"Never, never rest contented with any circle of ideas, but always be certain that a wider one is still possible."
"The next best thing to being wise oneself is to live in a circle of those who are."
Edward Elgar’s use of common time in such an uncommon work as the Enigma Variations is rich with symbolism and hidden meaning. Also known as imperfect time, common time is represented in the time signature either by two fours (4/4) or a broken circle (c). The symbol for common time resembles a capital C, the first letter in the words checkerboard, cipher, Christ and circle. Dick Santa’s intriguing research concerning Elgar’s cryptographic reference to Pi in the opening measure of the Enigma Theme is undoubtedly linked to the semicircle as a symbol for common time. 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). Notice Elgar used the first four notes of the G minor scale to approximate Pi with four numbers, thereby furnishing a subtle link to the Enigma Theme’s meter (4/4). The palindromic rhythmic pattern in the first two measures (two eighth notes, two quarter notes, two quarter notes and two eighth notes) is cycled three times over the first six measures, generating a sense of circularity.
Confirmation of Santa’s discovery may be found in the finger pattern employed on the violin when playing the first four notes of the Enigma Theme in the third position on the D string: 3-1-4-2. This conclusion is bolstered by the fact that the opening measures of the theme are given to the first violins. In violin music the D string is represented by the Roman numeral III because it is the third string. Consequently, the third position on the third string forms a clever numerological reference to Edward Elgar’s initials (EE = 33). Elgar was an accomplished violinist as well as cryptographer, so this inference is entirely plausible. In a covert manner Elgar initialed his greatest cryptographic work. For those who doubt this interpretation, consider the following: The intervals between B-flat/G and C/A are both minor thirds, so there is yet a second numerological equivalent to Elgar’s initials ensconced within the first measure of the Enigma Theme. There is also a third example when one considers that the third note of the Enigma Theme (C) occurs on the third beat of the first measure. The number three is important because it is cryptographically equivalent to the third letter in the alphabet (C), the symbol for common time (c). In the case of the Enigma Theme, the third note is C. Santa was kind enough to share an early draft of his paper with me, and I am delighted his discovery was recently presented in Columbia University
The discovery that Pi is encoded within the Enigma Theme invites a number of inferences, the uppermost being to Elgar’s circle of friends. While this conclusion is more than warranted (especially since the Variations are dedicated to Elgar’s ‘friends pictured within’), there are other less apparent but plausible inferences that compliment and expand this line of inquiry. For instance, music is based on the circle of fifths.
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| The Circle of Fifths |
In the circle of fifths, the major keys B-flat and G are arranged clockwise four steps apart. The same pattern holds true for the major keys C and A. Do these four step sequences of notes denoting Pi allude to the stacked numerals (4/4) found in the Enigma Theme’s time signature? Or is there something deeper some cryptographic significance to these repeated fours? The plagal cadence appears twice in the Enigma Theme (measures 6-7 and 16-17), representing another repetition of the number four as part of the Roman numeral harmonic formula (iv-I). Why so many number fours? The name for Elgar's God is a Tetragrammaton, a word consisting of four Hebrew letters (יהוה). Each of the first six measures of the Enigma Theme consists of four melody notes. Do the opening intervals of the Enigma Theme hint at the existence of a cipher? The inversion of a third is a sixth, so the two thirds formed in the first measure of the Enigma Theme may be viewed alternatively as a reference to two sixths. Is this possibly a subtle clue about the presence of a 6 by 6 checkerboard cipher?
There is a potent literary undercurrent to Elgar’s approximation of Pi and its association with the circle. This geometric form is referenced extensively in the first book Dante’s Divine Comedy – the Inferno – an allegory describing Dante’s trek through the bowels of the earth and the nine circles of hell.
Elgar makes multiple references to Dante’s epic poem in the Enigma Variations. One example is the title Nimrod for Variation IX, a movement that concludes with a dramatic blast from the brass section. In the Inferno Dante portrays Nimrod as a babbling giant imprisoned in the ninth circle of hell who blows a piercing blast from his horn to draw attention to himself.
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| Nimrod in the Ninth Circle of Dante's Hell |
In Dante’s hell Nimrod is cursed with confused speech because he built the Tower of BabelConfusion of Tongues. In imitation of that famous biblical narrative, Elgar follows Nimrod with Variation X, a movement that pokes fun at Dora Penny’s stutter – a speech impediment.
