Beginnings and endings

A New Year’s essay on music and chess

Many years ago, when I was studying for my PhD, my supervisor, the music analyst Derrick Puffett, remarked to me that it was odd that music scholars tend to spend much more time analysing how a piece begins, rather than how it ends. I think that this was a slightly barbed comment, given that I had just presented him with several pages of text and a complex graph analysing how the whole of Der Abschied, from Mahler’s Das Lied von der Erde, grows out of the single stroke on the tam-tam that begins it. Der Abschied is the last movement of Das Lied von der Erde, and its title means ‘The Farewell’, so I was at least writing about a sense of ending as well as concentrating on a beginning.

This post is appearing on 6 January, traditionally celebrated as the Feast of the Epiphany, marking the visit of the Magi to the infant Christ. It is the end of Christmas, and the beginning of the new year. Entirely suitable for some reflections on beginnings and endings, then.  T. S. Eliot also noted the relevance of beginnings that seem like endings in his poem on the Epiphany story:

[…] I had seen birth and death,
But had thought they were different; this birth was
Hard and bitter agony for us, like Death, our death.

(T. S. Eliot, ‘The Journey of the Magi’, 1927)

A sculpture of the Epiphany in Notre Dame cathedral, Paris. Two of the Magi appear to have brought chess-themed gifts. (Image: Bridgeman Education)

I have often thought about Derrick’s remark concerning beginnings and endings. It is quite true that analyses of musical works do often spend a lot of time on the opening of a work.  For more than two decades I taught music analysis to undergraduates studying at the University of Oxford here in the UK, and every year I tried to dissuade them from beginning their essays with the phrase, ‘In bar one…’.

The Encyclopaedia of Chess Openings runs to five thick volumes.

It is  also, of course, usual to write about the ‘opening’ of a game of chess. Indeed, the tendency to concentrate on openings is even more pronounced in writing about chess than in writing about music: hundreds and hundreds of volumes have been written about openings; they are often the largest section in a chess bookshop or a keen player’s library. At the beginning of the game, the first player has a choice of twenty possible legal moves. While some are much more popular than others, every single one of the twenty has been tried in master-level play at some point. Even apparently weird choices such as 1.Na3 (the ‘Sodium Opening’) have some theory attached to them.

Chess endings also have a five-volume encyclopaedia.

Endings, of course, are similarly fascinating to chess players, and endlessly discussed and analysed.  As the number of pieces left on the board diminishes, the paradoxical truth is that the need for precision and calculation actually increases. In the opening, almost all of the 400 different positions that can result from each player making a move can be viably played by either side; in an ending, there are often a similar number of possible legal moves as in the opening, but there may be whole sequences of play where only one of the moves available to either player can avoid defeat or secure victory.

A musical opening, and its ending

I now want to explore this inter-relationship of beginnings and endings in both music and in chess. My aim is to show once more how closely related these two ‘arts of playing’ can seem as technical, creative activities. To begin with, here is a remarkable opening to a piece of music. Indeed, one of my favourite pieces of music, both to listen to and to use in teaching. It is Mozart’s String Quintet in C, K515, composed in the Spring of 1787.

Mozart’s String Quintet in C, K515, bars 1-5

Here is a performance of this wonderful work. For the moment, you only need to listen to the first nine seconds; I urge you to come back and listen to the whole thing after you finish reading this post.

So, why did I describe this opening as remarkable? Well, as I used to point out to my student analysts, you can tell just from these first bars that the movement they introduce is going to be exceptionally long. In fact, I believe that the first movement of this quintet is the longest movement in ‘sonata form’ that Mozart ever wrote, at 368 bars. For comparison, the first movement of Mozart’s longest symphony, No. 41 ‘Jupiter’, K551, written the following year, is 313 bars long. I wrote a post early in the history of this blog entitled Is writing in sonata form like playing chess?, and it is not surprising that this form gives such a good example of how an ending is implied in a beginning.

The point is that Mozart’s opening bars announce themselves to be written in what is usually called the ‘Classical Style’, which relies on balance and symmetry of design; but at the same time they deliberately disrupt this balance. Mozart’s tune is very simple: just an arpeggio outlining a C major chord, played by the cello, and finished off (with a little twiddle) by the first violin. Not unlike another deceptively simple tune written by Mozart in the Summer of the same year (1787), featuring two arpeggios, and very well known:

Mozart, Eine kleine Nachtmusik in G, K525, bars 1-4

Returning to the tune that opens the quintet: it is apparently very straightforward, but there is one unusual thing about it. The tune is five bars long, when in the classical style, you would expect it to be four bars long, like the tune that opens Eine kleine Nachtmusik. Instead of a two-bar phrase answered by another two-bar phrase, the quintet opens with a three-bar phrase answered by a two-bar phrase.

