Enigma

The riddle 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 absolutely as ‘the definitive answer’ – it is a matter of subjective opinion if any solution is convincing, either musically or logically. The music of ‘Enigma Variations’ will always be greater than any proposed solution to the riddle, and yet we have been invited by the composer to contemplate this tantalising puzzle.

I have a new theory, which can be briefly summarised as follows:

  • The hidden theme of the Enigma is ‘The Representative Theme’ (aka ‘the Leitmotif’).
  • A musical counterpoint solution involves multiple Wagner leitmotifs.
  • The counterpoint themes help to point the way to the ‘dark saying’.

I will show here that this solution works both musically and logically, and that there is a plausible trigger for the Enigma riddle from shortly before the composition of the Enigma theme.

The Enigma Riddle.

Below is a reminder of Elgar’s program notes from the first performance:

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-e.g., Maeterlinck’s “L’Intruse” and “Les sept Princesses”the chief character is never on the stage.’

Dora Powell (nee Penny) expressed a view in her book ‘Edward Elgar – Memories of a Variation’ that the Enigma riddle is carefully divided into two parts. I believe there are as many as 3 or 4 parts to the puzzle, though the most important elements are ‘the larger theme’ and ‘the dark saying’, which are separate yet linked.

The Influence of Wagner.

Elgar is known to have been fascinated by Wagner’s music dramas, and he attended numerous performances of Wagner’s music dramas in Germany in the years leading up to the composition of the Enigma Variations. He played Wagner extracts on the piano and played violin in performances of Wagner’s orchestral music. An example of the Wagnerian influence on Elgar is his extensive use of the ‘leitmotif‘ technique, both before and after the composition of Enigma Variations. In late nineteenth century England the term ‘Representative Theme’ was often used instead of ‘leitmotif’.

The Genesis of the Enigma Riddle.

I quite unexpectedly found a very plausible trigger for the Enigma riddle, from reading ‘Elgar and the Press’ by Richard Westwood-Brookes. This book quotes an article from the Leeds Mercury, written shortly after the first performance of ‘Caractacus’ (5th October 1898) and about two weeks before Elgar started work on Enigma (21st October 1898). I believe the article would have still been fresh in Elgar’s mind when he “commenced in a spirit of humour & continued in deep seriousness”.

A substantial part of the article describes the importance of “the representative theme (aka ‘leitmotif’)” in Caractacus and goes on to add “Mr Elgar demonstrates his right to employ it much as though he were some Siegmund, and the representative theme, figured as the buried sword in the ash tree – to be used only by him who can draw it forth.”

Without doubt, Elgar would have appreciated this Wagnerian metaphor, which references a key moment from Act I of Die Walküre, where Siegmund draws a sword with special powers from an ash tree.

The article also describes how multiple ‘representative themes’ are used in succession in the opening chorus of Caractacus, “and yet the melodic phrase moves so naturally that the joinings are scarcely apparent.

I believe the article supports my theory as follows:

  • ‘The representative theme’ (as a concept) is the hidden theme of the Enigma, buried in the same way that Siegmund’s sword is buried in the ash tree.
  • Wagner’s ‘sword motif’ (from the Ring) is one of several Wagner representative themes that together form a counterpoint covering the 19 bars of the Enigma theme.
  • The Enigma theme itself becomes a ‘representative theme’, as its variants portray the 14 ‘characters’ of the variations, just as many of Wagner’s leitmotifs portray different characters in his music dramas.

The Musical Solution.

‘The Representative Theme’ is primarily a conceptual solution to the riddle of the Enigma, rather than having a single melody as an overall musical solution. However, there must be a counterpoint element in order to satisfy various statements that Elgar made, such as the one reported after an interview with the Musical Times in 1900: “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.”

Before going into any detailed analysis, I will present my complete ‘musical counterpoint’ for the Enigma theme. I firmly believe that this combination of themes (as demonstrated in the clip below) is the most musically interesting and satisfying of any of the proposed ‘Enigma solutions’ that I have heard:

I will now examine each of the counterpoint representative themes.

Enigma Bars 1-6 and ‘Brünhilde’.

