The puzzle of Elgar’s Enigma Variations has inspired a fascinating array of proposed solutions from diverse perspectives, each with their own merits and some seeming to have supporting evidence. No suggested solution for the Enigma riddle(s) can be proven as ‘the definitive answer’ (in spite of claims by some that the solution can be proven) – it is a matter of opinion if any solution is convincing, and Elgar’s music will always be greater than any proposed ‘solution’.

For those not exhausted by Enigma theories, I have a new theory which involves three Wagner ‘leitmotif’ themes, each linked to a distinct part of the ‘Enigma theme’ and to a different aspect of the puzzle. These themes link to other clues pointing towards an overall conclusion involving two more of Elgar’s major compositions.

The Enigma Puzzle(s).

From looking at Elgar’s program notes from the first performance, I firstly believe that the puzzle is divided into multiple parts and that the words of almost every part of it have been misinterpreted:

 (Puzzle 1:) ‘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, (Puzzle 2) through and over the whole set another and larger theme “goes”, but is not played . . . .(Puzzle 3:) So the principal Theme never appears, (additional hint?) even as in some late dramas-e.g., Maeterlinck’s “L’Intruse” and “Les sept Princesses” – (puzzle 4) the chief character is never on the stage.’

The idea of two separate Enigma puzzles is not a new one. Dora Penny expressed this viewpoint in her book ‘Edward Elgar – Memories of a Variation’ (1937). However, I believe there are as many as four parts to the puzzle, with the Maeterlinck reference providing an additional hint.

Before going into any detailed analysis, I will present the complete ‘musical solution’ to listen to, because if you do not find it musically convincing, you will not be interested in any logical explanation! I believe this combination of themes is the most musically interesting and satisfying of any of the proposed ‘Enigma solutions’:

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This clip uses high quality sampled sounds.

Puzzle 1: Bars 1-6 and the ‘Dark Saying’.

This part of the theory relates specifically to bars 1-6 of the Enigma Theme (up to the double bar line), and places particular emphasis on an unusual statement Elgar made:

“The drop of the seventh in the Theme (bars 3 and 4) should be observed.”

There aren’t a huge number of themes which involve a drop of a seventh, but one example is a leitmotif which is played many times in the final music drama (Gotterdamerung) from Wagner’s ‘Ring’ cycle and which is associated with the character Brunhilde. It is no longer fashionable to assign names to Wagner’s leitmotifs, but for convenience I will use the generally accepted leitmotif names. I first noticed that this ‘Brunhilde motif’ could work quite well as a counterpoint with bars 3 and 4, but was then surprised to realise that the theme can be repeated three times (without modification) across the first 6 bars of the Enigma theme and then again for bars 11-16, creating acceptable harmony (a bit like a ground bass except that it isn’t a bass). One weird feature is that for this to work, the motif has to start on the second beat of the bar each time, which is why it’s not obvious.

You can listen to the resulting harmony/counterpoint of the ‘Brunhilde theme’ played with bars 1-6 then 11-16 of the enigma theme here.

I think for a two bar phrase to repeat three times in this way across six bars of the Enigma theme without causing jarring dissonance is quite improbable unless by design.

To hear the original ‘Brunhilde motif’ played multiple times in the original Wagnerian context, you can listen to this recording (starting at 2:15) – from the Prologue Part II of ‘Gotterdamerung’ (Twilight of the Gods), where the theme first appears. ‘Gotterdamerung is the fourth and final part of Wagner’s ‘Ring Cycle’.

The question that springs to mind is ‘why should this theme should be referenced in this way?

The repeating nature of this two bar phrase played three times would make it very credible as a theme to improvise against, much in the same way as a jazz musician improvises against a repeating bass line or chord sequence. Some baroque music also works in a similar way, with a changing melody working in harmony with a repeating ‘ground bass’. Dora Penny wrote that Elgar often made a strange sound when he was playing the piano, as if he was filling in a missing part, so it seems quite feasible that he could have improvised against a repeating phrase (but a long and more complex phrase would be less likely).

