Note too that “lively debate” means something different to statisticians from normal people. You would be unlikely to split your sides laughing at conversations about whether building a model to use clinical data to predict outcomes (a core statistical activity), counts as “doing” or “using” math.

Whatever: my undergraduate degree required a lot of math, and my PhD thesis made use of lots of algebra and calculus. I call myself what I am: a statistician. But I do think of myself as belonging to the wider mathematical brotherhood. I believe that the inductive (statistical inference) and deductive (mathematical) logics are all we need to explain — in the sense of “make valid claims about” — the universe. Mastery of these fields are among our species’ proudest achievements.

All of which makes me worried, I think is the word, to read of the impact artificial intelligence and machine learning is having on (at least some) academic mathematicians. Recently, AI has started constructing proofs for some of the trickier unproven theorems. Which leads to the question: if a machine can prove a theorem, what’s the point of trying to do it oneself?

Kirwin Hampshire, who is in the process of working on his own PhD at the University of Victoria (in the department of Mathematics and Statistics, ha!), has just published a Substack essay in which he confesses that the ability of AI to solve problems is causing nothing less than severe existential angst. He feels “a profound spiritual crisis” and, in his worst moments of paranoia, wonders if it be the “express goal of these [AI] companies to make me kill myself”.

His essay is beautiful. To do him the disservice of summarizing it in a paragraph, he argues that the process of learning and proving is as important as the outcome, and that a machine-generated mathematics is no mathematics at all.

That reminded me of music, and I might suggest this to Kirwin as part-antidote to his fears (though he won’t like much of what I say). I am very fond of the Bach two-part and three-part inventions and have multiple recordings of these by some of the ablest pianists ever recorded: Glenn Gould and Andras Schiff are favorites. 

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AI and the false consciousness trap

By Yanis Varoufakis

Nothing I fumble out at the keyboard (I’m a constant piano student) will ever touch the divine musicality of Bach’s genius or the technical mastery of my favorite virtuosi. But it really doesn’t matter. Because few things give me more pleasure than trying. Few things feel more satisfactory than to master a complex passage even though I know no-one will ever hear it other than myself — and that even I would prefer to listen to Glenn Gould doing it properly.

In my analogy, the existence of digital recordings of music are the AI machines in Kirwin’s nightmare: they obviate the need for the task which gives my life meaning (“I am a piano student”) and pleasure (“I need to hear this music”). If a machine can “do” Bach for you, why try and do it yourself? Yet the pleasure persists, as does the choice to practice. I cannot prove this, but I believe it: a robot will one day produce music that sounds Bach-like. I do not believe it will improve upon him.

I suspect some similar “behavioral” consequence might happen to much of mathematics. A machine will be able to do algebra at least as well as a human. But that won’t rob humans of their need to do the algebra for themselves, nor diminish the beauty of any particular proof.

To which Kirwin might reply: so what? You’re talking about a hobby. I’m talking about the pitface of human endeavor, about what it means to be a mathematician. As he says “Mathematicians are paid to prove theorems” and, if you don’t need them for that, do you need them at all?

I cannot comprehend — this might be a failure of imagination — how the answer to that question could ever be “No, we do not need them”, not while there are humans in the world and a human society about which to be concerned. Math is special because it’s universal; no other discipline — save, perhaps, music — comes close. It is true that a machine could prove theorems in such a way as to be understandable and useful only to other machines, but if we reach that point then not only mathematicians should worry about superfluousness. In the meantime, humans will need to understand what the AI is “proving” and I can’t imagine how that could be achieved were those humans not themselves mathematicians.

Back to my own early practice at math. The point of my thesis was to take a noisy, distorted picture of something important (like a remotely-sensed heart scan) and reconstruct an approximation to the real object. In Chapter 4, I ended a few pages of algebra with this melancholic sentence: “Unfortunately we have not been able to prove this Lemma [a proposition].” In other words, I couldn’t demonstrate whether Chapter 4’s “great idea” had legs.

