Friday, September 17, 2010

Elgar's "Dark Saying": A Music Box Cipher

*** A more concise version of this article is available here. ***

It may well be doubted whether human ingenuity can construct an enigma of this kind which human ingenuity, if properly applied, may not also resolve.
While it is entirely plausible Ein feste Burg is the covert Principal Theme to Elgar's Enigma Variations, plausibility is not the same as proof. The real question is whether there is any way to decisively prove it. Absent confirmation, no solution has any hope of venturing beyond the purely speculative. This inevitably raises the question of whether Elgar surreptitiously supplied some way to authenticate the solution. Short of discovering a sealed envelope with the answer written in the composer’s own script, the consensus is a resounding no. Most scholars agree the riddle is impossible to resolve because Elgar ostensibly took his secret to the grave. Michael Kennedy opines, “People have ingeniously been trying to guess the tune ever since, a harmless but pointless recreation since the secret, if there was one, died with him.”[1] J.P.E. Harper-Scott echoes that staid opinion:
Although human nature guarantees that attempts to solve it will never end until the Ark of the Covenant and the Holy Grail are on permanent display in the British Museum, they all somehow fail to convince. It is easy to carp, since the riddle cannot be answered now its perpetrator is dead, but the evidence supporting all of the ‘solutions’ is weak.[2]
Just how do these scholars know the solution is unknowable? The brilliant Christian mathematician and philosopher Blaise Pascal argues humanity is incapable of certain knowledge and absolute ignorance, that too much and too little learning are extremes that escape us.[3] Centuries after Pascal arrived at these pivotal insights, Kurt Gödel conceived of a famous mathematical proof that affirms Pascal’s observations. The only thing we know with absolute certainty is that we can be absolutely certain of nothing. For better or worse, we reside in a universe predicated on faith. For academics to speak in such absolutes is contrary to their fashionable embrace of relativism, a dogma espoused with a degree of certainty only eclipsed perhaps by their fanaticism for it. Put another way, some scholars do not know what they do not know, elevating their ignorance to a form of pseudo-knowledge. Since they are incapable of unmasking the solution, they categorically deny that possibility for everyone else. If they cannot figure it out, they reason (rather unreasonably) that nobody else can either. No wonder Elgar was suspicious of career academics, balked when invited to join their ranks, and abandoned his lectures after enduring their scathing, cliquish criticisms.
What is known with great confidence is that Elgar held a lifelong fascination for a wide range of puzzles such as anagrams, crossword puzzles, riddles, and ciphers. Craig Bauer devotes an entire chapter to Elgar in his recently released history of cryptography titled Unsolved! Elgar's musical scores and letters are peppered with anagrams and secret codes. He also enjoyed creating new names. For example, the name he gave his only child – Carice – was a combination of his wife’s first and middle names (Caroline Alice). In March 1899 he called his new home Craeg Lea, a title created by reversing the letters of his last name (Craeg Lea) and adding the first letters of the first names of his daughter, wife, and himself (Carice, Alice, Edward).[4] C.A.E. are the initials for his wife in the Enigma Variations, a work completed a month prior to relocating to Craeg Lea.  He later devised the palindrome Siromoris to serve as his telegraphic address, a name based on his two honors – a knighthood (Sir) and the Order of Merit (OM). In his correspondence, he used this name as well as the opening bars of the Enigma Theme to represent himself. Since he wrote the Enigma Theme, this identification should be self-evident.
Elgar’s keen interest in ciphers is well-known, well-established, and well beyond any reasonable doubt. In April 1886 he attended a performance at the Crystal Palace conducted by August Manns in honor of Franz Liszt who was present for the occasion. Elgar expressed his opinion of the performance by writing a message in cipher on his program. A purported solution is “Gets you to joy, and hysterious.” The word hysterious is a portmanteau based on the words hysteria, mysterious, and tear.[5] In July 1897, Elgar sent a coded letter to Dora Penny who in 1899 was immortalized as the “variationee” for Variation X with the nickname Dorabella. This coded message known as the Dorabella cipher is among the most famous puzzles in cryptography because it remained unbroken for over a century.[6]  In Buckley’s 1905 biography, Elgar describes how he amused himself with cryptograms on railway journeys, solving an allegedly unbreakable cipher by John Holt Schooling featured in an 1896 issue of The Pall Mall Magazine.[7] He was so pleased with his discovery he painted the solution in black paint on a wooden box. That box is now in the possession of the Elgar Birthplace Museum. A box is ideal for displaying the solution because it is a Nihilist cipher, also known as a checkerboard cipher due to its grid pattern of cells arranged in columns and rows.
