Wednesday, May 5, 2021

Another Piece Of Elgar's Retrograde Puzzle

Your course as a candidate was perfectly clear. You took your canto fermo and on it built several species, and several cunning mixtures of species, of strict counterpoint. You took your fugal theme, and having to treat it tonally or otherwise, a vital point, you wrote your exposition, your episodes, your stretto and your pedal, by no means forgetting your augmentation and your diminution, and particularly remembering that while consecutive fifths meant relegation to the darkest depths of Tartarus, no university professor could resist the magic of a canon cancrizans, say in the Hypomixolydian mode.

Robert J. Buckley in Sir Edward Elgar (1905)

The British composer Edward Elgar composed his orchestral Enigma Variations in 1898-99. That masterpiece transformed his reputation from a provincial itinerant music teacher to a world-class composer.  The Enigma Variations is a riddle in three parts consisting of:

  1. An absent principal Theme

  2. A “dark saying” in the Enigma Theme, and

  3. A secret friend commemorated in Variation XIII.

Elgar advised the Enigma Theme is a counterpoint to a famous melody that is not heard yet plays “through and over” the set of Variations. The search for that absent tune spawned a speculative frenzy that continues unabated to this day. No purported melodic solution has ever gained widespread acceptance because scholars claim Elgar took his secret to the grave in February 1934. Even if the correct tune was proposed, the conventional wisdom insists there is no viable way to authenticate it.

Musicologists presume Elgar never wrote down the answer for posterity to discover. That presumption fails to take into account his lifelong obsession for cryptography. Elgar’s fascination for ciphers merits an entire chapter in Craig P. Bauer’s treatise Unsolved!  The bulk of its third chapter is devoted to Elgar’s meticulous decryption of an allegedly insoluble Nihilist cipher presented by John Holt Schooling in the April 1896 issue of The Pall Mall Magazine. That particular cryptogram is a derivative of the Polybius square. Elgar was so delighted with his solution to Schooling’s reputedly impenetrable code that he brags about cracking it in his first biography published in 1905. Those inclined to downplay Elgar’s expertise in cryptography are urged to consult the third chapter of Bauer’s book.

The recognition of Elgar’s cryptographic expertise raises the prospect that he encoded the solutions to the Enigma Variations within the score. A decade of concerted analysis has netted over ninety cryptograms in diverse formats. These ciphers encode a narrow set of mutually consistent and complementary solutions that provide definitive answers to its core riddles. 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 and subject of his first sacred oratorio, The Light of Life (Lux Christi).

The Enigma Variations embody a fusion of Elgar’s twin loves for counterpoint and cryptography. A stark gulf between these two disciplines prevents experts in those respective fields from uncovering and authenticating the answers. On the one hand, musicologists lack the expertise to plumb the depths of Elgar’s cryptographic genius. Their inability to detect and decrypt ciphers is routinely misattributed as proof against their existence. On the other hand, cryptographers are commonly recruited from the ranks of mathematicians and computer scientists with little or no background in music composition or counterpoint. Bridging the divide between these two divergent specialties demands an intimate familiarity with counterpoint and cryptography.

Scholars routinely argue that Elgar provided little or no guidance regarding the nature of his contrapuntal puzzle. On the contrary, he publicly challenged the world to decrypt his melodic cipher by offering a series of detailed clues. These criteria appear in four primary sources:

  1. The original 1899 program note

  2. An October 1900 interview in The Musical Time

  3. His 1905 biography, and 

  4. His descriptive notes for the 1929 pianola rolls.

The public record provides six precise conditions about the relationship between the Enigma Variations and the covert principal Theme. These specific clues are summarized below:

  1. The Enigma Theme is a counterpoint to the principal Theme.

  2. The principal Theme is not heard.

  3. The principal Theme is famous.

  4. Fragments of the principal Theme are present in the Variations.

  5. The principal Theme is a melody that can be played through and over the whole set of Variations including the entire Enigma Theme.