Having read Kirwin’s essay, I wondered if an AI could pick up where I’d left off in 1993. I wish I hadn’t. Here is what Grok told me:

You correctly identified the obstacle. You tried to adapt Eggermont’s argument (his Lemma 6.1 and the subsequent KL + residual Lyapunov function). The natural ordered-subset extension leads to the candidate inequality (your Lemma). That inequality does not hold in general, and the extra diagonal projector, which “switches on” only the current subset, prevents the global residual from decreasing monotonically. Consequently the Lyapunov argument collapses exactly where you left it.

There was a lot more. TL;DR: you couldn’t prove it because it was obviously unprovable, and you should have known this. It was quite clear that Grok already “knows” more about image reconstruction algorithms and their associated mathematics than I could ever hope to master. I think I preferred feeling sad, to feeling both sad and inadequate. Which is, of course, a version of Kirwin’s point.

But in any case none of the work I produced in 1993 is even vaguely relevant today, because the field has moved on. Ironically, image reconstruction was one of machine learning’s early successes: trained models can make better guesses at true images than my Pooterish attempts in Chapter 4.

But even without machine learning, I doubt many people’s theses from 30-odd years ago bear re-reading. I could make a joke here about some more recent contributions to the sociological literature, but I’ll rise above that. (Almost.)

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Must data centres be so ugly?

By Tom Ough

As with Bach, so with PhDs: the process is what matters. Learning how to read literature; how to build a hypothesis and investigate it, mathematically and empirically: this is why we train people to doctoral level in Mathematics and Statistics.

And the more machines produce technology or any other solution to any other problem, the more, I should think, we will need men and women like Kirwin.

I did, though, have long dark nights of the soul during those PhD; years, in fact, when I felt overwhelmed with futility. I remember walking towards the Math building in University Gardens and then just sort of veering off at the last minute, because of the sick feeling in my stomach. Not because of a machine, but because of my inadequacy.

Most PhD students have spent nearly 20 years of school and undergraduate life being told: “This is what you need to understand in order to pass an exam,” and most of us are extremely good at that way of learning. The PhD environment in mathematics and statistics — no classmates, no solutions to tutorials, possibly no solution at all to the problem you’re investigating (see Chapter 4 for details!), no one to tell you if the roll of the dice you’ve just made for the next three years will have any outcome beyond failure — is very different. It would almost be bizarre for a young person in such a situation not to develop angst, an existential dread.

And yet the sun rises, and yes, the work has purpose. Kirwin, your abilities will be needed in the age of AI more than ever before. Maybe just switch off your computer and close your notebook for a while, and think of something else. It was in those long dark nights, I recall, that I first fell in love with Bach.

White people, he said, have been “too polite” to state obvious racial truths. Like the superiority of Bach, Mozart and Beethoven over all other musical forms and practices. There is no equality between these glories — white glories — and the simplistic rhythms and disconsonant noises that prevail among other peoples (save for East Asians, he granted, who have admirably made Western classical music their own).

I was repulsed. Not, mind you, because I’m any sort of an aesthetic relativist. While liberality demands that we approach each artistic tradition on its own terms, respecting its inner integrity, there finally are objective standards; and by any measure, the Mass in B Minor leaves the drone of the didgeridoo in the Australasian dust. No, what got to me was the weird racialisation of classical music: the idea that Bach & co. embody the achievements not of Christian or even European civilisation, but of the white race, and that this racial “reality” is supposed to bear (unspecified) political consequences.

Race chauvinism is an all too typical “meme” these days, part of a global resurgence of particularism. Ever since the collapse of the Eastern Bloc shuttered the utopian horizon of socialism, questions of belonging and identity have shoved their way back to centre stage, usually at the expense of the more universalist aspirations that used to animate the modern world.

