Sunday, June 28, 2015

Four Integrated Enigma Theme Ciphers

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.
Edgar Allan Poe


It is no secret Edward Elgar (1857-1934) was captivated by secret codes, riddles and wordplay. As the respected biographer Michael Kennedy observes, Elgar “…loved puns, acrostics, secret codes and crossword puzzles.”[1] It should come as no surprise the Enigma Variations harbor several ciphers that answer its three core conundrums:
  1. What is the secret melodic Principal Theme?
  2. What is the ‘dark saying’ hidden in the Enigma Theme?
  3. Who is the secret friend portrayed in Variation XIII?

The Enigma Theme contains multiple ciphers that furnish specific, mutually reinforcing answers to these enduring questions. The covert melodic Principal Theme is Ein feste Burg (A Mighty Fortress) by Martin Luther. The ‘dark saying’ concealed by the Enigma Theme is a musical Polybius Square cipher (more playfully known as a Music Box Cipher) which encodes a series of phrases that are collectively an anagram of the complete German title Ein feste Burg ist Unser Gott. The secret friend to whom Variation XIII is dedicated is Jesus Christ. In support of this assessment, four integrated ciphers from the Enigma Theme will be described:
  1. Locks Cipher
  2. Keys Cipher 
  3. Psalm Cipher
  4. Music Box Cipher

The Locks Cipher

Ciphers are meant to be decoded, but first they must be found. In the case of the Enigma Variations, an obvious place to search is at the beginning with the oddly constructed Enigma Theme. Its very title suggests a cipher. These opening six measures are of special interest because of an oddly placed double bar at the end of measure 6. In music a double bar typically signals the end of a section, so the placement of one so close to the beginning is conspicuously anomalous. The most promising starting point to uncover a cipher is the Enigma Theme’s opening six measures.
The unusual position of the double bar at the terminus of measure 6 hints at a cipher in these opening measures. An analysis of these six measures revealed the total number of notes performed by each of the four active instrumental parts does not exceed the number of letters in the English alphabet. This feature suggests a rather basic Letter Number Cipher in which the total number of notes for each part is converted into the corresponding letter in the alphabet.
The total notes performed by each instrumental part were counted over the first six measures of the Enigma Theme (Figure 1). Instrumental parts that perform notes over these measures are the first and second violins, violas and cellos – the string quartet. The first violin part has the highest total number at 24 notes. The second violins have the second highest with 17 notes. The violas have the third highest with 15 notes, and the cellos with only 12 notes. This pattern presents an appealing symmetry because the number of notes decreases with each step down in the string choir. The lower the voice, the fewer the notes.

The next step in the decryption required converting these four note totals into corresponding letters from the alphabet (1 = A, 2 = B, 3 = C, etc.). The results of this elementary Letter Number conversion are displayed in Table 1. The plaintext solution is LOQX, a phonetic version of locks. Elgar employed trick spellings in his correspondence, so such a peculiar spelling is not unprecedented.

Why locks? Locks come with keys, and so do ciphers. This decryption indicates there are multiple ciphers lurking within the Enigma Theme. When the same note totals are applied to the alphabet in reverse order (i.e., 1 = Z, 2 = Y, 3 = X, etc.), the plaintext result is CJLO. When treated as an anagram, these letters may be reshuffled as LOJC.

Lo is a common biblical term meaning to look, see or behold. Lo is often associated with behold as in the phrase ‘lo and behold.’ J.C. are the initials for Elgar’s secret friend, Jesus Christ. These letters are covertly formed by the Roman numerals of his variation (XIII). X represents 10, and J is the tenth letter of the alphabet. III stands for 3, and C is the third letter. LOJC may reasonably be interpreted as Behold Jesus Christ.

The Keys Cipher

Returning to this idea of keys implicated by the LOQX decryption, it is vitally important to recognize the Enigma Theme is performed in two contrasting keys, the minor and major modes of G. The accidentals for these two keys are B-flat and E-flat for G minor, and F-sharp for G major. It is nothing less than extraordinary that this particular set of accidentals furnish the initials (E.F.B.) for these covert Principal Theme, Ein feste Burg by Martin Luther. Consistent with the forward Letter Number decryption of the Locks Cipher, the key signatures of the Enigma Theme literally furnish the keys to unlocking Elgar’s melodic vault.

