Intersections between the Enigma Theme and Mendelssohn Fragments: Cryptograms and Counterpoints

Felix Mendelssohn-Batholdy

People usually complain that music is so ambiguous; that it is so doubtful what they ought to think when they hear it; whereas everyone understands words. With me it is entirely the converse. And not only in regard to an entire speech, but also with individual words; these, too, seem to me to be so ambiguous, so vague, and so easily misunderstood in comparison to genuine music, which fills the soul with a thousand things better than words. The thoughts which are expressed to me by a piece of music which I love are not too indefinite to be put into words, but on the contrary too definite. 

Felix Mendelssohn in a letter to Marc André Souchay

(Berlin, October 5, 1842) 

The academic consensus reflexively maintains that the Mendelssohn fragments in Variation XIII are unrelated to the Enigma Theme and by extension the entirety of the Enigma Variations. As the Mendelssohn fragments originate from an entirely foreign work, scholars reason they must be independent and disconnected from the covert principal Theme, the “dark saying” mentioned by Elgar in the original 1899 program note, and the secret friend memorialized in Variation XIII. However, Elgar’s decision to superimpose these fragments over a pulsating ostinato drawn from the Enigma Theme’s palindromic rhythm of alternating pairs of eighth and quarter notes invites an alternative outlook. By deliberately pairing the Enigma Theme’s rhythmic structure with these Mendelssohn fragments, he firmly intimates a deeper connection between them and the Enigma Theme, and by extension, the core puzzles of the Enigma Variations. The nature and extent of these multifaceted interconnections are the focus of this overview.

The misguided assumption that the Mendelssohn fragments are somehow extraneous to the Enigma Variations is undermined by a variety of factors. Elgar cautioned for the original 1899 program note, “. . . I warn you that the apparent connexion between the Variations and the Theme is often of the slightest texture . . .” This warning must be carefully weighed when one is tempted to discount any links between the Enigma Theme and the Mendelssohn fragments. That no overt associations between the two may be easily spotted does not automatically render them aesthetically misaligned. It is paramount to recognize they are quoted in one of the movements as prominent features of a variation, so by definition, they must be in some way related to the Enigma Theme and its underlying mysteries. Uncovering those interconnections requires a fluency in music cryptography, an unfamiliar and baffling discipline for legacy scholars.

Far from being extraneous, the Mendelssohn fragments conceal a rich cache of cryptograms that divulge and authenticate the covert melodic Theme and the secret friend memorialized in Variation XIII. These cipher discoveries should come as no surprise because Elgar was an expert cryptographer, a prominent feature of his psychological profile that the alleged experts glossed over or ignored completely. An exhaustive analysis of the Mendelssohn fragments reveals they contain in whole or in part at least fourteen cryptograms. This distinct subset of ciphers is listed below with links to their detailed descriptions and descriptions:

1. “FAE” Cipher
2. “FACE” Cipher
3. “AMF” Cipher
4. Mendelssohn “EFB” Cipher
5. Mendelssohn Keynotes Cipher 
6. Mendelssohn Scale Degrees Cipher 
7. Variation XIII Music Anagram Ciphers 
8. Dual Initials Enigma Cipher 
9. Romanza Cipher 
10. Mendelssohn Pi Cipher 
11. Mendelssohn Pi-C Cipher 
12. Mendelssohn Fragments Melodic Intervals Cipher 
13. Dominant-Tonic-Dominant (5-1-5) Cipher 
14. “See Abba” Mendelssohn Cipher

My search for music cryptograms in the Enigma Variations was spurred by a marvelous discovery by Charles Richard Santa. A retired engineer and amateur musician, Santa realized the scale degrees of the Enigma Theme’s opening four melody notes in measures 1 and 11 encipher the mathematical ratio Pi. The scale degrees of the Enigma Theme's melody notes in measures 1 and 11 are B-flat, G, C, and A in G minor. The scale degrees of those four notes are 3, 1, 4, and 2, respectively. These scale degrees in melodic order are a coded reference to Pi which may be rounded from 3.1415 to four digits as 3.142. This is a remarkable cipher because a circle has 360 degrees, and the opus number of the Enigma Variations is 36. Santa’s groundbreaking research revealed for the first time how Elgar incorporated a cryptogram into the Enigma Theme, raising the tantalizing prospect of additional ciphers. Elgar uses four melody notes from the Enigma Theme’s first measure to encode Pi, and this furnishes a numeric parallel with the four Mendelssohn fragments in Variation XIII. Could there be a cryptographic connection between them? 

