Variation III (R. B. T.) with "Ein feste Burg"

A fool’s brain digests philosophy into folly, science into superstition, and art into pedantry. Hence University education.

George Bernard Shaw

Variation III of Edward Elgar’s Enigma Variations is dedicated to Richard Baxter Townsend (1846–1923), an Oxford-educated author and adventurer best known for his colorful memoirs of life in the American West. Townsend was the brother-in-law of William Meath Baker, the friend portrayed in Variation IV. Alice Elgar befriended the Baker family before her marriage, and Elgar himself became close friends with them in the years that followed. The warmth of that friendship is reflected in the fact that Elgar dedicated three of the fourteen variations to members of the Baker family circle: Variation III (R.B.T.), Variation IV (W.M.B.), and Variation X (Dorabella) — the last being Dora Penny, the niece of William Meath Baker.

The following contrapuntal mapping documents how Ein feste Burg plays “through and over” Variation III, consistent with Elgar’s 1899 program note. The hymn’s canonical phrase structure (ABCDEFB) is presented in an expanded sequence (ABCDEFAB), with Phrase A inserted before the concluding Phrase B — a subtle elaboration rather than a disruption of the chorale’s architecture. With the repeat, the phrase structure expands to ABCDEFAB CDEFAB for fourteen phrases in all. The ability to map both the notes and phrases of Ein feste Burg in their correct sequential order across the full extent of the variation constitutes compelling evidence of a deliberate and systematic counterpoint.

The phrases of Ein feste Burg mapped over Variation III are sourced from three contrasting versions of the hymn, forming a tribrid melody, a pattern likewise observed in the contrapuntal mappings of the Enigma Theme, Variation I, and Variation II. 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 both Bach's and Mendelssohn's distinct adaptation from the Finale of the Reformation Symphony, whose melodic contour aligns with Bach’s version. 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 next exhibit illustrates how Ein feste Burg was contrapuntally mapped above Variation III through a carefully aligned series of melodic and harmonic conjunctions. In the score, melodic conjunctions (exact matches between a melody note of the hymn and a melody note in Variation III) are marked with diamond-shaped note heads, while harmonic conjunctions (matches between a hymn melody note and any non-melodic note in the variation) appear with triangle-shaped note heads. Both types of conjunction require the notes to sound simultaneously to qualify as a match. As in Variation II, the dormant measures at the opening and close of the mapping serve to obscure the counterpoint's entry and exit points — a characteristic Elgarian strategy for concealing the hidden theme.

The mapping draws on the principles of melodic interval mirroring and counterpoint. Melodic interval mirroring occurs when note intervals from Ein feste Burg are reflected in the variation over comparable or identical distances between notes in the melody and harmony lines. In counterpoint, similar motion occurs when both voices move in the same direction, not necessarily by the same degree. Contrary motion occurs when the hymn moves in the opposite direction to the variation, again not necessarily by the same interval. For the purposes of this analysis, similar motion encompasses parallel motion, and contrary motion encompasses oblique motion. In some instances, the upper voice of the variation moves in parallel with Ein feste Burg while the bass line moves in a contrary manner. Similar motion is indicated by SM and contrary motion by CM. An effective counterpoint typically employs a fairly balanced mix of these two types of motion, and this mapping clearly reflects that balance.

The following table summarizes 30 melodic conjunctions between Ein feste Burg and Variation III. Shared melody notes are distributed across 21 of 36 measures, with note frequencies ranging from 2 (A) to 9 (F♯). The hymn is absent in bars 97, 105, 121–123, and 131a–131b for a total of seven measures. Melodic conjunctions are present in 21 of 36 measures, yielding a coverage rate of 58%. Excluding dormant measures, coverage increases to 21 of 29 bars, or approximately 72%.

The next table summarizes 41 harmonic conjunctions between Ein feste Burg and Variation III. Shared melody notes from the hymn with the short score of Variation III are distributed across 19 of 36 measures, with note frequencies ranging from 1 (D♯) to 10 (D). Harmonic conjunctions are present in 19 of 36 measures, yielding a coverage rate of 53%. Excluding dormant measures, coverage increases to 19 of 29 bars, or approximately 65%.

The combined melodic and harmonic conjunctions total 71, spanning 27 of the variation's 36 measures — a coverage rate of 75%. Excluding the dormant measures raises that figure to 93%, meaning Ein feste Burg maintains a contrapuntal presence across nearly all of the measures in which it is active. Thirteen measures contain both melodic and harmonic conjunctions simultaneously, representing nearly 45% of the active measures and reflecting the density and consistency of the counterpoint.

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: it plays “through and over” the set as a counterpoint.

Conclusion

The contrapuntal evidence presented above demonstrates that Ein feste Burg forms a compelling contrapuntal fit with Variation III (R.B.T.) in a manner consistent with Elgar’s 1899 program note. The mapping yields 30 melodic conjunctions and 41 harmonic conjunctions — a combined total of 71 — spanning 27 of 36 measures. Excluding the strategically dormant measures, Ein feste Burg maintains a contrapuntal presence across 93% of the remaining bars, a density of coverage that strongly supports deliberate compositional intent rather than coincidence.

Equally significant is the structural integrity of the mapping. The phrase structure of Ein feste Burg (ABCDEFB) unfolds across Variation III in an expanded sequence (ABCDEFAB CDEFAB), with Phrase A inserted before the concluding Phrase B. 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. This represents a subtle elaboration rather than a disruption of the chorale’s architecture, and the correct sequential order is preserved throughout.

The dormant measures at the opening and close of the mapping serve a concealing function, marking the boundaries of the counterpoint without disclosing them — the same strategic deployment of inactive bars observed in Variation II. These null measures are not weaknesses in the mapping but intentional features, the seams of a carefully constructed musical disguise. Thirteen measures containing both melodic and harmonic conjunctions simultaneously — nearly 45% of the active measures — further underscore the depth and consistency of the contrapuntal relationship.

The melodic and harmonic conjunctions, integrity of the phrase structure, and strategic deployment of dormant measures form a coherent and mutually reinforcing body of evidence. Variation III is a clear and convincing counterpoint to Ein feste Burg. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed. Please support my original research by becoming a sponsor on Patreon.

Soli Yah Gloria