Martin Gough’s Enigma 'Solution' Refuted

“All praise to Thee, my God, this night, for all the blessings of the light!

Keep me, O keep me, King of kings, beneath Thine own almighty wings!”

First stanza from  All Praise to Thee, My God

Martin Bird, the current editor of The Elgar Society Journal, is to be commended for raising Rushton’s moratorium by publishing a new solution to Elgar’s Enigma Variations. In the April 2013 issue, researcher Martin Gough theorizes the Enigma Theme is a puzzle canon that may be played with another canon by Thomas Tallis. Strangely Gough only introduces his candidate theme seven pages into the article: ‘Eighth Tune’ from Archbishop Parker’s Psalter of 1567. Never heard of it? Tradition has shortened that diffuse title to the Tallis Canon. Contrary to Gough's insistence, the Tallis Canon is not a puzzle canon, but rather a restricted canon. An excellent example of a puzzle canon is Bach's Crucigeros Canon. Below the canon Bach wrote the riddle, "Symbolum: Christus Coronabit Crucigeros." The translation of is, "Symbol: Christ will crown those who carry His cross." The solution is a double canon in contrary motion over a quotation from the Goldberg soggetto. Another more humble example of an enigma canon is shown below. Like the Bach puzzle canon, my riddle canon is only three measures long with a riddle beneath the title hinting at a solution. With the Tallis Canon there is no riddle beneath the title, no puzzle to solve, only a canon as its title makes quite clear. With a central tenet resting precariously on a false premise, the key to Gough's imaginative theory crumbles. Despite its enduring popularity in religious settings, the Tallis Canon has yet to deserve an article on Wikipedia. That omission does not bode well for its alleged popularity, a deficit that will probably not deter Wikipedia's Nomenklatura from soon adding Gough's theory to its growing list of flawed and incomplete enigma solutions.

Some Accurate Insights

Gough makes a number of stunningly accurate observations about the nature of the correct melodic solution to the Enigma Variations. The first is his conclusion that Elgar’s planning of the Variations ventured far beyond that of a brief improvisational foray on a relaxing Friday evening. He arrives at this assessment because canons “do not happen by chance.” Much could be said about a set of variations, for those too could hardly be described as the product of happenstance or luck. This opinion is one I advanced years ago, and it is decidedly at odds with the conventional wisdom that the Variations were the result of little or no advanced planning. Of course such a view is utterly inconsistent with Elgar’s known compositional style of accumulating ideas over years and even decades before finally fashioning them into a finished work. Gough’s second insight is to thoughtfully distinguish between the Enigma and the ‘larger theme’ that goes but is not heard. He emphasizes these are two separate parts of the puzzle, not overlooking the possibility they could be related in some way. His third contribution is the hypothesis the hidden melody to the Variations is a famous hymn tune from the sixteenth century inspired by the Book of Psalms from the Bible. On all of these points Gough is absolutely correct.

Enigma or Enigmas?

Although laying out some remarkably accurate premises, Gough soon veers off course, beginning with his fixation on the fugal qualities of the Enigma Theme most clearly exhibited in Variation IV. Correctly noting the opening bars of the Enigma Theme may be refashioned into a brief canon, Gough reverse engineers it to comport with this aspect of Variation IV. In essence he extrapolates one of Elgar’s own variation techniques to the Enigma Theme, and calls it an Old Canon. The canon itself is in three parts (Violin 1, Violin 2, Viola 1) accompanied by two other voices (Viola 2, Cello). Hence there are five parts in the Old Canon, but only four in the first six measures of the Enigma Theme (Violin 1, Violin 2, Viola and Cello).

It is surprising Gough limits his canonical treatment to just the first six measures of the Enigma Theme while ignoring the remaining eleven. His brief canon amputates a large portion of the Enigma Theme, bowing instead to the conventional wisdom. He writes, “…we know that the Enigma is specifically associated with the theme heard in the first six bars…” How precisely? He concludes this must be the case because Elgar asked his friend Jaeger to write Enigma in place of Theme on the title page. That is hardly a convincing argument, except for one already convinced at the outset. Gough presumes the Enigma Theme is limited to the first six measures without ever furnishing any objective proof. A major problem with this view is the opening material from measures 1-6 is recapitulated in measures 11-16 before the final cadence in measure 17. If the Enigma Theme was really restricted to the first six measures, its recapitulation should surely constitute a repetition. That means a more accurate title would be Enigmas (plural) rather than Enigma (singular). We know Elgar asked Jaeger to write the singular version, so this must mean the title Enigma applies to the entire 17 measures of the opening theme. There can be only one theme as the title makes clear, so it must refer to the entire opening movement rather than just the opening third.

     

It is a common error on the part of enigma detectives to confuse Elgar’s ‘dark saying’ (which is limited to the first six measures) with the Enigma Theme. The two are actually separate as Gough earlier points out, but not in the way he suspects. What Gough fails to grasp is Elgar’s ‘dark saying’ (a definition of enigma) is a music cipher embedded in the first six measures. Elgar is a recognized expert in ciphers, so this really should come as no surprise. As for the Enigma Theme, it remains intact as one complete movement in ternary form beginning in measure 1 and cadencing in measure 17. It may be argued the bridge in measures 18-19 constitutes an elaboration of the final cadence, making the Enigma Theme in reality 19 measures rather than 17. The double barline in measure 19 is identical to that found in measure 6, the alleged end of the Enigma Theme. The double bar in measure 19  marks the surreptitious end of the entire Enigma Theme, and would explain why Variation I does not begin until measure 20. Consequently, Gough’s failure to account for at least measures 7 through 17 renders both his Old Canon and New Canon incomplete, and inconsequential for a partial answer is no answer at all. In his New Canon, Gough alters the Tallis Canon in measure 7 to accommodate his novel harmonization of the Enigma Theme. These alterations to the source melody negate the whole point of the exercise insofar as Gough attempts to show how the Enigma Canon is a counterpoint to the Tallis Canon. One part can be changed to accommodate the other; but when both are modified it becomes a free transcription rather than a credible counterpoint.

Elgar’s Conditions – not Gough’s 

If the Tallis Canon was indeed the secret melody to the Enigma Variations, it must first satisfy four conditions given by Elgar soon after the 1899 premiere. These conditions are found in three primary sources: The original 1899 program note, the 1900 interview for The Musical Times, and the 1905 biography. Elgar’s four conditions are:

1. The Enigma theme is a counterpoint to the Principal Theme.
2. The Principal Theme is not heard.
3. The Principal Theme is a melody that can play ‘through and over’ the whole set of Variations including the Enigma theme.
4. The Principal Theme is famous.