There is a point of overlap here with an established theory from 2010 (by Charles and Matthew Santa), which highlights that the scale degrees of the Enigma theme’s first four notes are 3142, related to 3.142 or pi rounded to 3 decimal places. Pi links to a circle and given Elgar’s keen interest in Wagner, the obvious symbolic significance of a circle would be Wagner’s Ring.

Wagner’s Ring Cycle consists of four parts (Das Rheingold, Die Walküre, Siegfried and Götterdämmerung). There is only one character from Wagner’s Ring that is absent in part one (Das Rheingold), but present in parts 2, 3 and 4, and that character is Brünhilde. The opening six bars of the enigma theme each have a rest on beat one and music on beats 2, 3, 4 (and the same applies to bars 11-16).

The leitmotif which becomes associated with Brünhilde in ‘Götterdämmerung‘ is the one which forms my counterpoint solution for all of the bars in the Enigma theme that have a rest on beat one. Surprisingly, 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. For this to work, the Brünhilde motif has to start on the second beat of the bar each time, which makes sense because Brünhilde first appears in the second music drama of the Ring, known as ‘Die Walküre‘.

Above is the audio for Enigma bars 1-6 with Wagner’s Brunhilde motif, using sampled orchestral sounds (Click start arrow to listen).

A secondary significance of Pi and the circle is that in Act III of Die Walküre, Brünhilde is surrounded by a ‘circle of magic fire‘ and remains surrounded by the circle of fire until the Götterdämmerung Prologue, where the relevant Leitmotif is first heard. Interestingly, Dora Penny and a journalist described seeing a metalwork design over Elgar’s fireplace which he had designed and made himself, showing a phrase from the Die Walküre ‘fire music’.

The Brünhilde leitmotif contains a drop of a minor seventh. This could be what Elgar was hinting at when he made the following unusual statement in his notes for the ‘Pianola Rolls’ issued in 1929:

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

Click here to hear the Brünhilde leitmotif played multiple times in the original Wagnerian context (starting at 2:15) – This is from the Prologue Part II of Götterdämmerung, where the theme first appears.

It has been suggested that the Enigma theme was conceived as an improvisation. The repeating nature of the Brünhilde leitmotif 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 over a repeating ‘ground bass’.

Enigma bars 7-10 and ‘The Holy Grail’.

The second counterpoint theme is the ‘Holy Grail’ leitmotif from Wagner’s Parsifal. This theme, which is partially based on the ‘Dresden Amen’, fits with Enigma bars 7-10. It is just the top line of the ‘grail theme’ transposed into G major, but blending in with all of Elgar’s harmony as follows:

Above is the audio for Enigma bars 7-10 with Wagner Grail theme, using sampled orchestral and vocal sounds (Click start arrow to listen).

A visual inspection of the music shows that nearly all of the notes of the grail theme are either 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.

Enigma bars 16-19 and ‘The Sword’.

If the Enigma mystery was created in response to the Leeds Mercury article’s metaphor of Siegmund drawing the sword from the ash tree, then an obvious theme to use as a basis for counterpoint would be the Wagner leitmotif commonly known as ‘the Sword motif’, which is used in all four dramas of the Ring Cycle.

Click here for an extract from Die Walküre Act I, the moment where Siegmund draws the sword from the ash tree and the ‘Sword Motif’ sounds triumphantly (at 1:02:10).

The ‘sword motif’ is first used by Wagner at the end of Das Rheingold, just before the gods cross the rainbow bridge to enter Valhalla, so it is fitting that the theme fits with the ‘bridge section’ of the Enigma theme, leading into Variation I.

Above is the audio for Enigma bars 16-19 with Wagner’s Sword motif, using sampled orchestral sounds (Click start arrow to listen).

Combining the 3 Wagner Leitmotifs with the Enigma Theme.

The three leitmotifs discussed (Brünhilde, Holy Grail and the Sword) interlock to harmonise with all 19 bars of the Enigma theme.

Below, you can listen to a different arrangement of the complete Enigma/Leitmotif combination, this time using orchestral and vocal sampled sounds. Please click the start arrow:

The interesting question that arises is why would this particular combination of representative themes be referenced in this way? This is addressed in the next section.

How this leads us to the Dark Saying.

As you will remember, the Leeds Mercury article likened Elgar to Siegmund, and this casts some light on the relevance of Brünhilde.

