the greatest player of all time) stemmed from the fact that he learned the game so early, so that it was like a “native language” to him. Much the same could be said of Mozart. But many other great chess players learned the game later: for instance, Emanuel Lasker (eleven), one of his challengers for the World title, Carl Schlechter, (thirteen), another World Champion, Mikhail Botvinnik (twelve). Equally, while most musicians begin playing early in life, exceptional talent may not show itself until much later. Had Beethoven died at the same age as Mozart (35), he would have left just three symphonies, no operas, and only one set of string quartets.

When do artists reach their peak?

While some chess players and some musicians do show exceptional talent as children, this does not mean that they attain the greatest heights at that age. While most sportsmen and sportswomen reach their peak in their twenties or thirties (as I believe is true for some mathematicians), this hardly means that they are prodigies when they do, or have to have been prodigies in order to excel. Bobby Fischer learned the game of chess at the age of six, was hailed as the best player in America when he was thirteen, but did not become World Champion until he was 29. Chess and music are both reassuring (to people like me) in that age can be defied by the greatest exponents: Emanuel Lasker, having held the title of World Champion longer than anyone else (27 years), returned to competitive chess at the age of 66, having lost his fortune in Hitler’s persecution of Jews; he attained third place at the Moscow tournament of 1935, remaining unbeaten, defeating Capablanca (who came fourth), and ending just a half-point behind the winners (Botvinnik and Salo Flohr). The pianist Alfred Brendel caused dismay in the world of music when he announced his retirement at the age of 75, still considered by many to be the greatest living performer. The composer Havergal Brian produced his thirty-first and thirty-second symphonies at the age of 92.

Are chess, music and maths linked?

To me, the most irritating aspect of the statement with which I started this post is that I agree with its basic contention, which is that there is cognitive similarity between the intellectual skills and mental stimulation that chess, music and mathematics all provide. But I don’t think that this guarantees that talent in any of these fields must necessarily show itself in childhood. Nor do I think these are the only “areas of human endeavour” in which prodigies occur. Nor do I think that some competence in any of these fields is impossible for those who, like me, attempt in their middle life to apply the hard work and practice to these activities which they were incapable of mustering earlier on.

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.’

(p.21)

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.

(p.39)

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.