Elgar made it abundantly clear the Enigma Theme was a counterpoint to the unstated Principal Theme. In his first authoritative biography published in 1905 he explained:

"The ‘Enigma’ orchestral-piece is Op. 36. What the solution of the ‘Enigma’ may be, nobody but the composer knows. The theme is a counterpoint on some well-known melody which is never heard, the variations are the theme seen through the personalities of friends, with an intermezzo and a coda, the last added at the request of friends aided and abetted by Dr. Richter, who accepted the work on its merits, having received the score in Vienna from his agent in London, and who at the time had not met with the composer.”[1]

A counterpoint is by definition a counter melody, and logic dictates the unstated Principal Theme must therefore be a melody.  This observation is entirely consistent with Elgar’s history as shown by counterpoints he created to famous themes from Handel’s Messiah and Mendelssohn’s Wedding March. Since the unstated Principal Theme must be melodic in nature, this clearly precludes from consideration any symbolic, mathematical or literary themes.

A major implication of Elgar’s contrapuntal condition is the unstated Principal Theme must play ‘through and over’ the entire Enigma Theme. Again, this observation meshes with Elgar’s life history of composing melodic counterpoints to famous melodies. Like a home standing on its foundation, the Enigma Theme must fit with its foundational Theme. This demands that both must be the same size, in this case length.

A major flaw in Gough’s theory is the failure of the candidate melody to play 'through and over' the Enigma Theme. He contrives a brief canonical fit between the two themes by inserting a two-measure introduction in which only the secretive melody plays. A melody by itself can hardly be called a counterpoint. A second major departure is his realization of a completely different accompaniment in B-flat major rather than the original key of G minor. These changes represent substantial departures from the original score, and are more accurately described as a free and imaginative transcription rather than a counterpoint.  The length of Gough's New Canon is a scant eight measures, two of which feature only the purported secret melody. As we have already seen, a major shortcoming with this eight-bar solution is the Enigma Theme is seventeen measures in length, not eight. Basic math confirms that eight does not equal seventeen. Besides, there is no reasonable justification for ignoring the remaining nine measures of the Enigma Theme. Without a clear horizontal fit, the Tallis Canon cannot be considered as a serious candidate for the unstated Principal Theme to the Variations.

The acid test is to play the Tallis Canon intact over the original Enigma Theme without any alterations to either part. When mapped with its original note values over the Enigma Theme (and making allowances for the minor and major modes of G), the Tallis Cannon fails to form a horizontal fit or a credible counterpoint. It must be played twice just to accommodate the Enigma Theme's length. Gough surely recognized this failing, resorting to the ploy of claiming the Enigma Theme is limited to the first six measures. Such an obvious error really requires no refutation,  for the absence of the most basic horizontal fit between the two themes makes the Tallis Canon unfit. Another problem is the Tallis Canon produces an unacceptably high number of howling dissonances with the Enigma Theme. Hence there is not only the lack of a basic horizontal fit, but also a contrapuntal one as well. Gough strives to circumvent Elgar's old conditions by inventing a host of new conditions never offered up by the composer. In the final analysis, the Old and New Puzzle Canons Gough fabricates as 'solutions' are nothing more than imaginative and free transcriptions drawn from varied forms of the Enigma Theme.

The Tallis Canon fails to present a complete or convincing counterpoint over the entire seventeen measures of the Enigma Theme. Strike one. It produces an unacceptably high number of dissonant intervals in the process. Strike two. On top of these difficulties, Gough fails to show how the Tallis Canon could conceivably play “through and over” the remaining movements, a requirement Elgar imposes in the original 1899 program note. Strike three. To circumvent these obvious flaws, Gough invents a new set of conditions to rationalize his novel transcriptions of the Old and New Canons, incorporating elements of the Enigma Theme around the Tallis Canon to suggest some contrapuntal relationship. Moreover, Gough asserts the continuation of this contrived contrapuntal relationship between the two themes by cataloging from other movements some examples of thematic material drawn from the Enigma Theme without ever actually spelling out how the Tallis Canon plays over these other movements. Such a vain undertaking is more counterexample than counterpoint. It's all sizzle and no steak. If Gough desires a credible example of counterpoint between the hidden theme and the Variations, he may listen to one here. With so many strikes against it, Gough’s imaginative enigma theory may be safely rejected like so many others before it.

While beginning with a few sound principles, Gough quickly wanders into a wilderness of innuendo, musings and unrestrained speculation. So much of his thought process amounts to the stratification of varying assumptions, layering guess upon guess in a quest for some semblance of an answer. Instead of bringing clarity, Gough sows confusion. For instance, he loosely interprets the remarks 'for fuga' on an early sketch of the Enigma Theme as evidence for a puzzle canon. He further speculates Elgar likely showed that sketch to Dora Penny, anticipating that clue somehow would help her guess the solution. Seriously? Would any reasonable person view the comments 'for fuga' as evidence of a puzzle canon? How Gough's research ever cleared the peer review process is the real enigma. He emphasizes the concept of a puzzle canon, yet fails to mention Santa’s original research showing that the mathematical constant Pi is encoded in the Enigma Theme. Canons are also commonly identified as rounds, and Pi is a special ratio applied to circles. To overlook something so obvious and relevant to his research belies Gough’s lack of circumspection, not to mention Martin Bird's editorial insensitivity. The irony is that both are named Martin, a first named shared by the actual composer of the missing melody to the Enigma Variations. With the aid of the British academic establishment, Martin Gough's enigma theory attempts to accentuate Elgar's heritage by linking the Enigma Variations to one of England's great early composers, Thomas Tallis. What Gough overlooks is the fact Elgar was no Vaughan Williams, a votary of English folk music and song. On the contrary, Elgar was a fervid disciple of the German School. For answers to the Enigma Variations, one must look beyond the borders of England and across the channel to Germany.

