Elgar's Enigma Theme Unmasked: The Case for 'Ein feste Burg'

"If you want to change the world, pick up your pen and write."

"Next to the Word of God, the noble art of music is the greatest treasure in the world."

The evidence that Ein feste Burg is the missing Principle Theme to the ‘Enigma’ Variations is multifaceted, multivalent, and entirely consistent with Elgar’s character and Christian faith. From early youth well into adulthood, Elgar was drawn to creating counterpoints to famous melodies, and his 'Enigma’ Variations are no exception. Multiple streams of data converge into a mighty river proving Elgar’s elusive melody is the same quoted by Buxtehude, Pachelbel, Bach, Mendelssohn, Meyerbeer, Wagner, Liszt, and Raff. The preponderance of the evidence makes – not breaks – the case for Ein feste Burg as Elgar’s covert Principal Theme.

Full Coverage of the Enigma Theme

Ein feste Burg is the only theme ever proposed to convincingly play one full cycle ‘through and over’ the entire seventeen measures of the Enigma Theme. This feat is unprecedented in the history of Elgar scholarship. No other melody put forward over the past century surmounts this seemingly impossible hurdle. Ein feste Burg also satisfies five criteria prescribed by Elgar necessary for diagnosing the right melodic solution:

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.

5. Dora Penny was very familiar with Ein feste Burg as she was the daughter of an Anglican missionary and Rector.

'Through and over'

Consistent with Elgar's remarks in the original 1899 program note stating the hidden theme plays 'through and over' the set of variations, Ein feste Burg plays over each of the fourteen Variations. Table 1.1. summarizes how Ein feste Burg plays ‘through and over’ 591 of 780 measures, or virtually 76 % of the work. A detailed mapping of the Covert Theme over the Variations produces 854 melodic conjunctions, and 1754 chordal conjunctions. A melodic conjunction is defined as a shared note between the melody lines of the variation and Covert Theme. A harmonic conjunction is defined as any shared between the Covert Theme and the variation’s piano reduction excluding the variation's melody line. In total there are 2608 note matches between the Variations and the Covert Theme dispersed over 591 measures.

Table 1.1
Note Conjunctions between Ein Feste Burg and the ‘Enigma’ Variations
Variations	Note Conjunctions			Measures
Variations	Melodic	Harmonic	All	Active	Dormant	All
Theme	13	35	48	17	0	17
I C.A.E.	28	112	140	21	2	23
II H.D.S-P.	45	20	65	32	24	56
III R.B.T.	34	38	72	27	7	34
IV W.M.B.	26	87	113	28	4	32
V R.P.A.	68	98	166	22	2	24
VI Ysobel	39	66	105	21	0	21
VII Troyte	75	161	236	64	8	72
VIII W.N.	60	99	159	25	1	26
IX Nimrod	27	123	150	30	13	43
X Dorabella	104	68	172	41	33	74
XI G.R.S.	62	179	241	36	5	41
XII B.G.N.	23	77	100	23	5	28
XIII ***	46	127	173	43	8	51
XIV E.D.U.	204	464	668	159	77	236
Totals	854	1754	2608	589	189	778
Percentages	33 %	67 %	100 %	76 %	24 %	100 %

Variation I

Ein feste Burg plays ‘through and over’ Variation I C.A.E., producing 28 melodic conjunctions spread over 13 out of 21 measures, and 140 harmonic conjunctions spanning 21 measures. C.A.E. is 21 measures in length excluding a two bar bridge in measures 18 and 19. It was determined the Covert Theme is dormant in those two transitional measures, hence the absence of any note matches. Excluding these transitional measures, the Covert Theme plays in all 21 measures or 100 % of this movement.

Variation II

Ein feste Burg plays ‘through and over’ Variation II H.D.S-P., generating 45 melodic conjunctions in 31 out of 55 measures, and 65 harmonic conjunctions covering 32 measures. It was determined the Covert Theme is dormant in the first ten measures (41-50), and the last fourteen (83-96). Theses inactive sections are essentially symmetrical because both consist of ten measure segments at the beginning and end of Ein feste Burg with the last dormant section followed by a four bar codetta. Elgar uses this sandwich technique more than once in the Variations as a sort of camouflage to obscure the start and end points of the Covert Theme. Since it is dormant in 24 out of 56 measures, the Covert Theme plays over almost 43% of the movement.

