Monday, May 30, 2011

Elgar’s Enigma Theme, Pi and C

"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 checkerboardcipher, 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 the cryptographic equivalent of 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 insightful paper with me, and I am delighted his discovery was recently presented in Columbia University’s music journal Current Musicology. Like many Elgarians, I wait in eager anticipation for The Elgar Society Journal to publish Santa’s pioneering research.
The discovery that Pi is encoded in the Enigma Theme invites a number of reasonable inferences, the uppermost being to Elgar’s circle of friends. While this conclusion is more than warranted (especially since the Variations are 'Dedicated to my friends pictured within’), there are other less apparent but plausible inferences that compliment and expand on this line of inquiry. For instance, music is based on the circle of fifths

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 some deeper 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.

Nimrod in the Ninth Circle of Dante's Hell

There is a literary undercurrent to Elgar’s approximation of Pi and connection to the circle. This geometric form is referenced extensively in the first book Dante’s Divine Comedy, the Inferno, an allegory describing Dante’s journey through the bowels of the earth and the nine circles of hell. Elgar makes numerous references to Dante’s epic poem in the Enigma Variations. One example is the title Nimrod for Variation IX, a movement that concludes dramatically with a blast from the brass section. In the Inferno Dante portrays Nimrod as a babbling giant imprisoned in the ninth circle of hell who issues a piercing blast from his horn to draw attention to himself. In Dante’s hell Nimrod is cursed with inarticulate speech because he built the Tower of Babel in an attempt to make himself equal with God. As judgment the Lord dispersed the people by causing them to speak different languages, an even known as the Confusion 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.

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:

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.

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. Using this cipher Elgar's encodes the name for Jesus phonetically in measure 1 as GSUSThe pairing of Pie with Jesus in the first measure alludes to the Latin phrase Pie Gesu which means Pious Jesus. That phrase comes from the final couplet of the Dies Irae and is usually included in the Reqiuem Mass.

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 Roman 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: 

The circular Host and Wine Cup

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 that meter:

Enigma Variations in common time
A counterpoint to Ein feste Burg
Caroline Alice Elgar (wife of the composer)
Richard Penrose Arnold
Basil Nevison

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 EnigmaA and E are also the first letters in the names Alice and Edward, the first names for Elgar and his wife. In light of the number of coded references to the Divine Comedy, it is noteworthy Dante's name appears in the musical term Andante. 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.

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 whose head is the Pope. The central section of St. Peter’s Square in the Vatican is an elliptical semicircle, a feature that symbolizes the outstretched arms of the Church and closely resembles the symbol for common time.  Remarkably, common time is conducted in a manner that mirrors the Catholic practice of making the sign of the cross by directing the baton to the four corners of an inverted cross. According to Catholic historians, Peter was crucified upside-down.

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 and Prosperous Voyage (Meeresstille und glückliche Fahrt). In Variation XIII Elgar sonically portrays the sea by quoting a fragment from Mendelssohn’s concert overture Calm Sea and Prosperous Voyage. This early work by Mendelssohn was inspired by his friendship with Goethe and an admiration for his lyrical poetry. Three of these fragments are presented in the major modes A flat and E flat, and the fourth in minor mode of F. In an earlier post I describe Elgar’s many allusions to Christ in Variation XIII such as the Roman Numerals and their alphabetical equivalents (J = X, C = III). There is also a musical cipher within the three keys of the Mendelssohn fragments that translates in the German as Frei aber einsam (free but lonely).

Stradivari in his workshop

Elgar closely identified with the violin. Returning to the subject of Pi and its connection with the geometric circle, it is remarkable the design and construction of the violin involves the elaborate 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 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.

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 of 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. Four years after c was formally established as the symbol for the speed of light, Elgar composed the Enigma Variations in 1898-99. Elgar’s hobbies included scientific pursuits such as photography and chemistry, so he was surely aware of the letter c’s mathematical connection to light. He composed his first oratorio in 1896 with the original Latin title Lux Christi (Op. 29), but his publisher insisted on giving it the English title The Light of Life. This alternate title is based on the words of Jesus from John 8:12, “I am the light of the world. Whoever follows me will never walk in darkness, but will have the light of life.” Like sound, light waves propagate in circular patterns. Perhaps this best explains why Elgar identified the earliest sketch of Variation XIII with a solitary capital L, the first letter in the words Lamb, Lion, Life, Light, Lord, Lux and Land.
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.

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.  Elgar hinted at this combination by his dedication of the Variations to his friends 'pictured within.' For many a picture is worth a thousand words. For Elgar, one very special photograph of his crucified Lord was worthy of a ravishing constellation of musical notes popularly known today as the Enigma Variations. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

The Chi Rho with the Alpha and Omega

1 comment:

Robert Padgett said...

There is another feature of the Enigma Variations that lends support to Richard Santa's discovery. There are 360 degrees in a circle, and the opus number of the Enigma Variations is 36.