The fundamental allure of any puzzle is the prospect of solving it. Cryptograms were to Elgar what Mount Everest is to a mountain climber. He delighted in tackling supposedly insoluble puzzles and created a famous pair of his own with the Enigma Variations and the Dorabella cipher. For anyone to contend Elgar's substituted a practical joke in place of an actual melodic and cryptographic puzzle betrays a profound ignorance of his character. The Enigma Variations are one of his greatest puzzles, one obviously formed with the intent of concealing a melodic solution. The composer’s public and private remarks on this subject make that overwhelmingly clear. More importantly, Elgar did not take his secret to the grave as some would have us naively believe. On the contrary, he ingeniously enciphered the answer in the score itself. When found, the solution would be unguessed because it would be revealed by means of the composer’s principal form of amusementcryptanalysis.
To crack Elgar’s music cipher, it was first necessary to find the key to unlock it. With the discovery of Ein feste Burg as the covert Principal theme, that key was found. The next step was to find the lock, insert the key, and unlock the contents of Elgar's mysterious dark saying or hidden message. Instead of working from start to finish, my counterintuitive approach entailed working from back to front in the spirit of Jacobi's advice, Invert, invert, always invert.
Where was the lock, the location of the musical enigma cipher? The first six measures of the Enigma Theme seemed like the most obvious place to begin my search for the cipher principally because of the odd placement of a double bar at the end of measure 6. A double bar is commonly used to denote the end of a composition or a section within it, but neither is the case with measure six. The Enigma Theme is 19 measures in length, and the placement of a double bar so close to the beginning is incredibly conspicuous. It was reasoned this unusually placed double bar demarcated the section of the score containing Elgar’s musical cipher starting with measure one and terminating at the end of measure six. Ein feste Burg is the key, and measures one through six form the lock.
There is an array of uncanny coincidences supporting the hypothesis that the first six measures of the Enigma theme contain a music cipher. First, the number of letters in the title Ein feste Burg ist Unser Gott is the same as the number of melody notes over the first six bars: 24. Second, the number of measures is identical to the number of words in the missing melody’s title: 6. Third, there is an audible sense of separation achieved by the systematic placement of quarter note rests in the melody line at the beginning of each bar, a device suggestive of spaces between words. Dr. McClelland perceptively observed:
Elgar’s six-bar phrase is achieved by the characteristic four-note grouping, repeated six times with its reversible rhythm of two quavers and two crotchets. This strongly suggests the cryptological technique of disguising word-lengths in ciphers by arranging letters in regular patterns.[8]
Fourth, the original short score lends strong circumstantial evidence for a musical cipher in the first six bars of the Enigma Theme because the melody and bass notes are in black ink (like Elgar's painted solution on the wood box)  while the intervening notes are in pencil.[9]  Black ink is positively evocative of a dark saying. Fifth, at least three of Elgar’s favorite composers used musical ciphers in their scores: Johann Sebastian Bach, Robert Schumann, and Franz Liszt. In the unfinished Contrapunctus 14 of Die Kunst der Fuge (The Art of Fugue), Bach inserts his own name using the notes B-flat, A, C, and B. In German musical nomenclature, B-flat represents B, and B-natural the letter H. In Schumann’s Nordische Lied, he transforms the name of a Danish contemporary, Gade, into a musical motive, and in his Op. 60 fugues, he manipulates the Bach motive using inversion, retrograde, and augmentation.[10] In The Dream of Gerontius Op. 38, a work completed shortly after the Enigma Variations, Elgar encodes the names of some of his critics in the Demons’ Chorus with a music cipher. Like Schumann’s work for Gade, Elgar composed an Allegretto for the Gedge sisters using the letters of their name as a motive.[11] Finally, the original score has the word Enigma centered directly over the first six bars, suggesting the precise location of the cipher and its dark saying. As other researchers point out, the phrase dark saying is a definition of enigma.[12] With Elgar’s Enigma cipher, the evidence points to the first six bars as the most likely location of this mysterious puzzle. To confirm the presence of a musical cipher, a frequency analysis was performed on the letters from the full title of Luther’s hymn (Table 4.1).

