# Elgar's Enigma Breakthrough



## nimrod3142

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?


----------



## Elgarian

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.


----------



## nimrod3142

Elgarian[/quote said:


> 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.



Elgarian[/quote said:


> 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.


----------



## Edward Elgar

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.


----------



## Argus

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.


----------



## nimrod3142

Edward Elgar said:


> 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.


----------



## Elgarian

nimrod3142 said:


> 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.


----------



## Weston

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.


----------



## nimrod3142

Elgarian said:


> 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.


----------



## Elgarian

nimrod3142 said:


> '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.


----------



## teccomin

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.


----------



## nimrod3142

teccomin said:


> 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.


----------



## david johnson

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


----------



## nimrod3142

david johnson said:


> the solution is to listen to the work while eating *3* pizza *PI*es,* 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.


----------



## Serge

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?


----------



## Elgarian

teccomin said:


> 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.


I presume you're referring to my comments when you refer to negativity, but this is a misreading of my intention - which is to provide _constructive_ criticism of the kind that any serious new hypothesis should expect - in this case pointing out the ease with which, in these areas, it's possible to be misled by coincidences that are not as unlikely as we might think at first sight. I've also offered specific suggestions about what kind of further evidence might be sought to make the case stronger. If someone now managed to track down some correspondence of Elgar's referring to Pi at around 1898-ish - well, that would be a real feather in the theory's cap, wouldn't it? That would be a really interesting development, with the theory predicting an interest in pi that further research then actually discovered? So I wish Nimrod 3142 the best of luck in developing his theory, but I'd be dishonest if I pretended that I found it convincing as it stands.

When you say that Elgar wouldn't have gone for a more complex puzzle, I think the facts are against you, on the whole. His little jape called the 'Dorabella cypher' has eluded all attempts to decode it, so far. He loved tricky puzzles, and I don't think we have any good reason for supposing he'd necessarily settle on a simple one.

Incidentally, Nimrod3142 presumably set up this thread specifically in order to invite discussion of his interesting new proposal, and that's why we're 'dwelling' on this one, rather than others.


----------



## nimrod3142

Serge said:


> 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?


Yes that is a good point, however actually Elgar did appear as Variation XIV (Finale: Allegro Presto) "E.D.U." Elgar himself, nicknamed Edu by his wife, from the German version Eduard. The themes from two variations are echoed: "Nimrod" and "C.A.E.", referring to Jaeger and Elgar´s wife Alice, "two great influences on the life and art of the composer", as Elgar wrote in 1927. Elgar called these references "entirely fitting to the intention of the piece".[8]

You can "see" many of the other clues in the first 6 bars on the following link 
http://en.wikipedia.org/wiki/Enigma_Variations

If Elgar had been the enigma there would have been no need to hint at 22/7 in each of the three sentences he wrote at age 72 in 1929. 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.


----------



## Chi_townPhilly

It seems that today is going to be my day for word-clarification...


Elgarian said:


> my intention... is to provide _constructive_ criticism of the kind that any serious new hypothesis should expect


Yup! And thanks for your contributions in that regard...


Elgarian said:


> ...I wish Nimrod 3142 the best of luck in developing his theory...


Needs a little more work to graduate to the level of "theory." I think we were right the first time with "hypothesis."


Elgarian said:


> When you say that Elgar wouldn't have gone for a more complex puzzle, I think the facts are against you, on the whole. His little jape called the 'Dorabella cypher' has eluded all attempts to decode it, so far.


I didn't know that. (Thinks) I gotta find out more about this...

I can point to a passage in Wagner that seems to anticipate the Theory of Relativity... but that would be a digression...


----------



## nimrod3142

The 'Dorabella cypher' is composed of symbols, each made of one to four semi-CIRCLES. This could be considered another hint to Dorabella as to why he thought she might guess the solution. You know, circles -> Pi -> 3-1-4-2 scale degree. Elgar often said the enigma was very well know, not something he ever said about the 'Dorabella cypher' . I am constantly surprised that anyone would doubt the Pi solution once they look at all the connections. Of course most people are not even aware of the long unsolved "enigma" so they are reluctant to agree to a new solution. If you look at some of the old proposals on Wiki or elsewhere, you will quickly see the difference in factual connections versus contrived connections.


----------



## Vaneyes

Only one "NO" so far. I'm with the "MAYBE" majority. I like a good thriller, as I view safely from the sideline.


