Crosswords and Music

In my review of John Halpern’s book for the centenary of the crossword, I grumbled that he hadn’t spent as much time on the links between music and crosswords.  Rather than grumbling, I should take my instruction from Eric Sykes’ autobiography: If I Don’t Write it, Nobody Else Will.

And what you find is that it is an awfully difficult topic to get to grips with.  It’s rather like circling a mountain, and trying various paths up it, only to find them petering out in fields of scree.  However, the path marked ‘Mathematics’ looks promising.

There’s little doubt that maths and music are related.   There are mathematical qualities in chords: the numerical relationships based on plucked strings, and how these produce dissonance or consonance.  This leads to all sorts of analyses of harmony involving chords in various numbered positions.  There are the permutations involved in twelve-tone music.  And there’s the triangle player quietly counting ’48-2-3-4, 49-2-3-4, 50-2-3-4, damn! missed it’.  Just be careful not to confuse the ordinal musical fifth with anything fractional.

Can we see anything here between maths and music?  What I take from this – and from the wider views of mathematicians about the links between beauty and formal proof – is that both disciplines involve an intermingling of rigour and exploration, and that you can’t have the latter without the former.

Like many crossword setters, I have a scientific background.  I may not have pursued mathematics to its highest levels, but I have done enough to appreciate both the formal approach and the sense of discovery.  I regularly find myself looking on crosswords from just such a standpoint. 

The first piece of rigour is the grid.  Even before we start thinking about the words that go in it, we have a grid.  A set of lines, generally interlocking squares (occasionally hexagons and/or triangles) put together in a regular shape (rectangle, square, rhombus – or bigger hexagon, of course).  There have been puzzles that have adopted irregular shapes (e.g. Listener 3922 (, but even that was presented within a square grid, and the gimmick played on expectations of regularity for its effect.

Putting the words in the grid?  Here we start some of the interplay.  Certainly there is rigour – you have to know your common suffixes and prefixes, and your letter frequencies.  At the same time you will also be looking for interesting words to clue.  You may have a gimmick – latent letters or similar – or a constraint.  Once you bring things like that into play, then you’re exploring a bit more: a particular word or phrase might not be in the dictionary, but it fits, and…well, here we might be shading off into clueing possibilities, which I’ll come to later.

Here, though, we’re talking about how things fit together in a harmonious whole.  Yes, I’m playing up the link to music, though I’m thinking more about form than harmony per se.  I am constantly surprised at what is considered sonata form – or perhaps that is more ‘what you can get away with and still have some critic say: “Well, there’s the semblance of sonata form in there”.  It is a tremendously mutable concept, and should act as a reminder that form itself is not a straitjacket, but can be a source of invention.

So here we have one point of contact: the attitude to form.  I did initially call that ‘a relaxed but not dismissive attitude to form’ but that isn’t quite how I envisage it.  There is a spectrum from free jazz (an abomination devoutly to be dished, to my mind) to something like the ‘construct-your-own-minuet-by-rolling-dice’ game that has been foisted on Mozart.  Most of the good stuff is well within those boundaries.

If we turn to writing clues, we have a similar spectrum of opinion.  I could rehash the same sort of arguments over the various degrees of adherence to form, and reach a similar conclusion.

Instead, I want to try and elucidate some of the experience of writing clues and to speculate how that might align with music. 

The first point that strikes me as a link is the starting point, both of a grid fill and for writing any individual clue.  There you have it: a blank grid – what words do you put in? Or: there you have it: a word to be clued – where do you start?  This must be very similar to what a composer feels with a blank sheet of score-paper in front of him/her. 

There must be some impetus, of course, else whyever start?  Perhaps the composer has a commission (though I can’t help thinking here that Walton’s Belshazzar’s Feast started out as a chamber work, if you judge by the original commission) or perhaps there’s a melody that would just suit a cello.  Similarly, I might have a deadline for the BBC Music Magazine coming up, or a damn good clue for ARCHIPELAGO begging to be used.

But where do you go from there?  Birtwistle has somewhere said that he often just starts with a single note, generally an E, and waits for something to happen, and that’s also what a crossword setter has to do sometimes: bung in CANASTA (they’re all friendly letters) and see what fits round it.

And then you’re off, and something starts to build.  From then on, there may be something instinctual at play.  Consider a completed crossword: there should be a mix of words (nouns, verbs, adjectives, phrases) – but what is the right mix, and how much leeway do you have to vary it?  There should likewise be a mix of clue-types – but what is the right mix?  You can adjust the clue mix after completing the set – but how do you know you’re adjusting it correctly?  I don’t feel terribly comfortable about rules that say “Thou shalt have no more than X anagrams or hiddens in a puzzle” as I think the merits of a set of good clues of whatever type outweigh such strictures.  Why shouldn’t a symphony have two scherzos?

I suspect that, at the end, even the setter doesn’t know what the balance is.  There’s a story about Benjamin Britten, cornered by a devotee at a party.  The fan explained his harmonic analysis of one of the composer’s earlier pieces.  Britten (unusually, it seems) heard the fan out patiently, but as he was shepherded on to the next guest was heard to ask plaintively: “Did I really do all that?”  Instinct, probably partly innate, and partly learned, seems to be at play.

What is emerging is a shared basis of reasonably well-determined rules, allowed to interact guided by instinctive manipulation.  This seems to set up a mixture of known structure spiced with individual innovation, which seems to be common to music and crosswords.  One might even argue that the ability to appear individual while continuing to produce distinctive work is at the heart of a ‘style’ whether cruciverbal or compositional.

I could, I suspect, develop a longish argument setting up parallels between setting/composing and solving/listening, but I won’t.  But the idea of a recipient patiently, and successfully, working out a construction is tantalising.

That’s probably enough to be going on with.  Let’s just finish with an observation about gender imbalance.  You might like to compare the gender breakdown of audience/solvers (M:F roughly 50:50) with that of composers/setters (M:F >95:,5).  In music, some of it is certainly tradition, but are we also seeing the sort of divergence linked to autistic/Asperger’s spectrum divisions?

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