The significance of the ‘Brunhilde motif’ is less obvious. I think part of it is that in Act III of Die Walkure, Brunhilde is surrounded by a circle of magic fire and remains surrounded by the circle of fire until ‘Gotterdamerung’, where the relevant Leitmotif is first heard. The circle links to the longstanding theory (not mine) that the scale degrees of the Enigma theme’s first four notes are related to 3.142 – pi, rounded to 3 decimal places, which in turn connects to circles. The concept of the circle also links of course to the ‘circle of friends’ portrayed in the variations. I also think it possible that the ‘circle of fire’ which surrounds Brunhilde could be linked to ‘the loneliness of the artist’ which Elgar referenced in ‘The Music Makers’ (when quoting the Enigma theme).

Most interestingly, Dora Penny describes seeing a ‘poker-work’ design over Elgar’s fireplace which he had designed and made himself, showing a phrase from the Walkure ‘fire music’.

If I’m right about the ‘Brunhilde motif’ then I’m fairly sure that I now know what the dark saying is all about, but this is best explained ‘in context’ towards the end of this page – You will find it in the section ‘The Enigma and the Dark Saying’.

Although the ‘Brunhilde motif’ is not ‘well known’ amongst the general public, I think it’s fair to say it would have been very familiar to Elgar’s circle, to opera goers and to concert goers of the time. Anyone who has heard orchestral extracts from Wagner’s ‘Ring Cycle’ would know it. In her book, Dora Penny reports going to a complete Ring Cycle performance at Covent Garden and also reports hearing Elgar play extracts from RW operas on the piano (and may well have been turning the pages).

Puzzle 2: bars 7-10 and ‘Another and Larger Theme’.

I believe that the ‘larger theme’ relates to bars 7-10 (in the contrasting key of G major) and that this theme goes ‘through and over’ Elgar’s harmonies by starting low and rising gradually in pitch. This way, going ‘through and over’ does not necessarily mean going through the entire length of the Enigma theme, but could mean cutting through vertically and harmonising with one section. It is a ‘larger theme’ because (being 4 bars long) it is longer than the Brunhilde theme and (with a range of one and a half octaves) it is larger in range than both the Brunhilde theme and the Enigma theme.

The 4-bar theme that I believe fits well with enigma bars 7-10 is the leitmotif (partially based on the ‘Dresden Amen) which Wagner uses to represent the ‘Holy Grail’ in Parsifal. It is just the top line of the ‘grail theme’ transposed into G major, but fitting in with Elgar’s harmony.

A visual inspection of the music shows that nearly all of the notes of the grail theme are present in Elgar’s harmony or help to complete the chords (with the exception of 2 passing notes). Rising phrases in Elgar’s music foreshadow similar rising quaver phrases in the ‘grail’ melody, almost creating rising scales (particularly in the fourth bar).

You can listen to the resulting harmony/counterpoint of the ‘Grail motif’ played with bars 7-10 of the Enigma theme here, which I believe creates a harmonious and interesting effect.

A shortened version of Wagner’s grail theme can be heard here (in the original key of A flat major).

The Holy Grail obviously has a number of meanings both literal and symbolic. I think there are several reasons the ‘Grail’ theme might be referenced. The first is that the ‘holy grail’ is associated with something that is part of a challenging quest, or something unattainable. I think another reason is that in the English version of the grail legend (King Arthur), it is the knights of the Round Table who seek the holy grail, which involves another circle and also links to Elgar’s interest in medieval/mythical chivalry. I believe it has little or nothing to do with the details of the Parsifal story, but the link to the ‘spiritual side’ is significant as will be explained later.

The phonetic spelling of grail (‘GRALE’ or ‘GRAEL’) is an anagram of ‘ELGAR’, and he is known to have been keen on phonetic spellings and anagrams – This may or may not be relevant.

The third musical clue: Bars 16-19

There is a very clear logical link between the Arthurian legend (involving the grail) and Wagner’s Ring, because both involve a sword with magical properties which has to be removed from a rock/tree by one particular person. This led me to suspect that Wagner’s sword motif (from ‘The ring cycle’) might also be involved. The Sword motif indeed fits very well with the end of the Enigma theme and going into the bridge to the 1st variation (bars 18-19). This surprised me and I think it hints at the logical link between the King Arthur legend and Wagner’s Ring, but also to Brunhilde – in the story of ‘the Ring’, the broken pieces of the sword are safeguarded by Brunhilde before being given to Sieglinde.