Among the competing particularisms, the dumbest and most pernicious is race particularism. And yet I worry that it’s bubbling just beneath the surface of our “anti-racist” societies, in part as a reaction to the official pieties. If elite institutions applaud assertions of race-and-identity grievance, then why can’t white people celebrate their race and identity, with its ways of knowing and being in the world, its runes and cross stones, its Bach and Beethoven?

Liberalism, the last modern universalism still sort of hobbling along, has increasingly come to rely on racial disparities to perpetuate itself. In their neoliberal form, advanced capitalist economies did away with many of the social-democratic elements that once helped bridge the gaping inequalities in income and power generated by the unrestrained market. But fortunately for those getting rich, any remaining inequalities could be laid at the feet of “discrimination”.

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The problem with anti-woke liberals

By Sohrab Ahmari

No longer were political-economic explanations sought for social dysfunction, much less political-economic solutions. At its most ludicrous, this tendency impelled supposedly “progressive” institutions to adopt racialised modes of thinking scarcely different from the type of classical-music chauvinism espoused by my dinner companion. Excellence, punctuality, orderliness and objective thinking came to be regarded as “White” values, not to be expected of “Black” people (the capitalisation of these terms required by the new orthography underscored their essential, immutable, and “natural” quality). At times, it became genuinely difficult to distinguish the latest woke diktats — such as the National Museum of African American History and Culture’s claim that “hard work” is a white value — from the rantings of David Duke.

For Kenan Malik, this strange mirroring, of progressive identity politics and reactionary racism, is no accident. He argues, in his new history of race and racism, Not So Black and White, that both are reactions to one of the Enlightenment’s most persistent and bedevilling paradoxes: the fact that this new order asserted the radical equality of all human beings, and heralded their emancipation in the political sphere, even as it allowed profound inequalities and vicious exploitation in the material, economic sphere.

His history briefly touches on the premodern era before very quickly shifting to the modern. This is for good reason. The premodern world, as he rightly notes, knew tribe, nation, and cult, and it certainly knew prejudice. But race — as a dubious biological category sometimes elevated to the ontological — is distinctly modern. As he writes, “race did not give birth to racism”. Rather, “racism gave birth to race”. It was only after the Enlightenment proclaimed the basic equality of human beings that racism sprung up, as a way to justify the social realities of the post-Enlightenment world, its hierarchies and brutalities.

In Malik’s telling, faced with the tension between their self-proclaimed ideals and the realities of exploitation and colonialism, too many Enlightenment liberals ditched those ideals or narrowed their radius to only certain groups of people: those who looked like themselves.

Immanuel Kant, for example, claimed that the “greatest degree of perfection” lies in the white race, while at the bottom were “the Negroes”, who could at best be trained as “servants”. In between were “yellow Indians”, American natives, and “Moors”. That last group, he advised, should be punished using split canes, rather than sticks, lest their thick skins prevent the blood from finding release. Likewise, even as Thomas Jefferson declared that all men are created equal, the American Founder determined that black people were by “nature” childlike creatures, incapable of abstract thought and fine art.

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The narcissism of America's race politics

By Tomiwa Owolade

In the 19th century, these incipient racial attitudes hardened into supposedly “scientific” knowledge. And yet, as Malik shows, the new race “science” was anything but. Why, for example, did early race theorist Johann Blumenbach pioneer the term “Caucasian”? Get ready for the hard science: “I have taken the name of this variety from Mount Caucasus, because its neighbourhood … produces the most beautiful race.” In other words, aesthetic biases were transmuted into “scientific” categories that remain in use among government census-takers and statisticians to this day.

Malik’s book is full of delicious nuggets of the kind, and though his claims about the modern invention of race and racism aren’t news, he must be commended for the sheer accumulation of evidence in their favour. Through it all, he maintains a consistent and compelling argument: that race and racism served as alibis for class-based regimes of domination and exploitation that took hold — again, paradoxically — in the wake of the Enlightenment.

