The riddles of God are more satisfying than the solutions of man.
Variation V from Edward Elgar’s Enigma Variations is dedicated to Richard Penrose Arnold (1856–1908), the son of poet and critic Matthew Arnold. Arnold’s friendship with Elgar was driven chiefly by their mutual interest in golf. It is amusing that Arnold’s initials “RPA” are an anagram of “PAR,” the golfer's standard of excellence. In 1874, Arnold matriculated at Balliol College, Oxford, where he joined a vibrant circle of musical friends that included pianist Hugh David Steuart-Powell (Variation II, from Exeter College) and cellist Basil George Nevinson (Variation XII, also from Exeter College). Hubert Parry, another Exeter College alumnus, was deeply involved with the Oxford University Musical Club (founded 1872), in which Steuart-Powell and Nevinson were prominent and Arnold actively participated. This Oxford musical network is richly reflected in the Enigma Variations: Variation II portrays the pianist Steuart-Powell, Variation V the pianist-composer Arnold, and Variation XII the cellist Nevinson.
Although Parry is not overtly depicted, Elgar pays him a subtle coded tribute. The proximate title initials of Variation V (R. P. A.) and Variation VI (Ysobel) form the acrostic anagram “PARY” — a phonetic rendering of Parry. This hidden reference gains added resonance from the expressive bridge passage (bars 185–188) that links the two movements. It is especially fitting because Parry played a key behind-the-scenes role in persuading Hans Richter to conduct the premiere of the Enigma Variations in June 1899.
In 1899 — the same year Elgar published and premiered the Enigma Variations — Arnold published An Elegy for solo viola (or cello) and piano through Breitkopf & Härtel in London. A preliminary comparison of the two works reveals numerous striking parallels. Both open in C minor with a three-flat key signature, and both are set in common time. The tempo of Section B of An Elegy is marked “Andante” at a quarter note equal to 63 beats per minute, while Variation V is marked “Moderato” at a dotted quarter equal to 63 beats per minute — the same metronome value applied to different note values. Both works exploit rhythmic tension between melodic eighth notes and triplet accompaniment figures, and both feature octave leaps, register exchanges between melody and countermelody, and a sustained C pedal tone at the close. Arnold was not a violist, and it is likely that Elgar — himself a competent violist who taught the instrument — supplied the bowings and fingerings for An Elegy’s string part and helped guide Arnold through the publication process with Breitkopf & Härtel, a publisher Elgar had previously worked with. The bridge connecting Variation V (R. P. A.) with Variation VI (Ysobel), a movement featuring prominent viola solos, furnishes an instrumental allusion to Arnold’s An Elegy.
Shown below is a detailed contrapuntal mapping of the Lutheran chorale Ein feste Burg “through and over” Variation V. The notes of the hidden theme are based principally on J. S. Bach’s rendering from the final chorale of Cantata BWV 80. An audiovisual file of this mapping supports the efficacy of this contrapuntal solution.
Ein feste Burg was carefully mapped over Variation V based on a sequential series of similar melodic intervals and the principles of counterpoint. Melodic interval mirroring occurs when note intervals from the hymn are reflected in the variation over comparable or identical distances between notes. These notes do not necessarily appear in the melody line of the variation. The contrapuntal devices of augmentation, diminution, contrary motion, and parallel motion were also considered in this analysis. Contrary motion takes place when the hymn moves in the opposite direction from the variation, not necessarily by the same interval. Parallel motion is when both voices move in the same direction by the same degree. Contrary motion is indicated by CM, and parallel motion by PM. In some cases the upper voice of the variation moves in parallel with Ein feste Burg while the bass line moves in a contrary manner. An effective counterpoint typically employs a fairly balanced mix of contrary and parallel motion, something clearly evident in this mapping.