These results were compared with the first 24 notes in the Enigma theme based on note letters and durations (Table 4.2). After experimenting with strict substitution ciphers in which one plaintext letter is matched with one note name and value, this approach was ruled out as untenable. This outcome mirrors those reached by other researchers using the same methodology. Strict substitution simply will not do, and more importantly, it is far too simplistic for someone with Elgar's fluency in complex ciphers. For him to employ such a basic cipher would be too easy to crack, so a more sophisticated approach should be expected. Were there other more intricate methods of musical encipherment known to Elgar? The answer is yes.

Eric Sams theorized Robert Schumann learned about various musical ciphers from a book in his father’s bookstore by Ludwig Klübner called Kryptographik (1809).[13]  One method Klübner describes is a musical cipher wheel that encodes single plaintext letters using two-note combinations.[14] Schumann, one of Elgar’s favorite composers, was known to employ musical ciphers in his works. Based on Klübner’s musical cipher wheel, an analysis of note pairs in the Enigma melody was performed. However, this proved just as unproductive as the strict substitution method. Various attempts at decryption using a variety of possible cipher methods yielded no meaningful results over a three month period. 373 days after I concluded Ein feste Burg was the missing Principal Theme, I experienced an epiphany: Two-note combinations were possible, but it was necessary to consider both the melody and bass lines for the complete cipher.
The coupling of melody and bass notes was strongly suggested by Elgar’s use of six note letters in the melody (i.e., a, b, c, d, f & g), and six in the bass (a, b, c, d, e & g). Between the two lines, all seven musical note letters are used with the only difference appearing between the E and F with F used in the melody, and E in the bass. Later analysis revealed these notes were combined just as i and j or u and v are merged when enciphering entire alphabetical sequences. It is intriguing Robert Schumann (one of Elgar’s ideal composers) used the notes E and F in musical ciphers to symbolize his alter egos, Eusebius and Florestan. [15] A forceful literary basis suggesting the conflation of the letters E and F may be found in Canto XXXIII of Purgatory from Dante’s Divine Comedy in which Beatrice describes her enigma forte (“hard enigma”) because the first letters are e and f. Elgar makes numerous allusions to that epic poetic work bridging the divide between the Middle Ages and the Renaissance. By combining the note letters E and F, the end result permits the use of a 6 by 6 checkerboard configuration with 6 melody notes for each column and 6 bass notes for each row. By pairing a melody note with a bass note, a single cell in the checkerboard grid is designated at their intersection containing a plain text letter.
There is a far more compelling reason to conclude Elgar was inspired to create a musical checkerboard cipher, although I was unaware of it until only after I discovered the Enigma checkerboard cipher. Stowed away in Elgar’s personal library are four articles from the 1896 edition of The Pall Mall Magazine entitled Secrets in Cipher. These papers are now in the possession of the Elgar Birthplace Museum. The third article contains a musical cipher from the era of George II showing how twelve quarter notes and twelve eighth notes were used to encipher 24 letters of the English alphabet. In a surprising parallel, Elgar employs exactly twelve quarter notes and twelve eighth notes in the first six bars of the Enigma theme. The fourth article presents an allegedly insoluble Nihilist cipher Elgar reports solving in his 1905 biography.[16] The Nihilist cipher is a variant of the Polybius square and in some versions is comprised of a six-by-six grid “. . . to accommodate the 35 letters of the old Russian alphabet.”[17]
My suspicion Elgar devised a 6 x 6 checkerboard cipher was bolstered retroactively by the revelation of these articles from The Pall Mall Magazine. David Kahn reports the ancient Greek Polybius originally invented the checkerboard as a signaling method to relay messages over long distances at night using torches.[18] In this context, Elgar’s cryptic reference to a dark saying takes on a whole new light. The Polybius square is indeed a very old cipher which Elgar knew intimately from his studies of historical cryptography. Further circumstantial evidence hinting at the presence of a box cipher comes in the form of a large square Elgar drew on the lower left side of the original cover page of the Enigma Variations.

Besides containing the letters FEb (which is an anagram of EFB, the initials for Ein feste Burg), this unusually placed square directly overlays on the following page the very same staves suspected of harboring Elgar's musical Polybius square cipher.

The configuration of the Polybius square cipher key is hinted at by Elgar's use of six different names and titles which are each six letters in length. By stacking these names and titles, a six-by-six cipher table is created. It should be noted the German version of Elgar's first name (Eduard) is only half complete with the initials for Variation XIV. For this reason, the letters ARD are shown in italics.

The next step in the decryption process was to map out the bass/melody note pairs in the first six bars of Enigma Theme and compare them with the letter frequencies of Ein feste Burg (Table 4.3).  To identify note pairings, each bass quarter note was treated as a half note. These bass line extensions from the original quarter notes are suggested by the recapitulation of the opening six bars in measures 11 – 16 where they are played continuously as half notes. Bass notes not sounding continuously but implied by this analysis are shown in parentheses. In hindsight, Elgar’s decision to limit the majority of the bass notes to quarter notes in the opening six bars appears to be a means for obscuring the cipher.

Unmistakable correlations were found between bass-melody note pairings and plain text letter frequencies (Table 4.4). Discernible bass-melody note pairings were easily identified for letters with frequencies of 4 (e and t), 3 (s), and in three cases with letters with frequencies of 2 (g, i, n, r and u). The remaining two bass-melody pairings for letters with frequencies of 2 were not immediately apparent. The first to be paired were B flat-G and D-B flat because together they form a G minor triad, the opening chord of the Enigma theme. Also, they share a common note in the reverse positions (B flat). The final match pair was found to be A-C and E flat-A because of the shared note in reverse positions (A) as was the case with the previous pairing. A more nuanced explanation would be that the letters C, A, and E are the initials for Elgar's wife and form the subtitle for Variation I. Like the previous match pair, these notes also form a triad. In the circle of fifths the notes B, G, and D are closely aligned since G major is adjacent to D major, and B is the relative minor to D.  A similar pattern holds true for C major, A minor, and E minor. Remarkably these three-note clusters are adjacent to one another within the circle of fifths.

The remaining three bass/melody pairs (B-F, E flat-G, and E flat-B flat) were assigned to letters with single frequencies (b, f, and o).

After testing all possible plain text letter solutions restricted by bass/melody note frequency pairings over the first 6 bars of the Enigma Theme, an outcome that can only be described as breathtaking is realized (Table 4.5).