Slavery in the American South, for example, was racialised after the fact, as a way to break alliances between European indentured servants and African slaves, and to legitimate the greater use of slaves (whose bondage had no limits). In Europe, meanwhile, as capitalist development necessitated imperial expansion, good Enlightenment liberals increasingly adopted racialised claims about the need for the higher races to discipline the lower.

In the imperial cores, meanwhile, they came to treat their own outwardly “white” working classes as a different race. Indeed, race “scientists” ranked various European peoples according to the different quotients of Nordic, Alpine, and Mediterranean mojo that supposedly coursed in their veins; it just so happened that the Irish were found to have an outsize portion of Mediterranean “genes” — a fact that naturally explained their subjugation.

Even within individual European countries, the working classes came to be coded as black in their supposed laziness and antisocial nature. An item in The Daily Telegraph, for example, lamented that “there are a good many negroes in Southampton, who have the taste of their tribe for any disturbance that appears safe”; the paper, to be clear, was referring to the overwhelmingly white English working class.

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Why anti-racism should be resisted

By ASRA Q. NOMANI

Perhaps his most discomfiting argument — discomfiting in its unassailability — is that Nazi Germany didn’t rupture the ordinary development of Euro-American ideas on race and equality, but fulfilled them. Long before the National Socialists set out on their racial project, Theodore Roosevelt spoke of the moral rightness of subjugating Native Americans, for they were “but a few degrees less meaningless, squalid, and ferocious than… wild beasts”. In the Congo, Namibia, Australia, and, yes, British India, good liberals carried out their “compulsion to civilize”, as Malik puts it, with unspeakable tortures and mass atrocities.

America, especially, provided a racial template for the Nazis. The 1934 National Socialist Handbook for Law and Legislation noted that “the dominant political ideology in the USA must be characterised as entirely liberal and democratic” made it “all the more astonishing how extensive race legislation is”. The premier Nazi scholar of American law admired its “artificial line-drawing”, which dealt with the problem of “mongrels” by dividing the entire population into two groups, “whites and coloreds”, without fretting too much about details. In places, Nazi jurists felt American laws went too far, such as the rule that people with even a drop of “negro blood” are to be treated as black.

Did this affinity — between the world’s leading liberal regimes and their National Socialist foil in World War II — represent a betrayal of Enlightenment values? Yes and no, per Malik. The Enlightenment, he argues, may have inaugurated the modern ideology of race, but it also set forth the premises necessary to emancipate people from all arbitrary hierarchies.

The problem was that the radical, anti-racist Enlightenment of, say, a Diderot was eclipsed by the more moderate posture of a Burke or an Adam Smith, which was prepared to accept domination in the name of pragmatism and even “progress”. And as the liberatory promises of the Enlightenment crashed on the rocky shores of capitalist political economy, with its need for colonial expansion, darker racial sentiments took hold, as did the impulse for national purification and separation.

It fell to others — to Europe’s victims — to bring Enlightenment ideas to their logical conclusion. The heroes of Malik’s book are the “black Jacobins” of the Haitian revolution as well as C.L.R. James, Frantz Fanon, and even Malcom X in his later years. These were figures who saw — or in time came to see — that class and economic exploitation form the more fundamental power relationship in modern society. Race, in many ways, works to legitimate class-based domination and, especially in the United States, to forestall the emergence of a cross-racial labour movement.

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Race is a delusion

By David Mamet

Progressive identity politics, he suggests, obsessed with “cultural appropriation” and language-policing, harkens back to old ideas of racial separateness. It, too, helps forestall class solidarity across skin colour. At one point, Malik notes archly that one of the earliest “Black Power” conferences, in the Nixon era, was sponsored by… makeup brand Clairol.

Malik’s class-based analysis is largely correct: once you notice how 21st-century identity politics helps uphold today’s neoliberal political economy — offering diversity in the boardroom, but not living wages, good health care, and safe retirement — you can also see how the 19th-century variety served to uphold that era’s class-based hierarchies.