  6. The Enigma Theme consists of measures 1 through 19.

Elgar never elaborated on the exact nature of the counterpoint between the Enigma Theme and its secretive source melody. Virtually every proposed tune begins its contrapuntal mapping by overlaying the opening of both melodies. This reflexive approach fails to appreciate the possibilities afforded by contrapuntal techniques. Counterpoint offers some ingenious methods for manipulating a melody. Composers during the late Romantic period routinely modified melodic subjects using the standard contrapuntal techniques of stretto, augmentation, diminution, inversion, contrapuntal motion, and retrograde. According to Kent Kennan, the author of the textbook Counterpoint, the most rarified form is retrograde motion in which a melody is played in reverse from back to front. He explains:

Retrograde motion (cancrizans) is rare in tonal music. Not only is it difficult to write, but the average ear has trouble recognizing a melodic line when it is played backwards; consequently the point of the device tends to be lost.

Playing the covert Theme in reverse as a retrograde counterpoint sounds like the most effective tactic for camouflaging a melody.  The word cancrizans is medieval Latin for crab, a crustacean noted for its unusual ability to walk backward. For this reason, a retrograde counterpoint is also known as a crab counterpoint. In Variation XIII, Elgar repeatedly cites a melodic fragment of a subordinate theme from Felix Mendelsohn’s concert overture Calm Sea and Prosperous Voyage. The ostinato figure accompanying those melodic fragments reprises the Enigma Theme’s palindromic rhythm, providing a discernible link between these two ostensibly unrelated melodies. The Mendelssohn fragments sonically portray a calm sea, an environment inhabited by crabs. By conveying a marine atmosphere tied to the Enigma Theme’s distinctive rhythm, Elgar cleverly hints at a retrograde counterpoint.

Multiple lines of evidence point to such an unexpected backward counterpoint. For example, the ABA’C structure of the Enigma Theme is a phonetic spelling of aback, a word that means “backward” and “by surprise.” A retrograde counterpoint satisfies both of those definitions. Phonetic spellings are an idiosyncrasy of Elgar’s personal correspondence. The first six notes of the Enigma Theme’s bass line replicate in reverse order the last six notes of the ending phrase from Ein feste Burg. The discrete note letters of the Mendelssohn quotation in A-flat major (C, B-flat, and A-flat) provide three of the four letters in crab. Only the “R” is absent as the musical alphabet is restricted to the first seven letters. The Mendelssohn fragments encode the initials of Ein feste Burg in reverse order. Confirmation is provided by a retrograde mapping of Ein feste Burg above the Enigma Theme applying such standard techniques as augmentation and diminution.

A new piece of the cryptographic puzzle was recently found that intimates a retrograde mapping of the covert melody above the Enigma Theme. This discovery builds on prior research that determined proximate title letters encode answers to the Enigma Variations. Elgar’s sketches document five differing orderings of the movement, a process carried out to construct these varied cryptograms. The earliest example is the Letters Cluster Cipher that enciphers the initials of Ein feste Burg in the immediate vicinity of Variation XIII (***). A more recent revelation is how Elgar encodes the title of Ein feste Burg by proximate title letters in the Enigma Theme, Variations I-III, and XII-XIV. The latest discovery consists of adjacent title letters in Variations I, II, and III.  As shown below, nearby letters produce anagrams of CRAB, STEP, and HID.

The first and second initials of Variations I and III are an anagram of “CRAB.” The first two initials of Variation II in combination with a Roman numeral “I” is an anagram of “HID.” The last initials of Variations I, II, and III are an anagram of “STEP.”   Factoring in “Enigma” with these three anagrams permits the construction of the following remarkable phrases:

  1. “Enigma hid crab step.”

  2. “Crab step hid Enigma.”

