Sunday, November 1, 2015

The Enigma Theme with ‘Ein feste Burg’ in Retrograde

Amidst the worldly comings and goings, observe how endings become beginnings.”
A veritable phalanx of ciphers confirms the Covert Principal Theme to Elgar’s Enigma Variations is Ein feste Burg (A Mighty Fortress) by Martin Luther. Precisely how that gallant melody plays ‘though and over’ the Enigma Theme has been the subject of intense and prolonged deliberation. It was initially suspected a precise horizontal fit between both themes would be sufficient to substantiate this discovery, yet the absence of a credible counterpoint raised legitimate doubts about that melodic mapping. An alternative approach made it feasible to play Ein feste Burg over the Enigma Theme by applying free rhythm and varying its phrase order, producing a more credible vertical contrapuntal match. Even so, that mapping was greeted by some with skepticism. These and other questions fueled an ongoing reassessment, one that has now yielded an innovative charting of Ein feste Burg above the Enigma Theme by applying a rarely used contrapuntal device – retrograde motion. Before sharing this new contrapuntal mapping, it is advisable to consider how it was precipitated by two crucial breakthroughs.
The first key insight concerned just far Elgar’s counterpoint actually goes. The conventional wisdom as expressed by Dr. Clive McClelland asserts the counterpoint goes no further than the first six measures of the Enigma Theme, or merely the A section of its ABA ternary structure. The difficulty with that conjecture is it contradicts Elgar’s published position regarding the Enigma Theme’s actual length. In the late 1920’s he provided descriptive notes for a set of pianola rolls published in 1929. Regarding Variation I he wrote, “There is no break between the theme and this movement.”[1] That is a critical disclosure because it confirms the Enigma Theme does not terminate until Variation I begins in measure 20.

Based on his published statement, Elgar did not consider the two bar Bridge in measures 18 and 19 to be part and parcel of Variation I (something deceptively implied by the layout of the published score), but rather an elaboration of the Enigma Theme’s ending. A conspicuous tie between the notes of measures 17 and 18 validates this observation, linking the Enigma Theme and Bridge in a way not found with Variation I. The Bridge serves to unwind the Picardi cadence and return it back to the minor mode. Relying on Elgar’s published position, the correct melodic mapping of the Covert Principal Theme must account not only for the Enigma Theme’s Ternary ABA structure in measures 1 through 17, but also the two bar Bridge or C section in measures 18 and 19 that precede the launch of Variation I. In recognition of this fact, all alleged melodic solutions that neglect any part of the first nineteen measures of the Enigma Theme’s ABAC structure may be safely ruled out as invalid. This preclusion applies to the usual suspects as well as every solution now featured in Wikipedia’s article about the Enigma Variations.

A second breakthrough was the recognition that at various points throughout the Enigma Variations Elgar places a coded emphasis on the ending phrase of Ein feste Burg. For instance, at Rehearsal 68 in the Finale that ending phrase is stated as a counterpoint to the opening of the Enigma Theme. The pairing of Ein feste Burg’s ending with the Enigma Theme’s beginning prompted a meticulous reassessment of the Enigma Theme. On closer inspection is was found that the first six notes of the bass line are the last six notes of Ein feste Burg’s concluding phrase in reverse order.

This notable correspondence raises the very palpable prospect Elgar composed his counterpoint with the unstated Principal Theme in retrograde. This would mean that rather than mapping out the missing melody forwards as everyone would naturally expect, Elgar adopted the opposite tact by crafting his counterpoint with the absent theme play backwards.  The Enigma Theme’s ABAC structure subtly hints at this prospect because when read phonetically, ABAC sounds like aback. That term was originally used to describe when the sails of a ship are blown backwards into the mast In present usage it refers to being taken by surprise. Both of those definitions – backwards and surprised – would exquisitely express Elgar’s mapping of the Covert Principal Theme in retrograde over the Enigma Theme, not to mention his fondness for wordplay. The structure of the Enigma Theme hints at the strategy Elgar deployed to foil straightforward attempts at decoding his counterpoint. According to Kent Kennan, Professor Emeritus of Music at the University of Texas at Austin, retrograde motion is rarely encountered in fugal writing.[2] That Elgar was clearly contemplating various contrapuntal possibilities is reflected by the fact that on an early sketch of the Enigma Theme he wrote the phrase ‘for fuga’ above the first bar.[3] Fuga is another word for fugal. Considering the relative infrequency of retrograde counterpoint, mapping the Covert Principal Theme in this manner would be an extraordinarily effective tactic to foil detection.
After determining the scope of Elgar’s counterpoint and the potential of mapping the Covert Principal Theme from the end backwards to the beginning, a new mapping of Ein feste Burg in retrograde over the entire nineteen measures of the Enigma Theme was completed. Starting at the end of the bridge (Measure 19), the Covert Principal Theme is played backwards to the beginning with the reverse phrase order of BFEDCBA. The ending phrase (B) appears at both the opening and final cadence of the Enigma Theme with the opening phrase (A) deftly inserted over the Bridge. This mapping mirrors the minor and major modes employed by Elgar to camouflage the key of the Covert Principal Theme. Listening to this mapping with the Enigma Theme played in reverse makes it easier to recognize this chimerical version of Ein feste Burg.