In the face of this, what is desperately needed is a more robust universalism, capable of generating and sustaining solidarity across cultural divides. Malik puts his hope in the ideals of the radical Enlightenment. Yet as he concedes early on, the Enlightenment notion of equality is socially constructed — that is, it rests on a social, rather than metaphysical, claim made about the radically free and equal status of all members of the human race. That’s good, so far as it goes, but as his masterful history shows, it often didn’t go very far. Indeed, these very same claims about progress and liberation came to form the basis of new dominations.

I wonder if the way forward lies (partly) in going back, in recovering what the moderns too rashly swept aside. In his early chapter on the premodern, pre-race world, Malik notes in passing that the Enlightenment made explicit a universalism that was always “implicit” in Christianity. In fact, Christian universalism is very much explicit. In the secularised West, it’s easier said than done, but having endured the modern horrors of racism, it might be worth taking inspiration from the universalism that proclaims that there really is “neither Jew nor Greek”. As I shudder at sentiments like those of my dinner companion, which seem to be rising, I take great comfort in the presence, however residual, of a religious doctrine that human beings share fraternity, not according to social construct, but owing to a common, divine paternity.

For Christians, this week is the most important of the year. And this year’s Holy Week is, around the world, unlike any other. With churches shut, and services either cancelled or streamed online from all-but empty buildings, people will have to find their own space for contemplation. And that goes for non-believers, and lapsed or non-practising Christians, as well as the unambiguously religious.

For my own part, whether I have been in or out of faith, this week has always presented the richest musical opportunities. And though we can’t gather together these days, we can at least swop sources online; so I thought I might share some of the music which for me makes up Holy Week, and which can be heard for free. It is a feast rich enough to fill the long weekend, if not a lifetime.

St Matthew Passion, Bach — performed by Willem Mengelberg and the Royal Concertgebouw Orchestra

Normally in this week I would try to go to a performance of Bach’s St John or St Matthew Passion. I’ve heard some wonderful performances — and a few average ones — over the years, but in some ways the performance doesn’t matter because absolutely nothing can diminish the power of these works.

Of course, both have been recorded more times than can be counted. But this week I have been listening again, as I have most years, to a performance whose style is out of fashion, but which has an extra depth that never fails to move me.

This is the recording of the Matthew Passion broadcast on Dutch Radio on Palm Sunday 1939. The annual performance at the Concertgebouw in Amsterdam goes on to this day. But the conductor on this recording is the great Willem Mengelberg (1871-1951), who had been conducting the event since 1899.

While the circumstances of the performance should not overshadow the music, from the first bars of the opening chorus (“Kommt, ihr Töchter, helft mir klagen” / “Come you daughters, help me to lament”) there is a portentousness that makes you breathe differently for a moment. The performance is moving in so many ways, particularly because we now know what that audience — whose occasional coughs you can hear — were about to go through.

Naturally I would recommend listening to it all, but if you must skip, then wait until the end of the opening chorus, then move on to the great Dutch soprano Jo Vincent sing the aria ‘Aus Liebe will mein Heiland sterben’ (‘Out of love my saviour is willing to die’) which starts at 2:00:59. The whole performance is miraculously available on YouTube. Just listen to those repetitions of the words ‘Aus Liebe’, with those flute notes tumbling down.

Lamentatio Jeremiae Prophetae, Thomas Tallis — performed by the Deller Consort

Period recordings are always a fraught issue. And in general I listen to modern recordings. But sometimes a particular performance is the one you’ve been brought up with or heard first — or has some other quality which keeps it high above all others.

The Lamentations of Jeremiah by Thomas Tallis is one of the jewels of the Holy Week musical liturgy. There are several great recordings, but this one by the Deller Consort from 1958 is the one I listen to most often.

The voice of the countertenor Alfred Deller is not to everyone’s taste, and there are those weird gear-changes in his voice that a modern counter-tenor wouldn’t get away with. But he was a pioneer and it is the fragility of Deller’s voice soaring above the others that makes this recording so special. His voice sounds as though it is going to crack at any moment and in a way it is the sense of how nearly it could go wrong that makes it so clear that it is right.

