Sunday, August 9, 2020

Decoding Elgar's Descending Sevenths Enigma Cipher

Then Peter came up and said to him, “Lord, how often will my brother sin against me, and I forgive him? As many as seven times?” Jesus said to him, “I do not say to you seven times, but seventy-seven times.”

The British romantic composer Edward Elgar supplied brief explanatory notes in 1927 for a set of pianola rolls of the Enigma Variations produced by the Aeolian Company. These were eventually published in 1946 by Novello under the title My Friends Pictured Within. In his remarks about the Enigma Theme, Elgar draws unusual attention to its descending melodic sevenths. He states, “The drop of a seventh in the Theme (bars 3 and 4) should be observed.” This proviso compelled Julian Rushton to reason that the correct melodic solution to the Enigma Variations “...should take into account the characteristic falling sevenths in bars 3-4.” The absence of any cogent explanation for why those particular melodic intervals “should be observed” presents an enigma.

Could the two descending sevenths furnish clues about the absent Principal Theme or the secret friend portrayed in Variation XIII? Elgar’s characterization of these melodic sevenths with the term “drop” is revealing because one definition of that term is “a place or central depository to which something (such as mail, money, or stolen property) is brought for distribution or transmission.” Elgar’s carefully parsed language intimates that the descending sevenths are an information drop in the guise of a cipher. Those who reflexively reject this interpretation need to be reminded that Elgar’s obsession with cryptography merits an entire chapter in Craig P. Bauer’s treatise Unsolved! Elgar was an accomplished cryptographer with a record of constructing impenetrable coded messages like the Dorabella Cipher. Although Elgar’s expertise in cryptography is undisputed, evidence for his forays into music cryptography is practically nonexistent in mainstream music journals.
In consideration of Elgar’s enigmatic remark about the descending sevenths, an analysis was launched to detect and decrypt prospective music ciphers. The two descending sevenths in bars 3-4 use four notes (G-A-F-G) that consist of three discrete letters (A, F, and G). The figures three and four match the bar numbers 3-4 that contain those melodic sevenths. Previous research found that throughout the Enigma Variations, Elgar enciphers the three-letter initials (E. F. B.) for the covert Theme, Ein feste Burg. The three discrete note letters in the melodic sevenths present a conspicuous parallel with the three initials for the hidden melody. It is plausible that Elgar encoded the initials for the hidden melody by transposing the unique note letters of the melodic sevenths.
What type of cipher could have Elgar deployed with his conspicuous descending sevenths? One of the most basic forms of encryption that would lend itself easily to a musical context is a Caesar cipher. It works by shifting a plaintext letter by a fixed number of places in the alphabet. For instance, a shift right by 3 would replace the letter A with D. Alternatively, a shift left by 3 would replace D with A. The complexity of this cipher may be further enhanced by alternating the direction of the shift from left to right for alternating plaintext letters. For example, a bidirectional Caesar cipher would apply a fixed shift to the right for the first letter, left for the second, right for the third, and so on.
The equivalent of a Caesar shift in music would be transposition by a certain interval. Elgar described the distance between the notes in bars 3 and 4 as a seventh. The first melodic seventh is formed by a G dropping to A. The musical alphabet is limited to the first seven letters from A to G. This means that the musical interval of a seventh (A B C D E F G) would be the equivalent of a Caesar shift of 6. The explanation for this divergence is that a musical interval begins the count on the starting note, whereas the Caesar shift begins by counting the first letter to the right or left of the plaintext letter.
If Elgar utilized an interval transposition cipher, what interval would be prescribed as the fixed degree of the shift? The most obvious answer is the seventh due to Elgar’s association of the term “drop” with “seventh.” The next issue concerns the direction of the intervallic shift. Should the unique notes from the descending sevenths be shifted right (rising) or left (falling)? Restricting the shift to just one direction would be too simplistic for an expert cryptographer like Elgar. My analysis determined that he shifts the course of the intervallic shift from right to left based on the direction of the melodic interval that precedes each note in the melodic sevenths.
The decryption of Elgar’s Displaced Falling Sevenths Cipher unfolds in the following way. The first melodic seventh begins on G, a note preceded by a rising perfect fourth from D. This rising interval before G calls for a decryption of a seventh above that first note. The interval of a seventh above G is F. The second discrete note of the descending melodic seventh is A. The fall in the preceding interval demands the seventh below A which is B. The third distinct note in the melodic sevenths is F which is preceded by a rising minor sixth from A. This requires an interval shift of a seventh above F which is E. The plaintext solution FBE is an anagram of the initials (E.F.B.) for the covert Theme, Ein feste Burg. The initial for the first word in the title appears last in this decryption. This element will come into play later with the contrapuntal mapping of the covert Theme “through and over” the complete Enigma Theme.

