Friday, December 14, 2018

The Enigma Theme Relative Modes Cipher

After silence, that which comes nearest to expressing the inexpressible is music.

Elgar’s expertise in cryptography—the art of creating and decoding secret messages—is widely acknowledged. Craig Bauer, the editor in chief of the journal Cryptologia, devotes an entire chapter to Elgar’s obsession with secret codes in his book Unsolved! It should come as no surprise that the opening six bars of the Enigma Theme which comprise the first section of its ABA’C structure are permeated by a diverse array of cryptograms. These outwardly distinct yet interrelated ciphers encode solutions to three overarching riddles posed by Edward Elgar’s breakout symphonic masterpiece, the Enigma Variations. The primary one concerns a covert principal Theme to which the Enigma Theme is a cunningly crafted counterpoint. The second is a “dark saying” ensconced in the Enigma Theme. The third is the identity of a secret friend memorialized in Variation XIII.

One of the earliest cryptograms to be decrypted from the Enigma Theme’s opening section was the Enigma Locks Cipher. This secret code was first detected after it was determined the total notes played by each part in the full score does not exceed the number of letters in the alphabet. The note totals played through Section A by the first violins (24), second violins (17), violas (15), and cellos (12) are convertible to their corresponding letter in the alphabet relying on a basic number-to-letter key (a=1, b=2, c=3, etc…). The plaintext solution, LOQX, is a phonetic rendering of the word locks. This decryption is idiomatic of Elgar’s writing style because his personal correspondence bristles with inventive phonetic spellings.

Locks are opened by keys, and so are ciphers. Before venturing further, it is crucial to understand that tonal music is also written in a variety of contrasting keys. The unmasking of the Enigma Locks Cipher spurred a renewed interest in the musical keys of the Enigma Theme, a brief movement performed in the parallel keys of G minor and G major. The accidentals for those keys are B-flat, E-flat, and F-sharp. On closer inspection, the letters of those accidentals turn out to be an anagram of the initials for the covert Theme, Ein feste Burg. In a remarkable development, the Enigma Locks Cipher precipitated the discovery of the Enigma Keys Cipher, an exploratory progression described as a minor and major discovery.
Could Elgar have exploited other aspects of musical keys to encipher further corroborating information? To assess this possibility, a harmonic analysis of the Enigma Theme’s opening six measures was performed. The concept of tonicization is integral to harmonic analysis because the tonal center shifts temporarily due to the use of secondary dominants. The Harvard Dictionary of Music supplies the following definition of tonicization:
The momentary treatment of a pitch other than the tonic as if it were the tonic, most often by the introduction of its own leading tone or fourth scale degree or both. The resulting harmony is most likely to be the dominant of the tonicized pitch and is in such a case often termed a secondary or applied dominant. The triad formed on the leading tone of the tonicized pitch may also function in this way. Tonicization, which may be prolonged beyond a single chord or two, is nevertheless a local phenomenon, as distinct from modulation which implies an actual change in tonic. The boundary between the two, however, is not always easily fixed in practice
When a secondary dominant resolves to a degree other than the tonic, it makes the non-tonic chord sound like the tonic. This process is called tonicization. An accidental is a strong indicator of a secondary dominant because it alters a note’s pitch from what is specified by the key signature.

From the beginning to the downbeat of bar 3, the harmonic progressions are unequivocally based on the tonic key of G minor. The introduction of a C minor added sixth chord on the third beat of bar 3 followed by G dominant seventh chord on the downbeat of bar 4 tonicizes the fourth degree as it resolves to C minor. A German augmented sixth chord on the first beat of bar 5 heralds a return to G minor as it resolves to the tonic chord in the second inversion on beat 3. The tonic key is presaged by a Plagal cadence in bar 6 that resolves via a Picardy third to G major in bar 7 with the start of Section B.
One conspicuous feature of the harmonic analysis of the Enigma Theme’s Section A is the augmented German sixth chord on the downbeat of measure 5. This chord is a gigantic clue because the covert Theme’s complete title is six words in German. Other than the use of an augmented German sixth, the Enigma Theme’s harmonic progressions in Section A did not turn up any other obvious cryptograms.
Tonal music is defined by divergent keys that share certain relationships which are conveniently summarized by the circle of fifths. This geometric representation of a circle shows the twelve tones of the chromatic scale with their related key signatures and corresponding relative major and minor modes. It resembles a clock face with each number replaced by every fifth note in the musical scale beginning with C in the 12 o’clock position. With no sharps or flats in its key signature, C major begins the circle of fifths with a relative key of A minor. The minor key is defined as relative to a particular major key because they share the same key signature.
Proceeding clockwise to the next note a fifth above C is G major which has one sharp and a relative minor key of E. Following a fifth above G is D major with two sharps and a relative minor of B. This is succeeded a fifth above D by A major with three sharps and a relative key of F-sharp minor. This pattern of moving every fifth note higher continues with another sharp added at each step of the way until all seven sharps appear in the key of C-sharp major at the seven 0’clock position.