The standard phrase structure of Ein feste Burg with repeats is ABABCDEFB for a total of nine phrases. As mapped over Variation V, Elgar expands the hymn’s phrase structure to ABABABCDEFB with an extra repetition of phrases AB for a total of eleven phrases. At the conclusion of the extended Finale completed in July 1899, Elgar inscribed a quotation from stanza XIV of Henry Wadsworth Longfellow’s poem Elegiac Verse: “Great is the art of beginning, but greater the art is of ending.” This sentiment finds a striking resonance in the contrapuntal mapping of Ein feste Burg over Variation V. Of the eleven phrase statements, the opening Phrase A and the closing Phrase B together account for seven, with Phrase A appearing three times and Phrase B appearing four times. Phrase B provides both the penultimate and ultimate statements, framing the interior phrases C through F and delivering the final word. The marked emphasis on the beginning phrase (A) and the ending phrase (B) throughout this movement reflects precisely the artistic priority Elgar identified in Longfellow’s verse: that the art of ending is the greater achievement.
The phrases of Ein feste Burg mapped over Variation V come from three contrasting versions of the hymn to form a tribrid melody. This pattern is likewise observed in the contrapuntal mappings of the chorale with the Enigma Theme, Variations I, II, III, and IV. Phrases A, B, and F reflect Bach’s rendering in the final chorale (“Das Wort sie sollen lassen stahn”) from his Cantata BWV 80. Phrase C is based on Bach’s version and Mendelssohn’s distinct adaptation from the Finale of the Reformation Symphony, whose melodic contour aligns with Bach’s. Phrase D follows the pattern of Luther’s original version, which Bach faithfully preserved in his rendering, and which Mendelssohn likewise retained. Phrase E reflects Mendelssohn’s version exclusively. Ecclesiastes 4:12 declares that a threefold cord is not easily broken — and so it is with this tribrid theme, woven from the distinct but harmonious contributions of Luther, Bach, and Mendelssohn. Consult the following exhibit to easily compare phrases from all three versions of Ein feste Burg.
The following annotated short score documents an extensive series of melodic and harmonic note conjunctions. A melodic conjunction is represented by a diamond-shaped note head, and a harmonic conjunction by a triangle-shaped note head. A melodic conjunction is defined as any matching melody note between Ein feste Burg and the movement's melody line. A harmonic conjunction is defined as a match between a melody note from the hymn and any non-melodic note from the movement. Both melodic and harmonic conjunctions must sound together to qualify as a match.
The following table identifies 72 melodic conjunctions between Ein feste Burg and Variation V dispersed across 18 active bars, covering 75% of the movement’s 24 measures. The hymn is dormant in bars 172 and 173, a brief interlude that modulates to the dominant G major before cadencing in the tonic C minor at Cue 17. Excluding these dormant bars, the hymn forms a credible counterpoint over 83% of the remaining 22 bars, with shared melody notes appearing with remarkable consistency. The 72 melodic conjunctions encompass eight note types with frequencies ranging between 1 and 24. The dominant G leads with 24 matches (33%), followed by the tonic C with 22 (31%), A♭ and A each with 7 (10% each), B♭ with 5 (7%), F with 4 (6%), E with 2 (3%), and D with 1 (1%). Together the two most frequent notes — G and C — account for nearly two thirds (64%) of all melodic conjunctions, reflecting the tonic and dominant poles of C minor.
The next table breaks down 103 harmonic conjunctions between Ein feste Burg and Variation V across 20 active bars, representing 83% of the movement’s 24 measures. Backing out two dormant measures increases that coverage to nearly 91%. The 103 harmonic conjunctions encompass nine note types with frequencies ranging from 1 and 43. The tonic C leads decisively with 43 matches (42%), followed by dominant G with 30 (29%), A♭ with 12 (12%), B♭ with 6 (6%), B with 5 (5%), A with 2 (2%), D with 2 (2%), F with 2 (2%), and E♭ with 1 (1%). Together the two most frequent notes — C and G — account for more than two thirds (70%) of all harmonic conjunctions, once again reflecting the tonic and dominant poles of C minor. The dominance of C and G across both melodic and harmonic conjunctions is a striking feature of this mapping, underscoring the deep harmonic coherence between Ein feste Burg and Variation V.