Gough's conception of counterpoint (sans Tallis)

A Mighty Fortress

The only theme to successfully satisfy all of Elgar’s conditions is Ein feste Burg (A Mighty Fortress) by Martin Luther. That well-known hymn successfully plays one complete cycle ‘through and over’ the full seventeen measures of the Enigma Theme, establishing a precise horizontal fit. A vertical alignment between the two melodies illustrates Elgar's unique treatment of Ein feste Burg in an augmented form and modified phrase structure. Rather than present it in its traditional phrase structure (ABABCDEFB), Elgar begins his counterpoint with the final phrase first (BCDEFBA). This unconventional approach explains the profound difficulty in detecting a counterpoint because one usually plays the beginning of a prospective melody over the beginning of the Enigma Theme. Such a predictable approach produces a mismatch, throwing off researchers even when the right melody is tested. The correct contrapuntal mapping begins with the ending phrase of Ein feste Burg, something strongly suggested by the fact that same ending phrase is quoted twice in an augmented form by the inner voice of the tenth variation, Dorabella. This presents a parallel with the Enigma Theme because that same ending phrase also plays over it twice. No wonder Elgar suspected Dora Penny, the daughter of an Anglican Rector, would be the one to guess the solution because her Variation features the ending phrase of Ein feste Burg is quoted not once, but twice!

The case for Ein feste Burg as the unstated Principal Theme to the Enigma Variations is extensive and persuasive. Confirmation that Ein feste Burg is the hidden theme is given by a number of different music ciphers in the Enigma Theme and Variation XIII. Within the Enigma Theme is concealed a music box cipher, Elgar’s ‘dark saying’ linked to the Enigma mentioned in the original 1899 program note. Incredibly, Elgar did not take his secret to the grave, but rather enciphered the answer in the orchestral score. When discovered, the decrypted answer would remain unguessed just as Elgar predicted. He even went so far as to encode the initials for the hidden melody in the Enigma Theme which modulates between the minor and major modes of G. The accidentals for those two keys are E-flat, F-sharp, B-flat. Even Elgar’s odd nickname for Jaeger’s Variation (Nimrod) may be linked to the hidden theme's title by means of wordplay.

If he were alive today, Elgar's response to Gough’s pedantic theory would undoubtedly be, “I do not see that the tune you suggest fits in the least." If the theme does not fit, then one cannot commit. 

Soli Yah Gloria

Elgar's Enigmas Exposed

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[1] Buckley, Robert J. Sir Edward Elgar (1905). New York: Kessinger Publishing, Llc, 2009, p. 54-55

Elgar’s Other ‘Dark Saying’

I will incline my ear to a parable; I will open my dark saying upon the harp.            

Psalm 49:4

A Music Box Cipher Key

Hidden within the first six measures of the Enigma Theme is a Polybius square cipher, more lightheartedly known as a music box cipher. Elgar’s breathtakingly original music cipher holds a secret message – a ‘dark saying’ – confirming the identities of both the covert principal theme and the secret friend of Variation XIII. The key to this type of cipher is quickly and easily constructed using nothing more than a pencil and a small scrap of paper. The circumstances under which Elgar composed the Variations would seem to require any cipher be created speedily without difficulty. A Polybius square satisfies those requirements perfectly. In Elgar’s music box cipher, melody and bass note pairs combine to pinpoint a corresponding row and column in a checkerboard grid (Table 1). The intersection is a cell containing a solution letter or a null, non-cipher material intended to confuse cryptanalysis.

The cipher key in Table 1 present melody and bass note letters in alphabetical order to label columns and rows with plain text and nulls dispersed throughout the grid. There are fifteen movements in the Variations, and likewise there are 15 plain text letters in the cipher grid (b, e, f, g, g, i, n, o, r, s, s, s, t, u , u). With this key the melody/bass note letter pair C/A produces the plain text letter u. It should be noted accidentals are extraneous as the key relies on discreet note letters only. With this same key the melody/bass note letter pair B/E produces f. That is a remarkable combination since theses letters form the initials for the covert principal theme, Ein feste Burg. Additional evidence recently unveiled reveals this key letter combination is scarcely coincidental.

A Key within a Key

The Enigma Theme is performed in the minor and major modes of G. The key signatures for G minor and G major employ the letters B, E and F to identify the accidentals B-flat, E-flat and F-sharp. Incredibly those same letters form the initials for Ein feste Burg. The Enigma Locks Cipher suggests the key to discovering the secrets of the Enigma Variations rests in the keys. These identical initials are spelled out by the Mendelssohn Cipher in Variation XIII, ostensibly as the solution letters to the three asterisks (***) in the title of that movement. Elgar’s use of two parallel keys suggests an alternative treatment of his music box cipher key, namely adjusting the order of the bass and melody note letters to alter the configuration of the plain text solution letters within the grid. In a new twist, experimentation with the order of the row and column letters reveals a cipher within a cipher.

A Reconfigured Cipher Key

According to the Rule of product there are 518,400 possible combinations in a 6 by 6 checkerboard grid. As there are only 15 contain plain text solution letters in 36 cells, over half of the grid (58.3%) has no useful information (i.e., nulls). This substantially reduces the number of possible combinations. After extensive experimentation Table 2 was realized.  The order of the melody notes in the columns is B, D, G, F, C, A. The order of the bass notes in the rows is E, C, G, B, D, A. In both the melody and bass sequences A is the last letter, and G is the third. What is most striking about this reconfigured key are the resulting letter clusters.

A Germanic Matrix

There are at least four Germanic terms produced by the reconfigured cipher key. The first occurs in rows one and two. In the first row are the letters fou, and nestled around the u in the second row are the letters st. Together they spell foust, a phonetic version of Faust (Table 3).

The story of Faust is a classic German legend, the basis of many artistic works ranging from painting, literature to music. In German the word Faust means fist, implying the use of force to achieve a desired outcome. Faust makes a Faustian bargain with the devil who offers earthly pleasures and knowledge in exchange for his immortal soul. That famous legend serves as the backdrop for a tragic play by Johann Wolfgang von Goethe. His poetry inspired Felix Mendelssohn to compose the concert overture Calm Sea and Prosperous Voyage, a work quoted by Elgar in Variation XIII.

A second Germanic reference occurs in the second and third rows. Here we find the contiguous letters rine, a phonetic rendering of Rhine (Table 4). One of the most important rivers in Europe, the Rhine runs through the heart of Germany. It banks are populated with many historic castles and ancient fortifications, posing an interesting parallel with the title of the unstated principal theme (A Mighty Fortress). Elgar visited Germany on numerous occasions, composing From the Bavarian Highlands after vacationing in Upper Bavaria in 1894. In his youth Elgar studied German in the hopes of attending the oldest school of music in Germany, the Leipzig Conservatory founded by Felix Mendelssohn.

