View Poll Results: Do you think this is the correct solution to Elgar's enigma?

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Thread: Elgar's Enigma Breakthrough

  1. #1
    Junior Member nimrod3142's Avatar
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    Smile Elgar's Enigma Breakthrough

    1. Elgar's Enigma Variations (EV) written in 1898 were about his "circle" of friends. Pi is a constant in all circles. Pi is the circumference divided by its diameter.

    2. Pi is usually approximated as 3.142 as a decimal, or 22/7 as a fraction.

    3. The first four notes of EV are scale degree 3-1-4-2, decimal Pi.

    4. There is a drop of a seventh in bars 3 and 4.

    5. These 2/7 follow exactly after the first 11 notes. ie: 11 x 2/7 = 22/7, fractional Pi.

    (The first seven bars may be viewed in "Wikipedia, Enigma Variations"- I tried to cut and paste but it did not work here.)

    6. Elgar wrote EV in the year following the widely ridiculed Indiana Pi Bill of 1897 which attempted to legislate the value of Pi.

    7. In a programme note for the 1899 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.

    8. Elgar's "dark saying" could be, "Four and twenty blackbirds (dark) baked in a Pie (Pi). Within the first six bars there are exactly "Four and twenty black notes (with "wings" as ties/slurs) baked in a "Pi".

    9. Theme in the "literary" sense is the central concept or idea of a work. Pi is the Theme which "never appears", although the melody derived from Pi in the first six measures is heard through out as the "Original Theme".

    10. Elgar often said that the enigma was “well known.” Pi is taught to nearly everyone as part of a basic education.

    11. In 1929 Elgar was 72 years old, in ill-health and many of his friends had died. He probably wanted to leave some confirmation of the enigma's solution in case it were solved after his death. He wrote 3 sentences for release of his EV pianola rolls. These three sentences contain 3 hints at fractional Pi.

    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.


    12. In the first sentence he wrote of two quavers and two crotchets- at hint at "22" (of 22/7).

    13. In the second sentence he referred to the drop of the seventh in 3rd and 4th bar.

    14. In the third sentence he referred to "bar 7" which is a hint at "/7" of 22/7.

    15. Elgar wrote that "The EV were begun in a spirit of humour."

    16. Elgar was known for his interest in puzzles and his love of japes (jokes).

    I think this is the enigma solution? What do YOU think?

  2. #2
    Senior Member Elgarian's Avatar
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    I voted 'no'. As I mentioned in another thread, this kind of 'number magic' is notoriously prone to generating apparently startling correspondences which seem unlikely to be explicable by chance, but which actually are. (It's a bit like being startled to discover that out of two dozen people in a room, two have the same birthday; in fact the odds in favour of such a coincidence occurring are better than 50/50). I once encountered a paper demonstrating that the design of all the prehistoric stone circles in Britain showed the use of the 'golden ratio', but the apparently amazing diagrams were only the result of an excessive number of degrees of freedom, coupled with ingenuity (and persistence) on the part of the proposer of the idea.

    In these cases the burden of proof lies with the proposer of the solution, who must demonstrate the uniqueness of his solution - or at least, must demonstrate the unlikeliness of the 'coincidences' arising by chance.

    For example, let's take 4 and 5, which at first sight look startling:

    4. There is a drop of a seventh in bars 3 and 4.

    5. These 2/7 follow exactly after the first 11 notes. ie: 11 x 2/7 = 22/7, fractional Pi.
    I would ask the following crucial question:
    How easy is it to find similar relationships with other pieces of music (by Elgar or by anyone else) that have nothing to do with the 'Enigma', and which therefore we would know would be entirely spurious? Bear in mind that we would need to consider different variations on those relationships that we might find equally 'interesting', if we came across them. My instinctive reaction (based on some experience of this sort of thing, in non-musical fields) is that it's probably a lot easier than we might think - just like the two people with the same birthday in the same room. The onus is on the proposer of the theory to demonstrate otherwise.

