A numerologist and lover of puzzles, Bach invested his music with structures that underlie basic musical elements. As a man of faith, he imbued his works with praise of God in complex forms that continually surprise devotees who know his works note for note.
No man has a greater reverence for Bach than I. I play three or four preludes and fugues from the Well-tempered Klavier every day.
The numbers four and six turn up in a variety of notable ways in the Enigma Theme from Elgar's Enigma Variations. Its puzzling title—Enigma—has six letters. The dedication inscribed on the score—“Dedicated to my friends pictured within”—has six words. Elgar’s commentary cited in the original 1899 program note includes a cryptic reference to a “dark saying” lurking within the Enigma Theme. Notice that the words “dark saying” are four and six letters respectively. It was on a Friday, the sixth day of the week, that Elgar first performed the Enigma Theme at the piano for his wife. He composed the Enigma Variations between late October 1898 and mid-February 1899, a period of four months.
There are further allusions to the numbers four and six in the Enigma Theme’s melody and bar structure. It is divided into four parts resulting in an ABA’C format. The number of measures in the A and B sections is six and four respectively. The Enigma Theme’s melody note totals per bar and the number of measures in Sections A and B underscore a bond between the numbers four and six. Section A in G minor has exactly four melody notes in each of its six bars. Section B in the parallel major has precisely six mel0dy notes in each of its four measures. With these measure and melody note figures in sections A and B, Elgar repeatedly links together the numbers four and six.
The numbers four and six also reoccur in the orchestration, melody and bassline of the Enigma Theme. The orchestration in Section A is confined to four staves, the string quartet comprised of the first and second violins, violas and cellos. The note letters for the melody and bass lines in Section A are confined to six with the melody omitting the E, and the bass line the F. In bars 1-3 of Section A, the bass line rises stepwise from G to an E-flat to cover the span of a minor sixth before descending by a diminished fourth to B in bar 4. This is followed by another stepwise rise of a diminished fourth back to E-flat in measure 6. The two E-flats in the bassline found in measures 3 and 6 appear to be a coded version of the composer’s dual initials tied to the work’s opus number (36). The orchestration in Section B begins in measure 7 with instrumental parts dispersed over six staves (the string quartet, the B-flat clarinet, and bassoons) before additional lines weave briefly in and out of the score. The bassline in measure 9 descends from G to D producing a perfect melodic fourth. The glyph for nine (9) is an inverted mirror image of the number six (6).
In 1927, Elgar prepared some descriptive notes for a set of pianola rolls of the Enigma Variations later released in 1929. Portions of these notes were published in book form by Novello under the title My Friends Pictured Within. He made the following perplexing remark concerning the Enigma Theme, “The drop of a seventh in the Theme (bars 3 and 4) should be observed.” Why should these particular sequential intervals be observed? In mentioning these conspicuous and unusual melodic sevenths, Elgar draws indirect attention to the conventional melodic intervals just before, between and immediately after them. The first melodic seventh of a G descending to A is preceded by a D rising to G which completes a perfect melodic fourth. After the first descending melodic seventh, the line rises from A to F to form a minor melodic sixth. The second melodic seventh is formed by an F descending to G. This is followed by an A to produce a major melodic second. Elgar’s guidance to scrutinize the Enigma Theme’s melodic sevenths attracts implicit attention to the contiguous intervals. The first two adjacent intervals are a fourth and sixth, and the third is a second. The presence of a fourth and a sixth just before and between the descending sevenths is yet another case of these numbers in close proximity to a feature highlighted by the composer.
These recurring numeric associations demands a more careful search for one of Elgar’s favorite diversions: Cryptograms. Is there some explanation for why he would repeatedly invoke the numbers four and six throughout the Enigma Theme? Another cipher concealed in the first measure answers that probing question. There are seven performance directions in the opening bar that form an acrostic anagram. That particular integer is associated with the descending sevenths in bars 3 and 4. The first letters of those seven performance directions may be reshuffled to spell “EE’s PSALM.” The double E’s are an obvious reference to Edward Elgar’s initials. The term Psalm refers to a book of hymns in the Hebrew Bible.