The Psalm Cipher

How can we be certain the initials encoded by the Keys Cipher (E.F.B.) stand for Ein feste Burg? Important clarifying information is provided by another cipher hidden among the Performance Directions of the Enigma Theme’s opening measure. In that first bar there are seven distinct performance directions: Andante, molto espressivo, Piano, legato e sostenuto. The first letters of these seemingly unremarkable Performance Directions form the ingenious anagram EE’s PSALM. The initials EE evidently stand for the composer himself, Edward Elgar. The word Psalm indicates the book of Psalms in the Old Testament Bible which has a total of 150 chapters. This number presents a numerological parallel with the Enigma Variations which it is comprised of 15 movements, the Enigma Theme followed by fourteen variations.

Since the word psalm is in the singular case, this cipher singles out only one of those chapters. The question remains, which one? The Ternary ABA Structure of the Enigma Theme conveniently encodes the precise number. The opening A Section in G minor is 6 measures followed by the contrasting B section in G major which is 4 measures. Pairing these two numbers together creates the natural number 46. It is truly stunning that Martin Luther drew the title and inspiration for his most epic hymn, Ein feste Burg, from Psalm 46. The Performance Directions Anagram Cipher accurately identifies the book from the Old Testament (Psalms), and the number of measures in the A and B sections of the Ternary structure spell out the precise chapter (46). The biblical source of the melodic solution is intimated by Elgar’s use of Old Testament names for Variations VI (Ysobel) and IX (Nimrod).

Decoding Elgar’s Dark Saying

Armed with the title of the absent Principal Theme, the next step was to find the lock, insert the key, and unlock the contents of Elgar’s mysterious ‘dark saying.’ But where was that lock? Where was the location of this enigmatic music cipher? The first six measures of the Enigma Theme appeared to be the most obvious place to begin the search due to the odd  placement of a double bar at the end of measure 6 (Figure 3).

A double bar is commonly used to denote the end of a movement or a section, but neither was evidently the case here. The Enigma Theme is seventeen measures in length, hence the placement of a double bar so close to the beginning is highly conspicuous. It was reasoned Elgar inserted a double bar in measure 6 to demarcate not the close of a section, but the end of a cipher.
There is an array of preternatural coincidences supporting the hypothesis that the first six measures of the Enigma theme is indeed a music cipher. First, the total number of letters in the title Ein feste Burg ist unser Gott is the same as the number of melody notes played over the first six bars: 24. Second, the number of measures is identical to the number of words in the missing melody’s complete 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 observes:
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.[2]
Fourth, the original short score lends compelling circumstantial evidence for a music cipher in the first six bars of the Enigma Theme because the melody and bass notes are in black ink while the intervening notes are in pencil.[3] This presents a highly suggestive parallel with Elgar’s solution to the John Holt Schooling’s Nihilist cipher which was painted on a wooden box with black paint. Fifth, at least three of Elgar’s favorite composers included music ciphers in their scores: J.S. Bach, Robert Schumann, and Franz Listz. 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 the German musical nomenclature, B-flat is represented by B, and B natural by 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.[4]
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 musical motive.[5] Finally, the original score has the word Enigma centered directly over the first six bars, marking the precise location of the cipher and its ‘dark saying.’ As other researchers point out, the phrase ‘dark saying’ is one of the definitions for enigma.[6] The first word from the covert Principal Theme’s title (Ein) is found in the first three letters of Enigma with its last letter providing the correct translation (A). All the available evidence points to the first six bars of the Enigma Theme as the most likely location of a music cipher. The presence of the Keys and Performance Anagram ciphers only bolsters this suspicion.
To assess the presence of a music cipher, a frequency analysis was first performed on  the letters from the complete title of Ein feste Burg ist Unser Gott (Table 4). The results show there are a total of 24 letters with 11 distinct types.

These results were carefully compared with the first 24 notes in the Enigma Theme based on note letters and durations (Table 5).