The full Latin text (beginning “How doth the city sit solitary, that was full of people”) can be found online. For me the first rendition of “Jerusalem, Jerusalem, convertere ad Dominum Deum tuum” (“Jerusalem, Jerusalem, return unto the Lord thy God”) at about 7 mins in here, is the demonstration of Tallis’s — and Deller’s — greatness.

The Lamentations, Edward Bairstow — performed by the Choir of York Minster

Whilst we are on Lamentations, there is one other setting from the English choral tradition which I must flag up, because it is much less well known than the Tallis. This one from Edward Bairstow was composed in 1942. I had never heard the piece until I started attending the Good Friday service at St Paul’s Cathedral some years ago: a great service, during which the choir always sing Tallis’s Litany in procession, the Allegri Miserere and this piece from Bairstow.

This is a recording from York Minster, but you can imagine the effect of those organ chords each time the choir sings ‘Jerusalem’ in St Paul’s. It isn’t a masterpiece, but it is a magnificent setting of the words and there is something deeply moving about a piece written so firmly in the Anglican choral tradition.

Versa est in luctum, Alonso Lobo — performed by the Tenebrae Choir

One piece that most certainly is a masterpiece — and from a very different choral tradition — is this work by the sixteenth century Spanish composer Alonso Lobo. In my experience, Lobo is one of those composers who, whenever you hear anything by him, makes you immediately wonder why you don’t listen to him all the time. The recording of his magnificent ‘Versa est in luctum’ here is sung by the wonderful ensemble Tenebrae, and was recorded last year in the church of St Bartholomew the Great in London.

The Latin words have been set by many other composers, including Victoria. But I know no setting as intensely moving as this one.

Versa est in luctum cithara mea, et organum meum in vocem flentium.
Parce mihi Domine, nihil enim sunt dies mei.

[My harp is turned to grieving and my flute to the voice of those who weep.
Spare me, O Lord, for my days are as nothing.]

Officium defunctorum: Parce mihi Domine — performed by the Monteverdi Choir

Incidentally, some people may know the setting of the last of these words by the slightly earlier Spanish composer Cristobal de Morales. The Hilliard Ensemble made it famous again some years ago in a setting with saxophone improvisation on top, but the sparseness of the original saxophone-less version remains my favourite. Here it is courtesy of the Monteverdi Choir.

Tenebrae responsories: O vos omnes, Tomás Luis de Victoria — performed by the Cambridge Singers

I could go on, of course. Anyone thinking I unfairly skirted over Victoria earlier might be placated by the fact that I don’t think any Holy Week should be gone through without at least one listen to his setting of ‘O vos omnes’ (the words are “O all you who walk by on the road, pay attention and see if there be any sorrow like my sorrow”). Any choristers reading will know that every phrase in this piece (especially ‘Attendite’) is as beautiful to sing as it is to hear.

Here is a recording (with score, for anyone who wants to sing along) by the Cambridge Singers.

Apparition de l’Eglise éternelle, Olivier Messiaen — performed by Olivier Latry

Of course, all of these works are works of mourning and lamentation, composed to fit the dejection and desolation of the Holy Week story, leading up to the crucifixion on Good Friday. Easter Sunday of course changes everything, including the music. But that is to get ahead of ourselves. Perhaps I might finish this Holy Week playlist with a rather different final piece.

One of my favourite composers is Olivier Messiaen, the great expander of the organ repertoire, and one of the searing religious visionaries of the twentieth century. One piece of his which is worth turning the volume up on (especially if you have some good bass speakers) is this short work from 1932, ‘Apparition de l’Eglise éternelle’ (‘The apparition of the eternal church’).

I select it not just because it looks forward to what is to come, but because this recording (with score) was made on the great organ of Notre Dame in Paris. Perhaps one Easter soon it will be played in that great cathedral again. It will be very much in the spirit of the Easter story if it is.