In measure 1, the plain text solution is gsus, a phonetic spelling for Jesus. This special friend according to Elgar’s Roman Catholic faith is undoubtedly the hidden friend enshrined in Variation XIII, a subject that is explored more fully here. Elgar's use of phonetic spellings, particularly for names, is established by his own personal correspondence. Specifically, he sometimes signed his letters phonetically as Edwd.

In measure 2, the plain text solution is grts, the phonetic spelling of the Latin words “gratus,” “gratis,” and “gratias.” In his youth Elgar attended three Catholic schools and during this time received extensive instruction in Latin, so he was very familiar with this academic and liturgical language. According to Cassell’s Latin Dictionary, “gratus” means “pleasing, welcome, agreeable” and “loved.”[19] A Copious and Critical English-Latin Dictionary first published in 1871 and still in use when Elgar composed the Enigma Variations defines “gratus” as “beloved” and “favorite.”[20] The terms “beloved” and “pleasing” are used about Jesus after his baptism when a voice from heaven said, “This is my beloved Son, in whom I am well-pleased.”[21] An alternative realization of the plain text grts is the Latin word for grace – “gratis.”  As an adverb, it is defined as “without recompense, for nothing, gratis.”[22] As a noun “gratis” means “thanks” or “thanksgiving,” especially to a deity.
The phrase “Jesus Gratias” means “Thanks be to Jesus,” and closely mirrors a phrase from the Latin mass “Deo Gratias” meaning “Thanks be to God.” The alternative spelling “gratias” appears in the Ordinary of the Latin Mass in the seventh sentence of the Gloria as, “Gratias agimus tibi propter magnam gloriam tuam” ("We give thee thanks for thy great glory").[23] Following the first measure’s reference to Jesus, the appearance of the Latin words for beloved, thanksgiving, and grace are theologically elegant and compelling. In the Christian canon, Jesus is described as beloved and pleasing to God and serves as the supreme example of divine grace. This message is made plain in the book of Ephesians which states, “For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God—not by works, so that no one can boast.”[24]
As part of her conversion to Roman Catholicism four years after marrying Elgar, Alice received instruction in Latin. An entry in her diary on September 3, 1896 illustrates her very Roman Catholic penchant for sprinkling her writing with Latin phrases. It reads, To rehearsal at Queen's Hall about 11 – Perfectly lovely morning – Deo Gratias – for it.”[25] It is noteworthy the Latin terms in the opening of Elgar's 'dark saying' appear in the correct word order with the name gsus coming before grts. The use of the correct word order in measures 1 and 2 is significant because the same thing occurs with English words in measures 3 and 4. As Tim Roberts demonstrates with his alleged solution to the Dorabella cipher, the statistical odds of words from multiple languages occurring in meaningful pairs and in the correct order is far too remote to be the result of chance.

The Shroud of Turin and its photographic negative

Measure 3 produces the phonetic phrase inou, or “I know you.” In measure four the phonetic spelling is betr, or “better.” Combining the plain text results for measures three and four generates the phrase “I know you better.”  Following the plain text results from measures one and two citing Jesus and some of his attributes, the phrase definitely implies Elgar knows Jesus better. There is a historic photograph taken five months before Elgar began work on the Enigma Variations that would explain this cipher revelation. Secondo Pia took the first picture of the Turin Shroud in May 1898, and the photographic negative reveals a miraculous image of what many to be the crucified body of Jesus. This photographic negative became an international sensation in the media, and devout Catholics displayed copies as part of their devotion to the Holy Face. For Roman Catholics like Elgar, the opportunity to gaze at the actual face of their Savior would be a profoundly moving spiritual experience and a powerful confirmation of their faith. To see the actual face of Jesus would certainly prompt a Roman Catholic like Elgar to declare he knows Jesus better. Elgar's allusion to the Turin Shroud is bolstered by the discovery in Variation XIII of an elimination cipher that spells TURIN S, as in the Turin Shroud. The cipher references to Jesus contained within the Enigma Theme and Variation XIII are mutually reinforcing, thereby proving both ciphers are genuine.
The act of knowing Jesus is theologically significant for he told his disciples, “No one knows the Son except the Father, and no one knows the Father except the Son and those to whom the Son chooses to reveal him.” (emphasis added) [26] He also taught, “I am the way and the truth and the life. No one comes to the Father except through me. If you really knew me, you would know my Father as well. From now on, you do know him and have seen him.” (emphasis added) [27] Knowing Jesus means knowing his Father and being reconciled with Him. The phrase “I know you better” is nothing less in theological terms than a profession of Elgar’s faith in Jesus given the plain text results of measures one and two. The formation of a phrase based on the plain text solutions from bars three and four (“I know you better”) mirrors the pattern of generating a phrase from the plain text results from measures one and two (“Jesus Gratias” meaning “Thanks be to Jesus”). By gazing at the face of his crucified Lord as revealed by the miraculous 1898 photographic negative of the Turin Shroud, Elgar could rightfully claim to know his Lord better.

