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 or even disproven as ‘the definitive answer’ – it is a matter of opinion if any solution feels right, and Elgar’s music and his puzzle (or two puzzles) will always be greater than any proposed solution (but my confidence in my theory is growing daily).

For those not exhausted by Enigma theories, I have a new theory which combines links to three Wagner themes and which is also linked to a more established conceptual theory, and finally all of the parts together point to a surprising conclusion, which once seen is almost impossible to ignore.

The Enigma Puzzle(s).

From looking at Elgar’s program notes from the first performance, I firstly believe that there are at least three separate puzzles and that the words ‘through and over’ (applying only to the second puzzle) have been misinterpreted completely:

 (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, even as in some late dramas-e.g., Maeterlinck’s “L’Intruse” and “Les sept Princesses” – 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 fascinating book ‘Edward Elgar – Memories of a Variation’ (1937). However, I now believe there are at least three puzzles, with the third one concerning the ‘chief character’ linked to the other clues.

I have three separate musical solutions with the first relating to puzzle 1, bars 1-6 and 11-16 plus the ‘dark saying’. The second solution relates to puzzle 2, bars 7-10 and the words ‘through and over’. The third solution relates to bars 16-19 and links to the previous two and to the ‘Chief Character’. The first two musical solutions and the ‘chief character’ are all linked to a pre-existing conceptual solution which involves pi and circles.

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 Wagner’s ‘Ring’ music-drama cycle and which is associated with the character Brunhilde. I had 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 context please skip to 2:15 in this recording – from “Dawn” in the Prologue Part II from ‘Gotterdamerung’ (Twilight of the Gods), where it first appears.

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

Firstly, 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, but I think it is to do with the fact 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 connects 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 a circle. 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’ concept 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’.

Although the ‘Brunhilde motif’ is not ‘well known’ amongst the general public, I think it’s fair to say it would have been quite 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).

There are several ways in which Brunhilde can be associated with a ‘dark saying‘. However, I think my initial thoughts on this were wrong. I will provide an explanation of the dark saying towards the end of this page in the ‘conclusion’ (but only when I have thought this through carefully).

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

My theory is 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 mean going through the entire length of the Enigma theme, but cutting through vertically and harmonising with one section. It is a ‘larger theme’ because it is longer than the Brunhilde theme (4 bars) 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 with enigma bars 7-10 is the leitmotif (partially based on the ‘Dresden Amen) which Wagner uses to represent the Holy Grail in Parsifal. However, it is just the top line 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 also foreshadow similar rising quaver phrases in the grail melody, almost creating rising scales. Listening to the two themes played together, an interesting and harmonious effect is created.

You can listen to the resulting harmony/counterpoint of the ‘Grail motif’ played with bars 7-10 of the Enigma theme here.

In the recording above, I have set the tempo to be slower than the usual tempo of the enigma theme, partly to make the harmony more clearly audible and partly to bring it closer to the tempo of Wagner’s grail theme. 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. However, I think that the main reason is that in the English version of the legend (King Arthur), it is the knights of the Round Table who seek the holy grail, which links to another circle and also to Elgar’s interest in medieval/mythical chivalry. It almost certainly has little or nothing to do with the story of Parsifal.

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 link logical between the Arthurian legend 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. I then discovered that an extended version of 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 into confirms the logical link to the King Arthur legend, and also to Brunhilde, because in the story of ‘the Ring’, the sword is safeguarded by Brunhilde when broken, and the broken pieces 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 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 hear a recording of the combined themes, using high quality sampled sounds HERE:

This image has an empty alt attribute; its file name is Enigma-plus-3-Front-Page-1024x576.jpg
This clip uses high quality sampled sounds.

The Chief Character – The final Link?

The musical references I have mentioned all 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 and I am convinced he is the chief character. Finally, Caractacus is an oratoria 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 a brilliant bit of misdirection, and yet once the ‘Caractacus connection’ is identified, it seems obvious. 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, and this ‘something else’ might well be the ‘Principal theme’. I will publish my ideas on this in the ‘conclusion’ at the end, once I have clarified and organised my thoughts.

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

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.

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. also describes in her book how she spent time with Elgar on the ‘British Camp’ hill discussing the Caractacus story.

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.

Wagner’s Influence on Elgar.

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. 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 never too obvious.


The conclusion is under development and will be published here once complete.