So what is the effect of this lop-sided phrasing? In order to achieve the balance that the style in which he is writing requires – in order to obey the rules by which his music communicates – Mozart answers his five-bar phrase with another one. This creates a balanced, but still rather oddly-shaped, ten-bar period overall. Mozart then ‘balances’ these ten bars with another ten-bar period leading to a cadence. But by the end of bar nineteen, this curious competition between balance and lop-sidedness requires an entire bar of silence in bar twenty to ‘make up’ the proportions of the whole. And then, to use a chess term, Mozart plays an ‘opening surprise’:

Mozart String Quintet in C, K515, bars 17-25 (c. 0:25-0:35 in the video above)

The surprise is that in bar 21, Mozart reprises the opening of the work, with two differences: firstly, the violin begins the tune and the cello answers, instead of the other way around; secondly, and much more strikingly, the repeat is in the minor key, C minor instead of C major.

I hope that this has managed to explain why I said that the opening five bars could not belong to anything other than a long work in sonata form. Five bars are balanced by five bars. These ten bars are balanced by a further ten (the proportions only completed by a gap), and these twenty bars, which get no further in terms of form than most pieces of this sort do in eight bars, are then ‘balanced’ by a completely surprising reprise. Given that the form still requires a contrasting ‘second subject’ to be set against this first tune, you can see that Mozart is settling in for a lengthy operation: what turns out, in fact, to be a brilliant display of his total command of musical style and form. In fact, this fits in with what we know of Mozart’s reasons for writing this quintet. In 1787, he took out an advert in a Viennese newspaper, offering three string quintets for sale, in manuscript, copied under his personal direction and available from his publisher. In other words, he was at a point in his career where he wanted to make money from selling works directly to performers, rather than relying on a wealthy aristocratic patron (although he spent plenty of time cultivating the latter when he could). In contrast to Haydn, who remained a court servant more or less throughout his career, and anticipating Beethoven, who was to arrive in Vienna just a few years later, Mozart was behaving as an entrepreneur, a fully independent professional composer. All of which is a rather long way of saying that this quintet (and its companion, K516 in G minor – Mozart never got round to writing the third promised quintet, and had to arrange an earlier work instead) was written as a display piece, to show just how brilliant Mozart’s technique could be.

Having dealt with this work’s opening, what about its ending? I could of course write at great length about the way this movement finishes, but what I want to do is to point out how its conclusion, like its great length, is made necessary by the way that it opens. Its ending grows out of and finally resolves the imbalances of an overall well-proportioned design. In doing so, the ending carries within itself the legacy of the opening.

Here is the moment that heralds the very last phase of the movement. These are the bars that lead up to what a music analyst like me would probably call the ‘structural close’, the point after which the tonic chord is prolonged to the end – to borrow a phrase beloved of chess commentators, after this point it is ‘just a matter of technique’.

Mozart, String Quintet in C, K515, bars 256-272

Here, Mozart overlaps versions of the two-bar phrase with which the first violin originally answered the cello, in five-part canon. There are entries of the phrase on every instrument in turn, each coming one bar after the previous one, as I have annotated in the red boxes. As the first violin then leads the movement into the coda, the interruption to the opening at bar 21 still survives, with a hint of the minor key in the second viola and cello (the blue box). If you want to listen to this bit, it can be found at about 10′ 10″ to about 10′ 50″ in the video above.

A chess endgame, and its beginning

Mozart displays his brilliance of technique in  handling imbalances to achieve unsurpassable mastery of the situations he creates. That sentence could equally be written of the current World Chess Champion, Magnus Carlsen. Which goes a long way towards explaining the origin of the epithet I did not invent, but used in a previous post, Magnus Carlsen: the Mozart of the chess board.

There is for this post, on this date, only one game which is ideally suited to be placed beside Mozart’s wonderful display of how openings and endings reflect each other: the sixth game of the recently-concluded World Chess Championship, in which Carlsen defeated his latest challenger, the Russian Grandmaster Ian Nepomniatchi. This game was the first decisive one of the match, by far the most interesting, and indeed the turning point: after this game, ‘Nepo’ collapsed and Carlsen won easily, with a score of 7.5 / 3.5 after just eleven of the scheduled fourteen games.