Jesus in Jewish Aramaic

The plain text solution for measure 5 is teni. Popular biblical commentaries used during Elgar's lifetime explain when Jesus asked the Samaritan woman at the well for a drink of water, he began his request with that exact word by saying, "Teni li listosh." The word teni is indelibly linked to Jesus' encounter with the Samaritan woman at the well when he plainly revealed his identity to her as the Messiah. In view of the plain text results in measures 1 through 4 referring to Jesus, the theological context of teni is undoubtedly what Elgar intended. His personal library housed as many as 100 religious texts including Bibles, theological works and biblical commentaries, so Elgar was well versed in theology. In what language is the word teni? Multiple commentaries available during the 1890s claim that Jesus spoke to the Samaritan woman in Aramaic.  For instance, The Pulpit Commentaries dating from 1897 states:
The Samaritan woman therefore saith to him, How is it (compare this "how" with that of Nicodemus. Jesus had at once provoked inquiry, which he was not unwilling to gratify)—How is it that thou, being a Jew? She would have known that he was a Jew by his speech, for the Samaritans were accustomed to turn the sound of sh into that of s; and so, when Jesus said in Jewish Aramaic, Teni lishekoth, "Give me to drink," while she would herself have said, Teni lisekoth, his speech would betray him.
Another example occurs in The Preacher's Complete Homiletical Commentary on St. John dating from 1892 which also asserts the word teni is Aramaic:
The woman knew He was a Jew probably by His dress, but it may be also by His accent. It has been pointed out that the words of the question asked by Jesus in Aramaic would be תני לי לשׁחת (Teni li lish'ḥoth), whereas the woman would have said לשׂחת (lis'ḥoth) (vide Jud 12:5-6).
While these and other commentaries of his era would have reasonably lead Elgar to believe the word teni is Aramaic, it is actually Hebrew.  Charles C. Torrey of Yale University lays out a compelling case that the Gospel of John was originally written in Aramaic, the vernacular of Judea in the first century. Indeed, it is well established that Jesus and his disciples spoke primarily Aramaic. For this explicit reason, the commentaries correctly report that Jesus conversed with the Samaritan woman in Aramaic. However, the translation provided was mistakenly in Hebrew, a language very similar to Aramaic. The correct version from the Aramaic Peshitta is, "Hav li maya, eshteh," which translates as, "Give me water, I will drink."

Jesus meets the Samaritan woman at the well

In measure 6, the plain text solution is fete, a word defined as "a lavish party or religious festival." Phonetically it spells feat, a word Merriam-Webster defines as “an act or product of skill, endurance, or ingenuity.” Combining these cipher results from measures five and six produces “Night Feat,” denoting an ingenious act veiled in darkness. This is an appropriate description of Elgar’s "dark saying," a music box cipher. Remarkably, the plain text result for measure six may be respelled as “teef”, the phonetic spelling for the German word “tief” meaning “deep” as in a deep, dark secret. This intimates the fact that the language of the title of the missing Principal theme is in German. Fete is also phonetic for feet, and there are a number of biblical passages mentioning feet in connection with Christ's ministry. In the home of a Pharisee, a sinful woman washed the feet of Jesus with her tears, wiping them with her hair and anointing them with costly perfume. In a deeply symbolic act, Jesus washed the feet of his disciples on the eve of his crucifixion. A Messianic Psalms vividly describes his suffering on the cross, mentioning how his executioners pierced his hands and his feet and cast lots for his clothing.
An Elegant Anagram
The use of phonetic spellings is a diabolically difficult device used to defy decryption, particularly when done in multiple languages in a single, encoded message. Elgar’s personal correspondence is rife with trick spellings as Eric Sams meticulously mentions with “excuse” spelled as “xqqq”, and “score” as “ckor”, “skore”, “skorh”, “skowre”, “skourrghe”, “csquorr”, “skourghowore”, and “ssczowoughohr”.[30]  Even if such a cipher were compromised, the outcome would still not easily reveal the title of the missing melody since it is anagrammatized. The enigma is therefore multilayered as the solution letters must be rearranged to spell the correct solution. With 24 letters in the title of the missing melody, a minimum of 41,667 six-word combinations in English are possible with correctly spelled words. When phonetic spellings and multiple languages are added to the mix, the possibilities rise exponentially.
It is remarkable the first letters of the four Enigma Cipher languages – English, Latin, German and Aramaic – form the first four letters in the composer’s last name. This suggests a secret signature within the cipher. The use of multiple languages has a theological basis because the sign fastened to the cross announcing “Jesus of Nazareth, the king of the Jews” was written in multiple languages: Hebrew, Latin, and Greek.[31] This sign is commonly represented in works of art in the form of a rectangular plaque or parchment. Amazingly the phonetically spelled words and phrases from Elgar’s ‘dark saying’ may be rearranged to spell Ein feste Burg ist Unser Gott. Such an incredible outcome could only be the result of a deliberate, premeditated plan, one far beyond my limited powers of invention. To suggest any other explanation, particularly one devoid of forethought and detailed planning on Elgar's part, would be ludicrous. Elgar’s Music Box Cipher key is shown in Table 4.6.