The area of the score where the descending sevenths encode the initials (E.F.B.) for the covert Theme also employs the notes E-flat, B, and F. The cellos play E-flat on the third beat of bar 3 that coincides with the first note of the first descending seventh. For beats 1 and 2 of bar 4, the second violins play an F in conjunction with a B performed by the cellos. On the second quarter beat of bar 4, the first violins play F, the first note of the second descending seventh. As the first violins play the second note of the second descending seventh, the second violins play another E-flat. Two E-flats bookend the descending sevenths with the first performed by the cellos on the third bar of bar 3 and the second by the second violins on the third beat of bar 4. These two E-flats are a coded version of Elgar’s initials and make the beginning and end of the Displaced Falling Sevenths Cipher that encodes another set of initials for the covert Theme.

There is an added layer of encryption to Elgar’s Displaced Falling Sevenths Cipher. The melodic intervals that precede the two descending sevenths are a rising perfect fourth and a rising minor sixth. These intervals encode the numbers 4 and 6. When paired together, these two preparatory intervals are a coded version of the number 46. That is remarkable as the title of Ein feste Burg originates from the first line of Psalm 46. The word “psalm” is encoded in the first bar of the Enigma Theme where the performance directions are an acrostic anagram of “EE’s Psalm.”
There is another way to quantify the notes of the descending melodic sevenths in bars 3 and 4. The quarter note beats in bars 1-4 of the Enigma Theme may be numbered from 1 through 16.

The first note of the descending seventh begins on the 11th quarter beat of the Enigma Theme. That number is significant as there are precisely eleven unique letters in the complete six-word title of the covert Theme. The second note of the first descending seventh is positioned on the 12th quarter beat. The next melodic seventh in bar 4 starts on the 14th quarter beat and finishes on the 15th quarter beat.
The quarter beat note positions of the sevenths may be converted into plaintext using a simple number-to-letter key (A = 1, B = 2, C = 3, etc…). Counting forwards or to the right in the alphabet transforms the numbers 11, 12, 14, and 15 to the letters K, L, N, and O. These letters are an anagram of KNOL, a phonetic spelling of Noel. The definitions of “Noel” are “a Christmas carol” and “Christmas.” These definitions hint at the identity of the secret friend portrayed in Variation XIII, Jesus Christ. A phonetic reading of the letters KNOL as “Noel” is supported by Elgar’s use of phonetic spellings in his personal correspondence. A sampling of these atypical spellings are listed below:
  1. Bizziness (business)
  2. çkor (score)
  3. cszquōrrr (score)
  4. fagotten (forgotten)
  5. FAX (facts)
  6. frazes (phrases)
  7. gorjus (gorgeous)
  8. phatten (fatten)
  9. skorh (score)
  10. SSCZOWOUGHOHR (score)
  11. Xmas (Christmas)
  12. Xqqqq (Excuse)
  13. Xti (Christi)