These two decryptions implicate a crab counterpoint within the Enigma Theme. This latest cryptographic discovery bolsters the conclusion that Elgar deliberately concealed the covert Theme by disguising it as a retrograde counterpoint. To learn more concerning the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

Soli Yah Gloria

Thursday, April 29, 2021

Elgar's Enigma Theme's Encrypted Title

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 late romantic composer Edward Elgar excelled in cryptography, the science of coding and decoding secret messages. His obsession with that esoteric discipline merits an entire chapter in Craig P. Bauer’s book Unsolved! Bauer devotes much of the third chapter 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. Elgar was so gratified by his solution to Schooling’s purportedly impenetrable code that he specifically mentions it in his first biography released in 1905 by Robert J. Buckley.

Elgar painted his decryption in black paint on a wooden box, an appropriate medium given that another name for the Polybius cipher is a box cipher. His methodical solution is summarized on a set of nine index cards. On the sixth card, Elgar likens the task of cracking Schooling’s cipher to “...working (in the dark).” This confirms Elgar used the word “dark” as a synonym for a cipher.

This parenthetical remark is significant as he employs that same language in the original 1899 program note to characterize his eponymous Enigma Theme. It is an oft-cited passage that deserves revisiting as Elgar lays the groundwork for his tripartite 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 also uses the words “dark” and “secret'' interchangeably in a letter to August Jaeger penned on February 5, 1900. He wrote, “Well—I can’t help it but I hate continually saying ‘Keep it dark’—‘a dead secret’—& so forth.” One of the definitions for dark is “secret,” and a saying is a series of words that form a coherent phrase or adage. Elgar’s odd expression — “dark saying” — is coded language for a code. In his oblique manner, Elgar hints there is a secret message enciphered in the Enigma Theme. 

A compulsion for cryptography is a reigning facet of Elgar’s psychological profile. A decade of systematic analysis of the Enigma Variations has netted over ninety cryptograms in diverse formats that encode a set of mutually consistent and complementary solutions. Although this figure may seem astronomical, it is entirely consistent with Elgar’s fascination with ciphers. More significantly, 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 melodic foundation for the ensuing movements? Answer: Ein feste Burg (A Mighty Fortress) by the German protestant reformer Martin Luther. What is Elgar’s “dark saying” concealed within the Enigma Theme? Answer: A musical Polybius cipher situated 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.

The initials of Elgar’s secret friend are transparently encoded by the Roman numerals of Variation XIII using an elementary number-to-letter key (1 = a, 2 = b, 3 = c, etc.). “X” is the Roman numeral for ten. The tenth letter of the alphabet is J. “III” represents three, and the third letter is C. This cryptanalysis shows that the Roman numerals XIII are a coded form of “JC,” the initials for Jesus Christ. This is not an isolated instance of this encipherment technique in the Enigma Variations. Elgar uses the same number-to-letter key to encode August Jaeger’s initials in Variation IX (Nimrod). “I” is the Roman numeral for one. The first letter of the alphabet is A. “X” stands for ten, and the tenth letter is J.

With the secret friend’s initials thinly disguised by the Roman numerals of Variation XIII, what could be the significance of its cryptic title (***) consisting of three asterisks? That question was resolved in July 2013 by the discovery of the Letters Cluster Cipher that revealed the three asterisks represent the initials of Elgar’s mysterious missing melody. Those absent initials are encoded by the first letters from the titles of the adjoining movements: Variations XII (B.G.N.) and XIV (E.D.U., and Finale). These first letters are an acrostic anagram of “EFB,” the initials for Ein feste Burg. Elgar deftly frames the question posed by the three asterisks with the answer hidden in plain sight.

