Saturday, June 13, 2020

Elgar's Bridge Passage Tau Ciphers

Walking on Water, by Ivan Aivazovsky (1888)
It is doubtful whether anything more beautiful could be imagined, than the expression Elgar always gives to our Lord; in just such peaceful, soothing strains as these, we imagine, would the voice of Jesus sound. This impression is given us in the later oratorios, The Apostles and The Kingdom . . . It is an insight to the composer’s deeper religious feelings.
J. F. Porte writing about Lux Christi Op. 29 in Sir Edward Elgar

This is the third installment in a series of articles exploring a trove of cryptograms embedded within three bridge passages from the Enigma Variations by the British Romantic composer Edward Elgar. A section in classical music that smoothly connects one movement to another is called a bridge passage, and there are three in the Enigma Variations. The first in bars 18-19 forms the concluding phrase of the iconic Enigma Theme. It begins at Rehearsal 2 and precedes Variation I (C. A. E.). The second in bars 185-188 completes the closing section of Variation V (R. P. A). It starts four bars before Rehear-al 19 and links to Variation VI (Ysobel). The third bridge passage in bars 306-308 begins three measures before Rehearsal 33 and forms the ending phrase of Variation VIII (W. N.). A soulful melodic G from the tonic cadence is sustained by the first violins over the barline into Rehearsal 33 to herald the sublime dawn of the most elegiac of the movements, Variation IX (Nimrod).

My first essay covers the Opus Dei Cipher. This cryptogram is formed by three performance directions in the first bridge passage (bars 18-19) that stand out from the others because they end in a period: tempo., dim., and unis. These three performance directions are an anagram of two phrases and one word. The first is the Latin phrase “Opus Dei” which means “The work of God.” The next is “I m,” a phonetic spelling of “I am.” This phrase is a mysterious name given by God to Moses at the burning bush. The third is “mnt,” a phonetic rendition of “mount.” Moses first encountered God at the burning bush on Mount Horeb, a place also known as the Mountain of God. The decryptions “Opus Dei”, “I AM,” and “mount” exhibit a coherent theological context. They further hint at the identity of the secret friend memorialized in Variation XIII because Christian theologians classify the episode on Mount Horeb as a Christophany, an appearance of Jesus in the Old Testament.
My second article describes the Psalm 46 Ciphers. The word psalm is encoded as an acrostic anagram by five performance directions in the first bridge passage. The numbers 4 and 6 are enciphered in multiple ways by the orchestration. The first is conveyed by the breakdown of the notes in the opening G major chord in bar 18. This tonic major chord is constructed of ten written notes that may be categorized as four unisons and six discrete pitches. The numbers four and six turn up again in connection with the melodic eighth notes performed by the first violins (bars 18-19) and harmonic eighth notes played by the violas (bar 19). These eighth notes are beamed into groups of four, and there are a total of six beamed groupings. The encoding of the word psalm in conjunction with the numbers 4 and 6 is illuminating because the title of the covert Theme to the Enigma Variations originates from the first line of Psalm 46. The popular poem A Psalm of Life was written by Henry Wadsworth Longfellow, one of Elgar’s favorite poets and a fount of inspiration for numerous compositions.

The discovery of these ciphers is consistent with Elgar’s compulsion for cryptography, a subject that merits an entire chapter in Craig P. Bauer’s treatise Unsolved! A decade of concerted analysis of the Enigma Variations has netted over eighty cryptograms in diverse formats that encode a set of mutually consistent and complementary solutions. While this figure may seem incredible, it is entirely consistent with Elgar’s psychological profile. More importantly, their solutions provide definitive answers to the core questions posed by the Enigma Variations. What is the secret melody to which the Enigma Theme is a counterpoint and serves as the foundation of the ensuing movements? Answer: Ein feste Burg (A Mighty Fortress) by Martin Luther. What is Elgar’s “dark saying” ensconced within the Enigma Theme? Answer: A musical Polybius box cipher embedded in the opening six bars. Who is the secret friend and inspiration behind Variation XIII? Answer: Jesus Christ, the Savior of Elgar’s Roman Catholic faith.

The Tau Performance Directions Cipher

Two performance directions bookend the first and second violin staves in the first bridge passage (bars 18-19). They are “a tempo” and “unis.” The first letters of those performance directions are an acrostic anagram of tau: a tempo and unis.