As a geometric figure the circle contains chords, music too contains chords (also known triads). A simple musical triad consists of three notes spaced by one major and one minor third with the top note forming a fifth with the first, and the second and fourth notes omitted.
Similar to his description of Hell as a series of circular rings, Dante describes Paradise as a circular snow-white rose. A stunning print by Gustave Doré accompanying Longfellow's famous translation of Dante's magnum opus depicts this astonishing sight:
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| The White Rose of Paradise (Paradiso XXXI) |
As a geometric figure the circle contains chords, music too contains chords (also known triads). A simple musical triad consists of three notes spaced by one major and one minor third with the top note forming a fifth with the first, and the second and fourth notes omitted.
The Greeks are famous for their development of math and science. Hippocarus is known as the father of trigonometry in part for his creation of table of chord function values. He was a contemporary of Polybius, a prominent Greek historian whose major contribution to cryptography is the checkerboard cipher.
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| Polybius Cipher |
Elgar uses an ingenious musical checkerboard cipher in the opening measures of the Enigma Theme to encrypt the title of the unstated Principal Theme. Similar to a chord from a circle that has two endpoints, a Polybius cipher requires two variables to encipher a single plain text letter in a grid of cells resembling a checkerboard. In this instance, Elgar brilliantly employs the melody and bass notes of the first six measures of the Enigma Theme to create this unique musical checkerboard cipher.
Elgar’s cryptographic reference to Pi by means of a music cipher alludes to the circle as a symbol for the Enigma Theme. After contemplating Elgar’s devout Roma Catholic faith at the time he composed the Enigma Variations, careful consideration should be granted to the religious significance of this geometric form. In measures 7 through 10 Elgar uses a sequential modulation known as rosalia to circle back from G major back to G minor. The term rosalia suggests the rosary, a circular necklace of prayer beads used by Roman Catholics in their devotions. The circle is widely recognized as a symbol of eternity and the divine, and for this reason is found frequently in Christian art, symbols and rituals. Some examples are cited below:
- Chi Rho
- Crown of Thorns
- Borromean rings
- Celtic Cross
- Sacramental bread or host in the Catholic Eurcharist
- The wine cup use to celebrate the Eurcharist
- Rose Cross
- Luther Rose
- Shield of the Trinity
- Trefoil
- Vesica Piscis
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| The circular Host and Wine Cup |
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| Jesus at the Creation of the world |
Speaking of circles, the seventeenth measure of the Enigma Theme is the only one comprised entirely of whole notes. Out of all the possible range of note values, the one that most resembles a circle is the whole note. It highly appropriate the final measure of the Enigma Theme concludes with this note because the circle is a symbol of completeness.
Returning to the subject of common time, four of the fifteen movements of the Variations are set in this meter:
Enigma Variations in common time
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Movement
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Variation
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Title
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Dedicatee
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1
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nulla
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Enigma
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A counterpoint to Ein feste Burg
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2
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I
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C.A.E.
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Caroline Alice Elgar (wife of the composer)
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6
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V
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R.P.A.
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Richard Penrose Arnold
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13
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XII
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B.G.N.
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Basil Nevison
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I suspect it is more than just a coincidence four of the fifteen Variations are set in 4/4 time. Common time may also be represented by a broken circle (c), a symbol that resembles the capital letter for Omega. In light of Santa’s discovery of the Pi reference in the first measure of the Enigma theme, it is remarkable the capital O in Omega resembles a circle. Returning to the title Enigma, it is noteworthy the capital E looks like the lower case of Omega. The sixth and last letter in the word Enigma is a, or the lower case of Alpha. From a Christian perspective one may interpret the E and a from the word Enigma as an allusion to the Alpha and Omega since these letters occur in the first and last positions of the title (albeit in reverse order). As for the reverse order with the Alpha last and the Omega first, it says in Matthew 20:16, “So the last shall be first, and the first shall be last.” The tempo for the Enigma Theme is indicated by the Italian word Andante with the e and a in the opposite positions as the title Enigma. A and E are also the first letters in the names Alice and Edward, the first names for Elgar and his wife. One of the many titles for Jesus is the Alpha and the Omega, the beginning and the end, the first and the last. It is exquisitely appropriate that in the first measure of the Enigma Theme the name of Jesus is phonetically encoded along with the Morse code pattern for “I M”, a phonetic spelling for yet another title for Jesus, “I AM.” Elgar cryptically referred to this musical cipher as a ‘dark saying’, a description that meshes with the crucifixion of Jesus when darkness covered the land for three hours.
