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| Möbius Strip with music tape for a 15-note music box |
Amidst the worldly comings and goings, observe how endings become beginnings.
A veritable phalanx of ciphers authenticates Ein feste Burg (A Mighty Fortress) by Martin Luther as the covert principal Theme of Edward Elgar’s Enigma Variations. Precisely how that martial 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 mapped 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 a definitive mapping of Ein feste Burg above the Enigma Theme by applying a rarely used contrapuntal device: retrograde motion. Before presenting this contrapuntal solution, let us consider two crucial breakthroughs that precipitated that epiphany.
The first key insight concerns just how far Elgar’s counterpoint actually extends. The conventional wisdom, as expressed by Dr. Clive McClelland, holds the counterpoint goes no further than the first six measures of the Enigma Theme, Section A of its ABA’ ternary structure. The problem with that presumption is that it contradicts Elgar’s published position regarding the Enigma Theme’s actual length. In the late 1920s, he provided descriptive notes for a set of Aeolian Company pianola rolls issued in 1929. Regarding Variation I, he advised, “There is no break between the theme and this movement.” That disclosure is critical because it confirms that the Enigma Theme does not terminate until Variation I begins. As the first iteration of the Enigma Theme begins in bar 20, this must mean that the analytical scope of any contrapuntal mapping must cover bars 1–19.
Based on his published statement, Elgar did not consider the bridge in measures 18 and 19 to be part 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 seen with 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 proposed melodic solutions that neglect any part of Enigma Theme’s ABA’C structure may be safely ruled invalid. This preclusion applies to the usual suspects as well as a proliferation of attempted “solutions” featured in Wikipedia’s article on the Enigma Variations.
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| My Friends Pictured Within by Elgar: Variation I. (C. A. E.) |
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 that ending phrase appear at the beginning of the countermelody in the bass staff, and the remaining six emerge two bars later. This bifurcation of the ending phrase into four and six-note fragments alludes to “46,” the chapter from the Psalms that inspired Martin Luther to compose his most famous hymn. The four-note fragment also corresponds to the four-note melodic quotations in Variation XIII from Felix Mendelssohn’s concert overture Calm Sea and Prosperous Voyage (Meeresstille und glückliche Fahrt).
The pairing of the covert Theme’s ending phrase 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 Enigma Theme’s bass line state the last six notes of the covert Theme’s concluding phrase in reverse order.
This notable correspondence raises the very real prospect that 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 definitions — “backward” and “by surprise” — 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. That Elgar was openly contemplating various contrapuntal techniques is reflected by the fact that on an early sketch of the Enigma Theme, he wrote the phrase “for fuga” above the first bar. Fuga means fugue in Italian and Latin. Considering the relative scarcity of retrograde counterpoint, mapping the covert principal Theme in this manner would be an extraordinarily effective ploy to foil detection. The combination of retrograde motion and free rhythm presents a robust, multilayered strategy for concealing the principal Theme from straightforward detection.
At the conclusion of the extended Finale, Elgar cites 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 principle 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.
After determining the scope of Elgar’s counterpoint and the potential of mapping the hidden melody 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 (Bar 19), Ein feste Burg is played backward to the beginning with the reverse phrase order of BFEDCBA. It is intriguing that the opening three phrases spell “BFE,” a mirror of “EFB,” the acronym of Ein feste Burg. 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 obfuscate the key of the hidden Theme. An audiovisual demonstration of this contrapuntal mapping supports the efficacy of this solution.
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 assemble 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.
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 harmony notes in the Enigma Theme's short score are represented by triangular noteheads and classified as harmonic conjunctions. Both melodic and harmonic conjunctions must sound simultaneously to qualify as a match.
The retrograde mapping documents 29 shared melody notes between Ein feste Burg and the Enigma Theme. Melodic conjunctions are present in bars 1-3, 5, 7-10, 12-16, 18 and 19, for a total of 15 out of 19 measures or nearly 80% of the movement. There are seven note types with frequencies ranging from 2 to 8, the tonic G and dominant D being the most prevalent.
There are 45 harmonic conjunctions between Ein feste Burg and the short score of Enigma Theme for an average of 2.4 per measure. Ten shared note types have frequencies ranging from 1 to 13, the dominant D being the most common. The combined total of melodic and harmonic conjunctions is 74, covering 40 out of a total of 50 melody notes from Ein feste Burg. Remarkably, the total number of melody notes in the Enigma Theme across all 19 bars is 88 — precisely the number of keys on a standard piano keyboard. Furthermore, 80% of the melody notes from the covert Theme are embedded sequentially into the melody and harmony of the Enigma Theme.
The preponderance of the evidence outlined in the above Figures and Tables demonstrates that the Enigma Theme is a clear and convincing counterpoint to Ein feste Burg in retrograde. The contrapuntal mapping documented in Figure 6 reveals a relationship of remarkable depth and consistency. Twenty-nine melodic conjunctions confirm that the melody of Ein feste Burg in reverse aligns directly with the uppermost voice of the Enigma Theme across 15 of its 19 measures. Forty-five harmonic conjunctions establish that the covert theme is embedded still more pervasively in the inner voices and bass, with harmonic support present across every measure of the movement without exception. That harmonic conjunctions outnumber melodic conjunctions is entirely consistent with a deliberate strategy to obfuscate the principal Theme beneath the harmonic texture of the score, where it would resist detection by the casual listener and analyst alike. Together, these melodic and harmonic conjunctions account for 40 of the 50 melody notes of Ein feste Burg in retrograde — a sequential coverage rate of 80% that far exceeds what random coincidence or the casual application of free rhythm could plausibly produce.
Every bar containing a melodic conjunction is simultaneously reinforced by harmonic support, reflecting a compositional discipline consistent with deliberate design. The hidden source melody itself is a unique "tribrid" construction, assembled from complete phrases drawn from three distinct versions of Ein feste Burg — those of Luther, Bach, and Mendelssohn — fused into a single composite whole. Such a strategy is redolent of Ecclesiastes 4:12, “A cord of three strands is not quickly broken.” That Elgar wove together three strands from the German School into a single covert theme, then concealed it in retrograde within the very movement that introduces one of his most celebrated orchestral works, suggests the musical architecture carries profound personal and spiritual significance. In his original 1899 program note, Elgar advised that the solution to the Enigma Theme “must be left unguessed.” That carefully chosen phrase implies that the answer cannot be uncovered by random speculation or intuition alone, but only through systematic decryption. Like a fortress, a cipher secures and conceals. Of all the cryptograms embedded in the Enigma Variations, none is more audacious than the one hiding as a retrograde counterpoint at the threshold of the work itself.
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.


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