A third German term is found in the first two columns in the second through fourth rows where the word ring is formed (Table 5). This language is intriguing because the mathematical constant Pi is encoded in the first measure of the Enigma Theme. Pi is a special ratio at the very center of the mathematics of circles. The overlap of two of the letters with rine strongly suggests Wagner’s Ring Cycle, Der Ring des Nibelungen.  The first of these four operas is Das Rheingold (The Rhine Gold). Elgar was a huge admirer of Wagner's music.

In the opening scene, Alberich steals gold from the Rhine Maidens to forge it into a magical ring that enables him to rule the world. Wagner’s innovative orchestration includes 18 pitched anvils whose distinctive ding is literally spelled out by substituting the column heading D for the r in ring (Table 6). The legend of the Rhine Gold would later inspire Tolkien’s The Lord of the Rings.  In Scene 2 of Das Rheingold there are two giants, Fasolt and Fafner. In Dante’s Divine Comedy, the giant Nimrod is observed by Dante and Virgil imprisoned in the ninth circle of Hell. There is an obvious parallel with that epic Christina poem because Variation IX is called Nimrod. This association suggests Elgar saw his friend August Jaeger as a giant and champion of his music. It is also an excellent example of Elgar’s exquisite sense of wordplay. The assorted Germanic references point to the Teutonic character of the unstated principal theme.

In addition to these overt Germanic allusions, the reconfigured cipher key contain other suggestive letters in close proximity to one another. The first is the E, F and b in the upper left corner (Table 7), the initials for Ein feste Burg. In column 3 the word Goes is formed.  This exactly mirrors Elgar’s language in the original 1899 program note which reads, “The Enigma I will not explain – its ‘dark saying’ must be left unguessed, and I warn you that the connection 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..”[1] Together these may be read as EFB Goes.

In column six appears the German word aus. This term generally means from, out of, off of, made of, and for. One of these translations (out) is phonetically spelled in the upper right corner of the cipher key as Aut. This appears to indicate the translation of Aus is out. Adding this to the first two terms produces EFB Goes Aut, or EFB Goes Out. This brief phrase captures the essence of the Enigma Variations. The principal theme goes with the music, yet it is taken out, silent like the deathly stillness of the sea. Like Jesus before his accusers, the principal theme remains silent. With biblical names such as Ysobel and Nimrod, the Enigma Variations are rich with literal and implied theological references.

In 1898 to a letter to his friend Jaeger, Elgar wrote, “This is what I hear all day - the trees are singing my music – or have I sung theirs?” The letters in rows one and two of Table 8 show the plain text solution letters fou and rest may be combined to spell fourest, a phonetic rendering of forest. A forest has trees, and Elgar adored them, especially pine trees. He once told Newmann, “…as a boy he used to gaze from the school windows in rapt wonder at the great trees in the park swaying in the wind; and he pointed out to me a passage in Gerontius in which he had recorded in music his subconscious memories of them.” The appearance of fourest in this reconfigured cipher key suggests a source of inspiration for Elgar’s musical ideas. A checkerboard cipher has four sides surrounding a clump of cells in which to plant a forest of plain text solution letters and nulls. Some even liken tackling a difficult a cipher to wandering into a deep, dark forest. Elgar's fascination with trees is mentioned by Matthew Riley who writes, “The pine trees in particular seem to have been a recurring motif in his life.” In this context it is remarkably relevant the first six measures of the Enigma Theme are performed exclusively by the string section since those instruments are made of wood. Before launching his public ministry, Jesus’ vocation was as a carpenter, a wood-worker.

 Another ‘Dark Saying’

Further analysis of the reconfigured cipher table reveals another ‘dark saying’ (Table 9). In row one appears the French word for fool (fou). The term fool has a distinctly Christian context because in 1 Corinthians 4:10 it reads, “We are fools for Christ’s sake, but we are wise in Christ.” Jesus is the hidden friend of Variation XIII, so a theological perspective is more than warranted. In row two below the o in fou is e, permitting another reading as foe. It should be emphasized fou is a phonetic equivalent of foe. One definition of foe is enemy. Romans 5:10 states, “For if, while we were God’s enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life!”

Row two has the letters for rest. The downbeat of the first six measures of the Enigma Theme is a rest, and this pattern reappears in measures 11 through 16. Row three spells in. Row four contains the letters g and b. In the absence of a d among the solution letters, the conventions of cryptography permit reading b as the mirror image of d. Tim Roberts made a similar discovery in his ingenious decryption of the Dorabella Cipher. Roberts discovered Elgar substituted the letter b for p because these letters are shaped the same but have different orientations. The same holds true for b and d. Consequently the letters gb may be viewed as gd, a phonetic version of God. The last two rows contain the letters gsus, a phonetic rendering of Jesus. This is the exact same spelling found in the decryption of Elgar’s music box cipher for measure 1 of the Enigma Theme. Piecing together all of these key words produces the saying, “Fool, foe, rest in God, Jesus.” The phrase “rest in God” is found in Psalm 62 which begins:

Truly my soul finds rest in God;

    my salvation comes from him.

Truly he is my rock and my salvation;

    he is my fortress, I will never be shaken.

The number of that Psalm offers a tantalizing connection to Elgar’s 6 by 6 music box cipher because 62 is highly suggestive of two sixes. In the fourth line it reads, “God is my fortress…” This is a singular recasting of the secret theme’s title from the plural; A Mighty Fortress is our God.  In this analysis it has been shown that the reconfigured cipher key uses the following languages: English, French and German. The use of multiple languages is significant because this is also found with Elgar's Music Box Cipher and the Dorabella Cipher. Some will undoubtedly criticize this analysis as highly speculative and unworthy of serious consideration. With so many pieces of the puzzle pointing in the same direction, however, it would be nothing short of cavalier to dismiss this research so readily. The unusual concentration of Germanic terms is hard to ignore. Clearly there is more to Elgar’s Enigma Variations than meets the eyes...or ears.

Soli Yah Gloria

Elgar's Enigmas Exposed

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[1] Original 1899 program note by C. A. Barry citing a letter by Elgar

Elgar's Enigma, Pi and the Tower

The name of the Lord is a strong tower;

   the righteous man runs into it and is safe.

Proverbs 18:10

Richard Santa made the remarkable discovery Elgar encodes the mathematical constant Pi in the Enigma Theme. That special number captures the ratio of a circle’s circumference to its diameter. Santa’s research is featured in Columbia University’s music journal Current Musicology. He perceptively noted the scale degrees of the Enigma Theme’s melody in measure one 3-1-4-2, a rounded version of the first five digits of Pi (3.1415). The melody is recapitulated in measures 11 through 16, so Pi is quoted a second time in bar 11. Following a bridge in measures 18 and 19, Pi is quoted a third time in the first measure of Variation I. That uplifting movement is dedicated to Elgar’s wife, Caroline Alice Elgar. In all, Pi is quoted twice in the Enigma Theme (measures 1 and 11), and a third time in Variation I (measure 20).

