The Enigma’s Solution

Elgar’s Variations on an Original Theme for orchestra, Op. 36 ("Enigma"), commonly referred to as the Enigma Variations, is a set of a theme and its fourteen variations written for orchestra in 1898. It is Elgar's best-known large-scale composition, for both the music itself and the enigmas behind it. The piece was first performed at St James Hall, London, on 19 June 1899, conducted by Hans Richter and Elgar dedicated it to "my friends pictured within."

In an 1899 programme note for the first performance, Charles A. Barry rendered Elgar's own words:

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.

Elgar wrote the following in a set of notes issued with the Aeolian Company pianola rolls published 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 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] - E.E.


Elgar is known to have enjoyed puzzles, puns, nursery rhymes and jokes and he incorporated all of these in his enigma. The year before Elgar wrote the Enigma Variations, one of the great “japes” of all time occurred in the infamous Indiana Pi Bill of 1897. An amateur mathematician convinced the members of the Indiana House to vote for a bill to make “squaring the circle” the official way to calculate Pi. (This would result in a terrible approximation of anywhere from 2 to 4 depending on how the method was applied.) A real mathematician showed the Senate the folly of this bill and it was quickly tabled into obscurity.

In 1898, the year following the Indiana Pi Bill, Edward Elgar completed his Variations on an Original Theme. His original “enigma” melody was composed using three aspects of Pi. In the first six bars, Elgar incorporated Pi as a decimal, Pi as a fraction, and Pi as a pun. Pi is a constant in all circles (his circle of friends?) Pi is equal to circumference divided by diameter. Pi is approximately by 3.142 as a decimal or 22/7 as a fraction. Elgar’s first four notes are scale degree 3-1-4-2, decimal Pi. Elgar added “two drops of a seventh” after his first eleven notes, leading to 11 x 2/7 = 22/7, fractional Pi. Elgar, evidently amused at the pun contained in the line, “Four and twenty blackbirds baked in a pie (Pi),” worked this into his Pi melody. The first six bars of Elgar’s enigma melody are made up of exactly “Four and twenty blackbirds” (black notes with wings- slurs or ties.) baked in his “Pi.” This line from Sing a Song of Sixpence was humorously referred to as a “dark saying.” Obviously blackbirds are “dark” and the pun about Pi is unmistakable.



Pi satisfies all of the clues given in the 1899 program notes. When Elgar wrote that the Theme “goes over the whole set but is not played,” he was not referring to “theme” in a musical sense, as a melody. He was using the literary meaning of “theme” which refers to the idea or concept behind a work. That is why “the chief character (Pi) is never on the stage.”

In 1929, when Elgar was 72 years old and in ill health, no one had solved his enigma for 30 years. Although he was resolved never to reveal the secret, he found a way to confirm the “Pi solution” for posterity. He wrote three sentences about the enigma variations which appear to be simple descriptions of the music. However, hidden in each sentence is a hint at fractional Pi, 22/7. The second sentence states that “the drop of a seventh in the 3rd and 4th bar should be observed.” That leads to finding the 11 x 2/7 = 22/7 as already discussed. The first sentence points out his use of two quavers and two crotchets. This is a hint at 22 of 22/7. His third sentence refers to “bar 7” which hints at /7 of 22/7.

Two other things Elgar said during his lifetime are consistent with Pi being the solution. In 1912, Elgar wrote, “the work was begun in a spirit of humour.” He also often said that the solution was “well known,” and Pi is taught to all school children as part of a basic education. No other “solution,” as yet offered, has any relevance to Elgar’s 1929 hints including his “drop of a seventh in the 3rd and 4th bar.”

If this is not the solution, then we certainly have a lot of coincidences related to Pi.