----------



## Major Minor

If this is true how did encoding such things help the music at all?
I think these kinds of hermetic goose chases only reinforce a sense of elitism


----------



## nimrod3142

One should remember that Elgar loved riddles, puzzles and japes/jokes. As he wrote, "this work was begun with a spirit of humor," probably growing out of the ridiculous attempt to legislate the value of Pi in Indiana in 1897. Elgar never said his "enigma" was the answer to world peace. He expected that someone would guess it during the first performance. I guessed it the first time I heard the clues that he wrote in the program notes. It was just a riddle/joke. He enjoyed fooling people and he did a great job on the enigma. Even though he left many clues, it was not solved for 110 years.


----------



## Jeremy Marchant

Pardon my obtuseness, Mr Nimrod, but the theme, as cited on Wikipedia, clearly shows 25 notes in 7 bars (not 24 in 6). Now, had that been 22 in 7, I would have been impressed.

(In the full score, the second subject, on first clarinet, covers the final B natural of the first subject. The seven bar structure is clearer when the theme is represented, slightly altered, in bars 11-17 inclusive.)


----------



## nimrod3142

Mr. Marchant the statement which you inaccurately characterize is repeated below.

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".

Please note that the observation refers to the first six bars (not seven as you describe). It also defines the blackbirds as "black notes (with "wings" as ties/slurs) baked in a "Pi". The note in bar 7 lacks wings and may not be a blackbird.

In case you want to look at the Wiki orginal again, here is a link: http://en.wikipedia.org/wiki/File:Enigma_theme.png

How did you manage to overlook the other 15 reasons proving that Pi is the solution?

I am disappointed that you are not convinced by a logical argument but I am sure you have your reasons.


----------



## Jeremy Marchant

nimrod3142 said:


> How did you manage to overlook the other 15 reasons proving that Pi is the solution?
> 
> I am disappointed that you are not convinced by a logical argument but I am sure you have your reasons.


... and here they are, since you asked so nicely.

You say you have 15 other reasons "proving that Pi is the solution". Proving?? Nothing in your post proves anything, and only one point (3) is at all attractive. Your reasoning is meretricious rather than meritorious.

Let's take your points in order

1 - As you know, Elgar dedicated the EV to "my friends pictured within". You have projected your word, 'circle', onto this. Please provide a reference from Elgar's writings to demonstrate he, too, thought of his friends as a 'circle', as opposed to a 'group' or many other collective nouns.

2 - "Pi is usually approximated as 3.142 as a decimal, or 22/7 as a fraction." This is a mathematical statement. It doesn't refer to the EV, so it cannot be a 'reason' that 'proves' or disproves the truth of any assertion about the EV.

3- "The first four notes of EV are scale degree 3-1-4-2…" Agreed. But this isn't proof, though I accept it's an interesting observation.

4 - "There is a drop of a seventh in bars 3 and 4". There is indeed. But there are an awful lot of pieces of music with falling sevenths in them. So what? You didn't notice that there is also a unison later on, which is what a 22nd reduces to [ie, starting at G, each successive G going up is an octave, 15th, 22nd etc].

5 - "These 2/7 follow exactly after the first 11 notes. ie: 11 x 2/7 = 22/7" I'm not sure what this means. However, you seem to have missed that, if the first falling seventh occurs after the first eleven notes, there is a second [inversion of seventh] after the next eleven. And, taking the theme, as a whole, ie including the final B natural, in retrograde, then what is now the first seventh also occurs after eleven notes. None of this proves anything, of course. You need to look at the music of Berg or Maxwell Davies if you want to see what composers do when they want to introduce numbers into their music. My points are trivial.

6 - "Elgar wrote EV in the year following the widely ridiculed Indiana Pi Bill of 1897…" This is an example of the logical fallacy, _post hoc ergo propter hoc_, ie because B followed A, A necessarily caused B. I had some salmon for lunch and now it's raining. Therefore my eating salmon caused the rain.

7 - This point isn't a reason for anything, it's a quotation from a programme note telling us what we already know, namely that there is an enigma.

8 - Even you use the word 'could': 'Elgar's dark saying could be…'. So clearly you're not certain yourself. So I don't think this is a reason that proves anything. You didn't explain why the final note of the theme has been lost to fit your theory but, it sort of massively loses credibility by having to do so. You refer to 'ties/slurs'. There are no ties, the horizontal lines under the quavers are _tenuto _marks. So, why are some notes slurred and not the rest, if they're all supposed to be birds with wings?

9 - This statement falls into the logical fallacy of stating as truth that which you are seeking to prove. It isn't true just because you say it is.

10 - "Elgar often said that the enigma was "well known." Pi is taught to nearly everyone as part of a basic education." But so are many things which haven't found their way here. In any case, the reach of formal education over a hundred years ago in England was far less than it is now, so what is your evidence that "nearly everyone" then was taught pi?