I believe that the three leitmotifs (Brünhilde, Holy Grail and Sword) plus the Enigma theme have a strong logical relationship with a scene from Die Walküre, which is the second music drama of Wagner’s Ring Cycle. In Act II Scene IV, the valkyrie Brünhilde approaches Siegmund and tells him that he is doomed to die in battle and that she will take him to Valhalla, the afterlife of heroes and the castle of the gods.

The scene consists of a series of exchanges between Brünhilde and Siegmund, and I believe the first six verbal exchanges correspond to the first six bars of the enigma theme, for which the Brünhilde motif works as a counterpoint. The connections with the Walküre scene are not musical but symbolic.

The sixth exchange from this scene establishes a conceptual link to the ‘holy grail’ as follows:

Wish-maidens wait on thee there: Wotan’s daughter friendly there filleth thy cup!

Brünhilde to Siegmund, Die Walküre, Act II Scene IV

Fair art thou, and holy before me stands Wotan’s child:

yet one thing tell me, immortal!

Go brother and sister to Walhall together? Shall there Siegmund Sieglinde find?

Siegmund to Brünhilde, Die Walküre, Act II Scene IV

The mention of the words ‘cup’ and ‘holy’ connect logically with the ‘holy grail’ leitmotif and to bars 7-10 of the Enigma theme, for which the ‘holy grail’ theme can act as a counterpoint. At this point Siegmund considers the prospect of Valhalla, which corresponds to a change of mood in bar 7 of the Enigma theme from gloom to optimism, and a change of key from minor to major.

The next six exchanges between Brünhilde and Siegmund can be taken to correspond with bars 11-16 of the Enigma theme, where the G minor theme returns and where the Brünhilde leitmotif again works as a counterpoint.

At the end of this next set of verbal exchanges, a conceptual link to ‘the Sword’ is established, when Siegmund exclaims that he will defeat Hunding with the sword possessing magical powers, then Brünhilde’s replies:

He who bestowed it sends thee now death: for the spell he takes from the sword!

Brünhilde to Siegmund, Die Walküre, Act II Scene IV.

The Sword leitmotif can work as a counterpoint for bars 16-19 of the Enigma theme, which takes us through the bridge section to the end of the Enigma theme.

The symbolism of the three counterpoint leitmotifs and their logical connection to Act II scene IV of Die Walküre suggest that the heart of ‘the Enigma’ and the ‘dark saying’ are in some way encapsulated within this scene.

In a key phrase, early in the scene, Brünhilde states:

Death-doomed is he who looks upon me;

who meets my glance must turn from the light of life

Brünhilde to Siegmund, Die Walküre, Act II Scene IV.

I don’t wish to speculate about what significance this scene from Die Walküre had for Elgar, but its overall symbolism seems to be about mortality and the afterlife. It is likely that Elgar had an internal dialogue relating to one or both of these issues, and I believe the ‘dark saying’ is connected to this. It may or may not be relevant that The Light of Life was an earlier composition by Elgar.

I believe that Act II Scene IV of Die Walküre actually connects with the Enigma theme in ways that are too detailed to describe here. I am working on a separate explanation of this, for those who want the full details.

What about the Variations?

When I listen to the Variations that follow the Enigma theme, they sound complete, and it is impossible to imagine any counterpoint theme or sequence of themes covering the whole set without destroying the character of the music. For Elgar to have written the entire set of variations as a counterpoint would have put him in a musical straightjacket that would have made it impossible to create a masterpiece of such emotional power and imagination. I believe the assumption that any counterpoint theme(s) need to musically cover all of the variations is incorrect, and makes any solution impossible or un-musical.

So what did Elgar mean by ‘through and over the whole set?’

Crucially, the statement made after Elgar’s interview with the Musical Times in 1900 mentions the ‘original theme’, but makes no mention of the variations: “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.”

This might appear to contradict the statement that through and over the whole set another and larger theme “goes”, but is not played. However, this apparent contradiction can be resolved by recognising a conceptual theme that goes through and over the whole set of variations, linked to a counterpoint solution that specifically maps against the original Enigma theme.

