Thursday, April 18, 2013

Martin Gough’s Enigma 'Solution' Refuted

“All praise to Thee, my God, this night, for all the blessings of the light!

Keep me, O keep me, King of kings, beneath Thine own almighty wings!”

First stanza from  All Praise to Thee, My God

Martin Bird, the current editor of The Elgar Society Journal, is to be commended for raising Rushton’s moratorium by publishing a new solution to Elgar’s Enigma Variations. In the April 2013 issue, researcher Martin Gough theorizes the Enigma Theme is a puzzle canon that may be played with another canon by Thomas Tallis. Strangely Gough only introduces his candidate theme seven pages into the article: ‘Eighth Tune’ from Archbishop Parker’s Psalter of 1567. Never heard of it? Tradition has shortened that diffuse title to the Tallis Canon. Contrary to Gough's insistence, the Tallis Canon is not a puzzle canon, but rather a restricted canon. An excellent example of a puzzle canon is Bach's Crucigeros Canon. Below the canon Bach wrote the riddle, "Symbolum: Christus Coronabit Crucigeros." The translation of is, "Symbol: Christ will crown those who carry His cross." The solution is a double canon in contrary motion over a quotation from the Goldberg soggetto. Another more humble example of an enigma canon is shown below. Like the Bach puzzle canon, my riddle canon is only three measures long with a riddle beneath the title hinting at a solution. With the Tallis Canon there is no riddle beneath the title, no puzzle to solve, only a canon as its title makes quite clear. With a central tenet resting precariously on a false premise, the key to Gough's imaginative theory crumbles. Despite its enduring popularity in religious settings, the Tallis Canon has yet to deserve an article on Wikipedia. That omission does not bode well for its alleged popularity, a deficit that will probably not deter Wikipedia's Nomenklatura from soon adding Gough's theory to its growing list of flawed and incomplete enigma solutions.

Some Accurate Insights
Gough makes a number of stunningly accurate observations about the nature of the correct melodic solution to the Enigma Variations. The first is his conclusion that Elgar’s planning of the Variations ventured far beyond that of a brief improvisational foray on a relaxing Friday evening. He arrives at this assessment because canons “do not happen by chance.” Much could be said about a set of variations, for those too could hardly be described as the product of happenstance or luck. This opinion is one I advanced years ago, and it is decidedly at odds with the conventional wisdom that the Variations were the result of little or no advanced planning. Of course such a view is utterly inconsistent with Elgar’s known compositional style of accumulating ideas over years and even decades before finally fashioning them into a finished work. Gough’s second insight is to thoughtfully distinguish between the Enigma and the ‘larger theme’ that goes but is not heard. He emphasizes these are two separate parts of the puzzle, not overlooking the possibility they could be related in some way. His third contribution is the hypothesis the hidden melody to the Variations is a famous hymn tune from the sixteenth century inspired by the Book of Psalms from the Bible. On all of these points Gough is absolutely correct.

Enigma or Enigmas?
Although laying out some remarkably accurate premises, Gough soon veers off course beginning with his fixation on the fugal qualities of the Enigma Theme most clearly exhibited in Variation IV. Correctly noting the opening bars of the Enigma Theme may be refashioned into a brief canon, Gough reverse engineers it to comport with this aspect of Variation IV. In essence he extrapolates one of Elgar’s own variation techniques to the Enigma Theme, and calls it an Old Canon. The canon itself is in three parts (Violin 1, Violin 2, Viola 1) accompanied by two other voices (Viola 2, Cello). Hence there are five parts in the Old Canon, but only four in the first six measures of the Enigma Theme (Violin 1, Violin 2, Viola and Cello).

It is surprising Gough limits his canonical treatment to just the first six measures of the Enigma Theme while ignoring the remaining eleven. His brief canon amputates a large portion of the Enigma Theme, bowing slavishly to the conventional wisdom. He writes, “…we know that the Enigma is specifically associated with the theme heard in the first six bars…” Just how do we know that precisely? He concludes this must be the case because Elgar asked his friend Jaeger to write Enigma in place of Theme on the title page. That is hardly a convincing argument, except for one already convinced at the outset. Gough presumes the Enigma Theme is limited to the first six measures without ever furnishing any objective proof. A significant flaw with this view is the opening material from measures 1-6 is recapitulated in measures 11-16 before the final cadence in measure 17. If the Enigma Theme is restricted to the first six measures, its recapitulation surely constitutes a repetition. That means a more accurate title would be Enigmas (plural) rather than Enigma (singular). We know Elgar asked Jaeger to write the singular version, so this must mean the title Enigma applies to the entire movement rather than a six measure fragment.