11 - "He probably wanted to leave some confirmation of the enigma's solution… These three sentences contain 3 hints at fractional Pi." Your assertion. Where's the evidence? "Probably" tells me you're not sure of this point yourself, so how can it be said to "prove" anything? Elgar's three sentences read like dull programme notes making points about the melodic component of the music. Citation please.

12 - "In the first sentence he wrote of two quavers and two crotchets- at hint at "22" (of 22/7)." Hint's the word. Occam's razor suggests that, given two explanations for an event, we choose the simpler in the absence of a good reason to choose the other. I choose the simple explanation that Elgar was simply drawing attention to a basic rhythmic pattern he wished his listeners to observe throughout the variations. Since, so far, the only interesting thing you've observed is 3142, I suggest you haven't enough evidence to warrant anyone choosing any more exotic explanation.

13 - "In the second sentence he referred to the drop of the seventh in 3rd and 4th bar." Here, I am confident that Elgar is only making a superficial remark. The seventh is the key interval in the work, it occurs more or less in the middle of the theme and, at moments of emotion later, such as in Nimrod, it is the sevenths that get developed.

14 - "In the third sentence he referred to "bar 7" which is a hint at "/7" of 22/7." Tendentious. English speakers do not use the word 'bar' to refer to the symbol '/'.

15 - "Elgar wrote that "The EV were begun in a spirit of humour."" What does that prove? On another thread I recently read of someone's surprise that the Bartok third piano concerto was so life affirming given that he was dying as he wrote it. There need be no correlation between a composer's mental state and the content of the music he or she is writing. See also Stravinsky Symphony in C.

16 - "Elgar was known for his interest in puzzles and his love of japes (jokes)" Well, again, this is hardly proof that the overriding enigma is pi. It could just as easily be proof that there is no overriding enigmatic theme, and Elgar was having us all on.

"I think this is the enigma solution? What do YOU think?" I think you need to let go of your _need _to be right. If I may be flamboyant, I think you need to heed Thomas Cromwell, in his letter of 3 August 1650 to the General Assembly of the Kirk of Scotland, where he wrote: 'I beseech you, in the bowels of Christ, think it possible you may be mistaken.'


----------



## nimrod3142

Most people who view this series of evidence would find it compelling in favor of Pi. I am sorry that you do not want to see it that way. Perhaps, "Thou doest protest too much."


----------



## nimrod3142

Someone recently observed that the 1929 hints were issued along with release of Elgar's EV pianola rolls...Pi anola rolls. That is pretty far fetched but it could have been meant as another clue. It is certainly not inconceivable that Elgar intended "Pi-anola" to be a hint. We can certainly see that he had Pi on his mind in many other hints.


----------



## nimrod3142

The complete article, "Solving Elgar's Enigma" is now printed in the latest edition of the journal Current Musicology, published by Columbia University.


----------



## MJTTOMB

nimrod3142 said:


> Most people who view this series of evidence would find it compelling in favor of Pi. I am sorry that you do not want to see it that way. Perhaps, "Thou doest protest too much."


Every argument you have made is a logical fallacy. How you managed to publish anything whatsoever in a scholarly journal is beyond me.

"A lot of people would find this compelling"- Appeal to the majority. That is a childish and outright fallacious argument.

Quoting Shakespeare also adds no relevance or logical integrity to your case. He posted a very logically-sound 16-point rebuttal of your arguments, and you replied with one argument, which by its own merit wasn't much of an argument but rather a deluded, fallacious statement.

I recognize that pointing out another's fallacies is considered to be a fallacy in itself, so I will kindly suggest that you carefully re-read and reconsider Jeremy Marchant's well-stated argument.


----------



## nimrod3142

Thank you for considering the Pi solution. I would be happy to respond to each of the points made by Jeremy.

1 - As you know, Elgar dedicated the EV to "my friends pictured within". You have projected your word, 'circle', onto this. Please provide a reference from Elgar's writings to demonstrate he, too, thought of his friends as a 'circle', as opposed to a 'group' or many other collective nouns.

a. Elgar's use of the word "circle" is referenced on more than one occasion as pointed out in the "Solving Elgar's Enigma" paper printed in the latest edition of Current Musicology published by Columbia University. It may have only been coincidence that the "circle" is a variation of "My Friends Pictured Within." However it led me to investigate if 3.142 was used anywhere in the music. This is certainly not a proof of, or a proof against the Pi solution.

2 - "Pi is usually approximated as 3.142 as a decimal, or 22/7 as a fraction." This is a mathematical statement. It doesn't refer to the EV, so it cannot be a 'reason' that 'proves' or disproves the truth of any assertion about the EV.

a. This merely states two important facts necessary to understanding the significance of the later evidence.

