A Clever Musical Puzzle is Solved

[Nimrod]

Elgar's "Enigma" has remained unsolved for over 110 years, but I think we now have the solution.

In 1899, Edward Elgar wrote the following program notes for the first performance of his Enigma Variations:

"The Enigma I will not explain - its 'dark saying' must be left unguessed, and I warn you that the connection between the Variations and the Theme is often of the slightest texture; further, through and over the whole set another and larger theme 'goes', but is not played.... So the principal Theme never appears, even as in some late dramas ... the chief character is never on the stage."

In 2007, a retired engineer observed that the first four notes were scale degree 3-1-4-2, decimal Pi. Pi is a constant in all circles (circumference divided by diameter.) It is usually approximated by 3.142 as a decimal, or 22/7 as a fraction. Fractional Pi can be found within the first four bars by observing that two “drops of a seventh” follow exactly after the first eleven notes, giving us 11 x 2/7 = 22/7. Elgar included a “dark saying” into his first six bars by using “Four and twenty blackbirds (dark) baked in a pie (Pi).” The first four and twenty black notes each have “wings” (ties or slurs,) and they are followed by a double bar which usually indicates the end of a piece, but Elgar used it to indicate the end of his Enigma.

The first several bars can be viewed at http://en.wikipedia.org/wiki/File:Enigma_theme.png

Thus Pi fits all the clues given by Elgar in 1899. Viewing “theme” as the central idea/concept explains how Pi can be the “larger theme which 'goes', but is not played.” Pi “is never on the stage.” The 'dark saying' which must be left unguessed, turns out to be a pun from a familiar nursery rhyme.

As if to confirm "Pi", Elgar provided a Pi hint in each of the three sentences he wrote in 1929 at the age of 72, when no one had guessed the enigma after 30 years.

"The alternation of the two quavers and two crotchets in the first bar and their reversal in the second bar will be noticed; references to this grouping are almost continuous (either melodically or in the accompanying figures - in Variation XIII, beginning at bar 11 [503], for example). The drop of a seventh in the Theme (bars 3 and 4) should be observed. At bar 7 (G major) appears the rising and falling passage in thirds which is much used later, e.g. Variation III, bars 10.16. [106, 112]"

In the first sentence he referred to two quavers and two crotchets (hint at 22) and then in the third, he referred to bar 7 (hint at /7.) Putting them together yields another 22/7. In the second sentence he wrote, “The drop of a seventh in the Theme (bars 3 and 4) should be observed,” which leads us to find fractional Pi, 22/7, in the first four bars. Elgar said the solution was “well known.” Pi is taught to school children as part of a basic education.

Elgar wrote his Enigma Variations in the year following the very foolish Indiana Pi Bill of 1897 which attempted to legislate the value of Pi. Years later in 1910, Elgar wrote “the work was begun in a spirit of humour.” Elgar enjoyed such japes, as well as codes, puzzles and nursery rhymes. No other proposed “solution” has offered any relevance to Elgar’s 1929 hints including his “drop of a seventh in the 3rd and 4th bar.”

The complete paper "Solving Elgar's Enigma" is printed in the latest edition of Current Musicology published by Columbia University.

[Despina41]

[Balthazar]

Originally Posted by Nimrod

In 2007, a retired engineer observed that the first four notes were scale degree 3-1-4-2, decimal Pi.

Viewing “theme” as the central idea/concept explains how Pi can be the “larger theme which 'goes', but is not played.” Pi “is never on the stage.”

How can Pi be the "theme which is not played" if it's played in the first four notes of the composition?

[Nimrod]

Originally Posted by Balthazar

How can Pi be the "theme which is not played" if it's played in the first four notes of the composition?

Playing a theme based on Pi, having three hints at Pi, is certainly not the same as playing Pi.

[Nimrod]

Originally Posted by Balthazar

How can Pi be the "theme which is not played" if it's played in the first four notes of the composition?

Perhaps a better answer to your question would be that the "theme" which is never played is a theme in the literary sense. Pi is the central idea/concept upon which the work is based.

The 3-1-4-2 scale degree opening notes are a hint at decimal Pi but they are not Pi, just as 6-1-2 is my home address but it is not my home. It is a characteristic of my home, but it is not my home.

[Balthazar]

[Nimrod]

When Elgar wrote of a "Theme which is not played," he was making the distinction between the musical connotation of "theme" and the literary meaning. If it "is not played," then it must be the literary theme, the central idea/concept of a work.

Most musicians who tried to solve the enigma were obsessed with music and therefore they usually looked for a musical theme in the enigma, a melody that could be implied or an unheard counter melody. Most sleuths were also thrown off the track by the "dark saying," which most took literally and considered bible verses, etc. They forgot that Elgar often used nursery rhymes and puns in his daily life and he loved a good jape.

[Alex Daniels]

Originally Posted by Balthazar

[Nimrod]

Can I assume that you think this is a "dog-gone" good thread? If you have any questions I would be glad to discuss any aspect of the Pi solution in more detail.

[Astrovaan]

No offense, Nimrod, but your posts seem rather repetitive. I feel as though I've read this stuff before.