Here's a musical riddle that has kept people guessing for over a century.

English composer Edward Elgar's Variations on an Original Theme, ('Enigma') op. 36 is one of England's most beloved musical works. It's commonly known as the Enigma Variations.

It begins with a haunting theme and continues with 14 variations on that theme. One variation has become a national song of mourning in England, played at Princess Diana's funeral and annually at England's memorial ceremony for fallen soldiers.

When Elgar debuted the work in 1899, the word "Enigma" was written at the top of the score.

"The Enigma I will not explain," Elgar wrote in a cryptic note in the concert playbill. "Its 'dark saying' must be left unguessed." Then he added this: "... over the whole set another and larger theme 'goes,' but is not played..."

What is that dark saying, that enigmatic theme, that is present in the work but not played?

Elgar never said, and he took his secret to the grave. But it has been understood to be a famous tune that, if played along with the Enigma Variations, it would fit perfectly.

For decades, sleuths of all stripes have tried to figure out what the phantom melody is.

In the 1950s, a national magazine in the U.S. ran a guessing contest. And over the years, people have suggested all kinds of melodies, from "Twinkle, Twinkle, Little Star" to "Pop Goes the Weasel," to melodies from works by Mozart and Beethoven. The late violinist Yehudi Menuhin thought it was "Rule Britannia." The late British musicologist Eric Sams argued for "Auld Lang Syne" in a minor key.

None of these theories has ever convinced the majority of music scholars.

The North American branch of the Elgar Society is holding its annual conference in Madison, Wis., March 16 - 19 . Members will attend the Madison Symphony Orchestra's performance of the Enigma Variations, accompanied by a multimedia performance with actors telling the story of the composer and the work.

One man attending the Elgar Society conference has his own Enigma theory that he will be preaching to his fellow Elgar enthusiasts.

Bob Padgett of Plano, Texas, is not an academic; he used to work in insurance. But he's also a violinist who's played in professional orchestras, which is how he stumbled upon the Enigma Variations — from a conductor who recounted the mystery of the work.

"He made it sound so captivating," Padgett recalls. "Kind of like a murder mystery or something. Like a, 'whodunit'. At that point I decided, you know, this is one of the great mysteries of classical music. I thought this would be an interesting puzzle to try and unravel."

On his commute to work, Padgett used to listen to a CD of the Enigma Variations and hum tunes – like "Twinkle, Twinkle, Little Star" – to see if they'd fit. They don't, really. "You can try and shoehorn it in, but it doesn't work," Padgett says.

A devout Christian, Padgett says he prayed to God for help solving the puzzle. That's when he stumbled upon a church hymn he believes is the answer: Martin Luther's "A Mighty Fortress Is Our God."

In more than 100 posts on his blog, Padgett has laid out an elaborate theory involving cryptography, Christian symbols and dozens of other hidden clues he believes Elgar embedded in the music, too uncanny to be coincidences.

Padgett says when you play the hymn with the music, it fits perfectly – you just have to piece together three different versions, written by Luther, Bach and Mendelssohn, and then play it backwards, over Elgar's music.

Padgett recorded an example and uploaded it to YouTube, and presented the theory to Julian Rushton, an Elgar expert and professor emeritus of music at the University of Leeds in England.

Rushton was not convinced. He doubts a Roman Catholic composer such as Elgar would have embraced a Protestant anthem such as Luther's "A Mighty Fortress" (though Padgett has his own theory to explain that). More than that, he doubts Padgett's premise that Elgar reverse-engineered an entire symphonic work to fit a backwards-composite melody while sprinkling dozens of symbols and clues in the music.

"My problem with all this is to do with the way the music was composed in the first place," Rushton says. "Do you compose music by working out an elaborate form of symbolism, cryptography, or do you basically write music as a musician?"

But Elgar wasn't just a musician. He was a cryptography nut.

The year before he began writing the Enigma Variations, he wrote a coded letter to a friend that's come to be called the Dorabella Cipher. Code breakers are still trying to figure it out. Padgett is convinced Elgar did the same thing with the Enigma Variations.

"I believe he wanted someone to decrypt his cipher, to prove what the correct answer was," Padgett says. "He created a cipher, and ciphers are meant to be broken. He wanted someone to break the cipher in order to validate the correct answer."

Padgett has fought for recognition. He has tirelessly emailed skeptical music scholars who have been dismissive of his theory. He has fought pushback from Wikipedia editors reluctant to publish it — though recently, his theory was included in Wikipedia's entry on Elgar's Enigma Variations.

British scholar Rushton says there's evidence to suggest the enigma may not be a hidden tune at all, but rather a more abstract concept.

"We just don't know," Rushton says. "And in those words 'we don't know' lies the chief fascination of the Enigma Variations, and which is why I personally take more interest in studying the music itself rather than the riddle — which is just what Elgar suggested one should do."

In 1899, Elgar said the enigma should be left "unguessed." But 119 years later, the guessing game continues. Last year, a Cleveland police officer said he had cracked the enigma.

Copyright 2018 NPR. To see more, visit http://www.npr.org/.

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