Ed Newton-Rex
Apr 26 · 14 min read

A new solution to the enigma at the heart of Elgar’s most famous work.

Over a few months between 1898 and 1899, Edward Elgar composed what has become one of the most famous pieces of classical music in the world, the Enigma Variations. Its fame is due in large part to its beauty — its Nimrod theme must be one of the most moving passages of music ever written — but it has also captured people’s imagination for more than 100 years because, in its composition, Elgar set a puzzle that has never been solved.

An unheard theme

Elgar’s love of codes and ciphers was well-known, and, according to him, he placed a puzzle at the centre of this theme and variations. Here is the first thing he said in public on this central enigma, in a programme note that accompanied the piece’s first performance in 1899:

The Enigma I will not explain — its “dark saying” must be left unguessed, and I warn you that the connexion between the Variations and the Theme is often of the slightest texture; further, through and over the whole set another and larger theme “goes”, but is not played . . . . So the principal Theme never appears, even as in some late dramas — eg Maeterlinck’s L’Intruse and Les sept Princesses — the chief character is never on the stage.

In 1900, he clarified further the nature of the enigma in an interview with the Musical Times:

Mr Elgar tells us that the heading Enigma is justified by the fact that it is possible to add another phrase, which is quite familiar, above the original theme that he has written. What that theme is no one knows except the composer. Thereby hangs the Enigma.

This was backed up in a 1905 biography of Elgar, the writing of which had the cooperation of the composer himself:

The theme is a counterpoint on some well-known melody which is never heard.

And then, in 1924, when someone suggested to Elgar that the hidden theme was God Save the King, he replied:

Of course not, but it is so well-known that it is extraordinary no-one has found it.

Finally, when asked by his friend Dora Penny what the hidden tune was, since she had tried and failed to figure it out, he replied:

Well, I’m surprised. I thought that you of all people would guess it.

Elgar died in 1934, and he took the solution with him to the grave.

What do we know?

Because the hunt for the enigma has continued for over a century, there are dozens of conflicting views not only about what the solution is, but about what criteria the solution needs to satisfy. It is useful, then, to go back to basics and ask what we actually know. Here are some boxes we know must be checked by any solution we propose:

  1. We’re looking for a very well-known tune. (Elgar couldn’t believe no one had spotted it.)
  2. This tune must fit with the main theme of the Enigma Variations — the ‘Enigma theme’. (The Enigma theme is a counterpoint on some well-known melody.)
  3. It must involve a “dark saying”. (Elgar said as much in his programme note.)
  4. There should be some reason that Dora Penny, in particular, should have spotted it. (Elgar was surprised that she, “of all people”, hadn’t guessed it.)

But that second requirement — that the hidden tune fit with the Enigma theme — presents an immediate stumbling block.

What is the Enigma theme?

The first thing we need to do is figure out which bit of Elgar’s music we should be trying to fit a hidden tune alongside. Is it the opening, 6-bar, minor theme? The entire, 17-bar first movement? All of the 19 bars of music that precede the first Variation? The major version of the opening theme, most famous as the main theme of Variation IX (Nimrod)? Or something else entirely? Interpretations differ as to what actually constitutes the Enigma theme.

Drawing together all the available evidence, however, sheds a lot of light on this question:

  • The majority of times that Elgar referred to the theme, it was to versions of just the first six bars of the piece. Elgar wrote a set of notes about the piece to accompany the pianola rolls (which are reproduced in this collection of photographs, notes and manuscript pages). In these notes, he refers to the ‘theme’ five times. Of these, in three out of five instances, the passage he refers to is a version of just the opening six bars of the piece, in either the minor or the major, without the rest of the music of the opening movement. (In the fourth instance, describing the first Variation, he says “there is no break between the theme and this movement”, indicating the theme he is referring to here is the opening 19 bars — but in this context it seems likely he is simply giving a name to the untitled opening movement, for which ‘theme’ is the natural choice, rather than providing a conflicting opinion about what he considers the Enigma theme. In the fifth instance, he makes it clear that bars 3 & 4 of the opening movement are considered part of the theme, which doesn’t tell us much.) The ‘theme’ Elgar is predominantly concerned with in these notes, then, is that of the opening six bars of the piece, with both minor and major versions of this theme used throughout the work.
  • The only time Elgar specifically referred to a theme as the ‘Enigma’ theme, he was describing a version of just the first six bars of the piece. In an 1899 letter to his friend A. J. Jaeger, Elgar pointed directly to a specific appearance of “the principal motive (Enigma)”. The music he points to is a version of the first six bars, again without the rest of the music of the opening movement.
  • The word “Enigma” appears in the manuscript above the opening bars. In the original manuscript, the word “Enigma” has been added above bars two and three, in A. J. Jaeger’s handwriting (Jaeger was Elgar’s publisher). It is hard to see how or why he would have done this if not at Elgar’s request, and it suggests this music is part of the Enigma theme.
  • There is a double bar after bar 6. It’s unusual to have a double bar so early in a piece; its presence is explained if it is marking off what Elgar considers the Enigma theme.