It is a common error on the part of enigma detectives to confuse Elgar’s "dark saying" (which is confined to the first six measures) with the Enigma Theme. The two are actually separate as Gough earlier points out, but not in the way he suspects. What Gough fails to grasp is Elgar’s "dark saying" (a definition of enigma) is a music cipher embedded in the first six measures. Elgar is a recognized expert in ciphers, so this really should come as no surprise. As for the Enigma Theme, it remains intact as one complete movement in ternary form beginning in measure 1 and cadencing in measure 17. It may be cogently argued the bridge in measures 18-19 constitutes an elaboration of the final cadence, making the Enigma Theme in reality 19 measures rather than 17. This position is confirmed by Elgar's written remarks for a set of pianola rolls published in 1929. Regarding the first Variation he wrote, "There is no break between the theme and this movement." The double barline in measure 19 is identical to that found in measure 6, the alleged end of the Enigma Theme. The double bar in measure 19  marks the surreptitious conclusion of the entire Enigma Theme, and would explain why Variation I does not begin until measure 20. Consequently, Gough’s failure to account for at least measures 7 through 17 renders both his Old Canon and New Canon incomplete, and inconsequential for a partial answer is no answer at all. In his New Canon, Gough alters the Tallis Canon in measure 7 to accommodate his novel harmonization of the Enigma Theme. These alterations to the source melody negate the whole point of the exercise insofar as Gough attempts to show how the Enigma Canon is a counterpoint to the Tallis Canon. One part can be changed to accommodate the other; but when both are modified it becomes a free transcription rather than a credible counterpoint.

Elgar’s Conditions – not Gough’s 
If the Tallis Canon was indeed the secret melody to the Enigma Variations, it must first satisfy four conditions given by Elgar soon after the 1899 premiere. These conditions are found in three primary sources: The original 1899 program note, the 1900 interview for The Musical Times, and the 1905 biography. Elgar’s four conditions are:
  1. The Enigma theme is a counterpoint to the Principal Theme.
  2. The Principal Theme is not heard.
  3. The Principal Theme is a melody that can play ‘through and over’ the whole set of Variations including the Enigma theme.
  4. The Principal Theme is famous.
Elgar made it abundantly clear the Enigma Theme was a counterpoint to the unstated Principal Theme. In his first authoritative biography published in 1905 he explained:
"The ‘Enigma’ orchestral-piece is Op. 36. What the solution of the ‘Enigma’ may be, nobody but the composer knows. The theme is a counterpoint on some well-known melody which is never heard, the variations are the theme seen through the personalities of friends, with an intermezzo and a coda, the last added at the request of friends aided and abetted by Dr. Richter, who accepted the work on its merits, having received the score in Vienna from his agent in London, and who at the time had not met with the composer.”[1]
A counterpoint is by definition a counter melody, and logic dictates the unstated Principal Theme must therefore be a melody.  This observation is entirely consistent with Elgar’s history as shown by counterpoints he created to famous themes from Handel’s Messiah and Mendelssohn’s Wedding March. Since the unstated Principal Theme must be melodic in nature, this clearly precludes from consideration any symbolic, mathematical or literary themes.
A major implication of Elgar’s contrapuntal condition is the unstated Principal Theme must play ‘through and over’ the entire Enigma Theme. Again, this observation meshes with Elgar’s life history of composing melodic counterpoints to famous melodies. Like a home standing on its foundation, the Enigma Theme must fit with its foundational Theme. This demands that both must be the same size, in this case length.
A major flaw in Gough’s theory is the failure of the candidate melody to play 'through and over' the Enigma Theme. He contrives a brief canonical fit between the two themes by inserting a two-measure introduction in which only the secretive melody plays. A melody by itself can hardly be called a counterpoint. A second major departure is his realization of a completely different accompaniment in B-flat major rather than the original key of G minor. These changes represent substantial departures from the original score, and are more accurately described as a free and imaginative transcription rather than a counterpoint.  The length of Gough's New Canon is a scant eight measures, two of which feature only the purported secret melody. As we have already seen, a major shortcoming with this eight-bar solution is the Enigma Theme is seventeen measures in length, not eight. Basic math confirms that eight does not equal seventeen. Besides, there is no reasonable justification for ignoring the remaining nine measures of the Enigma Theme. Without a clear horizontal fit, the Tallis Canon cannot be considered as a serious candidate for the unstated Principal Theme to the Variations.
The acid test is to play the Tallis Canon intact over the original Enigma Theme without any alterations to either part. When mapped with its original note values over the Enigma Theme (and making allowances for the minor and major modes of G), the Tallis Cannon fails to form a horizontal fit or a credible counterpoint. It must be played twice just to accommodate the Enigma Theme's length. Gough surely recognized this failing, resorting to the ploy of claiming the Enigma Theme is limited to the first six measures. Such an obvious error really requires no refutation,  for the absence of the most basic horizontal fit between the two themes makes the Tallis Canon unfit. Another problem is the Tallis Canon produces an unacceptably high number of howling dissonances with the Enigma Theme. Hence there is not only the lack of a basic horizontal fit, but also a contrapuntal one as well. Gough strives to circumvent Elgar's old conditions by inventing a host of new conditions never offered up by the composer. In the final analysis, the Old and New Puzzle Canons Gough fabricates as 'solutions' are nothing more than imaginative and free transcriptions drawn from varied forms of the Enigma Theme.