Why Pi?

What possible explanation is there for encoding Pi in the Enigma Theme or Variation I for that matter? Santa suggests Elgar uses Pi allude to his circle of friends. After all, the Enigma Variations are dedicated “to my friends pictured within.” Note the letters pi in pictured. Was this Elgar’s way of hinting at his subtle use of numeric symbolism? Santa also detects an element of humor in Elgar’s Pi quotation. There are 24 melody notes in the first six measures set apart by an oddly placed double bar at the end of measure six. With Pi encoded in measure one, Santa creatively interprets these first six measures as four and twenty blackbirds baked in a pie. Like blackbirds, printed notes are black. The popular nursery rhyme begins with the phrase, "Sing a song of sixpence," and Elgar shows an unusual fascination for the number six in the Variations. In reality Pi is ‘baked’ into only the first four notes of the melody which repeat in measure 11 for a total of eight notes, not twenty-four. Besides the apparent allusion to his circle of friends, could there by some other explanation for why Elgar would quote Pi in the Enigma Theme and Variation I?

An Iconic Bridge

Elgar’s Pi reference in the Enigma Theme invites multiple interpretations, yet there is only one conceivable explanation that links Pi to the unstated Principal Theme. Spanning the Pi quotations in the Enigma Theme and Variation I is a two measure bridge. There is one very famous bridge that resembles Pi: London’s Tower Bridge. Constructed between 1886 and 1894, it was completed four years before Elgar began openly working on his Enigma Variations. Built as a combined suspension and bascule bridge, the Tower Bridge was deemed too unconventional by some authorities. For example, Builder Magazine condemned it as “the most monstrous and preposterous architectural sham that we have ever known.” Like that unusual structure, Elgar’s unusual treatment of the Principal Theme within the Enigma Variations was also decidedly unconventional.

How does the Tower Bridge resemble Pi? First consider the upper and lower cases of Pi are shown below:

With the bascules down, the Tower Bridge resembles the upper case of Pi.

With the bascules raised, the Tower Bridge resembles the lower case of Pi.

The bridge between the Enigma Theme and Variation I is two measures long. Similarly, the Tower Bridge has two towers and two bascules.

An Iconic Theme

What conceivable purpose could Elgar have entertained by using Pi to suggest one of London’s most iconic landmarks? The Tower Bridge secured its name due to its proximity to the Tower of London. The official name for that famous bastion is Her Majesty's Royal Palace and Fortress. Both the terms tower and fortress are associated with the covert theme of the Enigma Variations: Martin Luther’s Ein feste Burg. The complete German title Ein feste Burg ist unser Gott literally reads as A Mighty Fortress is our God. However, W. M. Bunting translated it as A Strong Tower is the Lord our God. In a fascinating coincidence, Variation IV is given the initials W.M.B., the same as those for Bunting. Like the Enigma Theme, Variation IV quotes Pi twice, first at Rehearsal 11 and again at Rehearsal 14. Interpreting Pi as a veiled reference to the Tower Bridge would draw attention to the terms fortress and tower, and these in turn hint at the title of the absent Principal Theme. And the Tower Bridge is a drawbridge, something associated with castles and fortresses. What could be more inventive or playful than to draw attention to something else by means of a drawbridge?

The Tower Bridge spans the River Thames. Thames sounds similar to themes, and both are spelled almost the same. With its retractable bascules that rise in quarter circles, the Tower Bridge can both be present and absent, a feature reminiscent of the Enigma Variations’ missing melody. The French term bascule means see-saw, and is used to describe a balanced bridge that moves up and down. The original steam-powered hydraulic system took six minutes to completely lift the bascules. This presents an interesting parallel with Elgar’s music box cipher in the Enigma Theme as it is based on a 6 by 6 checkerboard. Speaking of steam engines, the timpani rolls in Variation XIII sonically portray the sound of a ship’s steam engine. According to the Jewish historian Josephus, the Tower of Babel was built by Nimrod, the very name given to Variation IX. Observe that the title of that epic structure begins with words the Tower.

The Tower Bridge is in reality two bridges designed to fit together to form a larger one. In like manner the Enigma Theme is two themes that fit together by means of counterpoint to produce a larger one. Did Elgar seek to symbolize this correspondence by encoding Pi in the Enigma Theme and Variation I with a bridge inserted in between? The evidence suggests as much. The Tower Bridge took eight years to complete, and there are a total of eight quarter note beats over the two measure bridge spanning these movements. Could this be a clue, or simply a bridge too far?

 Soli Yah Gloria

Elgar’s Enigmas Exposed

A Minor (and Major) Discovery

Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn’t really do it, they just saw something. It seemed obvious to them after a while.

Steve Jobs

Why does Elgar modulate frequently between the G minor and major modes within the Enigma Theme? Besides serving as an excellent contrapuntal camouflage to obscure the source melody, there is an arcane yet obvious explanation, one that literally holds the keys to unmasking the secret melody to the Enigma Variations. The answer is so obvious even Julian Rushton must be prepared to acknowledge it.

The Enigma Key Cipher

The Enigma Theme cycles between the minor and major modes of G (Table 1). The key signatures for G minor and G major employ the letters B, E and F to identify the accidentals B-flat, E-flat and F-sharp. Incredibly those same letters form the initials for Ein feste Burg. The Enigma Locks Cipher suggests the key to discovering the secrets of the Enigma Variations rests in the keys. In is a remarkable coincidence these identical initials are spelled out by the Mendelssohn Cipher in Variation XIII, ostensibly as the solution letters to the three asterisks in the cryptic title of that movement. An ingenious Music Box Cipher in the Enigma Theme takes it step further by encoding all 24 letters of the title Ein feste Burg ist unser Gott into an anagram of phonetically spelled words and phrases in English, Latin, German, and Aramaic. The use of multiple languages undoubtedly hardens harden the cipher and confounds decryption, but there is a more subtle reason for Elgar’s linguistic foray. The first few letters of each cipher language forms a stealth signature for ELGAR: English, Latin, German, and ARamaic. In a deeply symbolic gesture Elgar signed his most elegant music cipher in code.