Variation III

Ein feste Burg plays ‘through and over’ Variation III R.B.T., producing 34 melodic conjunctions spread over 24 out of 34 measures, and 72 harmonic conjunctions spanning 27 measures. Since it is dormant in 7 out of 34 measures (97, 105, 121-123, and 131-132), the Covert Theme plays over approximately 79 % of the movement.

Variation IV

Ein feste Burg plays ‘through and over’ Variation IV W.M.B., generating 26 melodic conjunctions dispersed over 28 of 32 measures, and 113 harmonic conjunctions covering 28 measures. Since it is dormant in 4 out of 32 measures (178 through 181), the Covert Theme plays over almost 88 % of the movement.

Variation V

Ein feste Burg plays ‘through and over’ Variation V R.P.A., producing 68 melodic conjunctions spread over 20 out of 24 measures, and 166 harmonic conjunctions dispersed over 22 measures. Since it is dormant in 2 out of 24 measures (172 and 173), the Covert Theme plays over almost 92 % of the movement.

Variation VI

Ein feste Burg plays ‘through and over’ Variation VI Ysobel, generating 39 melodic conjunctions in 17 and 105 harmonic conjunctions spanning 21 measures. The Covert Theme plays over all measures or 100 % of this movement. It is remarkable the cover theme plays over the entire variation without any dormant measures in the first two movements dedicated to women (I and VI).

Variation VII

Ein feste Burg plays ‘through and over’ Variation VII Troyte, producing 75 melodic conjunctions over 39 measures, 161 harmonic conjunctions, and 236 total note conjunctions spread over 64 measures. Since it is dormant in 8 out of 72 measures (210 through 213, 223 through 225, and 252), the Covert Theme plays over almost 89 % of the movement.

Variation VIII

Ein feste Burg plays ‘through and over’ Variation VIII W.N., generating 60 melodic conjunctions and 159 harmonic conjunctions in 26 out of 27 measures. Since it is dormant in the final measure (307), the Covert Theme plays in just over 96% of the movement. If the final G of Ein feste Burg in measure 307 is tied over to the G major chord in measure 308, the case could be made the Covert Theme plays ‘through and over’ the entire movement without any dormant measures. This would present a third instance in which the covert Principal Theme plays over the entire length of a movement dedicated to a woman (I, VI and VIII).

Variation IX

Ein feste Burg plays ‘through and over’ Variation IX Nimrod, generating 27 melodic conjunctions spread over 20 measures and 150 harmonic conjunctions over 36 measures out of a total of 43. Since it is dormant in 13 measures (341, 349-350, 356, 361-364, 368-372), the Covert Theme plays over virtually 70 % of the movement.

Variation X

Ein feste Burg plays ‘through and over’ Variation X Dorabella, producing 104 melodic conjunctions spread over 35 measures, and 172 harmonic conjunctions over 41 measures out of a total of 74 measures. Since it is dormant in 33 measures (385, 397-404, 415-424, 437-450), the Covert Theme plays just under 58 % of the movement. It is remarkable that in both instances when the Covert Theme concludes one complete cycle it is immediately followed by a carefully placed double bar in the score (measures 414 and 436). The odds of such a coincidence are astronomically low, reinforcing the conclusion Ein feste Burg must be Elgar’s missing melody. More importantly, this phenomenon is not isolated to just one movement.

