nimrod
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In 1899 Edward Elgar introduced his Variations on an Original Theme with these 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.
After 30 years, no one had solved his enigma, so at age 72 he wrote these words:
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.
The first few bars of his music can be viewed at the following website:
File:Enigma theme.png - Wikipedia, the free encyclopedia
After three years of research I have found numerous hints at Pi. One or two hints might be coincidence but more than 10 hints becomes "proof" in my opinion.
1. The first four notes are scale degree 3-1-4-2, a common approximation of decimal Pi.
2. He dedicated his work to his "Friends Pictured Within". This is a "variation" of the more common phrase, "Circle of Friends", but he probably considered that too strong a hint. (incidentally, that is what led me to look for Pi.)
3. After the first 11 notes there are two "drops of a seventh." 11 x 2/7 = 22/7, a common approximation of fractional Pi.
4. Elgar said there was a "dark saying" involved. "Four and twenty blackbirds (certainly dark) baked in a Pie (Pi), could satisfy that requirement.
5. There are exactly Four and twenty black"birds" (black notes with wings-ties/slurs) baked in Elgar's Pi melody.
6. Elgar frequently said the solution was "well known." Pi is taught to almost everyone as part of a basic education.
7. Elgar said the work was "begun in a spirit of humor".
8. Elgar composed the Enigma Variations in the year following the humorous incident known as the Indiana Pi Bill of 1897, when the legislature passed a bill to propose the method to be used for calculating Pi. This bill was based on the erroneous assumption that Pi was difficult to calculate, but it was already know to more than 100 decimal places. The scheme they proposed, "squaring the circle" had been rigorously disproven by a real mathematician several years earlier. Elgar enjoyed "japes" such as that.
9. Elgar was known for his interest and skill in puzzles. John Holt Schooling devised a puzzle and declared that no one in all of England could solve it. Elgar did solve it and his six page solution is on display in his birthplace museum.
10. In Elgar's 1899 hints, he wrote that there was a "dark saying" in the first clue. In the second clue, he wrote that there was a theme that "goes but is not played." Pi is a theme in the "literary" sense in tht it is the idea or concept behind the work. In his third sentence he states that the enigma is "offstage," as Pi certainly is.
11. The 3 sentences from Elgar in 1929 each contain a hint at 22/7, fractional Pi. The first sentence refters to two quavers and two crotchets- a hint at 22. The second sentence refers to observing the "drop of the seventh in the third and four bars" which led me to find the 11 x 2/7 = 22/7. In third sentence he refers to a repeating pattern in bar 7, a hint at /7 of 22/7.
I cannot believe that all of this is just a coincidence, can you?
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.
After 30 years, no one had solved his enigma, so at age 72 he wrote these words:
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.
The first few bars of his music can be viewed at the following website:
File:Enigma theme.png - Wikipedia, the free encyclopedia
After three years of research I have found numerous hints at Pi. One or two hints might be coincidence but more than 10 hints becomes "proof" in my opinion.
1. The first four notes are scale degree 3-1-4-2, a common approximation of decimal Pi.
2. He dedicated his work to his "Friends Pictured Within". This is a "variation" of the more common phrase, "Circle of Friends", but he probably considered that too strong a hint. (incidentally, that is what led me to look for Pi.)
3. After the first 11 notes there are two "drops of a seventh." 11 x 2/7 = 22/7, a common approximation of fractional Pi.
4. Elgar said there was a "dark saying" involved. "Four and twenty blackbirds (certainly dark) baked in a Pie (Pi), could satisfy that requirement.
5. There are exactly Four and twenty black"birds" (black notes with wings-ties/slurs) baked in Elgar's Pi melody.
6. Elgar frequently said the solution was "well known." Pi is taught to almost everyone as part of a basic education.
7. Elgar said the work was "begun in a spirit of humor".
8. Elgar composed the Enigma Variations in the year following the humorous incident known as the Indiana Pi Bill of 1897, when the legislature passed a bill to propose the method to be used for calculating Pi. This bill was based on the erroneous assumption that Pi was difficult to calculate, but it was already know to more than 100 decimal places. The scheme they proposed, "squaring the circle" had been rigorously disproven by a real mathematician several years earlier. Elgar enjoyed "japes" such as that.
9. Elgar was known for his interest and skill in puzzles. John Holt Schooling devised a puzzle and declared that no one in all of England could solve it. Elgar did solve it and his six page solution is on display in his birthplace museum.
10. In Elgar's 1899 hints, he wrote that there was a "dark saying" in the first clue. In the second clue, he wrote that there was a theme that "goes but is not played." Pi is a theme in the "literary" sense in tht it is the idea or concept behind the work. In his third sentence he states that the enigma is "offstage," as Pi certainly is.
11. The 3 sentences from Elgar in 1929 each contain a hint at 22/7, fractional Pi. The first sentence refters to two quavers and two crotchets- a hint at 22. The second sentence refers to observing the "drop of the seventh in the third and four bars" which led me to find the 11 x 2/7 = 22/7. In third sentence he refers to a repeating pattern in bar 7, a hint at /7 of 22/7.
I cannot believe that all of this is just a coincidence, can you?