A compilation of shared melody and harmony notes between Ein feste Burg and the Enigma Theme was conducted.  Shared notes between both melodies are shown with diamond shaped note heads. Shared notes between the melody of Ein feste Burg and non-melodic or harmony notes in the Enigma Theme’s short score are represented by triangular shaped note heads.


With this mapping there are 30 matching melody notes, and 38 corresponding harmony notes dispersed over the Enigma Theme’s entire 19 measures. There is an average of 1.5 shared melody notes per measure with the highest concentration of seven in measure 14. On average there are 2 shared notes per measure between Ein feste Burg’s melody and non-melodic notes from the Enigma Theme’s piano reduction. The highest concentration of shared harmony notes is five, a figure found in both measures 13 and 15. The relatively regular distribution of shared melody and harmony notes between Ein feste Burg and the Enigma Theme is prima facie evidence for a retrograde counterpoint.

The version of Ein feste Burg used in Elgar’s retrograde counterpoint is culled together from multiple sources. A side by side comparison of Luther’s original composition with iterations by Bach and Mendelssohn reveals Elgar incorporated elements of all three to construct his hidden source melody. When combined with retrograde counterpoint, this ‘tribrid’ theme was undoubtedly constructed to complicate detection and description while paying homage to two paragons of the German School. Phrase A in measures 17 through 19 of the retrograde mapping is sourced from Mendelssohn’s more austere version characterized by rising and falling thirds, an attribute endemic to the A Phrase of the Enigma Theme. Phrase B in measures 14 through 16 bears the melodic imprimatur of Luther’s original hymn. Phrase C found in measures 12 through 14 matches up with both Bach’s and Mendelssohn’s versions which are virtually indistinguishable. Phrase D in measures 10 and 11 reflects Luther’s original as well as Mendelssohn’s faithful replica. Phrase E in measures 9 and 10 is based on Mendelssohn’s more florid adaption.  Phrase F in measures 6 through 8 and Phrase B in measures 1 through 5 both correspond with Bach’s rendering.

The prevalence of Mendelssohn’s adaption of Ein feste Burg in the retrograde mapping makes it remarkably clear why Elgar would feature four fragments from a symphonic work by Mendelssohn in Variation XIII. In a prescient parallel, four of the six phrases from Ein feste Burg are sourced from Mendelssohn’s adaption of Ein feste Burg.  The number four is also significant because Mendelssohn quotes Ein feste Burg in the fourth movement of his Reformation Symphony followed by a series of variations. The Mendelssohn fragments in Variation XIII harbor an alphanumeric cipher that encodes the initials EFB in reverse order, an element that now in retrospect cleverly alludes to Elgar’s retrograde treatment of the Covert Principal Theme.

It is intriguing Elgar extracts and combines fragments from three forms of Ein feste Burg to create a unique fourth version – his own. With each version representing a distinctive musical dialect, this parallels Elgar’s use of four different languages in a Music Box Cipher embedded within the opening six measures of the Enigma Theme. That unique cipher, originally known as a Polybius square, is strongly hinted at by a literal square Elgar drew on the cover page of the score.

What makes that rather ordinary looking square so extraordinary is it overlays the very staff lines on the next page of the full score that introduce the Music Box Cipher. No other cover page from Elgar's body of works has this unique feature, rendering it all the more significant from a cryptographic vantage point. It should also be noted the square on the cover page encloses the start and end dates of the orchestration in the month of February which Elgar abbreviates as Feb. Those three letters are an anagram for EFB, the initials for Ein feste Burg. Rather than X marks the spot, Elgar elected to do so rather symbolically with a square enclosing not one but two instances of the Covert Principal Theme's initials.