Dorabella’s ‘inner voice’
Concerning Variation X Elgar wrote the “inner sustained phrases at first on the viola and later on the flute should be noted”. His brief remarks draw attention to the inner melody line, yet give no particular reason why. Following the discovery of the Covert Theme, the reason becomes perfectly clear: Significant portions of Ein feste Burg are quoted verbatim by the inner counter melody. The first occurs in measures 408 through 452, and the second in measures 430 through 434. In both cases, the final cadence of Ein feste Burg is immediately followed mid-measure by a conspicuously placed double barline (414 and 436). No wonder Elgar told Dora that she ‘of all people’ would be the one to guess the correct melodic solution. Among all the variations, Dorabella most directly quotes a sizable part of the Covert Theme in an inner melody line, albeit in an augmented form and at the end rather than the beginning.

Variation XI

Ein feste Burg plays ‘through and over’ Variation XI G.R.S., generating 62 melodic conjunctions spread over 28 measures, and 241 harmonic conjunctions over 33 out of a total of 41 measures. The Covert Theme is dormant in 5 measures (457, 490 – 493) with four of these five inactive measures consisting of a codetta at the end of the movement. Consequently there are shared melody notes in 28 out of 35 active measures, or 80% of the movement when Ein feste Burg plays. There are matching notes dispersed over 33 of 35 active measures, or 92 % of the movement when Ein feste Burg plays. When factoring in all measures, matching notes occur in 80 % of the movement.

Variation XII

Ein feste Burg plays ‘through and over’ Variation XII B.G.N., producing 23 melodic conjunctions spread over 23 measures, and 100 harmonic conjunctions over 23 out of a total of 28 measures. Since it is dormant in five measures (494-495, 515, 520-521), the Covert Theme plays in just over 82 % of the movement. Inactive sections are symmetrical insofar as two consist of two measure segments at the beginning and end of Ein feste Burg, and the third near the middle at measure 515. This sandwich technique serves to camouflage the start and end points of the covert Principal Theme, and is also found in Variation II.

Variation XIII

Ein feste Burg plays ‘through and over’ Variation XIII Romanza, generating 46 melodic conjunctions in 29 measures, and 173 harmonic conjunctions over 46 out of a total of 51 measures. The Covert Theme is dormant over 21 quarter note beats dispersed over 8 bars (532-534, 548, 564-566, and 572). Consequently there are matching notes in 46 out of 51 active measures, or 90% of the movement when Ein feste Burg plays. When factoring all measures, the Covert Theme plays over almost 83 % of this section. Melodic conjunctions begin in measure 522 and continue through the double bar at measure 553 where Ein feste Burg finishes one complete cycle. The conclusion of Ein feste Burg precisely at the double bar is not an isolated coincidence as this pattern also appears in other variations containing double bars such as X.

Variation XIV

Ein feste Burg plays ‘through and over’ Variation XIV E.D.U., generating 204 melodic conjunctions in 85 measures, and 464 harmonic conjunctions over 148 out of a total of 236 measures. Since it is dormant in 77 bars (598-603, 626-634, 647-652, 671-674, 685-687, 702-703, 732-739, and 767-809), the Covert Theme plays in slightly over 67 % of the final movement. It is significant 55 % of dormant measures (41) are found in the extended ending Elgar added shortly after the 1899 premiere. This suggests Elgar tapered his sophisticated counterpoint to permit greater flexibility in the treatment and elaboration of the closing material.

Confirmation: The Enigma and Mendelssohn Ciphers

Elgar’s lifelong fascination with ciphers, wordplay, and anagrams is beyond dispute, so it is unsurprising he gives stealth confirmation of the correct melodic solution by means of an ingenious musical checkerboard cipher. This 'dark saying' is embedded within the first six measures of the Enigma Theme, and it is no coincidence the word ‘Enigma’ is written in pencil directly over the opening measures of the original score. An oddly placed double bar at the end of measure six marks the conclusion of this musical cipher. There are twenty four notes in the Enigma theme’s melody over the first six measures, and likewise there are twenty four letters in the six word title Ein feste Burg ist unser Gott. Six bars, six words, 24 notes, 24 letters – what are the odds of these uncanny parallels? It is fascinating the number 24, a multiple of 6, is reducible to 6 by adding the integers together. The varied references to the number six are not limited to measures or multiples of notes. The opus number for the Enigma Variations (36) is the product of 6 times 6. A second cipher in Variation XIII embedded in the Mendelssohn fragments produces E.F.B., the initials for Ein feste Burg.