Tau is the nineteenth letter in the Greek alphabet and is represented in English by the letter T. The number nineteen is intriguing as the last letter in tau is encoded in bar 19. With two proximate performance directions in the first and second violin parts, Elgar encoded the term tau as an acrostic anagram in the first bridge passage. This is consistent with a larger pattern within the Enigma Theme where the same technique is also applied in bars 1 and 18 to encipher the word psalm.
The significance of the Tau Cipher is that it refers to a type of cross. One of the four iconographic representations of the cross is the T-shaped cross called the tau cross. This symbol is also known as the Saint Anthony cross and the crux commissa. Artists like Konrad Witz portray Jesus crucified on a tau cross.

Crucifixion scene with a tau cross by Konrad Witz (1400–1447)

The presence of the Tau Cross Cipher within the first bridge passage is contextually appropriate because a bridge permits one to “cross” over an obstacle. The function of a bridge cleverly alludes to the word “cross.” Paintings of the penitent thief crucified at the right hand of Christ show him languishing on a tau cross.

Painting of the penitent thief on a tau cross (circa 1450).

The three bridge passages in the Enigma Variations are allegorical representations of the three crosses. This conclusion is reinforced by three Mendelssohn quotations in Variation XIII that sonically portray a sea crossing. This second corresponding series of three crossings within the Enigma Variations fittingly occurs in the movement secretly dedicated to Jesus who died on a cross. There were three crosses at the execution of Christ who was crucified between two criminals (see Luke 23:33). In a striking parallel, there are precisely three occurrences of the word “tempo” in the first bridge passage that begin with t, a letter that resembles the Latin cross. According to Roman Catholic tradition, Jesus was crucified at the age of 33. In a remarkable parallel, there are 33 written notes in the first bridge passage.

The 515 Tau Cipher

Two performance directions in the first bridge passage that are an acrostic anagram of tau may be broken down into three component parts: a, tempo, and unis. The number of characters in those three terms are 1, 5, and 5, respectively. These three numerals are an anagram of 515, a divine number that represents Dante’s “enigma forte” (hard enigma) from the Canto XXXIII of Purgatorio from the Divine Comedy. In that passage, the character Beatrice issues a cryptic prophecy about the coming of a future savior whom she identifies by the number “five hundred, ten, and five.” Elgar’s unusual title for the Theme is directly tied to that poetic riddle by the shared term “enigma.”
The remaining word “forte” is represented in musical scores by the initial f to indicate a loud dynamic. The performance direction forte has precisely five letters and occurs five times within the Enigma Theme’s orchestral score. The first three instances are on the fourth beat of bar 15 where a concert G is played forte by the first clarinet, second violins, and cellos. The lowest notes in this forte passage are octave Ds performed by the violas and basses. Consequently, the highest and lowest notes on the fourth beat of measure 15 are a phonetic spelling of “God.”

Measure number 15 conveniently provides the final two digits of 515 in the appropriate order. The last two occurrences of forte are located in the first violin and viola parts at the center of bar 19 of the first bridge passage. In all, the dynamic forte occurs five times on five different staves of the Enigma Theme with three in bar 15 and two in bar 19. The span of these two forte passages is five measures (bars 15, 16, 17, 18, and 19). The distance between these two forte markings is fifteen quarter beats. Consequently, the layout of the score encodes yet another form of the number 515 via five bars and fifteen quarter beats.

