The Enigma Theme with "Ein feste Burg" in Retrograde

An endless staircase depicted by M. C. Escher

Amidst the worldly comings and goings, observe how endings become beginnings.

Lao-Tzu

A veritable phalanx of ciphers confirms the covert principal Theme to Edward Elgar’s Enigma Variations is Ein feste Burg (A Mighty Fortress) by Martin Luther. Precisely how that gallant melody plays “through and over” the Enigma Theme has been the subject of intense and prolonged deliberation. It was initially suspected that a precise horizontal fit between both themes would be sufficient to substantiate this discovery, yet the absence of a credible counterpoint raised legitimate doubts about that melodic mapping. An alternative approach made it possible to play Ein feste Burg over the Enigma Theme by applying free rhythm and varying its phrase order, producing a more credible vertical contrapuntal match. Even so, that mapping was greeted by some with skepticism. These and other questions fueled an ongoing reassessment, one that has now yielded an innovative charting of Ein feste Burg above the Enigma Theme by applying a rarely used contrapuntal device: retrograde motion. Before presenting this new contrapuntal mapping, it is advisable to consider how it was precipitated by two crucial breakthroughs.

The first key insight concerned just how far Elgar’s counterpoint actually extends. The conventional wisdom, as expressed by Dr. Clive McClelland, holds that the counterpoint goes no further than the first six measures of the Enigma Theme, or merely the A section of its ABA’ ternary structure. The difficulty with that conjecture is that it contradicts Elgar’s own published position regarding the Enigma Theme’s actual length. In the late 1920s, he provided descriptive notes for a set of pianola rolls published in 1929. Regarding Variation I, he wrote, “There is no break between the theme and this movement.”[1] That disclosure is critical because it confirms the Enigma Theme does not terminate until Variation I begins in measure 20, extending the analytical scope of any contrapuntal mapping to all 19 bars.

Based on his published statement, Elgar did not consider the two-bar Bridge in measures 18 and 19 to be part and parcel of Variation I (something deceptively implied by the layout of the published score), but rather an elaboration of the Enigma Theme’s ending. A conspicuous tie between the notes of measures 17 and 18 validates this observation, linking the Enigma Theme and bridge in a manner not found in Variation I. The bridge serves to unwind the Picardy cadence and return the harmony to the minor mode. Relying on Elgar’s published position, any credible melodic mapping of the covert principal Theme must not only account for the Enigma Theme’s ternary ABA’ structure in measures 1 through 17, but also the two-bar Bridge (section C) in measures 18 and 19 that precede the launch of Variation I. In recognition of this fact, all alleged melodic solutions that neglect any part of the first nineteen measures of the Enigma Theme’s ABA’C structure may be safely ruled out as invalid. This preclusion applies to the usual suspects as well as purported “solutions” featured in Wikipedia’s article on the Enigma Variations.

The second breakthrough was the recognition that at various points throughout the Enigma Variations, Elgar places a coded emphasis on the ending phrase of Ein feste Burg. For instance, at Cue 68 in the Finale, that ending phrase is stated as a counterpoint to the opening of the Enigma Theme. The first four notes of the ending phrase are stated in the countermelody of Cue 68, and the remaining six appear two bars later. These four and six-note fragments allude to “46,” the chapter from the Psalms that inspired Martin Luther to compose his most famous hymn.

The pairing of Ein feste Burg’s ending with the Enigma Theme’s beginning prompted a meticulous reassessment of the latter. On closer inspection, it was found that the first six notes of the bass line are the last six notes of the covert Theme's concluding phrase in reverse order.

This notable correspondence raises the very real prospect Elgar composed his counterpoint with the unstated principal Theme in retrograde. This would mean that rather than mapping out the missing melody forwards as everyone would naturally expect, Elgar adopted the opposite tactic by crafting his counterpoint with the absent theme played backward. The Enigma Theme’s ABA’C structure subtly hints at this prospect because when read phonetically, “ABAC” sounds like aback. That term was originally used to describe the moment when a ship’s sails are blown backward into the mast. In present usage, it refers to being taken by surprise. Both of those definitions — backward and surprised — exquisitely express Elgar’s mapping of the covert principal Theme in retrograde over the Enigma Theme, and are entirely consistent with his well-documented fondness for wordplay.

