"Solving Elgar's Enigma", co-written by C R Santa and Matthew Santa, is now printed in Current Musicology, a journal published by Columbia University.
In 2007, a retired engineer observed that the first four notes of Elgar's Enigma Variations 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. Further research uncovered that 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 Elgar indicated that the enigma was contained only in the first six bars bar by inserting a double bar after the sixth bar. The double bar usually indicates the end of a section but Elgar inserted it before the end of the first phrase.
Pi fits all the clues given by Elgar in 1899. "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."
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 wrote three sentences 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 , 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."
Each sentence contains a Pi hint. Elgar was 72 old and no one had guessed the enigma after 30 years. In his 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 his 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.”
What do you think about this solution?