The cipher languages used in Elgar’s Music Box Cipher are English, Latin, German and Aramaic. This is hardly a random assortment because the first letters of each language encode the composer’s last name: English, Latin, German, and Aramaic. Elgar signed his cipher apropos in code. Three of these languages appear in Bach’s St. Matthew’s Passion. The original title is in Latin: Passio Domini nostri J.C. secundum Evangelistam Matthæum which translates as “The Passion of our Lord J[esus] C[hrist] according to the Evangelist Matthew”. The initials from that title (JC) are encoded by the Roman Numerals of Variation XIII with X representing the tenth letter (J), and III the third (C). The libretto is in German sourced from Martin Luther’s translation of the Bible. There is one exception. When Jesus cries out his last anguished but unvanquished words on the cross, he quotes Psalm 22:1 in Aramaic, “Eli, Eli, lama sabachthani!” It is possible Bach’s masterpiece informed and inspired Elgar’s selection of three of the four languages found in his Music Box Cipher, leaving only one – English – as an obvious connection to own linguistic and cultural heritage.
There is an indelible link between Bach and Mendelssohn forged at a momentous performance in 1829 when Mendelssohn conducted the St. Matthew’s Passion, a masterpiece that had not been performed publicly in over a century. This proved to be watershed moment because it “resulted in a full-scale revival and reevaluation of Bach’s works throughout Germany and beyond, and a universal recognition of their genius and significance.” Mendelssohn’s interest in Bach extended beyond the arts, for they shared a common faith. It was on March 21, 1816 – Bach’s birthday – that Mendelssohn was baptized as a Lutheran. The Mendelssohn fragments in Variation XIII combined with a capital L used to identify that movement on an early sketch serve as markers pointing to the famed composer of Ein feste Burg, Martin Luther. Through their faith, music and language there is an unmistakable bond between Martin Luther, Johan Sebastian Bach and Felix Mendelssohn. In the Enigma Variations, Elgar pays homage directly and indirectly to all three progenitors of the German School.
At the conclusion of the extended Finale, Elgar quotes a passage by Henry Wadsworth Longfellow from his Elegiac Verse. In Elgar’s script appears Longfellow’s prose, “Great is the art of beginning, but greater the art is of ending.” That literary fragment affirms the supremacy of the ending over the beginning, a feature reasserted by the coded recognition the ending phrase of Ein feste Burg marks the beginning rather than the end of Elgar’s counterpoint with the Enigma Theme via retrograde motion. The key to unraveling Elgar’s enigma is to begin at the end and work your way backwards. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

[1] Elgar, Edward. My Friends Pictured Within. The Subjects of the Enigma Variations as Portrayed in Contemporary Photographs and Elgar’s Manuscript (Sevenoaks: Novello, n.d. [1946], republication of notes for Aeoloian Company’s piano rolls, 1929)
[2] Kennan, Ken. Counterpoint Based on Eighteenth-Century Practice (3rd ed.). Englewood Cliffs: Prentice-Hall, Inc., p. 222.
[3] Rushton, Julian. Elgar: Enigma Variations (Cambridge Music Handbooks). New York: Cambridge University Press, 1999, p. 54

Tuesday, October 20, 2015

Elgar’s Contrapuntal Smoking Gun

Great is the art of beginning, but greater the art is of ending.”
Elgar quoting Longfellow at the end of the Enigma Variations

117 years ago on October 21, Edward Elgar first performed the transcendent Enigma Theme for his wife. It is for this reason October 21 is known to Elgarians as Enigma Day to commemorate the birth of the Enigma Variations, and a rebirth of English music. Elgar composed the Enigma Theme as a counterpoint to a famous melody, one that researchers have been unable to identify unanimously. Varying opinions have been proffered as prospective melodic solutions, yet they habitually fail to satisfy even the most basic condition of achieving a vertical fit with the Enigma Theme in its entirety. Far too many investigators content themselves with partial fits and pass them off as complete solutions. Like the misshapen stepsisters of Cinderella, they struggle in vain to shove on a glass slipper that simply will not fit.
The conundrum is compounded by the unexpected discovery Elgar’s counterpoint begins paradoxically with the final phrase of the hidden melody – Ein feste Burg by Martin Luther – and concludes with its opening phrase. Who would have ever suspected Elgar would begin his counterpoint with the concluding phrase of the mysterious missing melody? This would account for his odd explanation that the solution “…must be left unguessed.”[1] Without exception every mapping of an alleged solution melody starts with its beginning at the outset of the Enigma Theme. No one ever stopped to consider Elgar served for years as church organist at St. George’s Church in Worcester, and that in such a setting it was common practice to introduce hymns by playing their ending phrase as an introduction. And Ein feste Burg is an epic hymn.  The key to unraveling Elgar’s bewildering counterpoint is to search for the ending phrase at the beginning, and conversely the beginning phrase at the end.
Ein feste Burg is comprised of six distinct phrases (ABCDEF). With some repeated phrases that mighty theme extends to a total of nine parts (ABABCDEFB). In contrast to this rather elaborate phrase structure is the Enigma Theme’s much simpler ABAC structure. The ABA section is the more familiar Ternary Form (Measures 1 through 17) followed by the C section which is an elaborated and elongated ending (Measures 18-19) forming a bridge to Variation I. The surprising discovery is Elgar contrapuntally mapped the ending phrase of Ein feste Burg at the beginning of the Enigma Theme, and slipped the hidden theme’s opening phrase at the tail end ‘through and over’ the bridge. The efficacy of this analysis is sustained by mapping Ein feste Burg in this unexpected phrase order over the Enigma Theme, a method that produces a credible counterpoint consistent with Elgar’s compositional style.