A similar process involving the flats takes place in the counterclockwise direction. At the 11 o’clock position is the note a fifth below C is the key of F major with one flat and a relative minor of D. The next step counterclockwise a fifth below F is B-flat major with two flats and a relative minor of G. A fifth below B-flat is E-flat with three flats and a relative minor of C. This process cycles through every fifth note lower accompanied by the addition of another flat to the key signature until all seven flats are cited in C-flat major at the 5 o’clock position. There is a remarkable symmetry with the circle of fifths which commences with no sharps or flats in the key of C major and culminates with all seven sharps C sharp major and all seven flats in C flat major. The circle of fifths captures an elegant mathematical precision to the organization of the key signatures in tonal music.
At the 5, 6 and 7 0’clock positions of the circle of fifths are musical keys that may be spelled by either some combination of sharps or flats. For example, G-flat major with six flats sounds indistinguishable from F-sharp major with six sharps. This is possible because the notes F-sharp and G-flat are the same pitch. The ability to spell the same note in two different ways is known as an enharmonic equivalent. This concept proves pivotal in the harmonic analysis of the Enigma Theme’s Section A.
The circle of fifths conveniently summarizes the key relationships between the major and relative minor modes. A major key is related to a specific minor key because they share the same key signature. For example, G major and E minor are related because their key signatures both have an F-sharp. Elgar hints at the cryptographic significance of the circle by encoding the number Pi in the first bar of the Enigma Theme’s melodic scale degrees (3-1-4-2). This mathematical constant is the ratio of a circle’s circumference to its diameter. The Enigma Theme’s time signature (4/4) is also known as common time and may be represented by a capital C, a symbol that originated from a broken circle. This letter occupies the 12 o’clock position in the circle of fifths and is found in both key letters with all seven sharps and all seven flats. The most famous circle in music is indisputably the circle of fifths. By encoding Pi in the Enigma Theme’s first bar with a time signature of common time, Elgar subtly invites the savvy observer to refract the Enigma Theme’s harmonic progressions through the prism of the circle of fifths to reveal a coded message.
An analysis of the opening six measures of the Enigma Theme discloses that the relative modes of the tonal centers encode two of the three initials from the covert Theme’s title. The relative major keys of G and C minor are B-flat and E-flat respectively. These relative key letters are the first and third initials of the covert Theme’s three-word German title, Ein feste Burg. But what about the absent initial f? The German sixth chord furnishes the solution because its enharmonic equivalent is an E-flat dominant seventh with the C-sharp respelled as a D-flat. This alternate spelling comes from A-flat major with a relative minor of F. The enharmonic equivalent of the German sixth enciphers through its relative minor the remaining initial for Ein feste Burg. It is also salient to recognize that the sixth letter of the alphabet just so happens to be F.

The relative modes of the Enigma Theme’s tonal centers in Section A directly encipher two of the three initials for the covert Theme’s title. The absent initial is implicated by the relative mode of the enharmonic equivalent for the augmented German sixth chord. This cipher is merely one of at least seventeen different cryptograms within the Enigma Variations that encode the initials of the covert Theme.

The unique letters from the enharmonic equivalents of the tonicized progressions in Section A are an anagram of the word DEAD. The silence of the principal Theme is evocative of a passage from Psalm 37:17 that mentions the silence of the grave. In the original program note for the 1899 premiere of the Enigma Variations, Elgar likens the absent principal Theme to the mysterious protagonist who never appears on stage in various dramas by the Belgian playwright, Maeterlinck. That absent character is death. There was an indelible link between music and death for Elgar because as a boy he studied musical scores at a local churchyard while resting on a tombstone. In Variation XIII, Elgar repeatedly quotes a fragment from Mendelssohn’s concert overture Calm Sea and Prosperous Voyage (Meeresstille und glückliche Fahrt) to portray a ship crossing the open sea. This sonic symbolism was inspired by the poetry of the famed German playwright Goethe whose seemingly benign image of a boat adrift on a windless sea depicts the stillness of death (Todestille).
Why would Elgar make so many cryptic references to death in the Enigma Variations? The friend honored in secret by Variation XIII is Jesus Christ, the Savior of Elgar’s Roman Catholic faith who died and was miraculously resurrected. A musical cryptogram in that movement encodes DEAD G-D, and a discrete subset of ciphers in the Enigma Variations make veiled various references to Jesus’ burial cloth, the Shroud of Turin. That sacred relic still makes headlines today just as it did in the Spring of 1898 when Secondo Pia took the first official photographs that revealed for the first time on their negative plates the miraculous image of a crucified man many believe to be that of Jesus. The timing works because that historic event transpired five months before Elgar began to work seriously on the Enigma Variations.
Some scholars scoff at the vast trove of ciphers exhumed from the Enigma Variations and subjected to a detailed autopsy. What those career academics fail to appreciate is the old adage that “One man’s junk is another man’s treasure.” Although they contemptuously dismiss my research as dead wrong, the decryption of the Enigma Theme Relative Modes Cipher proves to be dead on. To learn more about the deep dark secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

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About Mr. Padgett

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Mr. Padgett studied violin with Michael Rosenker (a student of Leopold Auer), and Rosenker’s pupil, Owen Dunsford. Mr. Padgett studied piano with Sally Magee (a student of Emanuel Bay), and Blanca Uribe, a student of Rosina Lhévinne. He attended the Stevenson School in Pebble Beach, California, and Vassar College in Poughkeepsie, New York, where he graduated Phi Beta Kappa with a degree in psychology. At Vassar he studied music theory and composition with Richard Wilson. Mr. Padgett has performed for Joseph Silverstein, Van Cliburn, Arnold Schwarzenegger, Maria Shriver, Steve Jobs, Prince Charles, Lady Camilla, Marcia Davenport, William F. Buckley, Jr., and other prominent public figures. His original compositions have been performed by the Monterey Symphony, at the Bohemian Grove, the Bohemian Club, and other private and public venues. In 2008 Mr. Padgett won the Max Bragado-Darman Fanfare Competition with his entry "Fanfare for the Eagles." It was premiered by the Monterey Symphony under Maestro Bragado in May 2008. A member of the Elgar Society, Mr. Padgett is married with five children.