The structure of the Enigma Theme hints at the strategy Elgar deployed to foil straightforward attempts at decoding his counterpoint. According to Kent Kennan, Professor Emeritus of Music at the University of Texas at Austin, retrograde motion is rarely encountered in fugal writing.[2] That Elgar was openly contemplating various contrapuntal possibilities is reflected by the fact that on an early sketch of the Enigma Theme, he wrote the phrase “for fuga” above the first bar.[3] Fuga is Latin for fugue. Considering the relative infrequency of retrograde counterpoint, mapping the covert principal Theme in this manner would be an extraordinarily effective tactic to foil detection. The combination of retrograde motion and free rhythm presents a robust, multilayered strategy for concealing the principal Theme from straightforward detection.

After determining the scope of Elgar’s counterpoint and the potential of mapping the covert principal Theme from end to beginning, a new mapping of Ein feste Burg in retrograde over all nineteen measures of the Enigma Theme was completed. Starting at the end of the bridge (Measure 19), the covert principal Theme is played backward to the beginning with the reverse phrase order of BFEDCBA. The ending phrase (B) appears at both the opening and final cadence of the Enigma Theme while the opening phrase (A) is deftly inserted over the bridge. This mapping mirrors the minor and major modes employed by Elgar to camouflage the key of the hidden Theme. Listening to this mapping with the Enigma Theme played in reverse makes it easier to recognize this chimerical version of Ein feste Burg.

 
 

A systematic compilation of shared melody and harmony notes between Ein feste Burg and the Enigma Theme was conducted. Notes shared between both melodies are represented by diamond-shaped noteheads and classified as melodic conjunctions. Notes shared between the melody of Ein feste Burg and non-melodic or harmony notes in the Enigma Theme’s short score are represented by triangular-shaped noteheads and classified as harmonic conjunctions. Note conjunctions must sound simultaneously to qualify as a match.

 

This mapping yields 30 melodic conjunctions and 38 harmonic conjunctions dispersed across all 19 measures of the Enigma Theme. There is an average of 1.5 shared melody notes per measure, with the highest concentration of 7 in measure 14. On average, there are 2 shared harmony notes per measure between the hideden melody and non-melodic notes from the Enigma Theme’s short score, with the highest concentration of 5 found in both measures 13 and 15. The relatively regular distribution of shared melody and harmony notes across all 19 measures is prima facie evidence of a deliberate retrograde counterpoint.

The version of Ein feste Burg used in Elgar’s retrograde counterpoint is drawn from multiple sources. A side-by-side comparison of Luther’s original composition with iterations by Bach and Mendelssohn reveals that Elgar incorporated elements of all three to construct his hidden source melody. When combined with retrograde counterpoint, this “tribrid” theme was undoubtedly devised to complicate detection and decryption while paying homage to three paragons of the German School. The phrase-by-phrase sourcing is as follows:

• Phrase A (measures 17–19): sourced from Mendelssohn’s more austere version, characterized by rising and falling thirds — an attribute endemic to the A phrase of the Enigma Theme itself.
• Phrase B (measures 14–16): bears the melodic imprimatur of Luther’s original hymn.
• Phrase C (measures 12–14): matches both Bach's and Mendelssohn's versions, which are virtually indistinguishable from one another.
• Phrase D (measures 10–11): reflects Luther’s original as well as Mendelssohn's faithful replica.
• Phrase E (measures 9–10): based on Mendelssohn’s more florid adaptation.
• Phrase F (measures 6–8): corresponds with Bach’s rendering.
• Phrase B (measures 1–5): corresponds with Bach’s rendering.

 

The prevalence of Mendelssohn’s version of Ein feste Burg in the retrograde mapping makes it remarkably clear why Elgar would feature four fragments from a symphonic work by Mendelssohn in Variation XIII. Tellingly, four of the six phrases in the retrograde mapping are sourced from Mendelssohn’s rendering of Ein feste Burg. The number four is further significant because Mendelssohn quotes Ein feste Burg in the fourth movement of his Reformation Symphony, followed by a series of variations — a structural parallel to Elgar's own set of variations built upon a hidden statement of the same hymn. The Mendelssohn fragments in Variation XIII harbor an alphanumeric cipher that encodes the initials “EFB” in reverse order, an element that, in retrospect, cleverly alludes to Elgar’s retrograde treatment of the covert principal Theme.