‘The Representative Theme’ does indeed go ‘through and over the whole set’ of variations, because each variation is representative of a different ‘character’ in the circle of friends, in the same way that in Wagner’s music dramas each character is represented by a specific leitmotif. In the ‘E.D.U’ variation, themes from ‘C.A.E’ and ‘Nimrod’ are quoted as if they are leitmotifs. In this way, the concept of ‘The Representative Theme’ goes ‘through and over the whole set’ of variations, whilst specific examples of representative themes (leitmotifs) combine to form a counterpoint to the Enigma theme. However, I’ve identified three exceptions to this, as I believe additional counterpoints can be applied to three of the Variations. These are described in the two sections below.

‘Senta’ and ‘The Representative Theme’.

I’ve said that the variations that follow the Enigma theme do not generally involve any counterpoint, as the over-arching ‘larger theme’ is conceptual. However, I believe two of Elgar’s variations hint at ‘the Representative theme’ by referencing the name ‘Senta‘, which is embedded within the word ‘representative’.

Robert Padgett identified a possible connection between Enigma Variation XIII and Wagner’s ‘Senta’ theme from ‘Der Fliegende Holländer’ (the Flying Dutchman). Although he and I have very different viewpoints and reach different conclusions, I agree with him on this specific point, which you can read about here.

Investigating Variation XIII further, I can show how the intuitive connection between the first Clarinet solo and Senta’s theme can work as a satisfying counterpoint. The first part of this clarinet solo is reputed to be a quote from Mendlessohn’s ‘Calm Sea and Prosperous Voyage’, and yet it could also be a quote from the ‘Senta’ leitmotif from Der Fliegende Holländer. In the following clip, I show that the second part of the ‘Senta’ theme can be added as a counterpoint to the second part of the clarinet solo, with just a slight adjustment of the overall timing:

In addition to this connection, I believe that the ‘Senta’ leitmotif is hinted at in the ‘Dorabella variation’, as the top line of ‘Dorabella’ (first phrase) can form a counterpoint to the Senta theme (in G major), as demonstrated in this link:

Variation XIII and the ‘Dorabella Variation’ are both variations where the connection to the Enigma theme is ‘of the slightest texture’. It seems that these two movements (subtitled ‘Intermezzo’ and ‘Romanza’ respectively) are not variations on the ‘Enigma theme’ at all, but instead they make reference to the ‘Senta’ leitmotif, providing an additional hint that the theme that goes through and over the whole set of variations is ‘The Representative Theme’.

It is also interesting to note that Senta’s Ballad from Act II of Der Fliegende Holländer, which contains the ‘Senta leitmotif‘, starts in the key of G minor and with a metronome mark of 63 beats per minute – this is the same key and tempo as that written for the Enigma theme.

Enigmadämmerung.

The finale of the Enigma Variations (or E.D.U. variation) evokes Elgar himself, or arguably the more extrovert persona he presented to the outside world. In the extended revised version he quotes from the ‘C.A.E.’ and ‘Nimrod’ variations before bringing everything to a great climax. Right at the end, there is a sequence of chords which I always felt had some special significance. These chords feel quite dark and ambiguous, even though they resolve onto the tonic major chord. There is some similarity with the ending of Wagner’s Götterdämmerung, and although the chord sequence is not the same, I’ve found that the final leitmotif of Götterdämmerung, fits remarkably well with Elgar’s chords. The addition of the Wagner theme somehow relieves the dark ambiguity of Elgar’s chords.

The audio clip above combines the conclusion of the ‘E.D.U.’ Enigma finale with the final leitmotif of Wagner’s Ring.

This final Wagnerian leitmotif is sometimes known as ‘redemption’, sometimes ‘redemption through love’, sometimes ‘Sieglinde’s song in praise of Brünhilde’. There is no general agreement on what the theme represents, but the theme is certainly associated with the character Brünhilde. This final leitmotif is thematically linked to the other Brünhilde leitmotif that can act as a counterpoint for the opening 6 bars of the Enigma theme, right at the beginning of the piece. At the end of the revised score, Elgar quoted Longfellow – “Great is the art of beginning, but greater the art is of ending.” Perhaps this is a hint of this link between the ending and the beginning?

Is the Hidden Theme ‘quite familiar’?

Although the concept of the ‘Representative Theme’ and the specific Wagner leitmotifs mentioned here are not ‘well known’ amongst the general public, I think it’s fair to say they would have been very familiar to Elgar’s circle, to opera goers, to concert goers and to musicians of the time.