    Also, I think I'd need persuading that Elgar did have some particular interest in PI. I'm not aware of any such - but I may have missed something. If there were evidence of some central preoccupation of Elgar's with PI, that might swing the odds in favour of the theory. Then there's his famous comment to Dora Penny, where Elgar suggested that that she 'of all people' would be able to guess the enigma. That seems to me to work against the idea of anything related to PI - unless Dorabella had a fascination with circular geometry that I'm not aware of.

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  4. #3
    Junior Member nimrod3142's Avatar
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    Quote Originally Posted by Elgarian[/quote
    How easy is it to find similar relationships with other pieces of music (by Elgar or by anyone else) that have nothing to do with the 'Enigma', and which therefore we would know would be entirely spurious?
    Thank you for your comments. I invite you and anyone else to find Pi in both decimal and fractional form in any other music? I invite you and anyone else to find three consecutive sentences by anyone that can be linked to fractional Pi. It is not as easy or as common as you might think but give it a try. I await word of your success.

    Quote Originally Posted by Elgarian[/quote
    I think I'd need persuading that Elgar did have some particular interest in PI.
    A humorous incident occurred during the year before Elgar wrote the EV. The 1897 Indiana Pi Bill was a futile attempt to legislate the method for calculating Pi (and thus the value of Pi). This stupidity was widely ridiculed and Elgar loved stories like this of people doing silly things unintentionally. He called them "japes." Dorabella and Elgar shared one such jape at his home when the mail brought an invitation from the local temperance society. Their slogan was, "Let us hold up our fellow man." Elgar and Dorabella laughed together over that until they rolled on the floor, according to her book.

    On the subject of Dorabella, the is a famous puzzle sent to her by Elgar known as the Dorabella Cipher. Its symbols are composed of semi-CIRCLES. Elgar also sent Dorabella two letters which he signed with the first bar of the EV (the 3-1-4-2 scale degree). Dorabella was also the only person he knew who was just recently out of school (where one learns about Pi). All of Elgar's other friends were in their 40s or more. Dorabella was also a student of music who should have had recent familiarity with scale degrees.

  5. #4
    Senior Member Edward Elgar's Avatar
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    Your argument reads a bit like the "bible codes". They found predictions in the bible that had come true by analysing the word order in a numerically inventive way.

    It was also discovered that if the novel "Moby Dick" was analysed in a similar manner, it accurately described the death of Princess Diana and the alleged plot to kill her.

    You make a convincing argument and maybe you're right. However, I'd like to think the "Enigma" was more than a number-crunching exercise.

    Elgar took the secret to his grave. If it were discovered, the mystery and speculation would be lost. If you were right, that would reduce Elgar's organic melodies to mere serialism.

    I'm curious as to where you came upon this information. If you worked this out yourself I'm very impressed. It's good to have a theory about this work, but as we will never know, I'll always remain sceptical.
    When all the paint has been dried, when all the stone has been carved, music shall remain, and we shall work with what remains.

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  7. #5
    Senior Member Argus's Avatar
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    Where's the 'I don't care' option in the poll.

    All I care about is whether I like the music. And in the case of the Enigma Variations, I do.

    Elgar could have based the EV on the local football results in 1898 and it wouldn't alter my enjoyment of the music.

    Having said that, there's no harm in you or anyone else trying to solve these riddles if thats what you like to do.

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  9. #6
    Junior Member nimrod3142's Avatar
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    Quote Originally Posted by Edward Elgar View Post
    Elgar took the secret to his grave.

    I'm curious as to where you came upon this information.
    BEFORE Elgar went to his grave, he wrote 3 sentences in 1927 that confirm that the solution to the enigma being Pi. After he wrote 3 sentences in 1899 for the first performance which introduced the enigma , he wrote nothing more about it for 30 years. Why would he wait so long to describe the music using very simple terms that had been obvious to everyone who had looked at a score during the 30 years. He cleverly worded the three sentences in 1929 to give confirmation of the enigma's solution. It was very easy to spot scale degree 3-1-4-2 as the first four notes. (I did that even without looking at the score.) It was not so easy to find the fractional Pi. His 1929 hints made that discovery possible as I researched the enigma over the past 3 years.