Table 4.6 consists of a six-by-six checkerboard, an intriguing outcome when one realizes the opus number for the Enigma Variations is 36, the product of 6 multiplied by itself.  Plain text letters are shown while null cells contain only asterisks, although it would be simple enough to fill in the null cells with any combination of letters. To find a solution letter, locate the intersection of the melody and bass notes as outlined in Table 4.5. For instance, the combination of the melody note A with the bass note C yields the plain text letter t. Given the size of the grid, multiple pairings are possible for the same letter, furnishing another effective means to confuse attempts at unraveling the cipher. It should be emphasized Elgar did not provide homophones for the letter e but did so for letters typically having lower frequencies such as g and s.  This practice is also another proven method for sowing confusion and defeating attempts at cracking a cipher. That Elgar closely studied an allegedly unbreakable Nihilist cipher in the 1896 series of The Pall Mall Magazine – two years before he composed the Enigma Variations and one year before he created his still unsolved Dorabella cipher – is particularly relevant to this discovery. In May 2009  the Dorabella cipher was allegedly cracked by Tim S. Roberts, and his contribution confirms Elgars cryptological penchant for using phonetic spellings and multiple languages. This remarkable discovery is wholly consistent with my independent analysis and decryption of the Enigma cipher.
One curious aspect of the cipher table is the close proximity of solution letters that form identifiable words. Like the dark saying, these spellings occur in multiple languages. In the very center of the table, the letters s, i, and n form a triangle spelling the word “sin.” Two other triangular letter patterns intersecting on the s of the word “sin” spell “gsus,” the phonetic spelling for Jesus. According to scripture, Jesus became sin on the cross, so there is a theological justification for such a symbolic overlapping of these words. The first triangle is formed between the u in row one, the g in row two, and the s in row three. The second triangle is formed between the s and u in row one and the s in row three. The spelling for the word “fig” is found as an anagram in the last three cells of column two. One of the miracles of Jesus was cursing the fig tree.
Row three contains the letters “trse” forming the phonetic spelling for the word “trace,” a word meaning to discover, hint, locate, draw or outline. The phonetic for the word “begin” is formed by a triangular letter pattern beginning with the b in column five, progressing to the g in column four, and down to the n in the same column. The final column contains the letters e, o, and s that form the word “eos”. Elgar quotes a Gregorian chant in his oratorio The Apostles (1903) called “Constitues eos.”[32] It is noteworthy this particular chant is used in both Catholic and Lutheran services. In rows 3 through 5, the letters for the word “rift” are configured in the shape of an inverted L. The word “rift” can mean schism or split, an apt description of the Reformation. The letter L may be linked to the Great Reformation because it is the first letter from the last name of one of that movement’s most prominent leaders: Luther.
A comparison of Elgar's box cipher table with the six-letter name grid mentioned earlier produces some astonishing parallels. One example is the presence of four exact letter matches as shown in Tables 4.7 and 4.8. There are many other fascinating connections between the two grids, not to mention some revealing anagrams.

Alternating Sixths
The discovery of a six-by-six music checkerboard cipher draws renewed attention to Elgar's use of the music interval known as the sixth within the Enigma Theme. At Rehearsal 1 the Enigma Theme is played in sixths by the first and second violins. The inversion of the sixth is the third, and this interval is used extensively in the four measures preceding Rehearsal 1. The third and the sixth feature prominently in the Enigma Theme, and remarkable feature since the opus number for this work is 36.

In Variation XIII alternating sixths are indelibly linked to the Enigma Theme's palindromic rhythmic structure. For instance, one measure after Rehearsal 56 the violas play alternating sixths as an accompaniment figure to the Mendelssohn fragments to portray the soothing undulations of the sea. That the lowest note for the violas in this section is an open C string alludes to a ship traveling on the open sea. Elgar's use of the alternating sixths in conjunction with the Enigma Theme's distinctive palindromic rhythm may be reasonably interpreted as a clue regarding both the structure and location of his music cipher.

Contrary to the presumption of mainline scholars, Elgar did indeed write down the solution to his Enigma Variations while he was very much alive. He stealthily accomplished this feat in the opening six bars of the Enigma Theme using an ingenious Music Box Cipher. With the answer hidden in plain sight, Elgar evokes the words of Jesus who asked his disciples, “Do you have eyes but fail to see, and ears but fail to hear?”[33] For over a century the solution has been seen and heard countless times, yet ironically those with eyes and ears failed to perceive it. This is surely the pinnacle of cryptography, an art form Elgar found irresistible throughout his life. Now we know the secret he took to his grave. The covert principal Theme to the Enigma Variations is Martin Luther’s famous hymn Ein feste Burg ist unser Gott. The Enigma Variations is an enigma no more. This incredible discovery prompts one question for the career academic whose first three initials phonetically spell "jape" (J.P.E. Harper-Scott): When will the Ark of the Covenant and the Holy Grail go on permanent display at the British Museum? To learn more about the secrets behind one of Elgar’s most celebrated symphonic achievements, read my free eBook Elgar’s Enigmas ExposedPlease support my original research by becoming a sponsor on Patreon.