A careful analysis of the Mendelssohn fragments revealed that they also encode the first four digits of Pi. Elgar achieved this cryptographic sleight of hand by linking the scale degrees in G major — the key signature of Variation XIII — of each Mendelssohn fragment’s notes to the number of times it is stated in a given key by counting from the beginning of each fragment. This is how it works. The A-flat major Mendelssohn fragment is stated twice. The scale degrees of its first two melody notes, C and B-flat, are 4 and 3 in the G major mode. The F minor Mendelssohn fragment is played once. The scale degree of its first melody note, A-flat, is 2 in G major. The E-flat major Mendelssohn fragment is also performed once, and the scale degree in G major of its first note (G) is 1. The scale degrees of these melody notes encoded by the frequencies of each Mendelssohn fragment (4,3, 2, and 1) are an anagram of Pi.

The time signature for the Enigma Theme is 4/4 which is also known as common time. In early Christian music, duple time was called tempus imperfectum (imperfect time) and was indicated by a broken circle. In modern usage, the broken circle eventually became a capital C and came to represent common time. It was previously shown that Pi is encoded in the Enigma Theme’s first measure. The combination of Pi with the letter symbol for the Enigma Theme’s time signature “C” results in “Pi-C.” This is a nearly complete phonetic rendering of the twelfth Zodiac sign, Pisces. This name comes from the Latin term for fish, and the symbol for the constellation Pisces is two fish. In astrology, the fish are associated with the ichthyocentaurs who assisted Aphrodite when she was born from the sea. “Pi-C” sounds like Pisce, so this encoded Elgarian wordplay ostensibly represents the singular of Pisces or one fish rather than the pair. The significance of this decryption is that the ichthys — the sign of the fish — is a well-known Christogram or symbol of Christ, the secret friend memorialized in Variation XIII.

The twelve signs of the Zodiac are commonly represented on a wheel, a geometric shape closely tied to the mathematical ratio Pi. Pisces spans from 330° to 360° of the Zodiac, the latter figure representing a parallel with the Enigma Theme’s opus number 36. There is a historic fresco in the Svetitskhoveli Cathedral that portrays Christ in the center of the Zodiac Wheel. This remarkable church built in the Early Middle Ages reportedly holds the Mantle of Christ, a seamless robe worn by Jesus shortly before his crucifixion. The symbol for Pisces is two fishes, creatures that inhabit the sea which is expressly symbolized by the Mendelssohn fragments. The Mendelssohn fragments sonically portray the sea, a word that sounds like the letter C. The decryption of the Mendelssohn Pi Cipher may consequently be combined with the letter C to reproduce the Enigma Theme’s “Pi-C” Cipher and its coded reference to the sign of the fish.

The Zodiac Wheel

It has been shown that the Enigma Theme and the Mendelssohn fragments encode references to the mathematical ratio Pi and the letter C, and how these symbols may be paired together to form a revealing Christogram. There is yet another pair of ciphers shared by these two components of the Enigma Variations that encipher the initials for the covert Theme, Ein feste Burg (A Mighty Fortress) by the German Reformer Martin Luther. The Enigma Theme is written in the parallel keys of G melodic minor and G major. The accidentals for those key signatures are B-flat, E-flat, and F-sharp which serves as the leading tone. The letters of the accidentals for G melodic minor and G major cleverly encode the initials “E. F. B.”  This rather elementary music cryptogram is known as the Enigma Theme Keys Cipher. Its discovery was precipitated by the unmasking of the Enigma Locks Cipher, a cryptogram that encodes a phonetic version of locks in the Enigma Theme’s opening six measures. The realization that locks are opened by keys prompted careful scrutiny of the Enigma Theme’s key signatures, and the ensuing discovery of the Enigma Locks Cipher. 

The Mendelssohn fragments also encode the initials for Ein feste Burg in a cryptogram known as the Mendelssohn “EFB” Cipher. The decryption process involves identifying the number of times a fragment is stated in a given key and using that to pinpoint the letter of the corresponding scale degree. There are four Mendelssohn fragments in Variation XIII. Two fragments are in the key of A-flat major, and the second scale degree in A-flat major is B-flat. One fragment is in F minor, and the first scale degree of F minor is F. The final fragment is in E-flat major, and the first scale degree of that key is E-flat. The letters produced using this decryption methodology are E, F, and B. These are the initials for Ein feste Burg, the same encoded by the Enigma Theme Keys Cipher.