*

As an addendum, I might just say: these are tough times for many musicians, like everybody else. Huge amounts of work have been lost. So if these recordings or others that have been made available on YouTube do appeal to you, please do buy the artists’ albums, or those of other groups, and think about booking tickets for their next concerts. We will get back the joy of hearing live music again.

Not only have many of the churches remained closed, but unlike Giles Fraser’s, many — it is now clear — will not be reopening. Church administrators have used the opportunity that the Covid crisis has presented to do some of the things they had wanted to do anyway. My own family’s church, where worship had been continual for some 900 years, was closed by the Dean and Chapter of Westminster during this crisis: the choir dissolved, the congregation disbanded and all future services cancelled.

As it happens, St Margaret’s Westminster was the church in which I sang as a chorister, and as everyone else who has been through that experience will know, singing in a choir is not only one of the best ways to learn music but one of the finest ways for the liturgy and fabric of the Church to get into your bones.

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O come, all ye faithless

By Boyd Tonkin

Although Easter may be the most important festival for Christians, today’s feast is the most significant for cultural Christians. For many, the Christmas service was the only time in the year that they would go through the doors of their local church. Midnight Mass, or the service of Nine Lessons and Carols, would suddenly be filled with people who the church hadn’t seen for a year. And in a way that makes the absence of services and carol singing this year even sadder still. People who were only holding on to the church by a thread risk having that last thread frayed as well.

So I thought that, as at Easter, I would list some of the musical moments that always made Christmas special for me. I have — you might note — avoided all the most obvious ones. Anyone can find “Hark the Herald”, “O come, all ye faithful” and company on Spotify or YouTube. For many of us the beginning of Christmas was always the first notes of “Once in Royal David’s City” floating through the church, with the congregation and choir holding their cold breath in the hope that the chorister soloist wouldn’t go wrong.

But, as I say, you can find these easily. The selection below doesn’t include any rarities, but it includes music that shows that the Christmas music tradition is an ancient and very much a living thing. Even as we close a year in which singing has been made impossible.

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By Douglas Murray

At Easter I pointed readers to the classic Mengelberg recording of the St Matthew Passion. And I’ll start with Bach again, because he actually did write something for every season. The Christmas Oratorio was written for the Christmas period of 1734 for Bach’s church in Leipzig. There are a number of wonderful performances online. John Eliot Gardiner’s, from the Herderkirche in Weimar may be one of the cleanest musically. But this performance recorded in the 1980s, led by the great Nikolaus Harnoncourt, takes some beating. Not just the performance, but the fact that the setting and some of the performers look as though Bach would have recognised them.

Though it seems strange to imagine now, Bach was of course only adding to a musical tradition that was already rich when he found it. Every country in Europe had carols and anthems written for the season, some of which sound as though they reach back even further than they do. One of my personal favourites is the carol today known as ‘The Coventry Carol’. Probably dating from some time in the 1500s, its haunting open fifths give it exactly the sound of a sparse, wintry monastery. They are perfect for this verse in particular:

‘Herod the king in his raging
Set forth upon this day
By his decree, no life spare thee
All children young to slay’

This recording is from King’s College Cambridge, led by Stephen Cleobury (who died just over a year ago). For many people the sound of King’s is the sound of Christmas, so I make no apology for the number of selections here which rely on them. There are plenty of other recordings to find online but few ever beat the sound of King’s.

‘The Coventry Carol’ sounds as though it has been around forever — partly because it almost has — but occasionally a piece sounds that way despite being relatively new. The words of ‘Jesus Christ the Apple Tree’ are 18^th Century, but Elizabeth Poston wrote her setting in the early 20th. And it sounds as though it has been around for an age; one of those musical ideas that a composer seems to have found floating around the ether just waiting to be caught. As well as the beauty and naturalness of the melody and harmony, the almost shocking words make this piece so memorable. Lines like “For happiness I long have sought, / And pleasure dearly I have bought” sound like they should have no place in a carol, let alone “It keeps my dying faith alive.” Yet here they are, and once again perfectly sung by King’s.