There is a combined total of 175 note conjunctions (72 melodic + 103 harmonic) across the 22 active bars of Variation V, yielding a 92% coverage rate. When melodic and harmonic conjunctions are considered together, this rises to 100% of the 22 active bars — with the only exceptions being the two dormant measures (172–173) where Ein feste Burg rests entirely. Notably, 16 bars feature simultaneous melodic and harmonic conjunctions, showing that the hymn engages the full harmonic texture of the variation rather than merely skimming its surface melody.
This comprehensive, note-by-note penetration — from the opening bars to the final cadence — embodies the defining hallmark of a genuine contrapuntal mapping. Elgar’s own description of the hidden theme proceeding “through and over” the entire set of Variations is thus borne out with striking quantitative precision. Far from merely visiting Variation V in passing, Ein feste Burg permeates it at every structural level: melodically with the movement’s principal tune, harmonically with its inner voices, and formally with the eleven-phrase arc (ABABABCDEFB) from first note to last. Such a pervasive and structurally coherent alignment — encompassing 175 sequential note conjunctions across eight melodic and nine harmonic note types — provides compelling, quantifiable evidence that Ein feste Burg forms a clear and convincing counterpoint to Variation V.
The test Elgar set is simple but demanding: the covert principal theme must play “through and over” the entire set of Variations as a counterpoint. More than a century of purported solutions have failed to meet that requirement, for none has ever been successfully mapped contrapuntally above any complete movement. Ein feste Burg has met that test across every movement without exception, replicating sequential note content phrase by phrase while preserving the hymn’s phrase architecture from the Enigma Theme to the Finale. Ein feste Burg stands in a class all its own because it accomplishes what no other attempted solution can.
Conclusion
The contrapuntal evidence presented above demonstrates that Ein feste Burg forms a compelling counterpoint to Variation V (R. P. A.) in a manner consistent with Elgar’s 1899 program note. The contrapuntal mapping yields 72 melodic conjunctions and 103 harmonic conjunctions for a combined total of 175 spanning 22 of the movement’s 24 measures for a coverage rate of 92%. When melodic and harmonic conjunctions are considered together, every one of the 22 active bars contains at least one conjunction of either type, rising to 100% coverage of all active measures. Sixteen bars feature both melodic and harmonic conjunctions, representing 67% of the active measures and demonstrating that Ein feste Burg engages the full harmonic texture of the variation rather than merely skimming its surface.
Equally significant is the structural integrity of the mapping. The phrase structure of Ein feste Burg unfolds across Variation V in an expanded sequence of ABABABCDEFB — eleven phrases in all, with Elgar inserting an extra repetition of the opening AB pair before proceeding through phrases C through F and closing with a final restatement of B. The correct sequential order of the hymn’s phrases is preserved throughout without reordering, compression, or omission. The two dormant measures (172–173) coincide with a passage that modulates to the dominant G major before cadencing in the tonic C minor at Cue 17 — a structurally pivotal boundary at which the hidden theme briefly withdraws before returning, consistent with the strategic deployment of dormant measures observed in Variations II, III, and IV. These null measures are not weaknesses in the mapping but intentional features, the seams of a carefully constructed musical disguise. As with each variation, Elgar subtly varies the hymn’s phrase structure from movement to movement, a strategy that serves to confuse and camouflage the hidden counterpoint from casual detection.
The melodic and harmonic conjunctions, the integrity of the expanded phrase structure, and the strategic deployment of dormant measures form a coherent and mutually reinforcing body of evidence affirming that Variation V is a clear and convincing counterpoint to Ein feste Burg. Elgar’s description of the hidden theme playing “through and over” the entire set of Variations is borne out here with striking quantitative precision: 175 sequential note conjunctions across eight melodic and nine harmonic note types, permeating the movement at every structural level from first note to last. To learn more about the secrets underlying the Enigma Variations, read my eBook Elgar's Enigmas Exposed. Please support my original research by becoming a sponsor on Patreon.
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