The initials for Ein feste Burg are also encoded by the Enigma Theme Structure Cipher and the Mendelssohn Fragments Melodic Intervals Cipher. The Enigma Theme Structure Cipher requires a process of converting the number of measures for each of its four sections into their corresponding letters of the alphabet (A = 1, B = 2, C= 3, etc.). The Enigma Theme possesses an ABA’C structure. Section A is 6 measures, Section B is 4 bars, Section A Prime is 7 measures, and Section C is 2 bars. The application of a simple number-to-letter key to these measure totals (the same method used with the Enigma Variations Keys Cipher) produces the solution letters F, D, G, and B. The letters F and B stand out because they are the second and third initials from the covert Theme’s title, Ein feste Burg. In consideration of Elgar’s verve for phoneticisms, it is reasonable to consider that the letter F sounds like “EF.” This provides one way to unmask the absent E, which is also given by the Theme’s title, Enigma. E is the first letter in the first word of the hidden melody's title, and likewise is the first letter in the title of the Enigma Theme. It is further extraordinary that the first three letters of Enigma may be rearranged to spell the covert Theme’s first word, Ein. In a brilliant display of wordplay, Elgar provides with the carefully selected title Enigma not only the first initial of the covert Theme’s title but also all three letters contiguously of its first word Ein.

The remaining two letters (G and D) from the plaintext decryption are a phonetic spelling of God as “G-D.” This coded reference to God serves two purposes. The first is that it identifies the last word in the complete title of the covert Theme, A Mighty Fortress is our God. The second is it affirms the identity of the secret friend, Jesus, whom Roman Catholics such as Elgar identify as the Son of God and a member of the Trinity. It is undoubtedly for this reason that Elgar begins Variation XIII, the special movement dedicated in secret to Christ, with the two melody notes G and D.

The Mendelssohn Fragments Melodic Intervals Cipher is constructed from the melodic intervals of the Clarinet solos that begin with the A-flat and E-flat major Mendelssohn fragments. Of the three Clarinet solos that begin with Mendelssohn quotations, the first and third contain identical sequential melodic intervals. Those numbers are significant because they may be combined to form thirteen (13), the Roman numeral assigned to this movement. A melodic interval represents the difference between two adjacent notes in a melody. Only intervals greater than a unison were considered for the purposes of this sequential melodic interval analysis. Put another way, only melodic intervals between different notes were considered, a feature common to certain types of ciphers where redundancies are eliminated.

Each Mendelssohn quotation is performed by the Clarinet and is further elaborated into a plaintive seven measure solo. The structure of the Clarinet solo is based closely on the Mendelssohn fragments characteristic stepwise descent by melodic seconds. The opening Clarinet solo in Variation XIII begins with the first A-flat major Mendelssohn quotation (“C, B-flat, A-flat, A-flat”). Elgar develops this solo with a virtual restatement of the fragment a third higher (E-flat, D, C) that omits the repeated note. This is followed by an augmented version of the fragment in retrograde played a fourth lower (E-flat, F, G) which is also missing the repeated note. The final Clarinet solo in the movement starts with the E-flat major Mendelssohn quotation (“G, F, E-flat, E-flat”), and is followed by an almost complete restatement of the fragment up a third (B-flat, A, G). It concludes with an augmented version of the fragment in retrograde down a fourth (B-flat, C, D, D) with the first D appearing as a fleeting grace note. 

In both the first and third Clarinet solos in Variation XIII, there are precisely two E-flats. Each pair of E-flats conveniently furnishes a coded reference to Edward Elgar’s initials, a feature common to multiple ciphers in the Enigma Variations. Elgar took great pride in his cryptographic prowess, embedding his initials within varied decryptions to serve as a stealth form of identification and authentication. Returning to the decryption of Mendelssohn Fragments Melodic Intervals Cipher, the next step required identifying the melodic intervals used in the first and third Clarinet solos. There are three types of melodic intervals larger than a unison: 2nd, 5th, and 6th. The application of a simple number-to-letter conversion (A = 1, B = 2, C = 3, etc.) to these melodic intervals yields the letters B, E, and F. These plaintext solution letters are an anagram of the initials for Ein feste Burg, the covert Theme to the Enigma Variations. In an astonishing parallel, a count of the different key signatures in which the different movements of the Enigma Variations are written produces the exact same numbers as those found among the intervals in the clarinet solos beginning with the Mendelssohn fragments.