[1] Kennedy, M. (2004). The Life of Elgar. New York: Cambridge University Press. p. 67.    
[2] Harper-Scott, J. P. (2007). Elgar: An extraordinary life. Dorking: Associated Board Of The Royal School Of Music, p. 49.
[3] Pascal, B. (1995). Penseés. New York: Penguin, p. 63.
[4] Kennedy, M. (2004). The Life of Elgar. New York: Cambridge University Press. p. 66.
[5] Moore, J. N. (1999). Edward Elgar: A Creative Life (Clarendon Paperbacks) (New Ed.). New York: Oxford University Press, USA, p. 114.
[6] Kahn, David. The Code Breakers. New York: The Macmillan Company, 1968, p. 800.
[7] Buckley, Robert J. (1905). Sir Edward Elgar). New York: Kessinger Publishing, Llc, 2009, p. 41.
[8] McClelland, C. (2007, Winter). Shadows of the evening: new light on Elgar's 'dark saying'. Musical Times, Winter , p. 44.
[9] London British Library Add. MS 58003, f.2v.
[10] Daverio, J. (2008). Crossing Paths: Schubert, Schumann, and Brahms. New York: Oxford University Press, USA, p. 101.
[11] McVeagh, D. (2007). Elgar the Music Maker. Rochester, NY: Boydell Press, p. 3.
[12] Turner, Patrick. Elgar's 'Enigma' Variations - a Centenary Celebration. London: Thames Publishing, 1999, p. 46.
[13] Sams, Eric. Did Schumann use ciphers? London, The Musical Times, Aug., (1965), p. 584-591
[14] Daverio, John. Crossing Paths: Schubert, Schumann, and Brahms. New York: Oxford University Press, USA, 2008, p. 83.
[15] Dowley, T. (1982). Schumann: His Life and Times. Neptune City, NJ: Paganiniana Publications, Inc., p. 46-47.
[16] Buckley, Robert J. Sir Edward Elgar (1905). New York: Kessinger Publishing, Llc, 2009, p. 41.
[17] Kahn, David. The Code Breakers. New York: The Macmillan Company, 1968, p. 620.
[18] Ibid, p. 83.
[19] Cassell's Latin Dictionary (5th ed.). (2000). New York: Continuum, p. 268.
[20] Hall, W., & Smith, T. (1871). A Copious and Critical English-Latin Dictionary. New York: American Book Co., p. 75.
[22] Cassell's Latin Dictionary (5th ed.). (2000). New York: Continuum, p. 267-268.
[23] Randel, D. M. (1986). The New Harvard Dictionary of Music (Harvard University Press Reference Library). Cambridge: Belknap Press, pp. 471-472
[24] Ephesians 2:8-9
[25] The Elgar Society Journal, Vol. 15 No. 5, p. 12.
[28] Cassell's Latin Dictionary (5th ed.). (2000). New York: Continuum, p. 598.
[29] Ibid, p. 599.
[30] Cited from an unpublished paper by Eric Sams entitled Elgar’s Cipher Table (1970-71).
[32] Moore, J. N. (1987). Edward Elgar: A Creative Life. New York: Oxford University Press, p. 383.
[33] Mark 8:18


Anonymous said...

While I am happy for you that you are so convinced by your own theory, I have to say that I am not.

1) You can't just shoehorn Luther's melody into the Elgar theme by playing fast and loose with the accidentals. Luther's melody begins with a repeated phrase and either Elgar's supposed interpretation of it is in G minor or it's in G major, but not one followed by the other.

2) The miserable voice-leading resulting from forcing the Luther theme on Elgar's may be acceptable to 21st century ears but would never have passed muster in 1899. The parallel fifths in m. 12, the E-flat-D dissonance resolving to a dissonance in m. 13, and so forth. Dozens of other melodies can and have been shoe-horned onto Elgar's and with no better contrapuntal outcomes.

3) Why would the devoutly Catholic Elgar choose to encrypt the most famous hymn of the Protestant Reformation into this work? If it were true, then another interpretation might be that Elgar was secretly disaffected with the Catholic Church and longed to be a Lutheran. We can spin out theories like this all day long.

4) And as for the thirteenth variation and the encrypting of the letters J and C through the Roman numerals X and III, isn't it just as possible that Elgar might have meant XIII as the thirteenth letter of the alphabet, which is M as in Mary [Lygon]?

The most interesting part of the post has to do with Elgar's fascination with ciphers, and very complicated ciphers at that. Elgar told us that there was a cipher present in this work, but we all know that it could be anything: a cantus firmus in whole notes, one per bar of the theme, that spells out a name or a message -- a rhythm that suggests a spoken phrase -- anything at all. But I am certain that it is not Luther's melody, just as it's not Rule Britannia or For He's a Jolly Good Fellow. You may want it to be Luther's melody because it clearly means a great deal to you that this be true, but the overwhelming musical evidence as demonstrated in your own recorded musical examples tells me that you are sadly mistaken.

Robert Padgett said...

Anonymous rejects my thesis on the following grounds:

1) Elgar is not supposed to modulate between the minor and major keys while attempting to conceal a source melody. As no basis is given for such an assertion, no refutation is necessary. Modulating between major and minor keys would certainly be an effective camouflage for obscuring a source melody. As a composer, Elgar could and did write whatever he pleased.