    This information is the product of my original research undertaken after I noticed the first four notes were 3-1-2-4, and Pi was a fitting answer to the original clues about a Theme that is "not heard" and that is not "on stage." The four and twenty blackbirds (black notes with wings- ties/slurs) baked in a pie" was discovered while I was writing an "enigma" article for publication. I had suspected that was the "dark saying" but I had not noticed the 24 black notes until my son pointed it out.

    It is just a riddle. Elgar loved puzzles and riddles. It doesn't detract from his music. It enlarges the man to think that he could create a musical masterpiece while constraining himself to working with Pi. The man was super genius and appreciating another side of him should not detract from his compositions.

  10. #7
    Senior Member Elgarian's Avatar
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    Quote Originally Posted by nimrod3142 View Post
    I invite you and anyone else to find Pi in both decimal and fractional form in any other music? I invite you and anyone else to find three consecutive sentences by anyone that can be linked to fractional Pi. It is not as easy or as common as you might think but give it a try. I await word of your success.
    Well, if I shared your depth of interest in the puzzle, perhaps I might be tempted, but as I said in my post, the burden of proof lies with the proposer of the hypothesis. If this were a statistical problem (which it is, in a way, albeit one too loosely stated to be tested properly), then the question that would have to be addressed by the researcher would be: 'Can these results reasonably be explained by chance?' It's the job of the researcher to provide sound evidence for an answer to that question - not of his readers.

    A humorous incident occurred during the year before Elgar wrote the EV. The 1897 Indiana Pi Bill was a futile attempt to legislate the method for calculating Pi (and thus the value of Pi). This stupidity was widely ridiculed and Elgar loved stories like this of people doing silly things unintentionally. He called them "japes." Dorabella and Elgar shared one such jape at his home when the mail brought an invitation from the local temperance society. Their slogan was, "Let us hold up our fellow man." Elgar and Dorabella laughed together over that until they rolled on the floor, according to her book.
    Japes, yes. He loved them. And there are lovely examples in Dorabella's book. His love of japes is well documented and not in doubt. You don't need to defend that. But my question was, and remains: where is the evidence (other than your hypothesis) that Elgar showed any special interest in PI?.

    On the subject of Dorabella, the is a famous puzzle sent to her by Elgar known as the Dorabella Cipher. Its symbols are composed of semi-CIRCLES. Elgar also sent Dorabella two letters which he signed with the first bar of the EV (the 3-1-4-2 scale degree). Dorabella was also the only person he knew who was just recently out of school (where one learns about Pi). All of Elgar's other friends were in their 40s or more. Dorabella was also a student of music who should have had recent familiarity with scale degrees.
    Again I ask - where, specifically, is the evidence that Dorabella had any special interest or involvement with PI, sufficient to explain Elgar's comment to her? The use of semicircles in his cypher seems to be the closest we can come, and again that is really too vague. The 'fresh from school' argument is similarly vague: I assume Dora learned a good deal more at school than Pi!

    You'll think perhaps I'm being deliberately obstructive, but a good solution should be able to stand up to these kind of questions - just as the right approach to any new scientific hypothesis is to challenge it and see how it fares.

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  12. #8
    Senior Member Weston's Avatar
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    I voted maybe. I don't think I want to know. Pi seems a prosaic solution to the enigma, but Elgar was after all only human - not some mythic character in a Dan Brown potboiler.

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  14. #9
    Junior Member nimrod3142's Avatar
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    Quote Originally Posted by Elgarian View Post
    If this were a statistical problem (which it is, in a way, albeit one too loosely stated to be tested properly), then the question that would have to be addressed by the researcher would be: 'Can these results reasonably be explained by chance?'
    'Can these results reasonably be explained by chance?