You can here the ‘Sword motif’ played with bars 16-9 of the Enigma theme here.

The first time ‘the Sword’ motif is heard in Wagner’s Ring is just before ‘the gods’ cross the rainbow bridge to Valhalla, and it might be significant that this theme plays though the bridge between the enigma theme and Variation I.

Combining the 3 Wagner Leitmotifs with the Enigma Theme.

The three leitmotifs I’ve mentioned harmonise with sections of Enigma as described. Together, they interlock to fit with the whole 19 bars of the Enigma theme.

You can listen again to a recording of the combined themes, using high quality sampled sounds HERE:

Elgar is certainly known to have been fascinated by Wagner’s music dramas and leitmotifs including the Ring Cycle and Parsifal. Elgar attended two performance of Parsifal on a single trip to Bayreuth in 1892, and he later attended complete ‘Ring Cycle’ performances. He played Wagner extracts on the piano and attended many concerts with orchestral Wagner music. It is acknowledged by many that Wagner’s influence was absorbed into Elgar’s compositional technique, but by using his own unique style and musical language Elgar ensured that the Wagnerian influence was not too obvious. It would therefore not be too surprising if Elgar referenced Wagner themes in the way I’ve suggested.

Puzzle 3: The Principal Theme.

I think the ‘Principle Theme’ can be the interpreted in one of two ways.

The most likely explanation is that the principal theme is the over-arching concept of the leitmotif, which Elgar used in works before and after the Enigma variations, including ‘Caractacus’ and ‘The Dream of Gerontious’, and which covers the three unheard Wagnerian counterpoint themes.

Alternatively, it could relate to the fact that in a nineteenth century work in sonata form, ‘the principal theme’ was often described as masculine (being rhythmic, vigorous, bold), and the ‘subordinate’ second theme as feminine (being gentler, lyrical), forming a contrast. The Enigma theme is closer to the latter, hence ‘the principal theme never appears’ – this is self-evident from the fact that the enigma theme flows straight into the ‘C.A.E’ variation (associated with Elgar’s wife) without any break or any clear contrast.

A Singular Problem?

 One criticism of this theory has been that Elgar referred to the Enigma mystery in the singular (implying that there is one covert theme) and that this ‘solution’ involves multiple themes. However, the overarching concept of the leitmotif is singular, particularly when combined with the idea of ‘continuous melody’ or ‘infinite melody’ – another important aspect of Wagner’s approach to his music dramas, which were such an important influence on Elgar (particularly around the time of the Enigma Variations).

Puzzle 4: The Chief Character – The final Link? (I think not)

The musical references I have mentioned link to circles and swords. Elgar wrote several songs referencing swords, but the relevant one is the sword song from Caractacus, written one year before Enigma. In Caractacus, there is also a song called ‘tread the mystic circle round‘, and reference to the ‘mystic ring’. Caractacus was a chief of the Britons, so it is quite possible he is the ‘chief character’ hinted at in Elgar’s famous program note. Caractacus is a cantata, which is not performed on the stage (unlike the music dramas/operas that are referenced). Saying that ‘the chief character is never on the stage‘ is, I believe, a brilliant bit of misdirection, and might well have appealed to Elgar’s sense of humour. However, I don’t think this humorous part to the overall puzzle is quite the final link in the chain – there has to be something else, in order to give everything some significance. I explain my thinking on this towards the bottom of this page, in the section called ‘The Enigma and the Dark Saying’.

Was there a reason why Dora Penny should know the answer(s) so far?

In order to achieve his full potential for the type of composer he was, Elgar would have known that his music needed to express a wide range of feelings, including masculine, feminine and spiritual feelings, which I believe are each represented by one of the counterpoint Wagner themes.