Timing is everything, particularly in music, and this cipher epiphany is no exception. The discovery of the Enigma Key Cipher occurred on the evening of February 19, 2013. On that same day in 1899 Elgar completed his orchestration of the Enigma Variations. This is not the only example of extraordinary timing. The initial discovery of Ein feste Burg as the covert melody to the Enigma Variations took place on February 3, 2009 – the bicentennial of Felix Mendelssohn’s birth. The diverse music ciphers in the Enigma Variations make a profound and compelling case for Ein festeBurg, and still the evidence for Luther’s sublime hymn continues to mount into a veritable mountain.

Soli Yah Gloria

Elgar’s Enigmas Exposed

Elgar’s Enigma Theme with ‘Ein feste Burg’

The Enigma I will not explain – its ‘dark saying’ must be left unguessed, and I warn you that the connection 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 later dramas – e.g., Maeterlinck’s ‘L’Intruse’ and ‘Les sept Princesses’ – the chief character is never on the stage.[1]

Edward Elgar

1899 Program Note for the Enigma Variations

What is the missing melody to Elgar’s Enigma Theme? That haunting opening movement (Figure 5.0) has attracted a bevy of melodic candidates, yet none fully satisfy all of Elgar’s specific criteria. A careful analysis of three primary sources – the 1899 program note, the 1900 interview in The Musical Times, and the 1905 biography – identity four conditions concerning the relationship between the Enigma Theme and the covert Principal Theme. Those four conditions are:

1.      The Enigma Theme is a counterpoint to the Principal Theme.

2.      The Principal Theme is not heard.

3.      The Principal Theme is a melody that can play “through and over” the whole set of Variations including the entire Enigma Theme.

4.      The Principal Theme is famous.

Four Fragments

In early February 2009 the prospect first arose that Ein feste Burg (A Mighty Fortress) could be the covert principal theme of Elgar's Enigma Variations. What led to that surprising possibility were the incongruous Mendelssohn fragments in Variation XIII. In a standard theme and variations, it is not customary to draw attention to another composer’s work unless it has something to do with the original theme. In Variation XIII there are four musical fragments quoted from Mendelssohn’s concert overture Calm Seas and Prosperous Voyage. The original title of the overture is in German (Meeresstille und glückliche Fahrt), and the fount of inspiration was the poetry of the famous German poet, Wolfgang von Goethe. Three fragments are performed by the clarinet: Two in A-flat major and one a fourth lower in E-flat major. In the score these major fragments are enclosed in quotation marks to denote Elgar’s deliberate musical borrowing (Figure 5.1). A fourth fragment in F minor is performed by six members of the brass section (two trumpets, three trombones, and the tuba). Since it diverges from the original major version by being in a minor key, no quotation marks are situated around it. However, it most definitely comes from the same source. There are four Mendelssohn fragments, each four notes in length, and twelve of those notes from the major fragments are in quotation marks. Taken together, all four fragments are performed by a sum total of seven instruments from the woodwind and brass sections with the strings relegated to playing an accompaniment figure recapitulating the rhythmic palindrome from the Enigma Theme. Other than this rhythmic accompaniment figure, there appears to be absolutely no connection to the original Enigma Theme.

Four Clues

Why would Elgar insert four seemingly unrelated musical fragments into not just any variation, but one dedicated to a secret friend? Do these foreign fragments contain any clues about the identity of the hidden Principal Theme or the secret friend? One intriguing possibility is that the key letters of those fragments (A-flat, F and E-flat) are an anagram of the well known musical cryptogram F-A-E. That peculiar acronym forms the title of famous work for violin and piano composed collaboratively by Schumann, Brahms and Dietrich: The F-A-E Sonata. It was composed as a tribute to their mutual friend Joseph Joachim, a famous violin virtuoso who coined the romantic motto “Frei aber einsam” (Free but lonely). The initials for this motto form the title and basis for a curious musical cryptogram in each of the movements. Like the Enigma Variations, Joachim was challenged to guess the identity of the composer of each movement when he first performed the work at Schumann’s home. The two movements contributed by Schumann are a Romanze and a Finale. Interestingly, the Enigma Variations include a Romanza and a Finale. There is a historic connection between Joachim and Mendelssohn. When Joachim was thirteen years old he became Mendelssohn’s protégé, concertizing with him during his first tour of England in 1844. Obviously there far is more to the Mendelssohn fragments than a melancholy, motivic digression harkening back to some of the more important composers of the early Romantic era. Indeed, there is a hidden message, one much deeper than the F-A-E allusion to Joachim, Schuman, Brahms, and Dietrich. Elgar inserted these four Mendelssohn fragments as a cryptogram that, when decoded, unravels the mystery of the covert principal theme.

What is the significance of the Mendelssohn fragments? Fragments are like clues, for they are part of a larger subject. The quotation marks around the fragments imply by inversion that Mendelssohn “quotes” the same source melody in one of his own works. Since the Enigma Variations were composed for symphony orchestra, this suggests one of Mendelssohn’s symphonic works quotes the same principal theme. The number of notes in quotation marks is twelve, implying the number of letters in the theme’s title. The number of fragments (4) hints at the exact movement from the symphonic work featuring the mystery melody. The native language of Goethe, Mendelssohn and Joachim pinpoints the language of the principal theme’s title: German. Is there a symphonic work by Mendelssohn that could conceivably account for each and every one of these clues?

The answer is yes.

The work in question is Mendelssohn’s Reformation Symphony Op. 107. The fourth movement begins with a quotation of Ein feste Burg, proceeds through a series of variations on that sublime theme, and concludes with a rousing, augmented version of that historic hymn. Also known as A Mighty Fortress, Martin Luther’s most famous hymn is commonly known as Ein feste Burg, a title consisting of twelve letters in length. The Reformation Symphony was composed in 1832 for the tercentennial of the Augsburg Confession, but was not published until 1868 – well over two decades after Mendelssohn’s untimely death. For this reason it is numbered incorrectly as his fifth symphony when it was actually his first extended symphonic work. In an interesting parallel, Elgar’s first extended symphonic work is the Enigma Variations.

The Cipher Evidence

At least three music ciphers confirm the mysterious missing melody behind Elgar’s Enigma Variations is Martin Luther’s Ein feste Burg (A Mighty Fortress). The first and simplest is the F-A-E Cipher that encodes the initials for the literal English translation of the common three word title, A Mighty Fortress. The second is the Mendelssohn Cipher that encrypts the corresponding German initials for Ein feste Burg. The third and most sophisticated is Elgar’s Music Box Cipher embedded in the opening six measures of the Enigma Theme. This ingenious cipher encodes all 24 letters of the unstated principal theme’s title (Ein feste Burg ist unser Gott) in the form of an anagram that constitutes Elgar’s dark saying first mentioned in the original program note. This treatment of the Principal Theme's title is rather unexpected and unconventional. Rather than directly spelling out the answer. Elgar scrambles the letters of the missing title into phonetically spelled words and phrases to produce his dark saying.