The Tallis Canon fails to present a complete or convincing counterpoint over the entire seventeen measures of the Enigma Theme. Strike one. It produces an unacceptably high number of dissonant intervals in the process. Strike two. On top of these difficulties, Gough fails to show how the Tallis Canon could conceivably play “through and over” the remaining movements, a requirement Elgar imposes in the original 1899 program note. Strike three. To circumvent these obvious flaws, Gough invents a new set of conditions to rationalize his novel transcriptions of the Old and New Canons, incorporating elements of the Enigma Theme around the Tallis Canon to suggest some contrapuntal relationship. Moreover, Gough asserts the continuation of this contrived contrapuntal relationship between the two themes by cataloging from other movements some examples of thematic material drawn from the Enigma Theme without ever actually spelling out how the Tallis Canon plays over these other movements. Such a vain undertaking is more counterexample than counterpoint. It's all sizzle and no steak. If Gough desires a credible example of counterpoint between the hidden theme and the Variations, he may listen to one here. With so many strikes against it, Gough’s imaginative enigma theory may be safely rejected like so many others before it.
While beginning with a few sound principles, Gough quickly wanders into a wilderness of innuendo, musings and unrestrained speculation. So much of his thought process amounts to the stratification of varying assumptions, layering guess upon guess in a quest for some semblance of an answer. Instead of achieving clarity, Gough sows confusion. For instance, he loosely interprets the remarks "for fuga'"on an early sketch of the Enigma Theme as evidence for a puzzle canon. He further speculates Elgar likely showed that sketch to Dora Penny, anticipating that particular clue somehow would help her guess the solution. Seriously? Would any reasonable person view the comments "for fuga" as evidence of a puzzle canon? How Gough's research ever cleared the peer review process is the real enigma. He emphasizes the concept of a puzzle canon, yet fails to mention Santa’s original research showing the mathematical constant Pi is encoded in the Enigma Theme. Canons are also commonly identified as rounds, and Pi is a special ratio derived from the mathematical properties of circles. To overlook something so obvious and relevant to his research belies Gough’s lack of circumspection, not to mention Martin Bird's editorial insensitivity. The irony is that both are named Martin, a first named shared by the actual composer of the missing melody to the Enigma Variations, Martin LutherWith the aid of the British academic establishment, Martin Gough's enigma theory attempts to rehabilitate Elgar by linking the Enigma Variations to one of England's great early composers, Thomas Tallis. What Gough overlooks is the fact Elgar was no Vaughan Williams, a votary of English folk music and song. On the contrary, Elgar was a fervid disciple of the German School. For answers to the Enigma Variations, one must look beyond England and across the channel to Germany.