The number of Canto XXXIII is cleverly encoded by the first bridge passage that has precisely 33 written notes. The adjacent performance directions “a tempo” and “con” in bar 18 of the first and second violin parts permit the spelling of the word canto. This process involves combining all three letters of “con” with the first letters of “a” and “tempo” and reshuffling them to spell “canto.” The Roman numerals for Dante’s mysterious number 515 are DXV. Remarkably, the removal of all the vowels from the title of Elgar’s variation produces an anagram of DXV: XIV E.D.U. The reverse order of those remaining letters spells the Latin word for leader. This is feasible because the letters V and U are identical in the Roman alphabet. Consequently, DVX may be legitimately read as DUX.
A coded version of 515 within the Tau Cross Cipher is not a random coincidence. There is a distinct subset of cryptograms within the Enigma Variations that encipher that divine number. There are also other coded allusions to Dante’s Divine Comedy in the Enigma Variations. A longstanding debate regarding the identity of Dante’s future savior has spawned numerous books and scholarly papers. Elgar deftly enters the fray by offering his own solution through the guise of another enigma.
Through multiple coded allusions to Jesus and the number 515, Elgar answers Dante’s “enigma forte.” The encoding of the number 515 within the Tau Cross Cipher is merely one of numerous examples. The last four Roman numerals of Canto XXXIII match those for the movement secretly dedicated to Christ. Variation XIII begins at Rehearsal 55, includes measure 515 that falls in the center of the second Mendelssohn quotation, and consists of 51 bars. The discovery that Jesus is the secret friend memorialized in Variation XIII intersects elegantly with these interrelated cryptograms.

The Golden Section Ciphers

In professional mathematical literature, the Greek letter tau represents a unique number called the Golden Ratio. It is an irrational number that begins with 1.618 and never ends or repeats. An irrational number is one that cannot be represented by the quotient of two integers. Also known as the Golden Section, this ratio is produced by dividing a line into two sections such that the smaller section is to the larger as the larger is to the whole. The Greek letter tau was chosen by mathematicians to represent the Golden Section because it is the first letter in the Greek word meaning “the section” or “to cut.” This ratio has captured the imaginations of great mathematicians and artists as Mario Livio describes in his book The Golden Ratio:
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over the simple ratio and its properties. But the fascination with the golden ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the golden ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
The renowned mathematician Euclid defined this ratio in the context of a line divided or cut into two different segments:
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the great to the lesser.
The following exhibit captures this definition with a line divided into two shorter segments shown by points A, B, and C. For simplicity, the longer segment AB is labeled p, and the shorter segment BC as q. This subdivided line is said to be in extreme and mean ratio because the ratio of segment p is to q is the same as the ratio of segment (p+q) is to q. The American mathematician Mark Barr replaced the Greek letter tau with the letter phi (ᵠ) in the early part of the twentieth century. It is now standard practice to represent the Golden Section with the letter phi as shown below.

The use of points A, B, and C in this line is remarkable because the Enigma Theme has an ABA’C structure that employs all three of those letters. The first three parts are in ternary form (ABA’) followed by a short codetta (C) in the first bridge passage. The structure of the Enigma Theme hints at the Golden Ratio.