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| Conducting common time |
The letter C is the phonetic equivalent of the word see. The word see contains Elgar’s initials (E.E.), something also found in the word common with two capital cursive E’s turned downward in the form of two m’s. As a practicing Roman Catholic, Elgar was surely aware the word see is closely associated with the Roman Catholic Church. The Holy See is the central government of the Catholic Church in Rome Vatican
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| The Crucifixion of Petter |
The Enigma Theme's melodic line is performed exclusively by two instruments, the violin and clarinet. The first letters of these two instruments are V and C. A common acronym for the Pope is VC, an acronym for Vicar of Christ. The Apostle Peter is considered by Roman Catholics to be the first Pope.
The letter C is the phonetic equivalent of the word sea, a subject poetically described by Goethe's Calm Sea
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| Stradivari in his workshop |
Elgar closely identified himself with the violin as I described in this earlier post. Returning to the subject of Pi and its connection with the circle, it is significant that the design and construction of the violin involves the extensive use of circles.
The sound holes of the violin contain four broken circles. The scroll has eight circular holes in it for the pegs. The tail piece has four broken circles to secure the ends of the strings. The scroll also has circular features along with the upper, middle and lower bouts.
Some of world’s most legendary violins were created in the 1700’s by the great Luthiers like Antonio Stradivari, Guarneri del Gesù, Nicolo Gagliano, and Carlo Bergonzi. Stradivari’s Golden Era spanned from 1700 to 1720 with the construction of some of his greatest instruments like the ‘Messiah’ in 1716 and the ‘Red’ Mendelssohn in 1720.
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| Elizabeth Pitcairn |
Guarneri del Gesù made the ‘Il Cannone’ in 1743 a name given by its most famous owner, Paganini. Guarneri’s name is appended with Del Gesù (of Jesus) because he placed the nomina sacra and Roman cross on his instrument labels. Some of his other famous instruments are the Vieuxtemps Guarneri (1741) the Lord Wilton Guarneri (1742). Edward Elgar performed on a Gagliano. Consequently, it is entirely reasonable to draw a numerological association of the number seventeen with the violin. The Enigma Theme is seventeen measures in length, and the melody is almost entirely confined to the violins with the exception of measures 7 through 8 when the clarinet carries the melody. The clarinet later performs three fragments from Mendelssohn’s Calm Sea and Prosperous Voyage in Variation XIII. The first letter in clarinet is c, the third letter in the alphabet.
C is the symbol for the speed of light, a mathematical constant formalized in 1894 by the German physicist Paul Drude, an extraordinarius professor at the University of Leipzig
It was previously observed that Elgar’s Romanza Cipher in Variation XIII makes reference to the Shroud of Turin. The amateur photographer Secondo Pia took the first official photograph of the Turin Shroud in May 1898. When developing the photographic plate he made a startling discovery: The shroud image only becomes clearly visible when viewed as a photographic negative. Elgar began composing the Enigma Variations five months after Pia’s famous photograph was taken. Did this stunning photograph plant the seed in Elgar's fertile imagination to create a contrapuntal 'negative' of a well-known melody, one that celebrates the famous figure on the Turin Shroud? In the months leading up to Elgar’s Enigma epiphany, Pia’s photograph was popularized in the secular and Catholic press, and distributed widely among the Catholic faithful who wished to gaze and meditate on the Holy Face. The Shroud of Turin is viewed by many as the burial cloth of Jesus that captures the moment of his resurrection in the form a photographic negative millennia before the technology ever existed. To this day science has failed to provide a convincing explanation for the photographic negative on the shroud.
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| Shroud of Turin (Left) and its photographic negative (Right) |
I close with this intriguing insight: The letters Pi and C form the first three letters in the word picture. For many a picture is worth a thousand words, but for Edward Elgar, one very special photograph of his crucified Lord was worth a veritable constellation of musical notes we know today as the ‘Enigma’ Variations.
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| The Chi Rho with the Alpha and Omega |
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