Further evidence alluding to the title of the melodic solution is found within the Enigma cipher's choice of harmony. Elgar begins measure 5 with a distinctive chord known as the German Sixth, a feature that strongly alludes to the melodic solution’s German title consisting of six words.

The cipher employed by Elgar is a box cipher, also known as a Polybius square or checkerboard cipher. A box cipher relies on two data points to encipher a single solution letter using a checkerboard grid as a key with solution letters dispersed among the grid’s cells. The traditional Polybius square consists of a 5 by 5 grid pattern. Variations on this 'very old cypher' include a 6 by 6 grid pattern, and just such a solution grid is suggested by the presence of six different titles and names sprinkled throughout the Enigma Variations (Table 1.2). By stacking these titles and names, a 6 by 6 letter grid is realized.

Elgar's musical checkerboard cipher key is shown below in Table 1.3 with non-solution letters represented by asterisks (*). A careful consideration of the parallels between the 6 x 6 name grid and Elgar's box cipher table provides powerful circumstantial evidence he deliberately used six six-letter names within the Variations to hint at the nature and construction of his musical cipher.

Two data points identify the intersection of a specific column and row that contain within each cell a plain text solution letter. Elgar’s brilliant display of musical cryptography relies on melody and bass note pairs to encrypt solution letters, a feat never accomplished before or since its unique application in the Enigma Theme. The original short score of the Enigma Theme lends strong circumstantial evidence for a checkerboard cipher because the melody and bass notes are in black ink while the intervening notes are in pencil.[1] Elgar’s use of a box cipher is not without foundation as he bragged about cracking an allegedly impregnable checkerboard cipher in his 1905 biography.[2] The cipher appears in the fourth of a series of articles published in 1896 by The Pall Mall Gazette called Secrets in Cipher. These articles are now in the possession of the Elgar Birthplace Museum as part of the remains of Elgar’s personal library. Of all the papers he discarded and burned shortly after his wife’s death in 1920, why would Elgar retain those articles? Or why would he brag to his first biographer about cracking an insoluble checkerboard cipher, something found just thirteen pages from a revealing section about the ‘Enigma’ Variations? Were these not clues regarding the nature of his ‘dark saying’?

The solution letters of the first six measures of the Enigma Theme are shown in Table 1.4. The Enigma cipher solution is 24 letters in length forming phonetically spelled words in Latin and English that, as an anagram, may be rearranged to spell Ein feste Burg ist unser Gott. Elgar was fluent in English and German, and in his youth studied Latin in various Roman Catholic Schools in addition to attending Latin Mass in adulthood. The phonetic spelling of the name of Elgar's secret friend for Variation XIII is found in measure 1 – gsus for 'Jesus'. The second measure produces grts, a phonetic spelling for the Latin word for thanks, gratias. The combination of the plain text results for measures 1 and 2 of the Enigma cipher is gsus grts (Jesus gratias), the Latin phrase "Thanks be to Jesus."

Richter’s Gift: Longfellow’s Hyperion

Elgar was deeply grateful to the German conductor Hans Richter for conducting the premiere of the ‘Enigma’ Variations in June 1899. As a token of his gratitude, he presented Richter with a copy of Longfellow’s Hyperion. In a letter accompanying the gift, Elgar wrote, “I send you the little book about which we conversed & from which I, as a child, received my first idea of the great German nations.” Little did Richter realize that the identity of the unstated Principal Theme to the Enigma Variations is quoted within its pages. When Elgar gave Richter Hyperion, he literally gave away the answer. No wonder Elgar feared the answer would soon be discovered.

Elgar's Fragmentary Message

There are four Mendelssohn fragments in Variation XIII, each four notes in length. Twelve notes from three of the fragments in enclosed in quotation marks. In contrast, the remaining four are not in quotations because they, unlike the original source melody, are in the minor mode. 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 only an accompaniment figure recapitulating the rhythmic palindrome from the Enigma Theme. Other than this brooding accompaniment figure, there appears to be absolutely no connection to the original Enigma Theme.