The smaller segment q may be placed perpendicular to the longer segment p to form a tau cross (T). When segment q is positioned perpendicularly a short distance below the top of segment p, it also creates a Latin cross. When viewed in this context, Elgar’s cryptic allusions to this mathematical constant elegantly intersect with other coded references to Jesus in the Enigma Theme.
The Golden Ratio is hinted at in at least two ways in the first bridge passage. The first is the encoding of the word tau as an acrostic anagram via the performance directions “a tempo” and “unis.” The second coded allusion is provided by sixteen (16) melody notes performed by the first violins beginning in bar 18. The pairing of 16 with 18 furnishes the first four digits in the Golden Ratio (1.618).
A coded reference to a well known mathematical ratio in the Enigma Theme is not limited to the Golden Section in the bridge passage. There is another coded reference to the famous mathematical ratio Pi in the first bar of the Enigma Theme. Elgar encodes that irrational number using the scale degrees (3-1-4-2) of the first four melody notes (B-flat, G, C, A). That encrypted version of Pi is repeated by the melody a second time at Rehearsal 1 in bar 11. Consequently, the encoding of two famous mathematical constants in the Enigma Theme is complementary and mutually reinforcing. In both instances, Elgar enciphers the first four numerals from each mathematical ratio. The first occurrences of these two ratios mark the beginning and end of the Enigma Theme. This mirrors the enciphering of psalm in those same two regions of the score.
The first known use of the term “Golden Ratio” in English was in an article by James Sulley in an 1875 edition of the Encyclopedia Britannica. This predates the genesis of the Enigma Variations by 24 years. The Golden Section is often referred to as God’s number. This interfaces elegantly with multiple coded references to Jesus within the Enigma Theme with the first occurring in measure 1. The decryption of Elgar’s Polybius box cipher in bar 1 is “GSUS”, a phonetic version of Jesus. The pairing of the solution to the Enigma Theme’s Melodic Intervals Cipher in bar 1 (Pi) with the decryption of the Polybius box cipher in that same measure (GSUS) produces a phonetic variant of the phrase “Pie Jesu.” That is the Latin phrase for “Pious Jesus,” the final couplet from the hymn Dies Irae.
One of Elgar’s favorite authors from childhood was Henry Wadsworth Longfellow. So great was the admiration for this poet by the English public that two years after Longfellow’s death, a memorial bust was erected in the Poet’s Corner of Westminster Abbey next to Chaucer in 1884. Longfellow’s poetry and prose served as the stimulus for five of Elgar’s compositions. The first is Spanish Serenade Op. 23, a work for chorus and orchestra written in 1892 based on Act I of Longfellow’s play The Spanish Student. The second is The Black Knight Op. 25, an oratorio composed in 1893 and inspired by Longfellow’s translation of Uhland’s “Der schwarze Ritter” from his novel Hyperion: A Romance. The third is Rondel Op. 16 No. 3, a song for voice and piano set in 1894. The fourth is The Saga of King Olaf, a cantata composed in 1896 that was inspired by Longfellow’s epic poem sharing the same title. The fifth is The Apostles, a sacred oratorio premiered in 1903 that was based in part on Longfellow’s The Divine Tragedy (1871). Longfellow’s epic Christian poem forms a trilogy with The Golden Legend (1851) and The New England Tragedies (1868).
There is a famous compilation of medieval hagiographies about the saints compiled and written by Jacobus da Varagine called The Golden Legend. It is known by the Latin titles Legenda Aurea and Legenda Sanctorum. This is the original work that inspired the title for Longfellow’s Christian epic poem. An intimate association exists between the words dark, enigma and Christ in Longfellow’s The Golden Legend. The heroine Elsie says to Prince Henry in Chapter IV, “Faith alone can interpret life, and the heart that aches and bleeds with the stigma / Of pain, alone bears the likeness of Christ, and can comprehend its dark enigma.” For the original 1899 program note Elgar wrote, “The Enigma I will not explain — it’s ‘dark saying’ must be left unguessed . . .”
Longfellow’s prose inspired Arthur Sullivan’s cantata The Golden Legend. Elgar served as a sectional violinist in performances of that work in May 1887, September 1887, and November 1892. He also attended a performance of it in September 1898, a month before he began officially composing the Enigma Variations. Elgar’s daughter Carice wrote, “My father always spoke with great feeling and respect for Sullivan and admired The Golden Legend.” Coded references to the Golden Section in the Enigma Theme’s bridge passage allude to Longfellow’s The Golden Legend. The first two words in that title — “The Golden” — are identical to those in “The Golden” Section. The opening chord to the first bridge passage is G major, and the first letter in the first performance direction at the top of the score is L. Together, they furnish the initials for the Golden Legend. The function of the bridge passage further suggests a passage spoken by the character Prince Henry who likens Jesus and his Church to a bridge:
God’s blessing on the architects who build
The bridges o'er swift rivers and abysses
Before impassable to human feet,
No less than on the builders of cathedrals,
Whose massive walls are bridges thrown across
The dark and terrible abyss of Death.
Well has the name Pontifex been given
Unto the Church’s head, as the chief builder
And architect of the invisible bridge
That leads from earth to heaven.
In ancient Rome, a pontiff was a title awarded to a member of the College of Pontiffs, a group of priests who presided over the state religion. The Latin for pontiff is pontifex, a word formed by the root words pons (bridge) and facere (to do, to make). The literal translation of pontifex is “bridge builder.” This title alludes to the role played by the priests who bridged the gulf between humanity and the divine. The chief priest was known as the Pontifex Maximus, the same title given to the current pope. There are several coded references to Pope Leo XIII in Variation XIII.
There is an extraordinary reason for why Elgar would incorporate overlapping allusions to the Golden Section and Longfellow’s The Golden Legend in the first bridge passage that centers around the secret melody to the Enigma Variations. The first bridge passage begins at Rehearsal 2 and consists of two measures. The number two is significant because there is a “Second Interlude” in The Golden Legend with the title “Martin Luther.” It depicts that great German Reformer at Wartburg Castle where he went into hiding after his bold stand in 1521 at the Diet of Worms. In his homage, Longfellow alternates between quotations of each of the four stanzas from the hymn Ein feste Burg with more extensive intervening poetic passages. This part of The Golden Legend points to Ein feste Burg as the covert Theme to the Enigma Variations.
Luther was an artisan of hymnody and the founder of the Lutheran faith who translated the Bible into German. Out of respect and admiration for this champion of the Christian faith, Longfellow cites Luther’s most famous hymn not only in The Golden Legend but also in his novel Hyperion: A Romance. This is the “little book” that Elgar gave to the conductor Hans Richter in gratitude for conducting the premiere of the Enigma Variations. With that seemingly innocent gift, Elgar literally gave away the answer to his melodic enigma. Richter’s limited grasp of the English language undoubtedly prevented him from reading Hyperion and stumbling across the solution in its final chapter.