Extensive experimentation with strict substitution ciphers in which one plaintext letter is matched with each note type yielded no meaningful results. This was an expected outcome because it was also encountered by other researchers. For Elgar to employ such an elementary cipher would be too easy to unravel, so something more sophisticated should be expected. Were there other more complex cipher methods known to Elgar at the time he composed the Enigma Variations?
Eric Sams theorized Robert Schumann learned about an assortment of music ciphers from a book in his father’s bookstore by Ludwig Klübner called Kryptographik (1809).[7]  One method Klübner describes is a sophisticated music cipher wheel that encodes single plaintext letters using two note combinations.[8] Schumann was one of Elgar’s favorite composers and was known to employ music ciphers in his works. Recognizing the significance of Klübner’s music cipher wheel, an analysis of melodic note pairs in the Enigma melody was performed. However, this proved just as unproductive as the strict substitution method. Further attempts at decryption using a variety of cipher methods yielded no momentous results over a three month period. 373 days after I first concluded Ein feste Burg was the covert Principal Theme, I experience an epiphany: Two note combinations were possible, but it was necessary to consider the melody and bass notes together for the complete cipher. These are the same notes written in black ink on the original short score – Elgar’s ‘dark saying.’
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). Together the melody and bass lines employ all seven note letters with the only discrepancy between E and F. Later analysis revealed these notes were combined just as i and j or u and v are conflated when enciphering entire alphabetical sequences. Robert Schumann (one of Elgar’s ‘ideal’ composers) used the notes E and F in his music ciphers to symbolize his alter egos, Eusebius and Florestan. [9] With the conflation of the notes E and F, one distinct melody note may be assigned to each column, and one discrete bass note given to each row. This arrangement produces a 6 x 6 checkerboard configuration. By pairing a melody note with a bass note, a single cell in the checkerboard grid is designated at their intersection containing a plaintext letter solution.
There is yet another basis to suspect Elgar constructed a 6 x 6 checkerboard cipher because there are precisely six different 6-letter names and titles used in the Enigma Variations:
  1. Enigma for the Theme
  2. Ysobel for Variation VI
  3. Troyte for Variation VII
  4. Nimrod for Variation IX
  5. Eduard from the initials E.D.U. assigned to Variation XIV which are the first three letters of the German translation of Edward
  6. Finale, the subtitle for Variation XIV

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 6). For the purpose of identifying note pairings, each bass quarter note was treated as a half note. These base line extensions from the original quarter notes are justified based on the recapitulation of the opening six bars in measures 11 through 16 where they are played continuously as half notes (Figure 1). 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 stratagem for obscuring the cipher.

Unmistakable correlations were found between bass/melody note pairings and plaintext letter frequencies (Table 7). Discernable 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 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 is the letters A, C and E are the initials for the first names of Elgar, his wife and daughter. Like the previous match pair, these notes form a music triad. 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 plaintext 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 extraordinary is realized (Table 8).

Measure 1: GSUS

In measure 1 the plaintext solution is gsus, a phonetic spelling for Jesus. This special friend according to Elgar’s Roman Catholic faith is the hidden dedicatee for Variation XIII. His initials are ingeniously encoded by the Roman numerals for this movement. X represents the number ten, and the tenth letter in the alphabet is J. III stands for the number three, and the third letter in the alphabet is C. When the Roman numerals XIII are converted into letters using this Letter Number cipher method, the initials J.C. are realized. The efficacy of this cipher is demonstrated by Variation IX (Nimrod) dedicated to Elgar’s German friend, August Jaeger. Applying the same Letter Number encryption method to the Roman Numerals IX produces the initials A.J.
Richard Santa discovered Elgar encoded Pi in the opening measure of the Enigma Theme. Pi is a mathematical constant describing the ratio between any circle’s circumference and its diameter. In his groundbreaking research, Santa observed the first four notes of the Enigma Theme sequentially approximate the number Pi by means of scale degrees (i.e., B flat = 3, G = 1, C = 4, A = 2). The pairing of Pi with Jesus in the first measure of the Enigma Theme intimates the phrase “Pie Jesu” (Pious Jesus), a phrase from the final couplet of the Dies irae, a hymn in the Roman Catholic Requiem Mass.