Why would Elgar insert an unrelated musical fragment into not just any variation, but the one with a hidden dedicatee? There is a hidden friend, a hidden theme, and in Variation XIII a hidden message. I reasoned Elgar inserted these four Mendelssohn fragments to serve as a cryptogram that, when properly understood, would help unravel the mystery of the hidden Principal theme.

The quotation marks around three of the four fragments imply that Mendelssohn “quotes” the same source melody in one of his own works. Elgar quotes Mendelssohn to hint at the fact Mendelssohn quotes the covert Principal Theme. Since the Enigma Variations were composed for symphony orchestra, the implication is one of Mendelssohn’s symphonic works quotes the identical missing Principal theme. The twelve notes in quotation marks suggest the number of letters in the theme’s title. The four fragments hint at the number of the movement from Mendelssohn’s symphonic work that states the mystery melody.

Is there a work by Mendelssohn that could conceivably account for each and every one of these clues? The answer is affirmative. The fourth movement of the Reformation Symphony begins with a quotation of Ein feste Burg by the flute, proceeds through a series of variations, and concludes with a rousing, augmented version of the hymn. The parallels are truly striking: Four fragments, a fourth movement consisting of variations, three fragments in quotations, the covert theme's three word title, twelve notes in quotations, and twelve letters in the covert theme's three word title. With these melodic fragments prominently featured in Variation XIII, Elgar covertly suggests the hidden theme's title is in German, three words in length with twelve letters, and is quoted by Mendelssohn. Only one famous melody satisfies these three criteria: Ein feste Burg.

F-A-E and the initials for A Mighty Fortress

In Variation XIII Elgar uses a musical cryptogram to spell the initials for Joseph Joachim’s romantic motto Frei aber einsam . The German motto portrayed by the initials F.A.E. means "Free but lonely", a meaning that dovetails precisely with Elgar's comments about the Enigma Theme capturing his "sense of the loneliness of the artist." This motto forms the basis of a musical cryptogram made famous in a work for violin, the F-A-E Sonata. Elgar was a concert violinist who had aspirations of becoming a famous soloist like Joachim, but his hopes were dashed due to a lack of instruction during his formative years. Elgar continued to identify closely with the violin, and even composed a concerto for the instrument. As I explain here, Elgar achieves this cryptographic sleight of hand by his choice of keys for the Mendelssohn fragments: F minor, A flat major and E flat major. Variation XIII is the only movement lacking any initials or name that can be linked to one of the composer's friends. In place of the initials Elgar placed three mysterious asterisks (***). Based on my original discovery of the F.A.E. cipher in Variation XIII, the initials for this romanticized motto fill in those missing letters. More importantly, they pinpoint the identity of the unstated Principal Theme: A Mighty Fortress. How? By means of Elgar's favorite pastime, cryptography.

More Clues: Elgar's Wordplay

There are stunning examples of Elgar's highly refined sense of wordplay sprinkled throughout the Variations that allude to the covert theme's title. The six-letter word Enigma is a fascinating choice as the first three letters are an anagram for ein (the first word of the covert theme's German title), and the last is its English translation (a). The handwriting is not Elgar's, for he directed his German friend August Jaeger to pencil in 'Enigma' on the original score. In so doing Elgar subtly reinforced a sense of that title's German origin.

A second example of Elgar's wordplay is the odd six-letter nickname given to Jaeger for Variation IX: Nimrod. Elgar informed Jaeger of this nickname in a letter dated October 24, 1898, just three days after beginning work on the Variations. The book of Genesis describes Nimrod as "a mighty hunter before the Lord." This six-word description contains to sequentially matched words with the covert theme's title (A Mighty Fortress is our God) with the last two words being interchangeable (Lord and God). In the Old Testament Nimrod was known as a builder of great fortified cities – fortresses. His reputation for designing and building fortresses is so well established that a famous medieval castle on the northern slope of the Golan Heights is known today as Nimrod’s Fortress. By combining two well known descriptions of Nimrod as "a mighty hunter" and fortress builder, it is relatively easy to derive the title A Mighty Fortress. No wonder Elgar thought the hidden theme would quickly be discovered following the premiere of the Enigma Variations in 1899.