The ‘grail motif’ (based on the Dresden Amen and used in ‘Parsifal’) could be said to represent the spiritual side of Elgar’s music and personality, which came to the fore in Elgar’s next major work ‘The Dream of Gerontius’ (recognised as being influenced by ‘Parsifal’). The ‘sword motif’ could be said to represent the masculine character of much of Elgar’s music, evident in ‘Caractacus’, which was written the year before ‘Enigma’ and which includes ‘The Sword Song’. In contrast to this, the Enigma theme itself seems to express a much more sensitive side and in order to write this type of music, Elgar needed to access a part of his personality that he may have felt uncomfortable about because it could be seen as ‘unmanly’, particularly in Victorian England. I believe this is the basis of ‘the dark saying’, which ‘must remain unguessed’. In other words, Elgar was acknowledging (privately) a part of his personality that was important for his art, but which otherwise remained mostly hidden. Psychologist Carl Jung later defined ‘the anima’, existing in the subconscious of all men, and a source of creativity in artists. Interestingly, Jung saw Brunhilde (in Wagner’s Ring) as a metaphor for ‘the anima’. Although the writing of ‘Enigma’ was too early for Jung’s theory, Elgar might well have recognised the symbolic significance of Brunhilde, as it is self-evident in Wagner’s libretto that Brunhilde is a manifestation of part of Wotan’s personality. However, Elgar, the cigar smoking, golf playing, football loving gentleman of Victorian England could not have talked about a ‘sensitive side’ without ruining his public image, and yet he needed to acknowledge it in order to broaden as an artist. Secretly basing a theme around an improvisation on the ‘Brunhilde motif’ could have been a part of that process, and perhaps setting a baffling riddle for the public to struggle with was something he couldn’t resist.

The Enigma and the Dark Saying.

I think Elgar’s comment that she of all people should know the answer is partly a reference to the fact that she had a record of spotting similarities between themes in Elgar’s compositions and other existing themes. In her book she described pointing out that 2 themes in ‘The Dream of Gerontius’ resembled a Chopin piece and a hymn respectively. Elgar’s comment might have been due to his irritation at this, could have been half joking, or could have simply been recognition of her ability for spotting musical similarities. DP also describes in her book how she spent time with Elgar on the ‘British Camp’ hill discussing the Caractacus story.

Dora Penny (Dorabella) in her book makes at least three references to Parsifal, and it is clear that she was familiar with the opera and heard Elgar extracts on the piano. She also recalls going to a complete Ring Cycle performance at Covent Garden. She would therefore have been familiar with the three Wagner themes, and had a good musical knowledge generally. She was also aware of the ‘magic fire’ artwork above Elgar’s fireplace.

So Dora Penny probably had the knowledge to identify all of the various elements of the Enigma puzzle, even if she did not know how they could all be linked together.

The Eigen Connection.

In the oratorio ‘Caractacus’ (written just before Enigma Variations) the main female character is ‘Eigen’ who is the daughter of Caractacus. At the point where Eigen first makes an entrance, she sings “father” (to a falling seventh), then Caractacus sings “ ‘Tis Eigen”.

If we take that to mean “There is Eigen” it can be translated into welsh as “Mae Eigen”, which is a perfect anagram of “EE Enigma”. The language of the ancient Britons (i.e. the language of Caractacus) is closely related to the welsh language, and the Enigma theme contains many ‘drops of a third’, which we know Elgar associated with Wales.

There is a stage direction ‘Eigen Enters’ (initials ‘E.E.) and if we take that to correspond to the beginning of the Enigma theme (transposed into E minor), then the two ‘falls of the seventh’ would exactly match.

If Elgar’s instruction that “The drop of the seventh in the Theme (bars 3 and 4) should be observed” is applied to the relevant section of Caractacus, that would mean adding an additional three beats so that the two drops of a seventh are present –  then the top line of the Caractacus orchestral part (where there is no singing) plus the vocal line (where there is singing) can match with the Enigma theme from the point marked ‘Eigen enters’ to the end of ‘Tis Eigen’. I recognise that this is a bit of a stretch, but the point is that there does seem to be some connection between these two sections of music.

The ‘drop of the seventh’ is also a feature of the Wagner ‘Brunhilde motif’ which I believe is a repeating counterpoint to the first 6 bars of the Enigma theme (as explained above).

I think all of this draws attention to another point of connection. I think it is relevant that ‘Eigen’ is a german word with multiple meanings including ‘own, personal, private, eccentric, idiosyncratic, unusual, curious’ – is that not a description of the enigma and its mystery? and possibly a part of Elgar’s personality?

I think the hint here could be something along these lines – just as Brunhilde (Wotan’s daughter) is really a part of Wotan’s personality in Wagner’s Ring Cycle, the Enigma (here personified by the daughter of Caractacus) is a part of Elgar’s personality.

The Maeterlinck Reference.

