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Monday, October 25, 2021

Elgar’s German Sixth Enigma Ciphers

During railway journeys amuses himself with cryptograms; solved one by John Holt Schooling who defied the world to unravel his mystery.
Robert J. Buckley in his 1905 biography of Sir Edward Elgar

The British composer Edward Elgar relished phonetic spellings, wordplays, and anagrams. One notable illustration is the title “Craeg Lea” which he imparted to his Malvern home where his family resided between 1899 and 1904. That moniker is an anagram obtained from the reverse spelling of “Elgar” (Craeg Lea) mingled with the initials from the first names of his daughter Carice, himself, and his wife Alice (Craeg Lea). Elgar challenged Dora Penny to decipher the meaning of his home’s bemusing name. She caught on quickly as recounted in her memoir:
Edward called the place Craeg Lea and challenged me to guess how he had found the name. By some stroke of luck, I realized that the key lay in the unusual spelling of “Craeg” and immediately saw that the thing had been built up anagrammatically from (A)lice, (C)arice, (E)dward ELGAR. I think he was a little annoyed that this mystification had fallen flat.
Elgar’s enthusiasm for word games spilled over into his obsession with cryptography, the discipline of coding and decoding secret messages. His expertise in that esoteric art is amply documented by Craig P. Bauer in his treatise Unsolved! The bulk of its third chapter is devoted to Elgar’s brilliant decryption of an allegedly insoluble Nihilist cipher presented by John Holt Schooling in an April 1896 issue of The Pall Mall Magazine. A Nihilist cipher is a derivative of the Polybius square. Elgar was so delighted with his solution that he brags about it in his first biography published in 1905 by Robert J. Buckley. Elgar painted the solution in black paint on a wooden box, an appropriate medium as another name for the Polybius square is a box cipher.
Elgar’s methodical decryption of Schooling’s conundrum is summarized on a set of nine index cards. On the sixth card, Elgar relates the task of cracking the cipher to “...working (in the dark).” His use of the word “dark” as a synonym for a cipher is relevant to this investigation as this same adjective turns up later in the 1899 program note for the premiere of the Enigma Variations. It is an oft-cited passage that warrants revisiting as Elgar lays the groundwork for his melodic riddle:
The Enigma I will not explain – it’s ‘dark saying’ must be left unguessed, and I warn you that the connexion 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.
Elgar birthed the Enigma Variations in 1898-99. That extraordinary work elevated him from provincial obscurity to international acclaim, transforming his career from an itinerant music teacher to a celebrated composer. The original title appears on the autograph score as “Variations for orchestra composed by Edward Elgar Op. 36”. With the unconventional theme dubbed “Enigma,” the work is popularly referred to as the Enigma Variations. In the 1899 program note and other primary sources, Elgar explained the Theme is called “Enigma” because it is a counterpoint to a famous melody that is not heard but can play “through and over” the Variations. This secret tune is the cornerstone underlying the whole work, a subject that has provoked a prolonged debate about the correct solution.
Some contend there is no answer by insinuating Elgar concocted the notion of an absent principal Theme as an afterthought, practical joke, or marketing ploy. Others take Elgar at his word and accept the challenge that there is a famous melody lurking behind the Variations’ contrapuntal and modal facade. Regardless of what side is taken in the debate, mainstream scholars insist the answer can never be known with absolute certainty because Elgar allegedly took his secret to the grave in February 1934. They presume he never wrote down the solution for posterity to discover. This staid opinion glosses over or flagrantly ignores Elgar’s documented obsession with cryptography. That incontestable facet of Elgar’s personality raises the prospect that the solution is meticulously encoded within Enigma Variations’ orchestral score.
A decade of trawling that sublime symphonic masterpiece has netted over one hundred cryptograms in diverse forms that encode a set of mutually consistent and complementary solutions. Although that figure may seem extravagant, it is entirely consistent with Elgar’s lifelong fascination with ciphers. More significantly, the solutions give 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 melodic foundation for the ensuing movements? Answer: Ein feste Burg (A Mighty Fortress) by Martin Luther. What is the “dark saying” ensconced within the Enigma Theme? Answer: A musical Polybius box cipher embedded in its inaugural six bars cordoned off by an oddly placed double barline. Who is the secret friend and inspiration behind Variation XIII? Answer: Jesus Christ, the Savior of Elgar’s Roman Catholic faith. The cryptographic evidence supporting these discoveries is diverse yet mutually consistent, multivalent, and decisive. With such a vast trove of cryptograms, the Enigma Variations is Elgar’s musical homage to cryptography.