2) Elgar’s use of parallel fifths in measure 12 contradicts the rules of legitimate counterpoint. Perhaps if Anonymous consulted Elgar’s first biography by Robert J. Buckley, the following relevant passages would merit closer scrutiny:

From the Introduction Buckley writes:

“I have not given any space to consideration of Elgar’s wanderings from the paths of contrapuntal rectitude, as laid down by the theory formalists. The Roman soldiers tied weights to their sandals when marching for exercise, that by discarding them in time of war they might rejoice in comparative lightness and freedom. So, it would seem, are musicians weighted in the study of strict counterpoint, that in free composition they may derive additional inspiration from the joy of casting the load aside. It may be suggested that Elgar has cast away not only the weights but also the sandals. The sequence of consecutive fifths in ‘The Apostles’ is calculated to make the old theorists uneasy in their graves. But this is only history repeating itself. The Man of Progress is necessarily the Breaker of Laws, and if the Law-breaker is justified by results, we can demand no more.”

Buckley later quotes Elgar stating:

“You were talking of contrapuntal rules and restrictions. I have gone over them all: marked, learned, and inwardly digested everything available in theoretical instruction I could come across (and I think I have come across most of what has been written); and I cherish a profound respect for the old theorists. They were useful in their day, but they were not entitled to lay down hard and fast rules for all composers to the end of time.”

3) Elgar’s Roman Catholic faith barred him from quoting a Protestant hymn. Strangely enough, Elgar’s faith did not prevent him for quoting the music of a devout Lutheran in Variation XIII, namely Felix Mendelssohn. Even more bizarrely, Elgar produced some of his finest music for the Anglican Church, e.g., a setting of Psalm 48 ‘Great is the Lord’. It is highly coincidental the lyrics for ‘Ein feste Burg’ come from Psalm 46. The presumption Elgar’s Roman Catholic faith prevented him from surreptitiously quoting a famous Protestant hymn is resoundingly refuted by the facts.

4) The Roman Numerals for the thirteenth variation could be interpreted to represent the letter M instead of J and C. In focusing on the letter M, is Anonymous subconsciously alluding to the word ‘Messiah’? In acknowledging that the Roman numerals for Variation XIII do indeed form the initials for Jesus Christ, Anonymous all but concedes my point. Moreover, my interpretation is bolstered by the existence within that variation of a musical cipher that spells “S TURIN”, a clear reference to the burial cloth of Christ – the Shroud of Turin. Thanks to Anonymous, the 'Messiah' allusion is an added bonus.

Ironically, the one who is grossly ill informed on this matter is none other than Anonymous (which is likely why that individual chooses to remain such). The writing of that party reeks of the foul stench of academic ineptitude.

Robert Padgett said...

In Variation XIII Elgar’s use of the major and minor modes with the Mendelssohn fragments clearly reveals his intent to utilize both modes in his surreptitious treatment of the unstated Principal Theme. Since the Enigma Theme is in reality a contrapuntal ‘negative’ of the unstated Principal Theme, Elgar’s presentation of the Enigma Theme in both the major and minor modes throughout the Variations bolsters this conclusion. To naively insist he would arbitrarily limit himself to either the major or minor mode with his mapping of the unstated Principal Theme over the Enigma Theme overlooks these obvious facts. The modal duality of ‘Ein feste Burg’ serves as an effective smokescreen that defeats straightforward discovery, a strategy that should be expected of a master cryptographer like Elgar. Moreover, such a modal duality symbolically alludes to the two malleable parts (in this case, the top and bottom lines of the music) that together encipher one plaintext unit within a checkerboard cipher. In this instance, Anonymous is synonymous with preposterous.

Henry Pimpernell said...

It is not correct that Tim Roberts was the first to solve the Dorabella cipher. There is a much earlier solution proposed by Eric Sams in 1970 (The Musical Times, Feb. 1970)

Robert Padgett said...

Thank you for your comment. While you are correct in observing Eric Sams offered a 'solution' to the Dorabella cipher, he neglected to provide the correct one. This daunting task was only recently accomplished by Tim Roberts, and the overwhelming evidence he marshals makes that conclusion inescapable. Roberts should be congratulated for his brilliant and diligent work. The art of cryptography is not for the feeble minded or faint of heart.

escher7 said...

It is a simple substitution. No one used the correct English frequency table.

Anonymous said...

I don't think we can generally accept Tim Roberts's solution. The method used is partially fixed to fit the plain text he proposed as the solution. While it remarkably seems to make sense, there are just too many gaps in the decryption key he used. But it's seems like the most likely one so far.

Robert Padgett said...

We can and should generally accept and acknowledge Tim Rober's persuasive decryption of the Dorabella Cipher, particularly since it shares some uncanny parallels with my analysis of Elgar's Music Box Cipher. These overlapping features are phonetic spellings and the use of multiple languages in the cipher text. Tim Roberts made his remarkable discovery independent of my own, and the statistical probability of his solution is infinitesimally minute.

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.