Another cryptographic intersection between the Enigma Theme and the Mendelssohn fragments is that they both encipher the phrase “See Abba.” This particular cipher is a phonetic anagram built on the four note letters of the Mendelssohn quotation in A-flat major. The first and second Mendelssohn quotations in A flat major consist of four notes: C, B-flat, and two A-flats. The letters for these four note (C, B, A, and A) may be rearranged anagrammatically to form CABA. This reordering permits the phonetic reading “See Abba.” Elgar’s affinity for phonetic spellings is thoroughly documented by his personal correspondence, for this reason, a phonetic interpretation of CABA as “See Abba” is amply justified.

What is the significance of the decryption “See Abba?” According to Elgar’s Roman Catholic profession of faith, the central person of the Trinity is God the Father. As documented in the epigraph, Jesus called God “Abba” which is Aramaic for “Father.” Jesus further declared that those who have seen him have seen his heavenly Father. Jesus is the secret friend personified in Variation XIII, and the Romanza Cipher in that movement refers to his burial cloth, the Turin Shroud. This coded reference to Christ’s death would explain Elgar’s decision to quote a melody from Mendelssohn’s tone poem that represents the deathly stillness of the sea (Todesstille fürchterlich!) described so poignantly by the German poet Goethe. The “DEAD G-D” Cipher reinforces this interpretation, for Roman Catholics believe Jesus is divine and that he died at Calvary as an atonement. There are numerous cryptographic references to the Turin Shroud in the Enigma Variations. According to Elgar’s Roman Catholicism, to see the image on the Turin Shroud is to see an impression of Jesus, and by extension, his heavenly Father.

Why would Elgar encode a reference to seeing God the Father in Variation XIII? The explanation is provided by a famous photographic negative of the Turin Shroud first captured by Secondo Pia in May 1898, five months before Elgar began to work openly on the Enigma Variations. While developing the first photographic glass plates of the Turin Shroud in a darkroom, Pia made the remarkable discovery that the Turin Shroud is itself a photographic negative. A negative of a negative is a positive, so the image on Pia’s photographic negative unveiled for the first time a detailed positive image of a crucified man that many Catholic believe is the body of Christ. Pia was so shocked by his discovery that he almost dropped the photographic glass plate.

Pia’s remarkable discovery was widely reported in the secular and Catholic press, and the Turin Shroud remains a popular topic in the press to the present day. In witnessing for the first time a lifelike image of Jesus miraculously preserved as a photographic negative on his burial shroud, Roman Catholics like Elgar and Pia believed they were gazing at an actual image of their Lord and Savior, and by extension, their heavenly Father. My own grandmother was a Roman Catholic, and she proudly displayed a copy of Pia’s photographic negative of the Holy Face in her living room. Confirmation that Pia’s photograph of the Turin Shroud inspired Elgar to compose the Enigma Variations is found in Variation II which contains within its Roman Numerals and subtitle a coded reference to Secondo Pia.

The efficacy of the “See Abba” Mendelssohn Cipher is confirmed by a companion cryptogram in the Enigma Theme that encodes the identical phrase using the same letters. In a remarkable convergence, the four note letters of the A-flat Mendelssohn fragments are an anagram of the Enigma Theme’s ABA’C structure. When read phonetically in reverse, the Enigma Theme’s ABA’C structure sounds like “See Abba.” It is remarkable that the “C ABA” Cipher contained in the Enigma Theme’s structure is also present in the four-note Mendelssohn quotations in A-flat major. According to Elgar’s Roman Catholic faith, the central person of the Trinity is God the Father. So the A-flat Mendelssohn fragment encodes not only the four structural components of the Enigma Theme but also a revealing phrase that hints at the divine inspiration behind the Enigma Variations and the secret friend memorialized in Variation XIII.