The German Sixth Enigma Ciphers

The discovery of scores of ciphers within the Enigma Variations score invites a sustained search for even more cryptograms. One intriguing aspect of that work is the appearance of an augmented sixth chord called the German sixth near the beginning and original ending. The first arises on the downbeat of bar 5 of the Enigma Theme and is performed by the second violins (G), violas (E-flat and B-flat), and cellos (C-sharp). The German sixth is a transparent clue that betrays key attributes of the covert Theme’s complete title for it consists of six German words: Ein feste Burg ist unser Gott.


The label “German sixth” was in common usage when Elgar composed the Enigma Variations in 1898-99 as documented by numerous sources predating that work. “German sixth” appears in William Crotche’s 1812 edition of Musical Composition published in London. The April 1, 1879 issue of The Musical Times gives a probing analysis of the German sixth. The English music theorist Ebenezer Prout invokes this standard terminology in his 1889 text Harmony: It’s Theory and Practice published in London. There is no doubt Elgar was intimately familiar with the German sixth chord when he birthed the Enigma Variations in 1898-99.
The initials for Ein feste Burg are embedded within the first German sixth chord in bar 5 of the Enigma Theme. The E-flat and B-flat played as a double stop by the violas provide the first and third initials. The initial for flat rounds out “EfB” with the correct combination of upper and lower case letters for the commonly abridged title Ein feste Burg. Another way to arrive at f is through the application of a number-to-letter key (A = 1, B = 2, C = 3, etc.) which converts “six” to the sixth letter of the alphabet. The G in the second violin part gives the initial for Gott. Based on this analysis, the German sixth on the downbeat of bar 5 harbors the case-sensitive initials for the first, second, third, and sixth words of the hidden melody’s German title: Ein feste Burg ist unser Gott. With ten of its fifteen titles consisting of initials, the Enigma Variations places a marked emphasis on that predominant format. The detection of four of the hidden Theme’s six initials strongly suggests the remaining two initials are lurking in that conspicuous chord.
Unmasking the initials for ist and unser posed a more serious challenge partially because musical notes are limited to the first seven letters of the alphabet. A number-to-letter key permits the conversion of the number nine to the letter i. The number nine is encoded by the first German sixth chord in at least four ways. The label “German 6th” has nine characters. The glyph for 9 is identical to 6. Counting from the start of the Enigma Theme, C-sharp is the ninth note played by the cello section. Yet another way to arrive at the number nine centers on the interval formed between the lowest (C-sharp) and highest (E-flat) notes of the German sixth. The C-sharp and E-flat is a diminished tenth, the enharmonic equivalent of a major ninth. This leaves only u for unser to track down.
The application of a reverse number-to-letter key (Z = 1, Y = 2, X = 3, etc.) enables the conversion of the number six to the letter u. Consequently, the number six also encodes this absent initial. There is an alternate way to arrive at this missing initial. Elgar used the letter c — the initial for cipher — to generate 24 curlycue characters for his Dorabella Cipher dating from July 1897. In that baffling cryptogram, the letter c is written in different orientations to approximate the letters u and n. The genesis of the Dorabella Cipher predates the Enigma Variations by 464 days. Elgar’s flexible treatment of the c glyph permits the interpolation of the C-sharp as a coded form of the letter u, the initial for under.


A cryptanalysis of the German sixth chord in Enigma Theme’s fifth bar revealed it encodes all six initials for Ein feste Burg ist unser Gott. Three upper case initials are given as note letters: E, B, and G. The remaining three lower case initials are encoded by other indirect features of that chord. The notes E and B are flatted, and the initial for that accidental is f. C-sharp is the ninth note played by the cello section, leading to the ninth letter of the alphabet: I. The note letter C is also the glyph for U. This balanced encoding of three upper and three lower case initials by direct and indirect features of the German sixth reeks of design. Two threes intimate a coded form of Elgar’s initials as that number (3) is the mirror image of his capital cursive E. E-flat is the same pitch as a D-sharp, an equivalence that presents a coded spelling of “ED.” Ed is the short form of Edward and furnishes the first two initials from the title of Variation XIV (E. D. U. ), Elgar’s musical self-portrait. The first German sixth cipher efficiently enciphers Elgar’s initials, nickname, and initials for the secret melody.


The German sixth makes its final appearance in measure 683 of the original ending for Variation XIV (E. D. U.). On the third beat of that bar, the orchestra plays a conspicuous German sixth consisting of E-flat, B-flat, G, and C-sharp — the same notes used for the inaugural German sixth in the Enigma Theme. It was previously shown how that augmented chord encodes all six case-sensitive initials for the covert Theme’s German title. The last German sixth is positioned precisely six quarter beats from the end of the final bar.


In the final German sixth chord, the written notes for the F trumpets are B-flat, F, and D. These written notes resonate up a perfect fourth to generate in concert pitch the sounding notes E-flat, B-flat, and G. This combination of written and sounding notes for the F trumpets in the last German sixth chord provide the initials for Ein feste Burg. The written notes in the two adjacent staves for the F trumpet and trombone also present the initials for the covert Theme.