The cipher evidence Elgar meticulously worked into the fabric of the Variations is unanimous. Martin Luther’s most famous hymn is the absent theme that plays through and over the set of Variations. While the case for Ein feste Burg is multifaceted and compelling, one key piece of the puzzle resists discovery: How does Ein feste Burg play through and over the Enigma Theme?

A Perfect Horizontal Fit

A preliminary mapping of Ein feste Burg over the Enigma Theme proves they are a perfect horizontal match (Figure 5.2). Both themes begin and end precisely together, a phenomenon never before observed in the history of enigma research. The odds are astronomical for such a precise fit without resorting to any melodic and rhythmic alterations.

The familiar version of Luther’s hymn featured in the horizontal mapping comes from the final choral of Bach’s sacred cantata Ein feste Burg BWV 80. The structure of Ein feste Burg is divided into nine phrases (ABABCDEFB) with the second phrase (B) stated three times (Figure 5.3). It is fascinating the phrase structure concludes with the letters EFB, the very same initials for Ein feste Burg. Remarkably, an ingenious alphanumeric cipher embedded in the Mendelssohn fragments of Variation XIII spells out those very same initials in reverse order (BFE). Those are the missing letters for the three asterisks (***) used to identify Variation XIII. The reversal of the initials in that cipher hints at Elgar’s unconventional mapping of Ein feste Burg over the Enigma Theme.

An Imperfect Counterpoint

While remarkable, the horizontal match between Ein feste Burg and the Enigma Theme produces an unsatisfactory counterpoint due to an unacceptable number of dissonances. The G and F-sharp combination on beat three of measure 1, and the same note combination on beat 1 of measure 9 are just some examples. Considering that the cipher evidence is unanimous, this leads to the inescapable conclusion is Elgar must have created his counterpoint based on a variation of hidden theme’s phrase structure. This would explain why he desired to name the work more simply as Variations.

An Unconventional Approach

 What is the correct phrase structure of Ein feste Burg over the Enigma Theme? The Mendelssohn cipher implies an unexpected approach since it spells out EFB backwards. This suggests starting the melodic mapping with the principal theme’s ending phrase rather than its opening one. There is other evidence pointing in that same direction. Like his father, Elgar served for years as a church organist. A standard practice among church organists is to introduce a hymn by performing the closing phrase as an introduction. Consider the title Enigma. The letter E resembles the lower case of Omega, and a the lower case of Alpha. Both Omega and Enigma have four letters in common, and each word has three syllables ending in a. This suggests a link. Elgar's treatment of the letter E in his Dorabella cipher hints at viewing the capital E as a subtle reference to Omega, for he reorients the capital cursive E to resemble it and other letters as well as the number 3. The first letter in the series below is the lower case of omega.

Characters from the Dorabella Code

In the Greek alphabet, alpha is the first letter, and omega is the twenty-fourth and last. The term Enigma essentially places the first Greek letter last, and the last letter first. This is an intriguing observation because in the book of Revelation one of the appellations for Jesus is the Alpha and the Omega – the Beginning and the End. The title Enigma alludes not only to the hidden friend of Variation XIII, but also to Elgar’s unconventional treatment of the principal theme by beginning his counterpoint with its ending phrase first. The timing surrounding the addition of the word 'Enigma' to the title page further reinforces this view, for it was done in March 1899 only after the score was completed and received Hans Richter's consent to conduct its premiere. The final piece of the puzzle - the title Enigma - was added last. Elgar had a sound theological foundation for beginning his counterpoint with the ending phrase and ending it with the beginning phrase. Jesus, the secret friend and inspiration behind Variation XIII, is credited with saying, "So the last will be first, and the first will be last."

 In Variation X Elgar places a clear emphasis on the principal theme’s closing phrase by quoting it twice in the inner voice. Recognizing the importance placed on the number six throughout the Variations, it is significant Elgar virtually quotes the same ending phrase at Rehearsal 66 in the Finale. There may be a theological reason for this number. In Matthew 6:6 Jesus teaches about the importance of doing good works in secret: "But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you." The number 66 is also intriguing because the Music Box cipher in the Enigma Theme is a 6 by 6 checkerboard cipher. In that cipher he rearranges the 24 letters from the principal theme’s complete German title to create an anagram in Latin, English and Aramaic – his dark saying. The first few letters of these cipher languages spell Elgar (English, Latin, German, Aramaic). Just as Elgar scrambles the letters of the principal theme’s title, he rearranges the phrase structure of the melody. Evidently the purpose for this approach was to vastly complicate detection and decryption of the cipher as well as the melodic counterpoint.

Elgar famously described the genesis of the Variations as a work “…commenced in a spirit of humour & continued in deep seriousness…” What could be more humorous than starting his counterpoint with the ending phrase of Ein feste Burg?  That would surely throw off those trying to detect a counterpoint by mapping prospective themes from their beginnings. In the original 1899 program note he explained, “…and I warn you that the connection between the Variations and the Theme is often of the slightest texture…” This suggests a more flexible treatment of the principal theme within the counterpoint. Elgar’s sketchbook shows the lover’s theme for his overture Cockaigne is counterpoint to Mendelssohn’s Wedding March. His treatment of the source theme is revealing because it is simplified with some notes of shorter duration omitted entirely (Figure 5.4). Elgar was not going to make the process of mapping the missing melody over the Enigma Theme so straightforward or easy. After all, he was deliberately concealing the source melody.
      Elgar's decision to modify the source melody is in keeping with a pattern of altering other quotations featured in the Enigma Variations. In Variation XIII he changed a Mendelssohn fragment from the major to minor mode. At the conclusion of the original score he altered a quote from Tasso's Jerusalem Delivered. When he later added new material to the Finale, Elgar included a modified quotation from Longfellow's Elegiac Verse. Clearly Elgar had no qualms about changing his source material to suit his needs, so it is only reasonable to suspect he also would change the hidden melody to the Enigma Variations.