There are compelling contrapuntal links between the Enigma Theme and the deceptively disparate Mendelssohn fragments in Variation XIII. All or most of the concluding phrase from Ein feste Burg is encoded in the Enigma Theme and the Clarinet Solos commencing with the Mendelssohn fragments in A-flat and E-flat major. The prospect of uncovering fragments of the covert Theme was disclosed by an exchange in 1923 between Troyte Griffith and Elgar. Griffith, the friend portrayed in Variation VII, asked Elgar if the missing melody was God save the King. Elgar replied, “No, of course not; but it is so well-known that it is extraordinary no one has spotted it.” In addition to establishing its fame, such a reply suggests that fragments of the absent Theme are present in the Variations, for otherwise, there would be nothing to spot. This hunch is bolstered by the original program note that describes the link between the absent Theme and the Variations as being “. . . often of the slightest texture . . .” Merriam-Webster defines slight as “very small in degree or amount,” and one definition for texture is “the various parts of a song . . . and the way they fit together.” Elgar’s judiciously parsed words specify a discernable bond between the Variations and the absent Theme is comprised of short sequences of shared notes or fragments. This condition is further alluded to by the brief four-note Mendelssohn fragments quoted in Variation XIII.

Ein feste Burg is subdivided into six distinct phases labeled A through F with a comprehensive phrase structure of “ABABCDEFB.” It is remarkable that its German initials emerge sequentially in the final three phrases (ABABCDEFB). Among the six phrases, Phrase B is performed the most often with three cycles in the second, fourth and ninth positions. During the process of uncovering an efficacious contrapuntal mapping of the covert Theme through and over the entire Enigma Theme’s ABA’C structure, it was observed that the last six notes of Ein feste Burg’s Phrase B are played in reverse order over the first three measures in the bass line. This six-note fragment provided formidable evidence that Elgar skillfully mapped the covert Theme in retrograde above the Enigma Theme, the rarest form of counterpoint which is fiendishly difficult to detect.

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 played backward. 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 backward into the mast In present usage, it refers to being taken by surprise. Both of those definitions – backward and surprised – would exquisitely express Elgar’s mapping of the covert 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. That Elgar was openly 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. 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 backward 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 backward 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.

 
 

The same ending phrase from Ein feste Burg is also encoded as a music anagram by the Clarinet solos in Variation XIII that begin with the Mendelssohn fragments in A-flat and E-flat major. An anagram is composed of a word or phrase created by the transposition of another word or phrase. One example is that 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 those of another. This is what Elgar accomplishes with the Clarinet solos beginning with the first and third Mendelssohn quotations in A-flat and E-flat major. 

Elgar introduces the Mendelssohn quotations on the clarinet with the first in A-flat major (four measures after Rehearsal 56) and the third in E-flat major (four measures after Rehearsal 60). He further elaborated and extended these fragments into complete seven bar solos. A careful analysis of those clarinet solos reveals the notes are a music anagram of the concluding 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 in the fourth movement of the Reformation Symphony.

This overview has shown that the Enigma Theme and the Mendelssohn fragments harbor multiple cryptograms that encode a set of mutually consistent and identical solutions. These decryptions confirm and authenticate Ein feste Burg as the covert Theme to the Enigma Variations, and further identify Jesus Christ as the secret friend memorialized in Variation XIII. The Enigma Theme begins with a six-note fragment of Ein feste Burg’s concluding phrase in its bass line, and this is the identical phrase encoded as a music anagram by the Clarinet solos beginning with the A-flat and E-flat Mendelssohn quotations in Variation XIII. The Enigma Theme’s ABA’C structure is intimated by the Mendelssohn quotations in A-flat major which have the notes C, B-flat, and two A-flats. This shared compliment of four letters is an anagram of “CABA” which may be read phonetically as “See Abba,” a phrase rich with theological overtones implicating the secret friend who is mentioned by name in the second stanza of Ein feste Burg. The accidentals for the parallel major and minor modes of G in which the Enigma Theme is played are F-sharp, B-flat, and E-flat — the initials for the covert Theme. The Mendelssohn fragments encode this identical set of initials in multiple ways. The Enigma Theme and the Mendelssohn fragments encode the mathematical constant Pi and the letter C. These may be paired together to form “Pi-C,” a phonetic approximation of Pisce which alludes to the sign of the fish, a Christogram that points to the secret friend. To learn more about one of Elgar's greatest symphonic achievements, read my free eBook Elgar’s Enigmas Exposed. Please help support and expand my original research by becoming a sponsor on Patreon.

Soli Yah Gloria

Secondo Pia’s photographic negative of the Turin Shroud face region.