The reference to the Maeterlinck plays in the program note might simply be an illustration of the way ‘the chief character is never on the stage’, but it is such an unusual reference to make, it seems likely that there is more to it. I think the explanation could be one or more of the following:

(1) The name ‘Maeterlinck’ sounds like ‘metal link’, which could possibly hint that there is a chain of clues and connections.

(2) It could be a reference to the fact that the plays involve symbolism, hinting that there is some symbolism involved in the Enigma mystery.

(3) As the two plays mentioned are from the same period and linked in various ways, it might well be a hint that separate but adjacent works by the same writer can be linked together. Applying this to my Enigma theory, one of the Wagner themes (‘the Sword’) points backwards to Caractacus, while the ‘grail theme’ from Parsifal points forward to ‘The Dream of Gerontius’ – the connections in this case are more to do with contrast than similarity, as described in the ‘The Enigma and the Dark Saying’ section above. The three major works Caractacus, Enigma and Gerontius form a trilogy which express three different aspects of Elgar’s personality. Following on from this, this series of compositions can be seen as a larger set of variations. Elgar’s comment ‘I warn you that the connexion between the Variations and the Theme is often of the slightest texture’ then takes on a double meaning. Looked at this way, the Enigma variations exist within a larger set of variations where the overall theme consists of contrasting elements of Elgar’s music and character.

What about the Variations?

When I listen to the variations (as opposed to the theme), they sound complete, and it is impossible to imagine any counterpoint theme being added without destroying the character of the music. On the other hand, the Enigma theme itself sounds as if it is hiding something, as if it is asking a question that is never answered. I believe the view that any counterpoint theme(s) need to cover all of the variations as well as the theme is incorrect, as well as making any solution impossible (or un-musical). If I am right, then what did Elgar mean by ‘through and over the whole set?’ – I can see two possible explanations.

The first explanations is that ‘the larger theme’ (the Parsifal Grail motif) goes vertically ‘through and over the complete set’ of Elgar’s harmonies as described in the section above on ‘Bars 7-10 and Another Larger Theme’.

The second explanation is that as the ‘Parsifal Grail Motif’ is related to the ‘spiritual side’, Elgar could have been emphasising the strong influence of his beliefs, going ‘through and over’ other aspects of his personality (which are represented by the other counterpoint themes).


This theory has many parts and relates to what I see as a puzzle with many parts. As such, you might be convinced by one part of it and not another, or you might be convinced by all of it or none of it – in a way it doesn’t matter to me, and everyone is entitled to their preferred theory.

I feel comfortable myself that my theory and each of its constituent parts are plausible, and that the parts are linked in a logical way.  The three musical phrases by Wagner provide acceptable harmony when combined with the relevant sections of the Enigma theme. These three themes are from a source that Elgar was certainly interested in and each has a logical link to something in Elgar’s life. The three counterpoint themes together satisfy the various criteria of the Enigma puzzle, and cover all 19 bars of the Enigma theme. The first theme (Brunhilde) also forms a repeating pattern that would be viable as the basis for improvisation. The idea of Caractacus being the chief character, would have appealed to Elgar’s humour, while at the same time the subtle Caractacus references provide another link in a chain of connections. The three hidden Wagner themes pay homage to an important influence on Elgar’s music, and at the same time they each relate to a different aspect of Elgar’s music and his very complex personality.

If you accept this analysis, it is clear that this was not something that Elgar intended to be easily worked out. However, It would have been quite possible for some element of it to be correctly guessed, without necessarily understanding how the various pieces of this jigsaw puzzle fit together. I think the suggestion that the solution was obvious has been over-played, and was actually misdirection, providing amusement and increasing the level of curiosity. I believe the enigma puzzle was not really for the public but more of a message from Elgar to a part of himself, made public in an encrypted form. The metaphor of Wagner’s Brunhilde again comes into play, as it is clear that Wotan (in Walkure Act II scene II) is really talking to himself when he talks to Brunhilde:

Brünnhilde :
To Wotan’s will thou speakest,
when thou tell’st what thou wilt;
what am I, if not thy will alone?

Wotan :
What in words to none other I utter,
still will remain unspoken forever:
I speak in secret, speaking to thee.


If you wish to make any comment on this theory, please email me. Thank you.