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What is the solution to Elgar's Enigma Variations?


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May 23, 2011 7:42PM

Ein feste Burg (A Mighty Fortress) by Martin Luther

The melodic solution to Elgar's 'Enigma' Variations is Ein feste Burg (A Mighty Fortress) by Martin Luther. To learn more about this discovery, visit


The Pi solution is now printed in the latest edition of Current Musicology published by Columbia University

1. Elgar never wrote that the enigma was a melody. He referred to it as a "Theme." Theme, in the literary sense, is the central concept or idea of a work. Hence, Pi is the theme which is "not played."

2. Elgar showed that his enigma was completely contained in the first six bars by using a double bar after the sixth measure. There are exactly "four and twenty" black notes in the first six bars which confirms his "dark saying" as "Four and twenty blackbirds baked in a pie (Pi)." Elgar was well known to enjoy quoting nursery rhymes and puns. Here we have both.

3. Pi is taught to nearly everyone as part of a basic education. Dora was his only close friend who had recently completed her schooling. All of his other friends were in their forties. It had been 20 years since they learned about Pi. Elgar also signed to letters to Dora using the 3-1-4-2 scale degree first bar of the Enigma Variation.


Ein feste Burg (A Mighty Fortress)

On February 3rd 2009, Robert W. Padgett discovered the hidden principal theme to Sir Edward Elgar's Enigma Variations Opus 36: The Reformation hymn Ein feste Burg ist unser Gott by Martin Luther. This solution satisfies three specific rules proposed by the composer:

  1. The hidden melody is well-known.
  2. The principal them plays "through and over" the entire 17 bars of theEnigma theme.
  3. Dora Penny, the daughter of an Anglican Rector, was very familiar with this hymn.

A sound file of Ein feste Burg played on flute "over and through" the Enigma Theme may be heard at

The efficacy of this breakthrough is confirmed by playing the hidden principal theme "through and over" the most famous of the Variations - Nimrod.

A sound file of Ein feste Burg played on trumpet "over and through" Variation IX Nimrod may be heard at

The biblical name Nimrod means "A mighty hunter before the Lord." (See Genesis 10:9). Amazingly, the title of the missing principal melody literally translates from the German as "A Mighty Fortress is our God." It is noteworthy each title shares two identical words (i.e., a mighty) in the same position, and the final terms are interchangeable (i.e., Lord andGod). It should also be observed both titles consist of six words. The link between the two could not be more apparent. Martin Luther was German, and many prominent members of the German School quote Ein feste Burg in this music: J. S. Bach, Mendelssohn, Meyerbeer, Listz, Raff and Wagner. Elgar deeply admired the music of Bach, Mendelssohn and Wagner, so it should come as no surprise he would imitate these great masters in this way.

For Mr. Padgett's full report of this historic discovery, visit his blog at

March 2009


Elgar confirmed the "Pi" solution before his death

In 1929 when Elgar was 72 yrs old and in ill-health, no one had solved his enigma. He wanted to leave several more clues so the correct solution could be verified if it were found after his death. He wrote three sentences for the release of his pianola rolls. The three sentences sound on the surface like basic descriptions of his first several bars, however each sentence contains a hint at 22/7, fractional Pi. In the first sentence he writes of two quavers and two crotchets- a hint at 22 (of 22/7). In the second sentence he writes that the drop of the seventh in the 3rd and 4th bar should be observed- a hint at two sevenths (2/7 x first 11 notes = 22/7). In the third sentence he writes about a repeat in bar 7- a hint at /7 (of 22/7). All of this in four bars of music that begins with scale degree 3-1-4-2, decimal Pi. Can that be just a coincidence?


The enigma is "BACH"

Without any doubt. See it and hear it at

Elgar was passionate about Bach and it would not be possible for Elgar to have written the variations in the only key that fits the notes B-A-C-H without noticing. Bach himself wrote pieces with his own name embedded with, as did Schostakivitch and others. Elgar is paying the ultimate homage to the greatest musician that ever lived.

Listen to the clips, and follow the music. You will be presuaded.

Hugh Hunt

Trinity College


October 2007


The solution is as easy as Pi.

Sir Edward wrote a dedication on the score, "To My Friends Pictured Within".

As the entire piece is about variations, he could have written, "To My

Circle of Friends." This variation includes the word "circle," and in

math, characteristics of all circles are related by a universal constant,

Pi. Pi can be approximated as 22/7 which equals 3.142857.

When the first four numbers 3-1-4-2 are played on a musical scale with 1

being the root, 3 being the third, etc., we hear the opening Theme of his Enigma

Variations. Voila!

A story is told that Sir Edward at one time, had numbered the keys of his piano

to help a friend play a tune. His "student" gave up in confusion when he noticed

the same numbers repeated in other octaves. Sir Edward laughed so hard that he rolled

on the floor. This shows that he was very familiar with the note/number relationship

and it shows that he had a great sense of humor.

In order to confirm that the Pi solution is correct, it must be shown to answer

all of the clues which Sir Edward gave us during his lifetime. None of the previously

suggested solutions has been able to answer all of these clues which casts doubt on

their being the correct solution.

Sir Edward gave his first two direct clues when he wrote this note for the first

performance, "The Enigma I will not explain- its 'dark saying' must be left

unguessed, and I warn you that the connexion between the Variations and the Theme

is often of the slightest texture; further, through and over the whole set

(of variations) 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."

This note contains two clues, the "dark saying" and "the chief character (who)

is never on the stage". Pi could be described as the chief character as it

never appears on stage and this theme is the basis for all of the variations.

The second clue, the "dark saying", could be a clever reference to the line from

the very familiar English nursery rhyme "Four and twenty BLACKbirds baked in a


After 30 years in which no one guessed the Enigma, Sir Edward wrote in 1929, "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 the 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]- E.E."

Actually, there are two drops of the seventh after the first eleven notes.

Perhaps Sir Edward was suggesting, 11 notes times two sevenths = 11 x 2/7 = 22/7,

which is the common approximation of Pi.

Dora Penny Powell said in November of 1899 that Sir Edward, speaking of the Enigma,

told her, "It is so well known that it is extraordinary that no one has spotted it."

Later, when Troyte Griffith suggested, "God Save the King" was the answer, Elgar

responded, "Of course not...but it is extraordinary that no one has found it."

Shortly before he died, Sir Edward again said that he was surprised that no one had

correctly solved the enigma because it was so simple. Pi is universally

taught as part of primary education.

Dora said that Sir Edward told her privately, "I thought that you of all people

would guess it." Why would he say that? There are two very good reasons. Two

years before composing the Enigma Variations, Sir Edward had written a code

puzzle for Dora Penny which is still unsolved. "The Dorabella Cipher" is famous in

its own right, and it has become one of cryptography's most intriguing puzzles.

This hinted at the solution being a cipher. Additionally, in two separate letters

to Dora written in 1901, Sir Edward used the first measure of the Enigma Variations

as his signature. (The falling third, rising fourth, the 3-1-4-2). That is why he

thought that Dora, of all people, would guess it.

What do you think about this solution and its confirmation in the clues?

Dick Santa

Revised June 7, 2007