A Free Adaption

After extensive research and experimentation, a plausible mapping of Ein feste Burg through and over the Enigma Theme was identified based on an unconventional phrase structure (Figure 5.5). Beginning with its ending phrase, Ein feste Burg progresses through its standard phrase sequence (BCDEFB) in a largely augmented form. Is this what Elgar implied by mentioning another and larger theme, an enlarged melody? The two statements of the closing phrase (B) are eerily reminiscent of the two augmented quotations of that exact same phrase by the inner voice in Variation X. It is remarkable that in both statements the opening half of phrase B is in major, and the second part is in minor. In this mapping the twist comes at the end where the beginning phrase (A) is tucked away like an afterthought into the two measure bridge transitioning into Variation I.
      For some this melodic mapping of the unstated principal theme is a proverbial bridge too far as it continues past measure 17. But is it really? From a cryptographic standpoint it makes perfect sense, particularly since Elgar was bent on obscuring the source melody. There is an element of Elgar's exquisite sense of wordplay involved in this unusual phrase structure. When the letter a is combined with word bridge it produces abridge. Intriguingly phase A is the very part that plays over the bridge, meaning the unstated principal theme played over the Enigma Theme is abridged.
     The ties between the whole note chord in measure 17 with the first note in measure 18 hint at a continuation of the principal theme. The phrase “through and over” suggests as much, for this mapping credibly shows how the principal theme continues through and over the Enigma Theme into the bridge, only ending right before the first variation begins. By putting the proverbial cart before the horse, Elgar deftly conceals the counterpoint linked to famous opening phrase of the missing principal theme. That is a stroke of genius, for such a stratagem assuredly throws of even the most intrepid investigator by denying obvious access to the starting counterpoint. Where is one to begin if there is no beginning at the beginning?

Figure 5.6 shows all melodic and harmonic conjunctions between the Covert Theme and the Enigma Theme. Melodic conjunctions (or matching melody notes) are shown by diamond shaped note heads. Harmonic conjunctions (or matching notes between the Covert Theme and any non-melodic note in the Enigma Theme's score structure) are indicated by triangular note heads.

The unexpected phrase structure of Ein feste Burg above the Enigma Theme is hinted at by the note sequence over the first three beats of measure 7 (Figure 5.7). Did Elgar encode this letter sequence in just this place because the seventh should be observed? Elgar wrote, "The drop of the seventh in the Theme (bars 3 and 4) should be observed." Elgar used these numbers specifically in reference to measures, and the sum of three and four is seven. The melodic mapping of Ein feste Burg over Nimrod alludes to the unusual placement of the opening phrase at the end.

In German key notation a B-flat is represented simply as B. In measure 1 of the Enigma Theme the first melody note is a B-flat. This is not a coincidence, for it alludes to the correct starting phrase of the unstated Principal Theme within Elgar's contrapuntal sequence (Figure 5.8). To drive that point home, Elgar repeatedly places the note letter B ahead of A throughout much of the Enigma Theme, and not always strictly in the melody line. By adopting an unconventional phrase structure for Ein feste Burg, Elgar guaranteed its mapping over the Enigma Theme would remain unguessed.

     The most popular version of Ein feste Burg is an isometric variant of the more rhythmic form composed by Luther. The meter of this more widely performed variant is 87.87.66.66.7. It is intriguing Elgar's unconventional phrase structure produces a metrical palindrome (7.66.66.7), relegating the 8 (which stands for phrase A) to the bridge. Notice there are two sevens at both ends of this metrical palindrome (7.66.66.7). This is a remarkable coincidence because Elgar draws special attention to the two drops in the seventh of the Enigma Theme's melody in measure 3 and 4, and again in measures 13 and 14. Could his use of this musical interval hint at the importance placed on phrase B of Ein feste Burg since it is identified metrically by the same number? The answer is that it would appear to be so.
     The rhythmic palindromes in the Enigma Theme's opening six measures would also appear to allude to this metrical palindrome since it is six numbers long. The sum of all these numbers including the seventh (7+6+6+6+6+7+8) is 46, the same number as the Psalms that inspired the lyrics for Ein feste Burg. That is an astonishing coincidence, and more than likely a numerical clue.

     In the opening four measures of the Enigma Theme, the notes of the inner voice produces the letter sequence BCDEF. This captures almost the complete phrase structure of the covert principal theme. Starting in measure 2 the bass notes produce largely the identical letter sequence. As shown in Figure 5.9, it is feasible to trace these separate note tracks to generate the letter sequence BCDEFB with F and B played concurrently. This letter series represents the six part phrase structure of Ein feste Burg over the first 17 measures of the Enigma Theme (not including phrase A over measures 18-19). Based on this analysis, it appears Elgar encoded his unconventional phrase structure of Ein feste Burg within the opening measures of the Enigma Theme. By leaving only A out of these note series, this suggests Elgar also left out that particular phrase from the 17 measure Enigma Theme.

     Table 5.1 identifies 23 shared notes or melodic conjunctions between Ein feste Burg and the Enigma Theme spanning from measures 1 through 19. Column one indicates the measure number, column two the beat, and column three the shared melody note.

Table 5.2 breaks down melodic conjunctions between Ein feste Burg and the Enigma Theme by note type. There are 6 shared note types with frequencies range from 1 to 9: A, B-flat, C, D, F-sharp and G. It is remarkable there are an equal number of G's (9) and D's (9). These letters are a phonetic spelling for God (G-d). The number nine (9) is an inverted six (6), and Elgar displays an unusual fascination for the number six throughout the Variations.

Table 5.3 summarizes all melodic and harmonic note matches between Ein feste Burg and the Enigma Theme in each measure. There are 80 note matches between Ein feste Burg and the piano reduction of the Enigma Theme shown in Figure 5.5. There are 9 discreet note types (A, B, B-flat, C, D, E, E-flat, F-sharp and G).

     The melodic mapping in Figure 5.5 reveals Elgar as an unpredictable prankster who built his mighty contrapuntal fortress around an unconventional phrase structure enlarged and hardened by augmentation. Little wonder it took over a century to breach the walls of his melodic cryptogram to finally map the missing melody through and over the Enigma Theme. Contrary to the dominant impression of mainline scholars, Elgar did not make the process easy or straightforward. Only a circuitous route would do. No wonder he encoded the number Pi in the opening measure of the Enigma Theme. He surely realized such an unpredictable approach would keep researchers going around in circles for eons. Occam's razor need not apply. The mapping of Ein feste Burg over Nimrod is so self-evident that the melodic solution to Elgar's Enigma Variations should be as plain a pikestaff.

Soli Yah Gloria

Elgar's Enigmas Exposed

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[1] Original 1899 program note by C. A. Barry citing a letter by Elgar