Setting aside the notes letters that encode “EFB,” the remaining discrete note letters for the last German sixth chord in bar 683 are C, G, and D. When treated as an anagram, these three letters may be rearranged as “CGD.” When read phonetically, those letters produce the phrase “See God.” A phonetic decryption is called for by Elgar’s use of phonetic spellings in his correspondence. For example, he respelled “phrases” as frazes, “gorgeous” as gorjus, and “excuse” as xqqq. An alternative phonetic anagram is “GDC” which may be read as “God” and “sea.” In Variation XIII, Elgar depicts a calm sea by repeatedly citing a melodic fragment from Felix Mendelssohn’s overture Calm Sea and Prosperous Voyage. Variation XIII is dedicated in secret to Jesus Christ, the incarnation of God according to Elgar’s Roman Catholic faith. The combination of a marine atmosphere with a stealth dedication to Jesus poetically associates God with the sea. Jesus likened his death and resurrection to the Sign of Jonah, a prophet who spent three days and nights in the belly of a whale. This comparison provides a theological basis for linking Elgar’s covert friend with the sea. The word “sea” is a homonym of “C,” the initial for Christ. The first note of the opening two Mendelssohn quotations in A-flat major is also C. These opening two Mendelssohn quotations are accompanied by a soft metallic roll played by the timpani on C.
The positions of the first and last German sixth chords in the Enigma Variations provide the correct figures to encipher the initials for Ein feste Burg. The first German sixth occurs in the fifth bar from the beginning. The application of a number-to-letter key to that bar number converts 5 to E. The last German sixth is positioned two bars from the end, and precisely six quarter beats from the concluding quarter beat. A number-to-letter key converts 2 to B, and 6 to F. The F is also supplied by the label “German sixth” as it singles out its numeric equivalent. In this manner, the positions of the first and last German sixth chords encipher the initials “EFB” using an elementary number-to-letter key.
Elgar placed German sixth chords close to the beginning and original ending of the Enigma Variations. In a similar fashion, the titles of the Enigma Variations are bookended by two coded forms of his initials (EE). The first instance arises from the first letter of “Enigma” and the last initial of “C.A.E.” The second set is produced by the first initial of “E.D.U.” and the last letter of “Finale.” It should also be observed that the titles of the first and last movements (Enigma and E. D. U.) generate a third coded pair of initials. This final pair of initials associates the ending with the beginning.


There is also a coded form of those Elgar’s initials in the last German sixth chord from the original ending. That chord has precisely two unison E-flats played by the principal trumpet and principal trombone. Those two notes in the final German sixth are a transparently encrypted form of Elgar’s initials. This is part of a larger pattern of cryptograms in the Enigma Variations that harbor his initials. One notable example is the Enigma Theme Psalm Cipher that encodes “EE’s Psalm” and has precisely 46 characters, a figure that implicates Psalm 46. The title Ein feste Burg originates from the first line of that famous chapter known as “Luther’s Psalm.”


Elgar employs a similar flanking maneuver with the anomalous title of Variation XIII (***) by enveloping the asterisks with the three absent letters. He accomplished this cryptographic displacement using the first initials from the titles of the adjacent movements — XII (B. G. N.) and XIV (E. D. U. & Finale). Those first letters are an acrostic anagram of the covert Theme’s initials (EFB).


The answer is positioned so close to the question that it is shocking nobody spotted it sooner. Elgar created no less than five different lists of the Variations, a task carried out in retrospect to create this and other proximate title letters cryptogram.

The Finale’s AMDG Dedication Cipher

The initials on the Jesuit monogram are “AMDG” and signify the Latin motto “Ad Majorem Dei Glorium” (For the great glory of God). Elgar inscribed this monogram on his scores as a dedication to God. One of the most notable examples of this practice is The Dream of Gerontius.


There is a chord sequence beginning four bars from the original ending to the Finale that encodes three of the four initials for “AMDG.” Measure 681 opens with a forceful A minor seventh chord that decrescendos into the next bar. This is followed in bar 682 by a dramatic scale run upwards that arrives at a fortissimo D dominant seventh chord on beat four. This dominant seventh resolves on the downbeat of bar 683 to a tonic G major chord. The order of these chord letters is A-D-G, a pattern reinforced by the contrabass section that performs the identical note sequence. Remarkably, this chord and notes series presents the three available musical note letters of “AMDG” in the correct order. The lone holdout is M, a letter inaccessible in the musical alphabet. To encipher that letter, Elgar would need to resort to other indirect means.
One way the absent m is supplied in bar 682 is by the initial for the performance direction molto which appears four times in that measure. M is the alphabet’s thirteenth letter, a number embedded within that bar 682 in four discernable ways. The first is by the instrumental parts which have precisely thirteen coincident written notes at the outset of that measure. This pattern of thirteen concurrent written notes persists until the arrival of the dominant seventh on beat 4. The second is with the upward thirteen-note scale run that covers the interval of a major thirteenth. A third and less obvious way Elgar pinpoints the number thirteen in this bar is through thirteen performance terms dispersed over the first three quarter beats. There are six “ff”, four “molto”, and three “cresc.” The fourth method is by the sum of the characters in “ff molto cresc.” which adds up to precisely thirteen. These redundant encoded forms of the number thirteen implicate the thirteenth letter of the alphabet, the absent M.