It is intriguing that Elgar extracts and combines fragments from three versions of Ein feste Burg to create a unique fourth version — his own. With each version representing a distinctive musical dialect, this parallels Elgar’s deployment of four different languages in a Music Box Cipher embedded within the opening six measures of the Enigma Theme. That cipher is based on a cryptographic device originally known as a Polybius square — a form strongly hinted at by a literal square Elgar drew on the cover page of the score.

Cover page of the Autograph Score to the Enigma Variations

What makes that rather ordinary-looking square so extraordinary is that it overlays the very staff lines on the next page of the full score that introduce the Music Box Cipher. No other cover page from Elgar’s body of works bears this unique feature, rendering it all the more significant from a cryptographic standpoint. It should also be noted that the square on the cover page encloses the start and end dates of the orchestration in February, which Elgar abbreviates as “FEb.” Those three letters are an anagram of “EFB” — the initials of Ein feste Burg. Rather than marking the spot with an X, Elgar elected to do so symbolically with a square enclosing not one but two instances of the covert principal Theme's initials. The initials of Luther are furnished with equal cleverness by the L-shaped brackets enclosing the dates of orchestration.

The first page of the Enigma Theme from the Autograph Score

The cipher languages used in Elgar’s Music Box Cipher are English, Latin, German, and Aramaic. This is hardly a random assortment, for the first letters of each language encode the composer's last name: English, Latin, German, and Aramaic. Elgar signed his cipher, most appositely, in code. Three of these languages appear in Bach’s St. Matthew Passion. The work’s original Latin title — Passio Domini nostri J.C. secundum Evangelistam Matthæum (“The Passion of our Lord J[esus] C[hrist] according to the Evangelist Matthew”) — yields the initials JC, which are encoded by the Roman numerals of Variation XIII: “X” representing the tenth letter (J), and “III” the third (C). The libretto is in German, sourced from Martin Luther’s translation of the Bible. There is one celebrated exception: when Jesus cries out his last anguished yet unvanquished words from the cross, he quotes Psalm 22:1 in Aramaic — “Eli, Eli, lama sabachthani!” It is entirely plausible that Bach’s masterpiece informed and inspired Elgar’s selection of three of the four cipher languages, leaving only one — English — as a natural connection to his own linguistic and cultural heritage.

There is an indelible link between Bach and Mendelssohn forged at a momentous performance in 1829, when Mendelssohn conducted the St. Matthew Passion — a masterpiece that had not been performed publicly in over a century. This proved to be a watershed moment that resulted in a full-scale revival and reevaluation of Bach’s works throughout Germany and beyond, and a universal recognition of their genius and significance. Mendelssohn’s interest in Bach extended beyond the arts, for the two men shared a common faith. It was on March 21, 1816 — Bach’s birthday — that Mendelssohn was baptized as a Lutheran. The Mendelssohn fragments in Variation XIII, combined with a capital L used to identify that movement on an early sketch, serve as markers pointing to the famed composer of Ein feste Burg — Martin Luther. Through their shared faith, music, and language, there is an unmistakable bond between Martin Luther, Johann Sebastian Bach, and Felix Mendelssohn. In the Enigma Variations, Elgar pays homage — directly and indirectly — to all three progenitors of the German School.

At the conclusion of the extended Finale, Elgar quotes a passage by Henry Wadsworth Longfellow from his Elegiac Verse: “Great is the art of beginning, but greater the art is of ending.” That literary fragment affirms the supremacy of the ending over the beginning, a prinicple reasserted by the coded recognition that the ending phrase of Ein feste Burg marks the beginning rather than the end of Elgar’s counterpoint with the Enigma Theme via retrograde motion. The key to unraveling Elgar’s enigma is to begin at the end and work backward to the beginning. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed. Please help support and expand my original research by becoming a sponsor on Patreon.

Soli Yah Gloria

Footnotes

[1] Elgar, Edward. My Friends Pictured Within. The Subjects of the Enigma Variations as Portrayed in Contemporary Photographs and Elgar’s Manuscript (Sevenoaks: Novello, n.d. [1946], republication of notes for Aeolian Company’s piano rolls, 1929)

[2] Kennan, Ken. Counterpoint Based on Eighteenth-Century Practice (3rd ed.). Englewood Cliffs: Prentice-Hall, Inc., p. 222.

[3] Rushton, Julian. Elgar: Enigma Variations (Cambridge Music Handbooks). New York: Cambridge University Press, 1999, p. 54