Taking all of this together, it seems sensible to conclude that the Enigma theme is that of the first six bars of the piece, and any hidden tune should be a well-known tune that fits well with the theme in these bars. But finding such a tune has proved surprisingly difficult.

Suggested solutions

Over the years, a number of potential solutions have been suggested — but none of them really get anywhere near fulfilling the criteria outlined above, and particularly not the key first two criteria (a well-known tune that fits with the main theme). Here are what are probably the top four proposed solutions:

1. Rule Britannia

Rule Britannia has been proposed because it shares a characteristic five-note motif with the opening of the Enigma Variations: but Rule Britannia is in the major where the Enigma theme is in the minor, and it’s only this very short figure that’s shared between the two pieces. If you try the whole of Rule Britannia with the Enigma theme it doesn’t work at all.

The Enigma theme (left) and the passage from Rule Britannia (right)

2. Beethoven’s Pathétique sonata

Beethoven’s piece fits quite nicely, but only if you transpose it to the minor, which again rules it out on the grounds of the original Beethoven not working when you sing it over the top of the Enigma theme. What’s more, Elgar was open about the similarity of the Nimrod theme of his Variations (a version of the Enigma theme transposed to the major) and the Pathétique, whereas it’s generally accepted that he never disclosed the true hidden theme during his lifetime.

Enigma theme alongside Beethoven’s Pathétique sonata (Pathétique sonata transposed to the minor)

3. Ein feste burg

There’s an impressive and complex theory that argues that the Lutheran Hymn Ein feste Burg is the hidden theme, involving a whole host of hidden messages and ciphers. While it’s a thoroughly thought-through idea, it doesn’t work musically: the tune doesn’t fit well over the main opening theme of the Enigma Variations, and, even at points in the Variations where it can be made to fit, the fit does not come at all naturally. It’s a nice idea that Elgar built a complex web of codes of this nature into the Variations, but it seems like it’s almost certainly reading too much into things, especially given that the solution doesn’t meet the fundamental requirement of fitting musically with the Enigma theme.

4. Pi

The scale degrees of the opening of the Enigma theme

It’s worth mentioning another, non-musical solution: that the number Pi is the hidden theme. Proponents of this theory note that the opening notes of the Enigma theme are scale degrees 3, 1, 4 and 2, which they point out are the first four digits of Pi (3.142…). There are other numerical tricks you can perform on the Enigma theme to compute numbers that resemble Pi, which could be taken as backing up this theory. But it’s a theory that goes against all the evidence that the solution is an existing melody — and besides, you can pick any random number, take the scale degrees of the Enigma theme, and probably find a way of adding, subtracting, multiplying and dividing the scale degrees to give you the number you’re looking for.

There are many more hidden melodies that have been suggested over the years, but none of them work: at best they sound at least fairly wrong, and at worst you have to slice up the tune and totally rearrange it to make it fit. Put simply, no one has suggested a hidden melody that, on hearing it, is totally obvious, as Elgar suggested it should be.

A new solution: Pergolesi’s Stabat Mater

I heard the Enigma Varations in King’s College Chapel, Cambridge, the other day, and it got me thinking about this hidden tune. I started thinking about what I’d write if tasked with writing a counter-melody to the opening theme, improvising things that worked well with it. And almost immediately what I was writing reminded me of something: Pergolesi’s Stabat mater.