There is ample circumstantial evidence implicating Elgar’s devious decision to begin his haunting countermelody with Ein Feste Burg’s exultant ending phrase. First, consider the ABAC phrase structure of the Enigma Theme. When read phonetically, ABAC sounds like aback, a word that literally means in a backward direction. This term was originally used to describe when the sails of a ship are blown backwards into the mast. A more modern meaning of aback is to be taken by surprise. These definitions – backwards and surprised – synchronize perfectly with Elgar’s unforeseen tactic to begin his counterpoint with the ending phrase of Ein feste Burg, for it is surprising because it is backwards. Second, the puzzling title Enigma suggests just such a reversal because its first letter – the upper case E – resembles the lower case of the Greek letter Omega, while the last letter a is the first Greek letter Alpha. The word Enigma subtly places the Omega first and the Alpha last. In the New Testament book of Revelation, Jesus – the secret friend personified in Variation XIII – is quoted as saying, “I am the Alpha and the Omega, the First and the Last, the Beginning and the End.”[2]
A third reason to suspect Elgar began his counterpoint using the ending phrase of the covert Principal Theme is most of the Variations end with a partial or complete restatement of their opening phrases. This pattern holds true for nine of the fourteen Variations: I, II, III, V, VI, VII, IX, XII and XIV. By restating the starting phrase at the end of most movements, Elgar strongly implies the opening phrase of the unstated Principal Theme must also appear at the end of his contrapuntal mapping. This condition would further suggest the missing melody’s ending phrase would be found rather counter intuitively at the beginning.
A fourth reason may be found in passage by Henry Wadsworth Longfellow from his Elegiac Verse is quoted by Elgar at the conclusion of the extended Finale.  In Elgar’s script is Longfellow’s prose, “Great is the art of beginning, but greater the art is of ending.” This citation clearly affirms the supremacy of the ending over the beginning. The grand irony is Elgar transformed the ending of Ein feste Burg into a beginning with his unusually contoured counterpoint. Merriam-Webster defines an elegy as “a poem or song that expresses sorrow for someone who is dead.” The somber mood of the Enigma Theme and ‘deathly stillness’ embodied in Variation XIII both satisfy that definition. This is a remarkable insight because the central message of the Gospels is that God, personified in the form of Jesus Christ, died at Calvary for the remission of humanity’s sin. This would explain why Elgar would encode the phrase DEAD GOD in the score of Variation XIII and via the Mendelssohn fragments allude to the poetry of Goethe that describes the deathly stillness of the sea. In Matthew 12:40 Jesus likens his time in the tomb to that spent by the prophet Jonah in the belly of the whale. These layers of Biblical allusion were not lost on Elgar who wove an elegant tapestry of interlocking subtext in Variation XIII with music, literature and cryptography.
A fifth reason is found in Variation X Dorabella. Six bars before Rehearsal 42 and 45 the first four notes of Ein feste Burg’s ten-note concluding phrase are quoted verbatim by the inner melodic line in an augmented form. Five of the remaining six notes from that ending phrase follow the inner voice’s direct quotation in the outer treble and bass lines in sequential order. The probability of nine out of ten notes from the ending phrase from Ein feste Burg randomly occurring in the correct order is exceedingly remote. In each case the final cadence of Ein feste Burg is immediately followed in mid-measure by a double bar line, a feature commonly used to designate the end of a section. The double bars are a highly suggestive clue regarding the actual nature and significance of these passages.