Elgar’s sketches document five different orderings of the movements for the Enigma Variations. The discovery of the Letters Cluster Cipher verifies these divergent lists were generated to construct that particular cryptogram. This prospect eluded scholars like Julian Rushton who naively insist Elgar lacked the time to construct any ciphers. Rushton’s speculative rush to judgment is unsupported by the known timeline. Elgar began composing the Enigma Variations in earnest on October 21, 1898. The orchestration was completed on February 19, 1899. From inception to completion, the process consumed 121 days or four months. Such a lengthy period afforded more than sufficient time and opportunity for Elgar to indulge his passion for cryptography. Proffering the patently false claim there was inadequate time for Elgar to conceive of any cryptograms within the Enigma Variations conveniently relieves one from the obligation to search for any.

The Letters Cluster Cipher that encodes the covert Theme’s initials is a relatively simple cryptogram. Its discovery precipitated a much broader analysis of all the titles from the Enigma Variations to unmask other meaningful and relevant groupings of adjacent letters. Below is a summary of the Roman numerals and titles of the different movements in the Enigma Variations.

There is no Roman numeral for zero to assign the Enigma Theme that precedes Variation I. For this reason, it is identified by Null, a German term obtained from the Latin nullum that means “nothing.” That identical word turned up during a conversion between Elgar and his wife on the evening of October 21, 1898, when he first performed the Enigma Theme for her on the piano. After hearing it, Alice commented how she liked it and inquired, “What is that?” He replied, “Nothing — but something might be made of it.” Elgar used the word “nothing” to describe the Enigma Theme. At the end of the original score, he cites a paraphrase from Torquato Tasso’s Jerusalem Delivered that also employs the word “nothing.” He wrote, “Bramo assai, poco spero, nulla chieggio” (I desire much, I hope little, I ask nothing). The Italian word nulla is nearly identical to null, its German equivalent.

The discovery of the Letters Cluster Cipher fueled the hypothesis that Elgar may have encoded other terms within the Enigma Variations’ titles.  These additional words would be connected to the absent Principal Theme, the Enigma’s “dark saying,”and the secret friend commemorated in Variation XIII. This encipherment technique is markedly dissimilar from Stephen Pickett’s surgical cherry-picking of individual letters from titles and names allegedly associated with different movements to jerry-rig a presumed solution for the absent Theme. Given an adequate supply of letters, it is possible to reconstruct almost anything. The key difference between Pickett’s approach and this methodology is that it is narrowly restricted to smaller groupings of adjacent title letters.

A systematic analysis of proximate letters from the titles netted thirty different terms related to the riddles posed by the Enigma Variations. The mechanism for this particular cipher hinges on proximate title letters to form relevant words and names. The solutions expertly interwoven within the titles coherently relate to the riddles posed by the Enigma Variations. One example is the title Christ. This term is spelled by the first initials of Variations I through III (CHR), the Roman numeral I, and the third initials from Variations II and III (ST). Remarkably, the initials CHR and ST are sequential and align in two neat parallel rows.

The discovery of the covert Theme’s initials and secret friend’s title embedded among  proximate letters from the Enigma Variations’ titles spurred a renewed search for the hidden melody’s name. Remarkably, it is feasible to reconstruct the common three-word German title for the secret melody from adjacent title letters. The first word of that Teutonic title is conveniently nestled within the Theme’s name, Enigma. A Germanic context is affirmed by how that word was penciled on the Master Score by Jaeger, the only German friend portrayed in the Variations. The word enigma is also spelled the same way in English and German. The first three contiguous letters of Enigma are an anagram of Ein. There is a second way that word is spelled out by proximate title letters in the Theme and Variation I. “EIN” may also be fashioned from the initial E for Enigma, the initial N for Nulla, and the Roman numeral for Variation I. It is contextually appropriate that there is a coded link between the first word of the Enigma Variations and the first word of the covert Theme’s title.