Yet another example of Elgar's wordplay is the capital L he assigned to the earliest sketch of Variation XIII. This letter alludes to the last name of the covert theme's German composer – Luther. The movement quotes a concert overture by Mendelssohn, a German composer, inspired by the poetry of Goethe, a German poet. Like Mendelssohn and Goethe, Luther was German and a highly respected composer of both music and prose. By substituting the letter L for G in Goethe, the result is a phonetic spelling for Luther (Loethe). This approach is suggested by the well established fact Mendelssohn was a deeply religious Lutheran. In Variation XIII Elgar quotes the music of a well known Lutheran, just one step removed symbolically from quoting the music of Luther himself. The original language for the title of Mendelssohn's concert overture is in German, just as the original poetry by Goethe It is equally revealing Elgar used the German spelling of his name for Variation XIV. The initials E.D.U. are derived from the German spelling of Edward – Eduard. The Teutonic spirit of these references is difficult to overlook, and serve as a critical clue regarding the distinctly German character of the covert theme and its composer.

Enigma and the initials for A Mighty Fortress is our God

It is remarkable four letters from enigma have corresponding initials from the covert Principal Theme's title – A Mighty Fortress is our God. These four matching letters are clustered together in the word enigma. Although the remaining two letters from enigma (e and n) do not match the remaining two initials from the title (f and o), it is profoundly coincidental both immediately precede the correct letter within the alphabetical sequence. Put another way, e comes before f, and n before o.

The four matching letters (a,i, m and g) may be reshuffled to spell gaim, the phonetic equivalent of game. When the remaining two letters from enigma (e and n) are added to gaim, it forms engaim, a phonetic version of endgame. In Elgar's era the term endgame was commonly used to describe the concluding sequence of moves in a game of chess. This association with chess is a critical insight because a chessboard is indistinguishable from a checkerboard, and Elgar employs a checkerboard cipher to encrypt his 'dark saying.' A Polybius square is also known as a Polybius checkerboard, and Elgar's music box cipher is a variant of the Polybius square. Around the year 1927 Elgar encoded the 14-letter phrase A-V-E-R-Y-O-L-D-C-Y-P-H-E-R in one of his exercise books using symbols originally devised in 1897 for his Dorabella Cipher. The number 14 is tantalizing as there are 14 numbered variations in the Enigma Variations. The Polybius square is an ancient cipher studied closely by Elgar in an 1896 issue of The Pall Mall Gazette that he retained in his personal library and is now in the possession of the Elgar Birthplace Museum. In his first biography published in 1905, Elgar bragged about solving this allegedly unbreakable cipher, and painted his solution on the side of a wooden box.

Enigma Day: A Mighty Coincidence

On October 21, 1898 – the day he first played the Enigma Theme for his wife on the piano – Elgar wrote the following about his plans for a ‘Gordon’ Symphony:

’Gordon’ simmereth mighty pleasantly in my (brain) pan & will no doubt boil over one day.

Elgar's use of the word mighty on 'Enigma' day is remarkable when one realizes the covert theme to the Enigma Variations is A Mighty Fortress. Was the appearance of the word mighty in Elgar's correspondence on that pivotal day due to mere coincidence and nothing more? Or was it something else – a revealing slip of the pen? The evidence overwhelmingly favors the latter conclusion over the former. One coincidence is possible, two are highly unlikely, and three or more shatter the bonds of chance to announce something premeditated, intentional, and planned. In light of the overwhelming evidence, there can be no doubt Ein feste Burg is the unstated Principal Theme to Elgar's 'Enigma' Variations. The evidence literally sings for itself. Q.E.D.

Soli Yah Gloria

1. London British Library Add. MS 58003, f.2v.

2. Buckley, Robert J. Sir Edward Elgar (1905). New York: Kessinger Publishing, Llc, 2009, p. 41.