Progress is impossible without change, and those who cannot change their minds cannot change anything.
Edward Elgar dedicated Variation VII to Arthur Troyte Griffith (1864 - 1942), a member of an architectural firm based in Malvern operated by a brother of Basil Nevison. It is likely Elgar first met Arthur in 1897. Figure 16.1 documents how Ein feste Burg plays above Variation VII. This illustration is significant because Elgar claimed the covert Principal Theme must play “through and over” the set of Variations. To satisfy this critical condition, it must be shown precisely how Ein feste Burg fits over each movement.
Figure 16.2 illustrates how Ein feste Burg was carefully mapped over Variation VII based on melodic interval mirroring and the principles of counterpoint. Melodic interval mirroring occurs when note intervals from Ein feste Burg 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 similar and contrary motion were also considered in this analysis. Similar motion is when both voices move in the same direction, but not necessarily by the same degree. Contrary motion takes place when Ein feste Burg moves in the opposite direction than the variation, again not necessarily by the same interval. Similar motion is indicated by SM and contrary motion by CM. For the purposes of this analysis, similar motion includes any instances of parallel motion, and contrary motion any instances of oblique motion. In some cases, the upper voice of the variation moves 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 similar motion, something clearly evident with this mapping.
In Figure 16.2 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 covert principal Theme and any non-melodic note from the movement. Both melodic and harmonic conjunctions must sound together to be considered a match.
Table 16.1 summarizes 78 melodic conjunctions between Ein feste Burg and Variation VII. A melodic conjunction is defined as a shared note between the two melody lines. Share melody notes are dispersed over 42 of 72 measures in Variation VII or just over 58% of the time. Ein feste Burg does not play in 8 out of 72 measures, i.e., measures 210–213, 223–225, and 252. In bars where the covert Theme was deemed active, shared melody notes are present in 42 of those 64 measures or almost 66% of all active measures.
Table 16.2 breaks down melodic conjunctions between Ein feste Burg and Variation VII by note type. There are six shared melody note types (A, A flat, B, C, F, and G) with frequencies ranging from 2 through 35.
Table 16.3 gives a complete breakdown of shared notes between Ein feste Burg and the piano reduction of Variation VII. The number of shared notes is indicated by each measure number. There are 236 shared notes dispersed over 64 measures out of 72 measures. Of those conjunctions, 75 are melodic, and 161 are chordal. Ein feste Burg was deemed active in 64 measures, so 100% of active measures have shared notes. There are 8 shared note types (A, A-flat, B, C, D, E, F, and G) with frequencies ranging from 4 (D and E) to 105 (G).
Table 16.4 summarizes all matching notes between Ein feste Burg and Variation VII, giving totals and percentages for melodic and harmonic conjunctions.
Conclusion
The preponderance of the evidence presented in the above Figures and Tables demonstrates Variation VII is a clear and convincing counterpoint to Ein feste Burg. To learn more about the secrets behind the Enigma Variations, read my free eBook Elgar's Enigmas Exposed. Please support my original research by becoming a sponsor on Patreon.
4 comments:
Your numbers and statistics prove nothing.
When you choose to fudge the modality and actual melodic structure of Luther's tune to force it to "fit" the Troyte variation, you reveal your folly to the fullest.
This is not a musicological discovery here, it is merely a personal delusion amplified by verbiage and diagrams. You want this to be true and so you rig the evidence to make it so. But it is not so -- any reasonable musical ear can tell it is not so.
One would hope that if there is indeed a missing melody in Elgar's piece that if we were to hear if at long last it would add a musical dimension that would transcend the cleverness of the cipher.
But this ham-handed smearing of Luther's melody on top of Elgar's music is so hideous in its final audible result that it is a positive affront to the beauty of both original pieces.
Give this one up! The Enigma remains unsolved!
"Anonymous" rejects my thesis on the grounds the modality and melodic structure of Luther’s hymn does not fit cleanly and neatly over this particular variation. What "Anonymous" fails to appreciate is with any given variation, the melodic structure and modality are by necessity modified from the original. If this were not so, it would not be a variation. In a way, “Anonymous” bolsters my case by observing the obvious, namely that the melodic and modal divergences from the original structure of the hymn. Remember, Elgar was striving mightily to conceal the source melody, not facilitate its discovery.
Anonymous has clearly forgotten the determined and inspiring words of Sir Winston Churchill who said, "Never, never, never, never give up."
Anonymous disagrees with my mapping of "Ein feste Burg" over Variation VII using a bevy of derogatory terms instead of speaking to the evidence. The evidence speaks, or more specifically, sings for itself. The mapping is compelling, particularly to those with a musical ear. Moreover, Elgar made it perfectly clear in the original 1899 program note that “the connexion between the Variations and the Theme is often of the slightest texture.” In other words, the missing melody’s path over each of the variations is not apparent, but rather thin or trivial. Anonymous demands an obvious solution when Elgar made it perfectly clear at the outset that just the opposite would be the case. In this instance, Anonymous has overlooked the obvious.
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