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| Richard Penrose Arnold |
"The riddles of God are more satisfying than the solutions of man."
Variation V from Elgar's 'Enigma' Variations is dedicated to Richard Penrose Arnold (1856 - 1908), the son of poet Matthew Arnold. His friendship with Elgar was driven chiefly by their mutual interest in golf. Ein feste Burg plays 'through and over' Variation V as shown in Figure 10.1. The missing Principal Theme plays in the upper staff while the variation appears in the lower two staves in the form of a piano reduction. The notes of the Principal theme are based on Bach’s rendering of Ein feste Burg from the final chorale of cantata BWV80. A sound file of Figure 10.1 is available here.
Figure 10.2 shows how Ein feste Burg was carefully mapped over Variation V based on a combination of melodic interval mirroring and the contrapuntal devices of contrary and similar motion. Melodic interval mirroring is when note intervals from Ein feste Burg are reflected in the variation over similar or identical distances between notes. Similar motion occurs when voices from Ein feste Burg and the variation move in the same direction, but not necessarily by the same intervals. Contrary motion takes place when Ein feste Burg moves in the opposite direction than the variation, again not necessarily by the same interval. In some cases, the upper voice of the variation moves parallel with Ein feste Burg while the base line moves in a contrary manner. An effective counterpoint typically employs a fairly balanced combination of contrary and parallel motion, something very apparent with this mapping.
Table 10.1 summarizes 68 melodic conjunctions between Ein feste Burg and Variation V. A melodic conjunction is any shared note between the two melody lines. Share melody notes are dispersed over 20 of 24 measures of Variation V. Ein feste Burg was found to be dormant in 2 out of 24 measures (172 and 173). Ein feste Burg plays in 22 out of 24 measures, or 91.7 % of the time. In measures where the missing Principal Theme is deemed active, shared melody notes are present in 20 of those 22 measures, or almost 91% of all active measures. A total of 68 melodic conjunctions is truly remarkable.
Table 10.2 breaks down melodic conjunctions between Ein feste Burg and Variation V by note type. There are 8 shared melody notes with frequencies range from 1 to 21.
Table 10.3 gives a complete breakdown of all shared notes between Ein feste Burg and a piano reduction of Variation V. There are 166 shared notes spread out over 28 measures. Melodic conjunctions are indicated in bold enclosed in a double box. All other other note matches not shared between both melody lines are shown in bold within a single box. Note matches not occurring between both melody lines are also known as chordal conjunctions.
Table 10.4 condenses data from Table 10.3 according to note type and frequency with a total of 10 types of shared notes with frequencies ranging from 1 to 66. Of these shared notes, 9 are also shared by both melodies lines of Ein feste Burg and R.P.A. (i.e., A-flat, A, B-flat, B, C, D, E, F, and G).
Conclusion
Based on the data in Figures 10.1-10.2 and Tables 10.1-10.4, the preponderance of the evidence proves Variation V is a clear and convincing counterpoint to Ein feste Burg.
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