Elgar composed A Christmas Greeting Op. 52 in 1907 with the lyrics provided by his wife, Alice. The word “Nöel” appears twice in its final stanza. An alternative reading of KNOL is “Know El.” The Hebrew word for God is El. Jesus taught his disciples that those who know him know God (See John 14:7-9). This decryption of KNOL as the phrase “Know El” also hints at the secret friend of the Variations. Elgar identified the earliest sketch of Variation XIII with a solitary capital L. Recognizing that letter’s phonetic equivalence to the Hebrew word for God is revelatory. The number 77 is linked to Jesus in a variety of ways. The Gospel of Luke catalogues 77 generations in the genealogy of Jesus. When Jesus was asked by a disciple if he should forgive someone seven times, Jesus responded that he should forgive 77 times.
Just as a Caesar cipher may shift letters to the left or right of the alphabet, it is equally feasible to apply a number-to-letter key in reverse by counting backward in the alphabet (Z = 1, Y = 2, X = 3, etc…). The application of this inverted key to the numbers 11, 12, 14, and 15 yields the plaintext P, O, M. and L. The letters POML are a phonetic rendering of pummel, a verb that means “to strike repeatedly with the firsts.”  Following his arrest in the middle of the night, Jesus was beaten and punched by his captors (See Mark 14:65  and Luke 22:63).
The letters POML are an anagram of POLM, an alternative spelling of Palm.  Like Nöel, palm also appears in the lyrics of A Christmas Greeting. There is a distinct connection between the word “palm” and Jesus because his triumphal entry into Jerusalem the week before his crucifixion took place on Palm Sunday. As Jesus entered the city riding on a donkey’s colt in fulfillment of a prophecy from Zechariah 9:9, the people rejoiced as they waved palm branches and sang an excerpt from Psalm 118. That is remarkable as the title of the covert Theme comes from a different Psalm. This cryptogram is known as the Falling Sevenths Quarter Beats Cipher.

 Scrutinizing the two descending sevenths in bars 3 and 4 of the Enigma Theme has already netted two cryptograms: The Displaced Falling Sevenths Cipher and the Falling Sevenths Quarter Beats Cipher. These cryptograms encode a discrete set of interlocking answers regarding the covert Theme and secret friend. Further study of the two descending sevenths uncovered other fascinating elements. The sum of the bar numbers (3+4) with these melodic sevenths is itself seven. Two melodic sevenths suggest the sum of two sevens, or fourteen. This figure is tied to the Enigma Variations because there are fourteen variations assigned the Roman numerals I through XIV. These discernable mathematical patterns imply that these two sevenths somehow quantify the relationship between the covert Theme and the Enigma Theme.
The first minor seventh is formed by a G falling to A. The second minor seventh consists of an F descending to G. These two falling sevenths share a common pitch (G) separated by an octave. The descending sevenths form an integral part of the Enigma Theme, and it has been shown how they encipher the initials for the hidden melody. When considered in this context, the shared pitch between the two descending sevenths suggests that there are shared notes between the hidden melody and the Enigma Theme. The pairing of two sevenths intimates the number 77, implying that there are this many shared notes between the Enigma Theme and the hidden melody.
When constructing a counterpoint to another melody, some notes between the two will inevitably overlap to form conjunctions. This phenomenon is illustrated by Elgar’s sketch of the “lover’s theme” for his overture Cockaigne. The “lover’s theme” is a counterpoint to another famous tune, Mendelssohn’s “Wedding March.” This is not an isolated example of Elgar devising a counterpoint to a popular melody. Some overlapping notes are present between Elgar’s sketch and Mendelssohn’s original tune or Elgar’s slightly modified version.  In all, there are five melodic note conjunctions shown by diamond-shaped noteheads, and three harmonic note conjunctions indicated by triangular-shaped noteheads. These eight shared notes are present in three out of four bars, or 75 percent of the sketch.