    1. Elgar using scale degree 3-1-4-2 as first four notes (by chance 1 in 100).
    2. Elgar giving clues in 1899 consistent with Pi (by chance 1 in 100).
    3. Elgar composing a melody with four and twenty blacknotes-with wings (1 in 100).
    4. Elgar composing melody based on Pi after Indiana Pi Bill of 1897 (1 in 100)
    5. Elgar giving three more hints in 1929 at age 72, all hinting at 22/7 (1 in 100).
    6. Chance of all these being coincidences, greater than 1 in 10,000,000,000.

    I am not a statistian, obviously, but this may not be too inaccurate.

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  16. #10
    Senior Member Elgarian's Avatar
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    Quote Originally Posted by nimrod3142 View Post
    'Can these results reasonably be explained by chance?
    Well, I strongly suspect that they can. Those 1/100 probabilities you quote there look like mere guesses to me - and as with my original illustration about the chance of two people in the same room having the same birthday, mere guesses are notoriously unreliable.

    The problem here, as I've said before, is with the degrees of freedom that we have when we're looking for apparently startling numerical coincidences. For example, let's just take your third item (Elgar composing a melody with four and twenty blacknotes-with wings) and consider the number of degrees of freedom we have when selecting that song. There are many well-known songs which have numbers in them (Ten Green Bottles, the Twelve Days of Christmas, etc), and this gives us plenty of opportunities for finding one that (for any given circumstance) has some sort of resonance with what we're looking for. To settle on 'Sing a song of sixpence' in this way, because one of its lines seems to have some kind of correspondence with the problem at hand, requires us to interpret 'birds' as 'notes', 'wings' as 'ties/slurs', and 'pie' as 'pi', for no reason at all except that this way we can make them fit the hypothesis.

    Now, if we had some other evidence that Elgar had some special relationship with blackbirds, or with that particular song - if it was a favourite of his, perhaps, or if Dorabella and he had some little 'jape' concerning it, then it might start to be persuasive. But unless and until we find some evidence like that, I think we're in danger of accepting it merely because it happens, out of many other possibilities, to fit what we want to find.
    Last edited by Elgarian; May-25-2010 at 09:30.

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    After all the negativity in here, all I want to say that, if there is a solution to this enigma, the Pi solution is the most simple and elegant. Elgar wouldn't have gone for a more complex puzzle. The best way to prove a solution wrong is find an alternate solution which makes more sense. Dwelling on one solution will make no progress.

  18. #12
    Junior Member nimrod3142's Avatar
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    Quote Originally Posted by teccomin View Post
    The best way to prove a solution wrong is find an alternate solution which makes more sense. Dwelling on one solution will make no progress.
    I certainly agree that we need a solution that makes more sense. That is why I have been offering the Pi solution as an alternative to consider. There have been many solutions offered over the past 110 years and I think it is time to consider this new solution. I appreciate all feedback. It will help me develop a more effective plan going forward.

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    the solution is to listen to the work while eating 3 pizza PIes, 1 order of bread sticks, 4 mugs of beer, and 2 glasses of sangria. it's all amazingly clear everytime i do that.

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  21. #14
    Junior Member nimrod3142's Avatar
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    Quote Originally Posted by david johnson View Post
    the solution is to listen to the work while eating 3 pizza PIes, 1 order of bread sticks, 4 mugs of beer, and 2 glasses of sangria. it's all amazingly clear everytime i do that.
    Wow! You've taken this thing to a whole new level.

  22. #15
    Senior Member Serge's Avatar
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    Looks like a well-rounded theory overall, although, like some previous posters I didn’t buy some of the arguments.

    So, if the solution was actually “the circle of friends” with Pi given as a hint, wouldn’t it be logical to suggest that the composer himself was the central theme or character of the piece: he never actually appeared in it and was well known?
    When I hear John Cage’s 4’33”, I reach for my earplugs.

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