The location of these coded versions of M appears between the A minor seventh and D dominant chords, the correct location required to complete the stealth “AMDG” dedication. This secretive dedication is consistent with Elgar’s blueprint encompassing an absent principal Theme, a missing “dark saying” and an anonymous friend memorialized in Variation XIII.

Concluding Observations

Elgar’s mastery of cryptography is evinced by a broad spectrum of ciphers within the Enigma Variations. An augmented German sixth chord surfaces near both the Enigma Theme's beginning and the original Finale's ending. That particular chord furnishes multiple clues about the covert melody by identifying its language (German) and complement of words in the title (six). The first German sixth appears in bar 5 of the Enigma Theme. Three upper case initials are divulged directly by its note letters (E, B, and G), and the remaining three lower case initials (u, i, f) are encoded by other indirect features of that chord. These two groupings of three initials suggest a coded version of Elgar’s initials as the number 3 is the mirror image of a capital cursive E.
The final German sixth occurs two bars before the original ending of Variation XIV (E.D.U.), Elgar’s musical sketch of himself. The sounding notes of this last German sixth are identical to the first in bar 5 of the Enigma Theme. Precisely two E-flats are played in unison by the principal F trumpet and principal trombone, providing a coded form of Elgar’s initials within that augmented chord. The discrete written note letters that comprise the concluding augmented German sixth chord in bar 683 are B, C, D, E, F, and G. When treated as an anagram, these letters may be reshuffled to form the initials for Ein feste Burg (EFB), a phonetic version of the phrase “See God” (C G-D), and the words “God” (G-D) and “sea” (C). The two latter decryptions relate to Variation XIII, a movement with marine imagery that is dedicated in secret to Jesus, the physical manifestation of God. A phonetic analysis is supported by Elgar’s personal correspondence which exhibits creative phonetic spellings.
The positions of the first and last German sixth chords cleverly encode the initials for the covert Theme. The first German sixth appears five bars after the beginning, and the last occurs two bars from the original ending. Converting those bar distances into their corresponding letters of the alphabet generates the letters E and B, two of the three initials from Ein feste Burg. The last German sixth appears exactly six quarter beats from the end, and its label also furnishes the number six. A number-to-letter key transforms the number six into the letter F. Like so many other cryptograms in the Enigma Variations, the first and last German sixth chords encipher the initials to the hidden melody.
The last four bars of the original Finale encode the Jesuit monogram “AMDG” using a combination of chord letters (A, D, and G) and coded forms of the number thirteen, the numeric equivalent of the letter M. The chord in bar 681 is an A minor seventh. The next chord on the third beat of bar 682 is a D dominant seventh that resolves in bar 683 to G major. As previously discussed, the number thirteen is encoded in numerous ways in bar 682. One of the more obvious exemplars is its upward thirteen-note scale run that covers the interval of a major thirteenth. An elementary number-to-letter key converts thirteen to the thirteenth letter of the alphabet, M. The location of these various coded forms of thirteen is appropriately situated in between the A and D chords. Elgar inscribed “AMDG” on musical scores as a dedication to God. In the original ending, he encoded that dedication over three measures just before the final bar.
After the 1899 premiere of the Enigma Variations on June 19, August Jaeger counseled Elgar that the Finale’s ending was too abrupt and should be extended. The conductor Hans Richter also endorsed that assessment. After delaying a week, Elgar replied to Jaeger on June 27:
I waited until I had thought it out & now decide that the end is good enough for me...You won’t frighten me into writing a logically developed movement where I don’t want one by quoting other people! Selah! 
Selah is a Hebrew term used almost exclusively in the Psalms. Jaeger was apprised of the secret melody to the Enigma Variations, hence he would have quickly appreciated Elgar’s inside joke as a literary allusion to Ein feste Burg. Indeed, “Selah'' appears three times in Psalm 46. Elgar’s reluctance to alter the original ending makes perfect sense as he did not want to abandon his carefully crafted cryptograms in those final bars. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

Soli Yah Gloria


Original Ending to Variation XIV. (E. D. U.)

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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.