Measure 2: GRTS

In measure 2 the plaintext solution is grts, the phonetic spelling of the Latin words gratus, gratis, and gratias. In his youth Elgar attended three Catholic schools where he 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”.[10] 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”.[11] The terms “beloved” and “pleasing” are used in reference to Jesus after his baptism when a voice from heaven said, “You are my beloved Son; with you I am well pleased.”[12]
An alternative realization of the plaintext grts is the Latin word for grace – gratis.  As an adverb it is defined as “without recompense, for nothing, gratis.”[13] 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” which means “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).[14] 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, “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.”[15]

Measures 3 and 4: INOU BETR

In measure 3 the plaintext solution is inou, a phonetic rendering of the phrase “I know you.” In measure 4 the plaintext solution is betr, a phonetic version of the word “better.” Combing the plaintext results for measures three and four generates the phrase “I know you better”.  The formation of a meaningful phrase based on the plaintext solutions from bars 3 and 4 (“I know you better”) mirrors the pattern of producing a cogent phrase from the plaintext results from measures one and two (“Jesus Gratias” translated as “Thanks be to Jesus”). Following the plaintext results from measures 1 and 2 citing Jesus and some of his attributes, the phrase definitely implies Elgar knows Jesus better. But what possible explanation is there for why Elgar would encode such a declaration?
Almost five months before Elgar began openly working on the Enigma Variations, Secondo Pia took the first official photographs of the Turin Shroud. The photographic negative taken on May 28, 1898, vividly revealed for the first time the crucified body and face of the man many fervently believe to be Jesus Christ. It quickly became an international sensation, deluging the pages of both the secular and religious press. Copies of that remarkable image were soon shared and revered among Roman Catholics around the globe. For the first time many beheld the face of their Lord and Savior.
For a Roman Catholic like Elgar, the phrase “I know you better” conveys their view of the Holy Shroud’s significance and meaning. Elgar said if the Enigma Theme were presented as a ballet, the Enigma should be represented by a veiled dancer in a banquet hall. Like a shroud, a veil a cloth used to cover the body. Shortly before his crucifixion, Jesus met with his twelve disciples in a banquet hall to celebrate the Last Super. Excluding Elgar and his wife, there are twelve friends portrayed in the Variations. None of these theological allusions could ever be expected to register in a secular scholar’s worldview. In contrast, Elgar’s weltanshauung at the time he composed the Enigma Variations was decidedly Roman Catholic.

Measure 5: TENI

In measure 5 the plaintext solution is teni, an Aramaic word used by Jesus when he encountered the Samaritan woman at Jacob’s well.  When she came to the well to draw water, the first thing Jesus said to her was, “Teni li listosh,” which means, “Give me [something] to drink.” It was during this exchange that Jesus revealed his identity as the Messiah. In view of the plaintext results in measures 1 through 4, this theological assessment of teni is amply justified. This conclusion is bolstered by the recognition Elgar’s personal library contained numerous works on theology and biblical exegesis.

Measure 6: FETE

In Measure 6 the plaintext solution is fete, a word defined as a lavish party or religious festival. In light of the coded reference to Jesus in measure 1, the latter definition involving a religious context is warranted.

The use of phonetic spellings is a diabolically difficult device that vastly complicates decryption, particularly when done with multiple languages encoded in the same 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”.[16]  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 because the solution letters must still be rearranged to spell out the correct solution: Ein feste Burg ist Unser Gott.
Akin to the four sides of a box cipher key or four instruments in a string quartet, there are four languages employed in Elgar’s Music Box Cipher: English, Latin, German and Aramaic. Similar to the Performance Directions Anagram Cipher in which Elgar encodes his initials (E.E.), the first letters of these cipher languages spell out his last name:
  • English
  •  Latin
  •  German
  • ARamaic