Giovanni Battista Pergolesi was an Italian composer, and his setting of the Stabat mater, composed in 1736 and the last piece the composer wrote before he died, is one of the best-known pieces of choral music ever written. Its opening movement is a hauntingly beautiful duet for two singers, the text of the Stabat mater reflecting Mary’s torment as Jesus is crucified, the central moment of the Christian faith.

It had been a popular piece for a long time before Elgar came along: it was first published in London in 1749, and was the most frequently printed piece of music of the 18th century. Indeed, there was a new edition published by Novello in 1894, just four years before Elgar wrote the Enigma Variations. There is no doubt at all that Elgar would have known the piece, and considered it extremely well-known.

The fit between the opening (and most famous section) of the Stabat mater and the Enigma theme is pretty astounding, as you can hear below.

Enigma theme alongside Pergolesi’s Stabat mater (Stabat mater transposed up a tone)

Key to spotting this similarity is how the counterpoint is constructed. When seeking solutions in the past, people have often fallen into the trap of listening to the fully-scored Enigma theme and trying to hum another tune over the top. But this isn’t how Elgar said the counterpoint should work. In the 1900 Musical Times interview, he said that the two themes (i.e. not mentioning the harmony) could be combined. His 1905 biography put this in even clearer terms: The theme is a counterpoint on some well-known melody which is never heard. The Enigma theme is a counterpoint on the hidden melody, not the other way around. This is important: it means that, when auditioning hidden themes, we should be playing the hidden theme and humming the Enigma theme over the top. Any harmony should be provided by the music accompanying the hidden theme, not by that accompanying the Enigma theme.

(It’s worth noting that the word ‘counterpoint’ is defined by the Harvard Dictionary of Music as “music consisting of two or more lines that sound simultaneously.” There are more specific types of counterpoint, such as that outlined in Johannes Fux’s Gradus ad Parnassum in 1725, and the term is sometimes used to describe these more specific types — but we have no reason to think that Elgar wrote the Enigma theme as a counterpoint to the hidden tune according to any one specific set of contrapuntal rules. From his interview in the Musical Times in 1900, we know the counterpoint we’re looking for is the addition of “another phrase, which is quite familiar, above the original theme that he has written” — that is, counterpoint in the sense of two or more musical lines sounding simultaneously and working well together.)

Using harmony provided by the music accompanying the hidden theme is the approach used in the video above — and, when looked at like this, the Enigma theme not only works, it complements the vocal parts of the Stabat mater beautifully. There is musical analysis we could do, but there’s almost no need, it works so well. In the whole thing, there are perhaps three notes that work less well, but each can be explained in harmonic terms:

  • In bar 4, the F in the Enigma theme clashes with the F# in the Stabat Mater’s alto part: but as the major and minor third over the chord of D in the Stabat Mater, these form a false relation, and their falling on different beats reduces the effect of any dissonance.
  • In bar 4, the Bb in the Enigma theme clashes with the B natural in the Stabat Mater’s soprano part: but, again, as the major and minor third over the chord of G in the Stabat Mater, these form a false relation, and it only lasts for a single quaver on a weak beat, meaning its effect is minimal.
  • In bar 6, the first G in the Enigma theme clashes with the F# in the Stabat Mater’s alto part: but, as an on-beat dissonance that resolves by step, this is little more than an appoggiatura.

Coming relatively late as they do in the melody, these three notes do very little to detract from the overall sense of fit. What’s more, when you remove the soprano and alto lines of the Stabat mater and play the Enigma theme alongside just the Stabat mater’s characteristic bass line, the two false relations and the clash formed by the appoggiatura disappear, and you’re left with two parts that fit perfectly together (demonstrating not only how well the Enigma theme fits with the Stabat mater’s bass line, but also how well it fits with the Stabat mater’s underlying harmony):

There’s one piece of musical analysis that is worth pointing out: the notes that form the basis of the rising Stabat mater sequence are played in the bass line that accompanies the Enigma theme:

This gets even more obvious in the first Variation, when an alteration Elgar makes to the rhythm of the Enigma theme results in every note of the famous rising Stabat mater motif being played in one instrument or another:

Enigma Variations, start of Variation I, alongside the Stabat Mater

As if that weren’t enough, there’s the length of the Enigma theme to consider. As Clive McClelland pointed out in the Musical Times in 1901, “because [Elgar’s] arrangement of notes produces a six-bar phrase, a precise metrical alignment with a well-known tune is unlikely.” Regular, four-bar phrases are far more common in the musical canon — so McClelland assumes the hidden melody can’t run in parallel with the six-bar Enigma theme. But it makes more sense to take Elgar at his word, assume the theme does run in parallel, and therefore conclude that it’s a six-bar theme we’re looking for. And, sure enough, the famous opening theme of the Stabat mater is six bars long.