Contiguous initials from Variations I-III and XIV furnish the letters needed to spell FESTE, the second word from the hidden Theme’s German title. Although Variations I and XIV are not neighboring movements, they are intimately connected for three reasons. First, these two movements are musical portraits of Elgar (XIV) and his wife Caroline Alice Elgar (I). Second, this musical union is affirmed by a partial restatement of Variation I in XIV. Third, Elgar is identified by a phonetic rendering of “Edoo” (E.D.U.), a pet name Alice coined from the German spelling Eduard. Like Enigma, “Edoo” is distinctly Germanic. The first initials from the titles of XIV (E and F) and third initials of I (E), II (S), and III (T), are an anagram of FESTE. Alternatively, the E in Variation XIV could be substituted with the E from Enigma. However, the E from Enigma was skipped in this instance as it is already used as part of the first word in the title (EIN).

Neighboring initials from Variations XII, XIII, and XIV provide the letters required to spell BURG. The first and second initials of XII (B.G.N.), the only known initial from XIII (Romanza), and the third initial of XIV (E.D.U.) are an anagram of BURG. Elgar’s phonetic rendering of Alice’s nickname “Edoo” as “E.D.U.” furnishes the crucial adjacent “U” to complete the spelling. Like the covert Theme’s title, Elgar’s pet name is German.

This cryptanalysis determined that it is feasible to assemble the three-word German title of the covert Theme from adjacent letters in the titles of the Enigma Variations. The first (Ein) is an anagram of the first three letters in Enigma. Alternatively, it may be fashioned from the E in Enigma, N from Nulla, and I from Variation I. The second (feste)  is encoded by proximate title letters in Variations I, II, III, and XIV. The third (Burg) is enciphered by adjacent title letters in Variations XII, XIII, and XIV. A discernable German antecedent furnishes a part of each word in the decryption. This is the case because the titles of the Theme (Enigma) and Variation XIV (E.D.U.) are Germanic. The distance between Variations III and XII was ostensibly intended to foil recognizing the covert Theme’s name spliced in among the titles of the Enigma Theme, Variations I through III, and XII through XIV.

Elgar expertly interlaced the covert Theme’s title within particular titles of the Enigma Variations using anagrams of adjacent letter groupings. Eight titles from seven contiguous movements are required to construct this particular cryptogram. There is a distinct symmetry as it spans the foundational Theme, the first three variations, and the final three movements. The prominence of two threes suggests a coded version of Elgar’s initials (EE) because that numeral is the mirror image of a capital cursive E. A coded form of Elgar’s dual initials is also detectable in the first and final movements (Enigma and E.D.U.).

Could there be yet another layer to this proximate title letters cipher the encodes the title of the covert Theme? A number-to-letter key converts numerals into their corresponding letters of the alphabet. For example, the number one becomes the letter A, the number two the letter B, and so on. Applying this key to the Roman numerals of the movements required to assemble the title of the covert Theme produces the plaintext “ABCLMN” as shown below:

I = A






The Enigma Theme has no Roman numeral and consequently is assigned a null or zero. The glyph for zero (0) duplicates the letter O. This completes the list of seven number-to-letter conversions in alphabetical order as “ABCLMNO.” When treated as an anagram, those letters may be rearranged as “BLAC NOM.” The first term is a phonetic spelling of black with the letter k absent. It was observed earlier that Elgar generated a phonetic spelling of “Edoo” as “Edu.” Phonetic spellings are an idiosyncratic feature of his correspondence. Some examples of these inventive 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)

A synonym for black is dark, a term Elgar used to denote a cipher.  An office that specializes in encoding and decoding secret messages is called a Black Chamber. The second term “NOM” is an exact spelling of the French word for name. This word is found in such expressions as “nom de plume” and “nom de guerre.” Consequently, the anagram “BLAC NOM” may be translated as “Black Name.” The complete French translation as “Nom Noir” is alliterative. The ancillary decryption “Black Name” is an apt description for a concealed title. This decryption suggests a password key for pinpointing the specific movements required to reconstruct the covert Theme’s title from contiguous title letters. To learn more concerning the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

Soli Yah Gloria

About Mr. Padgett

My photo
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.