Elgar literally signed his cipher so it could be independently authenticated as genuine and correct. The phonetically spelled words and phrases from Elgar’s ‘dark saying’ are an elaborate anagram sourced from the title of the unstated Principal Theme, Ein feste Burg ist unser Gott. Such an incredible outcome could only be the result of a deliberate, premeditated plan, one far beyond my powers of invention. To suggest any other explanation, particularly one devoid of forethought and careful planning by Elgar, would be beyond absurd.
The Enigma Theme Music Box Cipher key is summarized in Table 10. It consists of a 6 x 6 checkerboard, an intriguing outcome when one realizes the opus number for the Enigma Variations is 36, the product of 6 times 6.  Plaintext letters are shown while null cells contain only asterisks. To find a solution letter, locate the intersection of the melody and bass notes as outlined in Table 8. For instance, the combination of the melody note A with the bass note C yields the plaintext 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 the Dorabella Cipher. Mathematician Tim S. Roberts successfully cracked the Dorabella Cipher in 2009, confirming Elgar’s use of multiple languages and phonetic spellings.

There was a far more compelling reason to suspect Elgar was inspired to create a musical Polybius square, although I was unaware of it until only after my discovery of the his Music Box Cipher. In his personal library are four articles from the 1896 edition of The Pall Mall Gazette titled Secrets in Cipher. These papers are now in the possession of the Elgar Birthplace Museum. The third article contains a music 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 remarkable 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.[17] The Nihilist cipher is a variant of the Polybius square which in some versions uses a 6 x 6 grid “…to accommodate the 35 letters of the old Russian alphabet.”[18] The suspicion Elgar devised a 6 x 6 checkerboard cipher was bolstered retroactively by the revelation of these articles from The Pall Mall Gazette. 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.[19] Elgar’s cryptic reference to a ‘dark saying’ takes on a whole new light in this context. The Polybius square is a very old cipher, one Elgar knew intimately from his personal studies.
   Elgar did indeed write down the solution to his Enigma Variations while he was very much alive, and accomplished this feat in the opening six bars of the Enigma Theme by means of 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?”[20] For over a century the solution has been seen and heard countless times, yet ironically those with eyes and ears failed to recognize it. Such is the pinnacle of the art of cryptography, a discipline Elgar found irresistible throughout his life. Now we know the secret he ostensibly took to his grave.

Four Integrated Ciphers

The preceding descriptions and decryptions of four ciphers nestled in the opening measures of the Enigma Theme demonstrate they are integrative with a complimentary and mutually reinforcing set of answers. When decoded forwards using an elementary Letter Number conversion key, the Locks Cipher from the Enigma Theme’s opening six measures indicates that multiple keys are required to unlock the secrets of the Enigma Variations. Applying this insight to the actual keys in which the Enigma Theme is performed, it was determined the letters for the accidentals of the G minor and major modes are E.F.B. This is a remarkable find because those initials are an exact match for the famous Reformation hymn Ein feste Burg.
The Performance Directions Cipher in the Enigma Theme’s first measure encodes the composer’s initials (E.E.) with the word Psalm. This coded message suggests one out of a possible 150 chapters from the Old Testament Book of Psalms. The Ternary structure of the Enigma Theme cleverly provides a solution culled from the total number of measures for the A and B sections which are 6 and 4 respectively. Pairing these two digits in reverse order produces 46. The title for Ein feste Burg comes from the first line of Psalm 46. In the second stanza of that epic hymn, the name of Elgar’s secret friend is cited.
When decoded backwards using the Letter Number conversion key, the Locks Cipher provides the initials for Jesus Christ (J.C.) with the word lo, biblical shorthand for behold. The Locks Cipher reveals how to obtain the initials for the unstated Principal Theme from the keys in which the Enigma Theme is played, and it also encodes the initials for the secret friend portrayed in Variation XIII. The lyrics from the hidden Principal Theme provide only one name, Jesus Christ, which is an exact match with the Locks Cipher decryption.
These relatively basic Enigma Theme ciphers implicate Ein feste Burg as the covert Principal Theme. This melodic solution accounts for the seemingly anomalous Mendelssohn fragments quoted in Variation XIII since Mendelssohn quotes Ein feste Burg in his first extended symphonic work, the Reformation Symphony. By quoting Mendelssohn, Elgar subtly suggests by inversion (a common contrapuntal technique) that Mendelssohn also quotes the same Principal Theme in one of his own works. The number of Mendelssohn fragments – four – cleverly specifies the correct movement from the Reformation Symphony that cites Ein feste Burg – the fourth. The Roman numerals for that movement are in fact a simple Letter Number Cipher that encodes the initials J.C. X represents the number ten, and the tenth letter in the alphabet is J. III stands for the number three, and the third letter in the alphabet is C. These are the identical initials encoded by the Locks Cipher, a variant of the Letter Number Cipher in which the number of notes from each active orchestral part serves as the key.
The most complex and compelling cryptogram in the Enigma Theme is the Music Box Cipher. Through an elegant anagram it encodes the entire 24 letter title of Ein feste Burg ist Unser Gott. Elgar explained in the original 1899 program note the Enigma contains a ‘dark saying,’ and this is born out by the realization the hidden theme’s title as well as its anagrammatized plaintext consists of multiple phrases or sayings. Similar to the Performance Direction Anagram Cipher which encodes Elgar’s initials, the first letters of the four  languages used in the Music Box Cipher cleverly encode his last name – English, Latin, German, Aramaic. As a stealth form of authentication, the composer ingeniously encodes his initials in the Performance Directions Anagram Cipher and his last name in the Music Box Cipher. Like a consummate artist, Elgar meticulously initialed and signed his work. A phonetic version of the secret friend’s first name (GSUS) is encoded in the first measure. This name Jesus is cited in the second stanza of Ein feste Burg, and his initials (J.C.) are encoded by the Locks Cipher. With so many ciphers encoding the same set of answers, we may be exceedingly confident the solutions are accurate and authentic. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