This game was the longest in the match, and indeed the longest game in the history of chess World Championships. Even more reason to place it alongside Mozart’s longest sonata form movement. Like the quintet, the game began conventionally enough, Carlsen playing 1.d4 (P-Q4) and Nepo answering 1…d5 (…P-Q4).  A completely ordinary beginning, just as an arpeggio is the most ordinary of tunes with which to begin a piece of music. But on move six, Carlsen introduced the first hint of imbalance with a rarely-played move, not unlike Mozart’s decision to create a five-bar phrase out of his opening material:

Carlsen vs Nepo, Game 6, White’s 6th move

And two moves later, Carlsen brought about a position never seen before in any recorded chess game:

Carlsen vs Nepo, Game 6, White’s 8th move

The imbalance in the position, which in general terms remains very even, already indicates that Carlsen is anticipating a long game, in which he will attempt to demonstrate his superiority in understanding the potential of the imbalance he has created. And this he does: I am not going to comment on the ‘middlegame’ of this tremendous contest any more than on the middle part of Mozart’s quintet, except to show the moment at which Carlsen chose to make the imbalance a structural feature of the game, so to speak, when he exchanged his queen for Nepo’s two rooks on the twenty-sixth move:

The equivalent to Mozart’s technically accomplished five-part canon is the moment at which Carlsen decided to sacrifice a rook and reduce the struggle to an unbalanced collection of just a few pieces on each side, on the eightieth move of the game:

Carlsen vs Nepo, Game 6, White’s 80th move (Carlsen has taken a pawn and delivered check)

Thirty-five moves later, Carlsen steered the endgame to a total of just seven pieces:

Here begins the equivalent of the musical coda: an exercise in pure technique, as Carlsen, keeping all his pieces close together, gradually pushed his two pawns up the board towards the ‘final cadence’ of queening one of them. Here, he was following a mixture of calculation and creative instinct truly the equal of Mozart’s, since the ‘correct’ moves at each turn can only be calculated by powerful computers. The actual moment at which Nepo (a phenomonally strong player) eventually went astray was on his one-hundred-and-thirtieth move:

Carlsen vs Nepo, Game 6, position after White’s 130th move

Here, Black has twenty-six legal moves; more than the twenty available on the first move of the game. Of these twenty-six, only two avoid defeat. Nepo chose one of the other twenty-four moves, the entirely reasonable-looking Qe6 (…Q-K3), pinning the white rook:

Carlsen vs Nepo, Game 6, Black’s 130th move

For the curious, the two moves that preserved the draw were …Qb1 or …Qc2 (…Q-QN8 or …Q-QB7). As one Grandmaster commenting on the game put it, ‘Who knows why?’.

From here, though, with the certainty of a ‘strong perfect cadence’ in the Classical Style, Magnus Carlsen brought about his challenger’s resignation in another seven moves:

Carlsen vs Nepo, Game 6, position after White’s 137th move (the end of the game)

The final position of the game still reflects the opening: the choice of queen’s pawn rather than king’s pawn on the first move of the game leads directly to the king’s pawn and king’s bishop’s pawn being the two that eventually survive to reach Black’s end of the board; the imbalance introduced on moves six and eight leads directly to the unbalanced forces on the white and black sides with which the game ends. Just as Mozart’s final section perfectly reflects the opening of the quintet, Carlsen’s brilliant endgame grows perfectly out of the apparently quiet opening of the game. This is indeed a display by a true World Champion.

In my beginning is my end

The subtitle of this concluding section is taken from T. S. Eliot, whose reflection on the Epiphany I quoted earlier. ‘In my beginning is my end’ is the opening line of ‘East Coker’, the second of his Four Quartets. The poem is a meditation on time, and its final words are ‘In my end is my beginning’, reversing the formulation with which it starts. It is a powerful notion, that as a process unfolds in time, each phase it passes through is both determined by what came before (in my beginning is my end), and yet a transformation of it (in my end is my beginning). It might describe a meaningful human life; it might also describe a meaningful piece of music (the collection is called Four Quartets in allusion to Beethoven’s last string quartets, whose effect Eliot was trying to reproduce in poetry); or it might also describe a satisfying game of chess. Beginnings and endings demarcate and define a span of time, and the way something begins can determine how it is likely to end.

In placing a masterpiece by Mozart alongside a masterpiece by Carlsen, I have intended to show how the combination of rule-respecting technique, precise calculation, and creative flair are united in the minds of both the composer and the grandmaster. Beyond that, I have wanted to unpick a little more the reasons why music and chess can both provide metaphors that illuminate aspects of lived human experience. Both music and chess can illustrate our instinct as creative human beings to make sense of the world around us and our path through it. Framing my attempts to analyse great music and a recent great chess game with quotations from T. S. Eliot may seem pretentious; but I believe that the correspondences I have tried to describe here account for a large portion of the enduring fascination both of music that appeals to the intellect, and of the Royal Game.

After a long pause in my contributions to the blog, as the whole world has paused in the midst of a global health crisis, I offer these observations to my readers with very best wishes for the coming year of 2022.

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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