Tim Smith of The Baltimore Sun was the first journalist to report on my original research in March 2009. My melodic solution to the Enigma Variations was first mentioned in a respected  music journal in July 2009 by Dr. Clive McClelland on page 50 of The Elgar Society Journal. This was only five months after I published my preliminary results on Google Blogger. By the Fall of 2009, Dr. Clive McClelland dared me to put my theory to the test by mapping Ein feste Burg over any of the Variations besides the Enigma Theme. I readily accepted his challenge and soon traced the course of Ein feste Burg through and over Variation IX (Nimrod). The process proved far easier than I anticipated. Even the composer Martin Barnaby recently acknowledged the efficacy of this contrapuntal mapping of Ein feste Burg over Nimrod. No other alleged solution has ever been mapped successfully above any complete movement of the Variations. Consequently, my mapping of Ein feste Burg over Nimrod is unprecedented.
Determining how Ein feste Burg plays over the Enigma Theme proved to be a far more daunting task. A major hurdle was identifying the full extent of the Enigma Theme. There are competing schools of thought regarding the Enigma Theme’s actual length with some advocating six measures, and others seventeen bars. It was not until 2015 that I eventually realized that the Enigma Theme encompasses nineteen measures. This is established by Elgar’s explanatory notes for the pianola rolls that plainly state, “There is no break between the theme and this movement.” The first iteration of the Enigma Theme is not introduced until bar 20. The plain implication of this statement is that the Enigma Theme must cover the opening nineteen bars. The two-bar bridge in measures 18 and 19 does not belong to Variation I (something deceptively implied by the layout of the score), but rather represents an elaboration of the Enigma Theme’s final cadence.
The ties connecting the notes of measures 17 to 18 link the Enigma Theme to the bridge passage in a way not found with the first variation. The bridge passage in bars 18-19 unwinds the Picardy cadence, returning it back to the minor mode in preparation for the first variation from which it is separated by a conspicuous double bar. At first glance, measure 17 only appears to mark the end of the Enigma Theme. Elgar’s published statement makes clear that this is a faux ending. The correct melodic mapping of the covert Theme must account not only 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 precedes the launch of Variation I. The complete layout of the Enigma Theme is ABA’C form.

My preliminary attempts to map different versions of Luther’s hymn focused exclusively on the opening seventeen measures of the Enigma Theme and generated some abrasive dissonances. For example, my mapping of Bach’s version of Ein feste Burg over the Enigma Theme yields some “howling dissonances” and ignores the bridge section in bars 18-19. While seemingly unproductive, these early efforts determined through a process of trial and error that Elgar must have constructed his counterpoint in a less predictable manner.
The Displaced Falling Sevenths Cipher encodes the initials of the hidden melody out of order with the first initial appearing last in the sequence. A similar reversal exists with the notes of the first descending seventh with a G falling to A. This is the case as G is the last letter in the musical alphabet, and A is its first. This ordering suggests that the correct contrapuntal mapping of the covert Theme must begin with its end and conclude with its beginning. In layman's terms, this entails mapping the ending phrase of Ein feste Burg over the beginning of the Enigma Theme, and its opening phrase above the Enigma Theme's ending in bars 18-19. Such a counterintuitive approach would deserve the title “Enigma.”
Elgar's citation from the last stanza of Longfellow's Elegiac Verse at the end of the completed Master Score emphasizes the importance of the ending over the beginning. Longfellow's words ring true regarding Elgar's unexpected counterpoint, "Great is the art of the beginning, but greater is the art of ending." The ending would be more decisive than the beginning if Elgar began his counterpoint using the concluding phrase of the hidden melody. Mapping the ending of the covert Theme above the beginning of the Enigma Theme literally places the ending over the beginning. There is evidence from other areas of the score that support this hypothesis. At Rehearsal 68, the Enigma Theme’s opening phrase overlays a counter melody constructed entirely of fragments from Ein feste Burg’s concluding phrase. This contrapuntal smoking gun known as the Rehearsal 68 Cipher combines the absent Theme’s ending with the Enigma Theme’s beginning.