Gough's conception of counterpoint (sans Tallis)

A Mighty Fortress
The only theme to successfully satisfy all of Elgar’s conditions is Ein feste Burg (A Mighty Fortress) by Martin Luther. That well-known hymn successfully plays one complete cycle "through and over" the full seventeen measures of the Enigma Theme, establishing an uncanny horizontal fit. A precise vertical alignment between the two melodies illustrates Elgar's unique treatment of Ein feste Burg in an augmented form as a retrograde counterpoint. This unconventional method accounts for the profound difficulty in detecting a contrapuntal fit because one typically plays the beginning of a prospective melody over the beginning of the Enigma Theme. Such a predictable approach produces a mismatch, throwing off researchers even when the right melody is tested.
The case for Ein feste Burg as the covert Principal Theme to the Enigma Variations is extensive and persuasive. Confirmation that Ein feste Burg is the hidden theme is given by a diverse range of music ciphers in the Enigma Theme and Variation XIII. Within the Enigma Theme is concealed a music box cipher, Elgar’s "dark saying" linked to the Enigma mentioned in the original 1899 program note. Incredibly, Elgar did not take his secret to the grave, but rather enciphered the answer in the orchestral score. When discovered, the decrypted answer would remain unguessed just as Elgar predicted. He even went so far as to encode the initials for the hidden melody in the Enigma Theme which modulates between the minor and major modes of G. The accidentals for those two keys are E-flat, F-sharp, B-flat. It is remarkable the initials for Ein feste Burg are E.F.B.
The odd nickname for Jaeger’s Variation (Nimrod) is linked to the title A Mighty Fortress by of one Elgar’s favorite pastimes, wordplay. When he gave a copy of Longfellow’s novel Hyperion to the conductor Hans Richter following the premiere, Elgar literally gave away the answer.  No wonder he suspected the solution would soon be found. Even the wrong date on the original score is a revealing clue since it falls on the anniversary of Luther’s death. According to an alphanumeric cipher within the Mendelssohn fragments, the missing initials for Variation XIII (***) are E.F.B. – the initials for Ein feste BurgThe mapping of Ein feste Burg over Nimrod is so self-evident that the melodic solution to Elgar's Enigma Variations is as plain a pikestaff.
If he were alive today, Elgar's response to Gough’s theory would undoubtedly be, “I do not see that the tune you suggest fits in the least." If the theme does not fit, then one cannot commit. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar’s Enigmas Exposed.

[1] Buckley, Robert J. Sir Edward Elgar (1905). New York: Kessinger Publishing, Llc, 2009, p. 54-55


Robert Padgett said...

Martin Gough is welcome to offer a defense of his imaginative 'solution' here in the comments section. I am curious to know why he chose to cut the Enigma Theme down from 17 measures to just 6. The double bar and plagal cadence in measure 17 makes it abundantly clear the Enigma Theme concludes in measure 17, not 6. The case can be made the Enigma Theme actually continues with an elaboration of the final cadence until measure 19 because Variation I does not start until measure 20. It is a pervasive error on the part of enigma researchers to reduce the scope of the challenge to 6 measures rather than at minimum 17. The problem with that approach is that a partial answer is really no answer at all.

Robert Padgett said...

Unlike this blog, Martin Gough's videos on YouTube presenting his conjectured solutions to Elgar's Enigma Variations are not open to public comment. What is he afraid of? His reluctance to engage his audience is as disappointing as it is revealing. Gough clearly does not welcome any comments critical of his free adaptions of the opening six measures of the Enigma Theme. He has yet to muster any defense in this open forum, leaving only one obvious implication - he has none worthy to offer.

About Mr. Padgett

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Mr. Padgett studied violin with Michael Rosenker, and Rosenker’s pupil, Owen Dunsford. Mr. Padgett studied piano with Sally Magee (a student of Emanuel Bay), and Blanca Uribe, a student of Rosina Lhévinne. He attended the Stevenson School in Pebble Beach, California, and Vassar College in Poughkeepsie, New York, where he graduated Phi Beta Kappa with a degree in psychology. At Vassar he studied music theory and composition with Richard Wilson. Mr. Padgett has performed for Joseph Silverstein, Van Cliburn, Arnold Schwarzenegger, Maria Shriver, Steve Jobs, Prince Charles, Lady Camilla, Marcia Davenport, William F. Buckley, Jr., and other prominent public figures. His original compositions have been performed by the Monterey Symphony, at the Bohemian Grove, the Bohemian Club, and other private and public venues. In 2008 Mr. Padgett won the Max Bragado-Darman Fanfare Competition with his entry "Fanfare for the Eagles." It was premiered by the Monterey Symphony under Maestro Bragado in May 2008. A member of the Elgar Society, Mr. Padgett is married with five children.