The significance of the numbers four and six is that together they designate the precise chapter out of 150 Psalms that unveils the title of the hidden melody to the Enigma Variations. Psalm 46 inspired Martin Luther to compose his hymn, Ein feste Burg (A Mighty Fortress). A diverse and compelling array of contrapuntal and cryptographic evidence proves that the Battle Hymn of the Reformation is the hidden Theme to the Enigma Variations. No one would ever guess that Elgar, a practicing Roman Catholic, based his breakout symphonic masterpiece on a hymn composed by a heretic excommunicated by Pope Leo X. And yet that is precisely what Elgar did, first in a “spirit of humour” and then “continued in deep seriousness.”
For those who doubt the encrypted connection between the Psalms and the chapter number 46, consider the performance directions as they appear in the first bar of the Enigma Theme in the Master Score:
As shown in the table below, the total number of characters for the performance directions in the Enigma Theme’s first measure is 46. The link between “Psalm” and the number “46” is firmly established by this stunning convergence in the first bar’s performance directions.
The numbers four and six are closely tied (pun intended) to the Mendelssohn fragments in Variation XIII. Elgar cites those melodic snippets to sonically portray the “deathly stillness” of a calm sea. There are precisely four Mendelssohn fragments. The manner in which they are written produces four sounding notes, but requires six written notes with ties over the bar lines. Again we observe the numbers four and six mingled together by Elgar’s unique treatment of Mendelssohn’s melody.
In the orchestral score, the ostinato accompanying the Mendelssohn quotations performed by a solo clarinet is comprised of alternating sixths played by the violas. Its palindromic rhythm is derived from the Enigma Theme’s six bar melody in Section A with the quarter rests stripped out. This rhythmic fingerprint establishes an organic link between the two movements, implying a more profound connection between them. The accompaniment figure includes a soft metallic timpani roll on C, the fourth degree of that movement’s G major mode. With so many coded references to the numbers four and six, it should come as no surprise that these Mendelssohn fragments harbor multiple ciphers that identify Ein feste Burg as the covert Theme.
Elgar quotes Mendelssohn’s symphonic oeuvre to imply through imitation that this towering figure of the German School quotes the secret melody in one of his own works. The number of fragments (4) and their sounding notes (4) further suggest to seek out the fourth movement of one of Mendelssohn’s symphonic works for the answer. In the fourth and final movement of the Reformation Symphony published posthumously in 1868, Mendelssohn cites Luther’s Ein feste Burg followed by a series of variations. It was composed in 1829-30 to commemorate the tricentennial of the Augsburg Confession, the primary confession of faith of the Lutheran Church. Elgar’s coupling of Mendelssohn’s music with water is richly symbolic because Mendelssohn was baptized a Lutheran on the March 21, 1816, the 131st anniversary of Johann Sebastian Bach’s birth. Elgar’s decision to feature the music of a devoted Lutheran in Variation XIII serves two purposes. First, it hints at the identity of the composer of the covert Theme. Second, it decimates the myth still proffered by legacy scholars such as Julian Rushton that Elgar’s Roman Catholicism would bar him from quoting a famous Protestant work.
Although no coded references to the Psalms have yet been discovered in the Mendelssohn fragments, it is important to recognize that Mendelssohn composed numerous symphonic and choral works inspired by that scriptural collection of hymns. The Finale of his Reformation Symphony is one of the more outstanding examples with its quotation of Ein feste Burg inspired by Psalm 46. He employs Psalm 51 in his sacred oratorio Saint Paul to convey the contrition of the Pharisee Saul of Tarsus following his miraculous conversion on the road to Damascus. Mendelssohn produced large choral cantatas based on Psalm 115 (1830), Psalm 42 (1837), Psalm 95 (1838), Psalm 114 (1839), and Psalm 98 (1843). Mendelssohn composed some of his Psalm settings specifically for English audiences. One example is Psalm 55 (1844). His oratorio Elijah was premiered in 1846 at the Birmingham Festival. In that large-scale work he employs Psalm 6, 7, 10, 16, 25, 55, 86, 88, 91, 93, 104, 108, 121, and 128. His other choral settings include Psalm 66 (1822), Psalm 5 (1839), Psalm 31 (1839), and Psalm 100 (1844).