There is another basis for believing that Elgar engineered his counterpoint in reverse by pairing the last phrase of the hidden melody with the opening phrase of the Enigma Theme. As previously noted, the Enigma Theme is constructed in ABA’C form. The letters ABAC are a phonetic spelling of “aback,” a term that means “backward” and “by surprise.” This reading is consistent with Elgar’s proclivity for phonetic spellings and wordplay. What could be more surprising than to start his counterpoint at the beginning of the Enigma Theme with the ending phrase of Ein feste Burg? This inkling is bolstered by the Mendelssohn fragments in Variation XIII that encipher the initials for Ein feste Burg in reverse order.
A counterintuitive mapping is not beyond the realm of possibility, for if it were that simple then it would not be what the title describes as an enigma. The word enigma means something difficult to understand or explain. In the 1899 program note, Elgar advised that the solution must remain unguessed, a qualification inconsistent with a straightforward mapping that could conceivably be guessed. No one would ever guess that a Roman Catholic like Elgar would surreptitiously cite the battle hymn of the Reformation, a work composed by a renegade priest excommunicated by the pope. Likewise, Elgar’s counterpoint must be unexpected and beyond the grasp of sheer conjecture.
The standard phrase structure of Ein feste Burg without repeating the first two phrases is ABCDEFB. It is feasible to superimpose its ending Phrase B over the Enigma Theme’s beginning with the remaining phrases CDEFB mapped in order and the beginning Phrase A played above the Enigma Theme’s ending in bars 18-19. The unconventional phrase structure of Ein feste Burg in this mapping is BCDEFB’A with the starting phrase shifted to the end. This mapping is made possible by applying free rhythm, an approach advocated by Dr. Clive McClelland who reasons, “Most of the solvers make the false assumption that the hidden melody fits in real time with Elgar’s theme; but…a precise metrical alignment with a well-known tune is unlikely.” Like the alternating minor and major modes, free rhythm serves to obscure the meter and structure of the covert melody. An early form of this contrapuntal mapping was attempted seven years ago in 2013. A revised version with slight adjustments to the mapping is exhibited below. 

There are 26 shared melody notes shown by diamond-shaped note heads. These melodic note conjunctions are present in 16 out of a total of 19 measures, or 84 percent of the movement for an average of 1.37 per bar. Measures 6, 11, and 17 have no shared melody notes between Ein feste Burg and the Enigma Theme. Measure 8 has the highest number with 3 melodic conjunctions. There are 51 shared harmony notes shown by triangular shaped note heads. These harmonic note conjunctions are present in 18 out of  19 measures with an average of 2.68 notes per bar. Only measure 19 has no shared notes between Ein feste Burg and the Enigma Theme’s harmonic structure. In all, this contrapuntal mapping has exactly 77 shared notes between Ein feste Burg and the Enigma Theme’s score.  This figure is consistent with the hypothesis that the falling sevenths encode that number as the sum of shared notes between the hidden melody and the Enigma Theme. 