[1] Kennedy, Michael. The Life of Elgar (Musical Lives). illustrated edition ed. New York: Cambridge University Press, 2004, p. 68
[2] McClelland, C. (2007, Winter). Shadows of the evening: new light on Elgar's 'dark saying'. Music Times, Winter , p. 44.
[3] London British Library Add. MS 58003, f.2v.
[4] Daverio, J. (2008). Crossing Paths: Schubert, Schumann, and Brahms. New York: Oxford University Press, USA, p. 101.
[5] McVeagh, D. (2007). Elgar the Music Maker. Rochester, NY: Boydell Press, p. 3.
[6] Turner, Patrick. Elgar's 'Enigma' Variations - a Centenary Celebration. London: Thames Publishing, 1999, p. 46
[7] Sams, Eric. Did Schumann use ciphers? London, The Music Times, Aug., (1965), p. 584-591
[8] Daverio, John. Crossing Paths: Schubert, Schumann, and Brahms. New York: Oxford University Press, USA, 2008, p. 83.
[9] Dowley, T. (1982). Schumann: His Life and Times. Neptune City, NJ: Paganiniana Publications, Inc., p. 46-47.
[10] Cassell's Latin Dictionary (5th ed.). (2000). New York: Continuum, p. 268
[11] Hall, W., & Smith, T. (1871). A Copious and Critical English-Latin Dictionary. New York: American Book Co., p.
[12] English Standard Version
[13] Cassell's Latin Dictionary (5th ed.). (2000). New York: Continuum, p. 267-268.
[14] Randel, D. M. (1986). The New Harvard Dictionary of Music (Harvard University Press Reference Library). Cambridge: Belknap Press, pp. 471-472
[15] Ephesians 2:8-9 NIV
[16] Cited from an unpublished paper by Eric Sams entitled Elgar’s Cipher Table (1970-71).
[17] Buckley, Robert J. Sir Edward Elgar (1905). New York: Kessinger Publishing, Llc, 2009, p. 41.
[18] Kahn, David. The Code Breakers. New York: The Macmillan Company, 1968, p. 620.
[19] Ibid, p. 83.
[20] Mark 8:18 (NIV)

Tuesday, March 17, 2015

The Enigma Variations: Beginnings as Endings

Great is the art of beginning, but greater the art is of ending.”