For example, Elgar and his wife attended numerous Wagner performances at Bayreuth and various German cities. Austin Jaeger (Nimrod) was also an ardent Wagnerian, and Hans Richter conducted the first performance of The Ring as well as the first performance of Enigma Variations. Dora Penny attended a complete performance of the Ring at Covent Garden with William Meath Baker (of Variation IV) and also mentions Parsifal three times in her book. I would argue that amongst Elgar’s close circle, the better known Wagner themes would have been at least as well known as the folk tunes, nursery rhymes, patriotic songs and hymns that many people think should hold the key to the Enigma.

The Maeterlinck Connection.

even as in some late dramas-e.g., Maeterlinck’s “L’Intruse” and “Les sept Princesses”

Edward Elgar, from the original program note of the Enigma Variations premiere.

Maeterlinck was a Belgian playwright, and Elgar’s reference to the Maeterlinck plays in the program note has probably been assumed by most to be merely an illustration of the way ‘the chief character is never on the stage’. However, it is such an unusual reference to make that it seems highly likely that there is more to it, for example:

  • I have explained that the ‘dark saying’ of the Enigma could be concerned with human mortality, and that is certainly a theme that is present in the two Maeterlinck plays that are mentioned.
  • The Maeterlinck plays are known for their symbolism, and the section of my theory leading to the ‘dark saying’ involves symbolism.
  • The plays that are referenced are part of a group of plays by Maeterlinck that are separate, but containing common themes and characteristics. The reference could be a hint that ‘the Enigma’ shares a common theme with other compositions by Elgar, written either before of after the Variations. It does not require much stretching of the imagination to see how that indeed could be the case.

Was there a reason why Dorabella should have known the answer(s)?

I think Elgar’s comment that she of all people should have known 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.

Dora Powell (nee Penny) in her book makes multiple references to Wagner and it is clear that she was familiar with his music. She reports hearing Elgar play Wagnerian extracts on the piano, and may well have been turning the pages. She also recalls going to a complete Ring Cycle performance at Covent Garden, and mentions Parsifal three times. She would therefore have been familiar with all of the Wagner themes mentioned here, and had a good musical knowledge generally. She was also aware of the ‘magic fire’ artwork above Elgar’s fireplace, and knew Elgar’s personality well.

If the ‘dark saying’ of the enigma is concerned with mortality or the afterlife, then a vicar’s daughter such as Dora should perhaps have known more about that than most.

So, Dora Penny 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.

There is another possible explanation for Elgar’s comment regarding Dora. This is that there could be a specific clue in the ‘Dorabella Variation’, which would be consistent with what is explained in the section ‘Senta and the Representative Theme’ above.

Conclusion.

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.

I am comfortable that this theory and each of its constituent parts are plausible and logical.

  • The musical phrases by Wagner provide acceptable and interesting harmony when combined with the Enigma theme and the three relevant sections of the variations.
  • These themes are from a source that Elgar was passionate about and which was a key influence on his musical thinking.
  • The ‘Senta theme’ (hinted at in variations X and XIII) provides a cryptic link to the concept of ‘The Representative Theme’, which is a plausible conceptual theme that goes ‘through and over the whole set’ of variations.
  • The Leeds Mercury article about the Caractacus premiere and the metaphor of Elgar drawing forth the ‘representative theme’ as Siegmund draws forth the sword provides an interesting and plausible trigger for this aspect of the Enigma riddle.
  • I believe that the three leitmotif counterpoint themes and their symbolism point the way to the dark saying.

If you accept this analysis, it is clear that this was not something that Elgar intended to be easily worked out, particularly the ‘dark saying’ element, which ‘must remain unguessed’. However, It would have been quite possible for some elements of it to be correctly guessed, without necessarily understanding how the various pieces of this jigsaw puzzle fit together. I think the ‘Enigma Riddle’ was really a message from Elgar to a part of himself, made public in an encrypted form. The metaphor of Wagner’s Brünhilde again comes into play, as it is clear that Wotan (in ‘Die Walküre‘ Act II scene II) is really talking to himself when he talks to Brünhilde:

Brünhilde :
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.

Feedback.

I will be pleased if you wish to provide any feedback or ask any question on this theory. If so please email me. Thank you.