Elgar deliberately concealed the covert Theme by aligning the bulk of its melody notes with the accompaniment rather than the melodic line of the Enigma Theme. Consistent with the objective, the majority of the note conjunctions occur between the covert Theme and the Enigma Theme’s harmonic structure. The Enigma Theme consists of 88 notes, and only 26 intersect with Ein feste Burg. That represents just under 30 percent of the Enigma Theme’s melody. It was previously theorized that Elgar emphasized the importance of the two descending sevenths with one note in common to imply that there are 77 shared notes between the covert Theme and the Enigma Theme’s score.  My contrapuntal mapping of Ein feste Burg over the Enigma Theme generates exactly 77 note conjunctions dispersed over every measure of the Enigma Theme with an overall average of 4.05 shared notes per bar. The odds of finding precisely 77 note conjunctions is far too remote to be casually attributed to chance.
It is feasible to trace a second contrapuntal mapping of Ein feste Burg above the Enigma Theme. Rather than mapping the missing melody forwards in the ordinary manner as everyone would naturally expect, it is conceivable Elgar took the opposite tact by crafting his counterpoint with the absent Theme played in reverse.  Such a technique is known as a retrograde counterpoint. On an early sketch of the Enigma Theme he wrote “for fuga” above the first measure, an unmistakable indication he was contemplating several fugal possibilities. According to Kent Kennan, Professor Emeritus of Music at the University of Texas at Austin, retrograde motion is rarely encountered in fugal writing. In the April 2013 issue of The Elgar Society Journal, Martin Gough theorized Elgar may have “…disguised the melody, perhaps by putting it in retrograde or contrary motion, thus preventing easy recognition…” Given the relative rarity of retrograde counterpoint, mapping the hidden melody in reverse would be a clever tactic to foil detection and discovery. That no one has ever attempted to map a candidate theme in retrograde over the Enigma Theme only reinforces this suspicion.
Certain features of the Enigma Theme hint at a retrograde counterpoint. First, the opening six notes of the cello line are the last six notes of Ein feste Burg in reverse order. Second, the Enigma Theme’s ABA’C structure is a phonetic spelling of aback. That term was originally used to describe when a ship’s sails are blown backward into the mast. In modern usage, it refers to being taken by surprise. Both of these definitions – “backward” and “surprised” – would exquisitely express a retrograde counterpoint over the Enigma Theme. Finally, the odd title denotes something difficult to understand or explain. A retrograde counterpoint is like an enigma because when played in reverse, the melody is obscured and not easily recognizable. In multiple ways, the Enigma Theme alludes to an unexpected contrapuntal mapping in which the absent Theme’s beginning goes at the end, and its end at the beginning.
It is feasible to play Ein feste Burg in retrograde “through and over” the Enigma Theme starting from bar 19 and working in the correct phrase order in reverse backward to bar 1. Ein feste Burg’s phrase structure in reverse order without the usual repetition of the A and B phrases is BFEDCBA. The ending Phrase B appears at both the opening and final cadence of the Enigma Theme with the starting Phrase A played over the bridge section in bars 18-19.

This mapping mirrors the alternating minor and major modes employed by Elgar to camouflage the original key of the covert principal Theme. Remarkably, the accidentals for the alternating keys of G minor (B-flat and E-flat) and G major (F-sharp) encode the initials for Ein feste Burg. Some notes in the covert Theme were lengthened or shortened to facilitate this mapping. These are standard contrapuntal techniques known as augmentation and diminution. Musicologists who insist Elgar would never employ these tried and true methods in his counterpoints are demonstrably ignorant of his methods. For example, Elgar used both augmentation and transposition to insert the melody of God save the King as a counterpoint to the 5/4 waltz from Tchaikovsky’s Pathétique. Elgar deliberately altered the key and note values of his national anthem to accommodate another melody. Consequently, one may reasonably expect the same flexible approach towards his treatment of the covert Theme to the Enigma Variations.

A contrapuntal mapping Ein feste Burg in retrograde above the Enigma Theme generates 30 shared melody notes as indicated by diamond-shaped note heads. These melodic note conjunctions are found in 16 out of 19 measures which captures 84 percent of the movement for an average of 1.68 melodic conjunctions per bar. Only measures 4, 6, and 11 are bereft of melodic conjunctions. The first two bars without matching melody notes — 4 and 6  — are remarkable because the title of the covert Theme heralds from Psalm 46. The third and last bar without melodic conjunctions is measure 11, and that number is also significant as there are precisely eleven unique letters in the covert Theme’s complete title.
47 shared harmony notes are shown by triangular shaped note heads. These harmonic note conjunctions are present in all 19 measures with an average of 2.47 harmonic note conjunctions per bar. In all, there is a combined total of 77 note conjunctions dispersed over all of the Enigma Theme’s 19 measures with an average of 4.05 shared notes per bar. Amazingly, this is the same number of note conjunctions found between the Enigma Theme and Ein feste Burg with an BCDEFB’A phrase structure. Two different mappings of Ein feste Burg that begin with its ending phrase and conclude with its starting phrase “though and over” the Enigma Theme each generate 77 note conjunctions. This numeric convergence could be a coded homage to the 77 generations from Adam to Christ in Luke's genealogy, or the teaching of Jesus to forgive someone 77 times. 