What of criteria (3) and (4) — the “dark saying”, and the fact that Dora Penny should have been particularly well-placed to spot the hidden theme?

Regarding the former, the text of the Stabat mater, relating as it does to the crucifixion, seems as good a fit as any as the “dark saying”. It certainly seems a more obvious fit than Rule Britannia, the Pathétique Sonata, Ein feste burg or any of the other proposed solutions.

And the latter — Elgar’s surprise that Dora Penny hadn’t spotted the hidden theme — makes perfect sense when you consider Dora’s background. Her father was Rector of St. Peter’s, Wolverhampton, a church whose impressive organ and roster of previous organists (including A. H. Mann, who would go on to conduct the first Festival of Nine Lessons and Carols at King’s College, Cambridge in 1918) suggests a strong musical tradition which she would have been exposed to when growing up. And she herself had singing lessons and sang in Wolverhampton Choral Society, in either or both of which she almost certainly would have sung the Stabat mater at one point or other, given its fame. Taking these two facts together, it is easy to see why Elgar would have expected her, “of all people”, to recognise the Pergolesi hiding in his Variations.

We could, if we wanted, find numerous other hints that Stabat mater is the hidden melody:

  • The 4-note phrases of Elgar’s tune match the metric structure of the words Stabat mater.
  • The veneration of Mary in the Catholic Church, of which Elgar had been brought up a member, makes the Stabat mater a natural choice for him.
  • The tune of the Stabat mater is hinted at in retrograde in the two bars before the start of the first Variation.
  • When writing a set of notes on the piece to accompany the pianola roll edition, Elgar specifically pointed out the two drops of a seventh in bars 3 and 4, which, taken together, form a pictorial cross, in a manner known to have been intentionally used by other composers such as Bach (the cross being the focal point of the text of the Stabat mater).

But searching for more incidental clues such as these can lead you to almost any answer you want to justify. Ultimately, Occam’s Razor is a better judge: the solution that requires the fewest assumptions is the best. Without rearranging notes or identifying ciphers, the Stabat mater gives us a solution that satisfies the four key criteria we know are relevant:

  1. It was an extremely well-known tune in Elgar’s time. It had been around for 150 years and was seen as one of the greatest pieces of sacred music in existence.
  2. It fits uncannily well with the Enigma theme. The Enigma theme forms a beautiful counterpoint to the Stabat mater, following its harmony and even, unlike many melodies of the time, matching its six-bar length.
  3. It involves a “dark saying”. The subject matter of the Stabat mater — the crucifixion — provides a compelling reason Elgar would have chosen to refer to it this way.
  4. There is a good reason Dora Penny should have been expected to spot it, “of all people”. As the daughter of a Rector in a musical church and an enthusiastic singer, she was probably the most likely of Elgar’s friends to know the Stabat mater well; it’s conceivable she had even sung it and relayed this to Elgar.

Each of these four points, when taken on their own, point to the Stabat mater being a more likely solution to Elgar’s enigma than the solutions previously suggested: when taken together, the evidence seems almost overwhelming. But stronger even than the appeal to logic is the appeal to the ears: when played alongside each other, the two themes fit astonishingly well. And that, taking Elgar at his word, should be the ultimate test.

Of course, given that it’s 85 years since Elgar’s death, we may never know what the true solution to the Enigma Variations is. And perhaps that’s part of their beauty — that they keep us guessing. But I now can’t help humming the Enigma theme when I hear the Stabat mater, and vice versa — possibly as Elgar intended.

Re / verb

Words about music

Ed Newton-Rex

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Founder of @Jukedeck // Composer with Boosey & Hawkes // Artificial intelligence & Music // www.ed.newtonrex.com

Re / verb

Re / verb

Words about music

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