Elgar quoting Longfellow at the end of the Enigma Variations

A persistent trait displayed throughout Edward Elgar’s Enigma Variations is the partial or complete restatement of the opening material as a concluding phrase. This is sometimes accomplished while overlaying the opening phrase with some variant of the Enigma Theme’s starting phrase. In all, ten of the Variations restate the beginning phrase in whole or in part as endings: I (C. A. E.), II (H. D. S-P.), III (R. B. T.), V (R. P. A.), VI (Ysobel), VII (Troyte), IX (Nimrod), X (Dorabella), XII (B. G. N.), and XIV (E. D. U.). Absent from this series are IV (W.M.B.), VIII (W. N.), XI (G. R. S.) and XIII (***). In the search for the covert principal theme, it is critically important to recognize Elgar’s repeated restatement of the opening phrase at the conclusion of the majority of the movements. This is the case because Elgar unpredictably starts his counterpoint between the Enigma Theme and the covert principal theme with Ein feste Burg’s final phrase, and unexpectedly concludes it with its starting phrase. From a contrapuntal standpoint, Elgar puts the proverbial cart before the horse.
Variation I (C. A. E.) begins in measure 20 with a rhythmic variation of the Enigma Theme in G minor played by the flute, second violins and violas. The opening two bars of this rhythmic variant (measures 20-21) are reprised in G major as a tierce de Picardie by the clarinet as the ending phrase (measures 30-40).

Variation II (H. D. S-P.) commences in measure 41 with a toccata figure stated by the first violins. Four bars from the end in measure 93 the flute repeats this opening figure verbatim from measure 41, continuing over into measure 94 with the first note (C) from measure 42. This is promptly followed by rest of the material from the second bar (measure 42) performed by the clarinet in measure 95. At Rehearsal 6 this opening toccata figure plays over a variant of the Enigma Theme played by the cellos and basses. One major implication of this pairing is the repetition of the opening toccata figure at the conclusion of this movement contrapuntally alludes to the Enigma Theme’s starting phrase.

Variation III (R. B. T.) starts with a basic accompaniment figure (measure 97) which is restated at the end (measure 132). Unlike the preceding movements, the entire opening phrase in measures 98-104 is reprised at the end (measures 124-130). This mirrors the ABA ternary structure of the Enigma Theme. What is noteworthy is the identical accompaniment figure begins and ends this movement.

Variation V (R. P. A.) begins with a haunting countermelody played by the violins over a variant of the Enigma Theme performed by the cellos and basses.  Four bars from the close of this movement the violins reprise the countermelody’s opening phrase twice in measures 185-186 as the Enigma Theme’s first phrase is played again by the cellos and basses. In the last two bars the first four notes of the countermelody are repeated four times in a transition section leading into the next movement. This steady recurrence of the first four notes of the countermelody casts a contrapuntal shadow of the opening phrase of the Enigma Theme which plays below this figure at the beginning of the movement.

Variation VI (Ysobel) begins with a countermelody distinguished by large intervallic leaps played by the violas as the bassoons perform a truncated version of the Enigma Theme. The countermelody’s first phrase reappears as the concluding phrase (measures 209-210) without any sign of the Enigma Theme’s variant.

Variation VII (Troyte) concludes dramatically with an augmented variant of the Enigma Theme’s opening phrase (measures 275-279) performed triumphantly by the brass section. While this movement does not restate counter-melodic material from the opening at the ending, the appearance of some form of the Enigma Theme’s starting phrase as the concluding passage is important. As previously shown, contrapuntal material played over some version of Enigma Theme’s opening phrase is repeated at the conclusion of Variations II, V and VI. The Enigma Theme’s opening phrase is repeated at the conclusion of Variations I and VII.

Variation IX (Nimrod), the most elegiac of the series, begins slowly with a poignant variant of the Enigma Theme played pianississimo (ppp) in measure 309. This inaugural phrase is restated as the ending (measure 348) in a dramatic fortissimo (ff) before diminishing rather suddenly to pianissimo (pp) before fading away. This type of ending in which the Enigma Theme’s opening phrase is restated is also found in Variations I and VII.