This relatively even distribution of shared melody and harmony notes between Ein feste Burg and the Enigma Theme is prima facie evidence for a retrograde counterpoint with the source melody’s notes and phrase structure in sequence and intact. More importantly, this series of corresponding notes silence any objections based on too many lingering dissonances. If any dissonances are there, they are Elgar’s by design. To dismiss this mapping due to some dissonant intervals would require rejecting Elgar’s similar use of dissonance within the Enigma Theme.
This analysis has shown that it is possible to map Ein feste Burg both forward and backward above the Enigma Theme. Each approach begins by overlaying its ending phrase over the Enigma Theme’s beginning and concluding with its starting phrase above the Enigma Theme’s ending. It is feasible for these two contrapuntal mappings of Ein feste Burg to play concurrently “through and over” the Enigma Theme.

There are seven phrases in Ein feste Burg in these two contrapuntal mappings. The adjacent melodic sevenths in the Enigma Theme could be a coded reference to these two different contrapuntal phrase structures of the covert Theme in seven parts. The first mapping of Ein feste Burg with the modified phrase structure of BCDEFB’A results in 26 melodic conjunctions and 51 harmonic conjunctions with the Enigma Theme. The second mapping of Ein feste Burg in retrograde with the reverse phrase structure BFEDCB’A produces 30 melodic conjunctions and 47 harmonic conjunctions with the Enigma Theme. The difference between the melodic conjunctions in these two mappings is four  (30 - 26 = 4). This same difference is also found between the harmonic conjunctions (51 - 47 = 4). The numeric symmetry of these differences points to design.
There are exactly seven phrases in the forward (BCDEFB’A) and backward (BFEDCB’A) mappings of Ein feste Burg over the Enigma Theme. By drawing attention to the drop in the two sevenths the Enigma Theme, Elgar gave a coded allusion to these two sets of seven phrases from the hidden melody above the Enigma Theme. There are two versions of Section A in the Enigma Theme. Section A covers bars 1-6 and is repeated in a more elaborate form in bars 11-17 with a final cadence. There are two different descending sevenths, and there are two bars in the bridge section that begins at Rehearsal 2. These allusions to the number two suggest two different contrapuntal mappings of the hidden melody.
crab canon is a counterpoint in which two musical lines are played in retrograde to one another. It is the musical equivalent of a palindrome. The opening six phrases in both mappings of Ein feste Burg over the Enigma Theme are a palindrome (BCDEFB’ and BFEDCB’). Although these two contrapuntal mappings of Ein feste Burg over the Enigma Theme are not a strict crab canon, their nearly palindromic phrase structure does bear striking similarities to one. A second palindrome is formed by the seventh and final phrase of Ein feste Burg in these mappings is its opening phrase played simultaneously both forward and backward. The Mendelssohn fragments in Variation XIII portray a calm sea, and crabs are creatures of the ocean.

A palindrome is a word, phrase or sequence that may be read the same backward as forward. For this reason, a palindrome may be represented by the geometric figure of a circle. A rounded form of the mathematical constant Pi is encoded by the opening four scale degrees of the Enigma Theme (3-1-4-2) in bar 1 and 11. This number represents the ratio of a circle’s circumference to its diameter. The letters “pi” appear in the dedication to the Enigma Variations, “Dedicated to my friends pictured within.” These coded references to Pi were likely inserted to allude to a circular or crab canon phrase structure of the contrapuntal mapping of the covert melody above the Enigma Theme.
The phrase pattern of Ein feste Burg in the first mapping is BCDEFB’A. In the second retrograde mapping the phase structure is all but reversed as BFEDCB’A. The only commonalities are the positioning of phrases A and B. A comparison of these two phrase patterns reveals three matches and four divergences. The numbers three and four correspond to the bar numbers with the descending sevenths in the Enigma Theme.

The phrases that differ are remarkable because two spell ED, a shortened version of Edward. This is consistent with other cryptograms in the Enigma Variations that divulge the composer’s first name, last name, and initials. The initials for Variation XIV (E.D.U.) begin with ED.