Drei Psalmen Op. 78 was published after Mendelssohn’s death. These three a cappella choral works are settings of Psalm 2 (1843), Psalm 22 (1844), and Psalm 153 (1844). Drei means the number three in German. This figure presents an uncanny parallel with Elgar’s use of the Mendelssohn fragments in Variation XIII because there are three quotations drawn from the concert overture Meeresstille und glückliche Fahrt. It was previously observed that Elgar’s act of citing Mendelssohn’s music served to suggest the inverse, specifically that Mendelssohn quotes the secret melody in one of his own works. It may be argued that the specific number of Mendelssohn fragments enclosed by quotations in Variation XIII is another clue regarding the source of the covert Theme. The three Mendelssohn quotations herald from a work with a German title, and the German word for three is not coincidentally the first word in the title Drei Psalmen. The number three is directly linked to a work by Mendelssohn associated with the Psalms. There is a distinct impression of Elgar’s sense of wordplay as the phonetic equivalent of drei in English is dry, the opposite of a marine environment. With so many musical renditions of the Psalms attributed to Mendelssohn, it is not a stretch to associate the numbers four and six highlighted in the Mendelssohn fragments with Psalm 46.
Like his muse Mendelssohn, Elgar’s output includes a number of Psalms set to music. Susan Gillingham catalogues these in her book Psalms of the Centuries:
The most significant English composer associated with Romantic Movement who also arranged accompaniments for psalms is Edward Elgar (1857—1934). Drawing much of his inspiration from the Worcestershire countryside, from British culture and from his continental contemporaries, Elgar’s symphonies, oratorios and his nationalistic works gave him huge popular appeal. By the time he had started the major choral work using Newman's The Dream of Gerontius (1900), he had already established himself with his Enigma Variations and Sea Pictures, both performed in 1899. In The Dream of Gerontius, Elgar demonstrated something of his personal Catholic faith and, despite the muted reception and Elgar’s consequent distress at its first performance, it placed him as amongst the best of British performers of his day because of its universal import—the death of everyman. In The Dream, Elgar set to music Newman's Psalms—Psalm 31:5 (‘into thy hands I commend my spirit’), Psalms 147 and 150 as the subtext for 'Praise to the Holiest’, and especially Psalm 90, sung as Gerontius descends to purgatory. Later, Elgar composed other liturgical works from Psalms: in 1907 he arranged two single chants for the Venite (Psalm 95), and two double chants for more nationalistic Psalms 68 and 75. In 1912 he also wrote an accompaniment to Psalm 48 for a service at Westminster Abbey. But, in terms of psalmody, nothing perhaps excels his dramatic use of Psalm 90, with its balance of expression from orchestra and choir and soloists alike.
The phenomena of overlapping decryptions is a remarkable element of Elgar’s cryptographic brilliance. One example is provided by the combined decryptions of the Enigma Pi Cipher and Music Box Cipher. In the first bar of the Enigma Theme, the Pi Cipher encodes a rounded form of the mathematical constant Pi using the scale degrees of the melody (3-1-4-2). In that same measure, a musical Polybius square cipher encodes GSUS, a phonetic rendering of Jesus—the secret friend portrayed in Variation XIII. The combination of these two decryptions produces the phrase “Pi Jesus,” a form of “Pie Jesu” which is Latin for “Pious Jesus.” This phrase is the final couplet of the Dies irae and is traditionally included in popular settings of the Requiem Mass as a motet by such renowned composers as Cherubini and Fauré. Early in his career before he rose to prominence, Elgar composed three motets Op. 2. In his youth, he also carefully studied Cherubini's treatise on counterpoint.
The multiple coded references to the numbers four and six in the Enigma Theme take on added significance with the discovery of the Enigma Psalm Cipher in the first measure. This is another instance of two decryptions that mingle to produce a complementary and more complete answer. One identifies the book, and the other the chapter. These overlapping decryptions are connected together by location and an expanded sense of meaning that are mutually consistent and precise. More important is that jointly they confirm the correct melodic solution as the title of Luther’s hymn originates from the first line of Psalm 46. To learn more about the secrets of Elgar’s Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.