Regarding Variation X Elgar wrote the “…inner sustained phrases at first on the viola and later on the flute should be noted.”[3] His cryptic commentary draws attention to the inner melody without furnishing any specific reason except for the word noted. Such an overtly suggestive wordplay beckons the reader to observe the notes of the inner voice. The discovery that Ein feste Burg is the hidden melody provides a compelling explanation for Elgar’s odd statement because of the uncanny resemblance between its ending phrase and the inner melody of this movement. No wonder Elgar chided Dora by confessing he thought that she of all people would be the one to guess the melodic solution. Dora made numerous speculative attempts to unmask the hidden melody, all to no avail. When she begged Elgar for the answer, he replied, “Oh, I shan’t tell you that, you must find it out for yourself.” “But I’ve thought and racked my brains over and over again,” she insisted. He then replied, “Well, I’m surprised. I thought that you of all people would guess it.”[4] This confession makes complete sense when one recognizes that out of all the movements, Variation X provides the most complete quotation of Ein feste Burg’s ending phrase in the inner voice not once, but twice.
A sixth reason is that the ending phrase of Ein feste Burg is ingeniously encoded by a musical anagram in two of the four Mendelssohn fragments of Variation XIII. In standard practice, an anagram is a word or phrase created by the transposition of another word or phrase. For instance, the letters from debit card may be reshuffled to spell bad credit. The same can be done with the notes from a musical phrase in which one melody is constructed from the notes of another. This is precisely what Elgar does in Variation XIII with two of the three clarinet solos beginning with the Mendelssohn fragment.

The clarinet solos in A-flat major and E-flat major begin with a 3 measure fragment from Mendelssohn’s concert overture Meeresstille und glückliche Fahrt. This fragment is elaborated by Elgar into a complete 7 bar solo. A careful analysis of those two clarinet solos reveals the notes are a music anagram of the ending phrase from Ein feste Burg. This is subtly hinted at by the Mendelssohn Keynotes Cipher which encodes the last three notes of that ending phrase as quoted by Mendelssohn himself in the fourth movement of the Reformation Symphony.

A seventh reason has now surfaced from the rousing Finale of the Enigma Variations which all but confirms Elgar intended his counterpoint to commence with the concluding phrase of Ein feste Burg. At Rehearsal 68 the beginning of the Enigma Theme is stated with augmented triplets accompanied by a rhythmic descending G major scale as a countermelody. The back to back triplets suggest Elgar’s initials, for 33 is the mirror image of EE. A carefully study of the countermelody at Rehearsal 68 reveals it starts and ends with the ending phrase of Ein feste Burg. The beginning and ending sections of this concluding phrase are separated by note fragments (designated A and B) sourced from it. One of these intervening fragments (B) is an exact interval match the F minor Mendelssohn fragment found in Variation XIII. In the B fragment the notes are the third, second and first degrees of the descending A minor scale (C, B and A). These are the identical scale intervals cited in the F minor Mendelssohn fragment (A-flat, G, and F). This is an extraordinary congruence because it has previously been shown the concluding phrase of Ein feste Burg is encoded by the Mendelssohn fragments in several ways, demonstrating unequivocally that Elgar’s use of interlocking ciphers extends beyond the Enigma Theme itself.

The more acute observer will observe that the third, sixth and ninth notes of the countermelody at Rehearsal 68 are E, B and F-sharp respectively. These note letters may be rearranged as E-F-B, the initials for Ein feste Burg. There are at least four other ciphers that encode those same initials:
  1. Keys Cipher
  2. Mendelssohn Cipher
  3. Letter Cluster Cipher
  4. Enigma Date Cipher

The countermelody at Rehearsal 68 is a veritable smoking gun that reveals Elgar began his counterpoint with the concluding phrase of Ein feste Burg. The key to unraveling Elgar’s enigma is to begin with the end, honoring Jacobi’s maxim, “Invert, always invert.” To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

[1] Original 1899 program note by C. A. Barry citing a letter by Elgar
[2] Revelation 22:13 New Century Version
[3] Elgar, Edward. My Friends Pictured Within. The Subjects of the Enigma Variations as Portrayed in Contemporary Photographs and Elgar’s Manuscript (Sevenoaks: Novello, n.d. [1946], republication of notes for Aeoloian Company’s piano rolls, 1929)
[4] Powell, D. M. (1947). Edward Elgar: Memories of a variation (2nd ed.). London: Oxford University Press, p. 23

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)