Remarkably, these coded spellings of Elgar’s first name overlap with the initials of the covert Theme (E.F.B.) also embedded within these phrase patterns of Ein feste Burg. Like the dual counterpoints, the initials of the covert Theme are presented both forward and backward. 

Three phrases are exact matches with one another (BB, B’B’, and AA). Elgar refers to three sets of dual initials in connection with the Enigma Variations. For the original 1899 program note, he mentions the Belgian playwright Maurice Maeterlinck (MM). At the end of the original Finale, Elgar wrote a paraphrase of a passage from Jerusalem Delivered by the Italian poet Torquato Tasso (TT). As the composer of the Enigma Variations, Elgar’s own initials (EE) are two Es. The names of all three of these artists consist of dual initials. Three sets of matching phase letters mirrors this pattern in these two mappings of Ein feste Burg above the Enigma Theme.
Three dual initials associated with the Enigma Variations is also reflected by three matching pairs of numbers. The first is the Enigma Theme with 88 melody notes. There are 77 note conjunctions between the Enigma Theme’s short score and two different contrapuntal mappings of the covert melody. A comparison of these two mappings reveals a difference of 4 between their melodic conjunctions and 4 between their harmonic conjunctions. These repeated number patterns hint at a dual contrapuntal solution to the Enigma Theme similar to a crab canon. 
The Enigma Theme has a Polybius box cipher in its opening six bars that encodes Elgar’s “dark saying” first mentioned in the original 1899 program note. A Polybius box cipher uses fractionated text to encode a particular cell within a checkerboard grid that is assigned a plaintext letter. Elgar’s use of melody and bass note pairs to encipher his “dark saying”  alludes to a binary contrapuntal solution to the Enigma Theme. Just as the combination of two note letters encodes a third solution letter, and the merger of two counterpoints above the Enigma Theme generates a third solution. A binary  contrapuntal solution to the Enigma Theme has never been proposed or cogently addressed. In Ecclesiastes 4:12 is says that "a threefold chord is not easily broken." The same holds true for a three-part contrapuntal cipher.
A decade of concerted analysis of the Enigma Variations has netted over ninety cryptograms in diverse formats that encode a set of mutually consistent and complementary solutions. While this figure may seem incredible, it is entirely consistent with Elgar’s psychological profile. More importantly, their solutions provide definitive answers to the core questions posed by the Enigma Variations. What is the secret melody to which the Enigma Theme is a counterpoint and serves as the foundation of the ensuing movements? Answer: Ein feste Burg (A Mighty Fortress) by Martin Luther. What is Elgar’s “dark saying ensconced within the Enigma Theme? Answer: A musical Polybius box cipher embedded in the opening six bars. Who is the secret friend and inspiration behind Variation XIII? Answer: Jesus Christ, the Savior of Elgar’s Roman Catholic faith. To learn more concerning the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

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About Mr. Padgett

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Mr. Padgett studied violin with Michael Rosenker (a student of Leopold Auer), and Rosenker’s pupil, Owen Dunsford. Mr. Padgett studied piano with Sally Magee (a student of Emanuel Bay), and Blanca Uribe (a student of Rosina Lhévinne). He attended the Stevenson School in Pebble Beach, California, and Vassar College in Poughkeepsie, New York, where he graduated Phi Beta Kappa with a degree in psychology. At Vassar he studied music theory and composition with Richard Wilson. Mr. Padgett has performed for Joseph Silverstein, Van Cliburn, Arnold Schwarzenegger, Maria Shriver, Steve Jobs, Prince Charles, Lady Camilla, Marcia Davenport, William F. Buckley, Jr., and other prominent public figures. His original compositions have been performed by the Monterey Symphony, at the Bohemian Grove, the Bohemian Club, and other private and public venues. In 2008 Mr. Padgett won the Max Bragado-Darman Fanfare Competition with his entry "Fanfare for the Eagles." It was premiered by the Monterey Symphony under Maestro Bragado in May 2008. A member of the Elgar Society, Mr. Padgett is married with five children.