Variation X (Dorabella) begins with two rapid accompaniment figures of three 32nd notes answered by a four-note 16th note figure intended to mimic Dora Penny’s stutter. This movement is distinguished by the absence of any clear indications of the Enigma Theme’s opening phrase.  Four bars from the end at Rehearsal 46 the initial accompaniment figures of three 32nd notes reappears and is again answered by the four-note 16th note stuttering motif. Six notes followed by four at Rehearsal 46 may be seen as a coded reference to the number 46, the same chapter in the Psalms that inspired the lyrics for Martin Luther’s famous hymn, Ein feste Burg (A Mighty Fortress). What makes this movement vitally important to resolving the mystery of the covert principal theme is that the inner voice restates in an augmented from the first four notes of closing phrase from  Ein feste Burg in measures 383-387, and again in measures 406-410. More remarkable still, these first four notes and the final four from the closing phrase of Ein feste Burg are restated by the stuttering motif in measures 422-424.

Variation XII (B.G.N.) commences in measures 467-468 with a tender cello solo capturing the consecutive dropping sevenths drawn from the Enigma Theme (measures 3-4 and 13-14). Just as the movement opened, the cello once again restates this excerpt from the Enigma Theme in measures 493-494. While not the final phrase of the Enigma Theme, this excerpt serves as the beginning and concluding passage for this movement.

Variation XIV (E.D.U.) does not begin and end with the same thematic material. The reasons for this divergence from the other Variations are it has a sixteen measure introduction with a considerably expanded ending. The first real thematic material is not introduced until Rehearsal 62 (measure 565). At the behest of conductor Hans Richter and August Jaeger, the original ending was expanded by nearly 100 measures following the June 1899 premiere. Consistent with a pattern exhibited by earlier movements, the opening thematic material presented in measures 565-566 is restated in measures 683-684 almost exactly 100 measures before the appended ending. The originally shorter Finale actually mirrored a pattern displayed in Variations II, V, VI, IX, namely that the opening thematic material reappears close to or at the end.

An examination of the Enigma Variations reveals a persistent pattern in which the first phrase is restated at or near the conclusion of the majority of the movements. This trend holds true for Variations I, II, III, V, VI, VII, IX, XII and XIV. The exceptions to this pattern are the Enigma Theme and Variations IV, VIII, XI, and XIII. As an aside, it is remarkable to observe the sum of these latter Roman numerals (4+8+11+13) is 36, the opus number for the Enigma Variations.
In the search for the covert principal theme, it proves critical to recognize that most of the Variations conclude with their beginning phrases sourced either from the countermelody, some variant of the Enigma Theme, or both. As most of the movements end with their beginning phrase, this insight strongly implies Elgar’s counterpoint between the Enigma Theme and the covert principal theme models this approach. That would mean the Enigma Theme’s counterpoint concludes with the covert theme’s opening phrase, and more decisively, that it begins with the covert theme’s final phrase.
The initial mapping of Ein feste Burg with its original phrase structure (ABABCDEFB) ‘through and over’ the Enigma Theme proved it was a perfect horizontal fit. Even so, it produced unacceptable dissonances which precluded a credible counterpoint. When applying Elgar’s counterintuitive tact of placing the beginning phrase at the end (and by implication the ending phrase at the beginning), a credible counterpoint between Ein feste Burg (Phrase structure: BCDEFCA) and the Enigma Theme is realized.
Regarding the Enigma Theme Elgar wrote, “The drop in the seventh in the Theme (bars 3 and 4) should be observed.” For over a century no one could discern the cryptographic significance of that statement. Both the statement and the number seven are odd. By observing the seventh, Elgar was alluding to the importance of the seventh and final phrase of the covert principal theme (ABCDEFC) because it unpredictably marks the beginning of the counterpoint between the covert melody and the Enigma Theme.
This analysis of the Enigma Variations reveals the supremacy of the ending phrase over the beginning, an insight amplified by the quotation from Longfellow’s Elegiac Verse Elgar penned at the conclusion of the expanded Finale. “Great is the art of beginning, but greater the art is of ending.” To learn more about the secrets of the Enigma Variations, read my eBook Elgar’s Enigmas Exposed. Like my heavenly Father’s gift of salvation and forgiveness, the price is free.

About Mr. Padgett

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Mr. Padgett studied violin with Michael Rosenker, 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 ShriverSteve 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.