There are a number of settings of ‘In the Bleak Midwinter’, but two jostle for the lead. Gustav Holst’s is near impossible to beat, but Harold Darke’s does it.  It is a choral favourite, not least because it gives one of the tenors a verse in which to show off. But it is a stony-hearted person who can listen to all four verses and not be moved by the simplicity and beauty of the final verse, “What can I give Him, poor as I am?”.

One of the wonderful things about Christmas music is that it doesn’t just rely on major pieces by major composers.  Strange pieces have made it into the repertoire, sometimes by strange composers. None is stranger than Peter Warlock (real name Philip Heseltine), who as well as being one of the most innovative figures in early twentieth century British music was also among the most infamous. Perhaps best known today for the Capriol Suite, some of his music – such as the song-cycle “The Curlew” — is as dark as he was.  In a strange act of posthumous outing the art historian Brian Sewell earlier this decade revealed in his memoirs that Heseltine was his biological father.

Heseltine left other strange gifts to posterity, including a couple of pieces which are firmly established in the Christmas repertoire. Curate’s egg though he was, Heseltine’s setting of ‘Bethlehem Down’ is one of the most knotty, satisfying and moving Christmas pieces I know:

Of course like any tradition that aspires to live, a repertoire must continue to be added to if it is to continue. In regular times church choirs in the English-speaking world have been careful to keep commissioning where they can. Like all new-music commissions, this is a hit and miss affair, with many first performances also being the last. But occasionally a piece settles above the water-line and grows a life of its own.

The American composer Morten Lauridsen is easy to be slightly snotty about. Some of his harmonies and clusters sound like the spillage from composers that have gone before him. But his setting of “O Magnum Mysterium” (“Oh great mystery”) is deeply affecting. It has entered the repertoire party because it is so wonderful to listen to, but also because unlike a lot of modern church music it is as enjoyable from the inside, to sing, as it is from the outside to listen to.

One final addition to the repertoire. Eric Whitacre is a composer who it’s even easier to be sniffy about than Lauridsen. Many of his pieces seem to be second-presses from earlier composers. But occasionally even a comparatively minor composer (as with Warlock) hits on an absolutely first-rate idea. Whitacre did with his piece ‘Lux Aurumque’, which although just over ten years old has already settled into the repertoire.

I first heard it when it was performed by King’s earlier this decade, and here the composer seems to have written something perfectly suited to the acoustic of a vaulted cathedral or Chapel building. The soaring solo treble line is a spine-tingler if ever there was one. And the arrival of this piece is a reminder that the Christmas music tradition is a living one, that will live again.

Finally, a great Christmas service always sees the congregation played out with a great, thundering organ voluntary. As a chorister I was lucky enough to hear Thomas Trotter — one of the greatest living organists – every Sunday. One of the few bright spots this year was Trotter being awarded the Queen’s Medal for music in November. Among other things I owe him my early acquaintance with a composer who continues to give me more joy than almost any other, Olivier Messiaen.

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A lot of people find Messiaen hard-going to begin with. Once you get used to his musical language it all makes perfect sense, but perhaps like learning new languages it is best to learn it early. I still listen to the whole of his organ cycle ‘La Nativité du Seigneur’ each year as I put up the Christmas decorations. One thing that is so remarkable about this 1935 piece is the restraint and pacing. Throughout the full cycle it bursts out only a couple of times.

But the greatest and most famous eruption is in the final movement — ‘Dieu Parmi Nous’ — when a toccata suddenly appears, sounding as though the composer could no longer hold back his joy at “God [being] among us”. There are some magnificent recordings online, including Trotter and also the extraordinary Naji Hakim playing on the organ of Messiaen’s own church. But perhaps this performance by the great Gillian Weir is best.

It’ll play me out. Happy Christmas!