Concluding Remarks

There is a coded reference to the Greek letter tau in the first bridge passage of the Enigma Variations. It occurs in bars 18-19 as an acrostic anagram by proximate performance directions (a tempo, and unis.) in the first and second violin staves. The significance of the word tau is its connection to the tau cross, one of the four iconographic representations of the cross. The encoding of this term in the first bridge passage is contextually appropriate because a bridge is a crossing point. Jesus is the friend portrayed in Variation XIII, a movement that depicts a sea crossing through repeated quotations of a melodic fragment from Mendelssohn’s overture Calm Sea and Prosperous Voyage. The image of a sea crossing turns up in the second bridge passage, a subject that will be addressed in a future article.
The number of characters in each performance direction of the Tau Cross Cipher is an anagram of the number 515. This divine number is the “enigma forte” from Canto XXXIII of Purgatorio from Dante’s Divine Comedy. The first bridge passage alludes to this Canto because it has precisely 33 written notes. Roman Catholics believe Jesus was crucified at the age of 33, injecting another layer of significance to the Tau Cross Cipher in the first bridge passage. There are multiple coded allusions to the Divine Comedy and the number 515 within the Enigma Variations, particularly in Variation XIII. The Roman numerals for that movement secretly dedicated to Jesus match the final four in XXXIII. Variation XIII begins at Rehearsal 55, includes measure 515 during the second Mendelssohn quotation, and has a total of 51 bars.
Like the divine number 515, there are at least two coded references in the Enigma Theme’s bridge passage to a mathematical ratio known as the Divine Number or Golden Section. This number begins with 1.618 and continues without repetition forever. The first is conveyed by the number of notes in the first violin’s melodic line (16 notes) in conjunction with the measure number in which that bridge passage begins (18). The second is the word tau formed as an acrostic anagram from two proximate performance directions in the first and second violin staves (a tempo and unis.). Before the earlier 20th century, mathematicians use the Greek letter tau to represent the Golden Section. Similarly, there are two coded references to Pi in the Enigma Theme formed by the sequential scale degrees of the melodic line in bars 1 and 11. These parallels between the Pi and Tau ciphers are compelling evidence for a deliberate construction. Incredibly, there is a trinity of divine numbers enciphered within the Enigma Theme: Pi (3.142), Tau (1.618), and Dante’s “enigma forte” (515).
The American poet and educator Longfellow took over two decades to painstakingly complete his popular English translation of Dante’s Divine Comedy published in 1867. A coded reference to the Golden Section in the first bridge passage alludes to another work by Longfellow, The Golden Legend published in 1851. This is the second part of his Trilogy of Christus. The first part is The Divine Tragedy (or Life of Christ), and the third is The New England Tragedies. In The Golden Legend, Longfellow employs a bridge metaphor to represent the role of Jesus and his church. Through the redemptive work of his death and resurrection, Jesus fabricated a proverbial bridge over the “abyss of Death.”
A bridge is an apt metaphor for a cross because it serves as a crossing point. There are three bridges in the Enigma Variations, and likewise, there were three crosses at the crucifixion of Jesus where he was executed between two criminals. Finally, a chapter in The Golden Section with the title “Martin Luther” cites all four stanzas of the hymn Ein feste Burg, the covert Theme to the Enigma Variations. Although divergent in their construction, the bridge passage ciphers encode a set of mutually consistent and complementary set of answers to the core riddles posed by the Enigma Variations. To learn more about the 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.