3- "The first four notes of EV are scale degree 3-1-4-2…" Agreed. But this isn't proof, though I accept it's an interesting observation.

a. This could either be intentional or unintentional by the composer. If it is intentional we should like to see other evidence of Pi in the melody.

4 - "There is a drop of a seventh in bars 3 and 4". There is indeed. But there are an awful lot of pieces of music with falling sevenths in them. So what? You didn't notice that there is also a unison later on, which is what a 22nd reduces to [ie, starting at G, each successive G going up is an octave, 15th, 22nd etc].

a. The drop of the seventh in bars 3 and 4 was pointed out by Elgar in his 1929 comments leading one to suspect that they may have a special significance as opposed to those in other places.

5 - "These 2/7 follow exactly after the first 11 notes. ie: 11 x 2/7 = 22/7" I'm not sure what this means. However, you seem to have missed that, if the first falling seventh occurs after the first eleven notes, there is a second [inversion of seventh] after the next eleven. And, taking the theme, as a whole, ie including the final B natural, in retrograde, then what is now the first seventh also occurs after eleven notes. None of this proves anything, of course. You need to look at the music of Berg or Maxwell Davies if you want to see what composers do when they want to introduce numbers into their music. My points are trivial.

a. Elgar added the two sevenths after his first 11 notes. 2/7 x 11 = 22/7, fractional Pi. One must decide if this is intentional or unintentional, but now we have two incidents of hints at Pi.

6 - "Elgar wrote EV in the year following the widely ridiculed Indiana Pi Bill of 1897…" This is an example of the logical fallacy, post hoc ergo propter hoc, ie because B followed A, A necessarily caused B. I had some salmon for lunch and now it's raining. Therefore my eating salmon caused the rain.

a. Again we have an unusual sequence of events and we must consider if it was a coincidence that Elgar used Pi in the year following the humorous jape, Indiana Pi Bill. Was it just another unintentional event or was it intentional.

7 - This point isn't a reason for anything, it's a quotation from a programme note telling us what we already know, namely that there is an enigma.

a. Elgar's careful choice of words is important to solving his enigma. 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 - Even you use the word 'could': 'Elgar's dark saying could be…'. So clearly you're not certain yourself. So I don't think this is a reason that proves anything. You didn't explain why the final note of the theme has been lost to fit your theory but, it sort of massively loses credibility by having to do so. You refer to 'ties/slurs'. There are no ties, the horizontal lines under the quavers are tenuto marks. So, why are some notes slurred and not the rest, if they're all supposed to be birds with wings?

a. Although I am criticized for being both uncertain and too certain, I will explain the information in another way. Elgar's "dark saying" appears to be, "Four and twenty blackbirds baked in a pie (Pi). The are a number of facts pointing to this. Elgar used a double bar after the sixth measure which was most unusual since the first phrase was not complete. What was complete? Four and twenty black notes baked in Elgar's Pi. The tied notes and slurs appear to be wings to me but that is not significant in any case. The double bar after bar 6 explains why the black note in bar 7 is not counted. (It also does not have a slur or a tie to another note.)

9 - This statement falls into the logical fallacy of stating as truth that which you are seeking to prove. It isn't true just because you say it is.

a. Elgar referred to his enigma as a Theme and it is important to point out that Theme refers to melody in a musical sence but Theme in a "literary" sense refers to the central concept or idea of a work. Elgar hinted that the enigma Theme was literary by stating that "it is not played.... So the principal Theme never appears, even as in some late dramas ... the chief character is never on the stage." What king of melodic theme is not played? His reference to "late dramas" is another reason to suspect Elgar's theme is a literary theme not a melodic theme.

10 - "Elgar often said that the enigma was "well known." Pi is taught to nearly everyone as part of a basic education." But so are many things which haven't found their way here. In any case, the reach of formal education over a hundred years ago in England was far less than it is now, so what is your evidence that "nearly everyone" then was taught pi?

a. Can anyone honestly believe that Pi was not taught in England in the 1860-1890's. It was even taught in Indiana, although the legislators were not paying close attention. Ha Ha. (a little Pi humor)

11 - "He probably wanted to leave some confirmation of the enigma's solution… These three sentences contain 3 hints at fractional Pi." Your assertion. Where's the evidence? "Probably" tells me you're not sure of this point yourself, so how can it be said to "prove" anything? Elgar's three sentences read like dull programme notes making points about the melodic component of the music. Citation please.

a. Again I am attacked for not being certain. The facts are that Elgar's three carefully worded sentences each contains a hint at 22/7, fractional Pi. They do read like elementary school program notes which part of Elgar's genius and why the enigma was unsolved for so long. After 30 years and hundreds of performances, was it really necessary to point out that the first bar contained two quavers and two crotchets? I think not. It was a hint at 2 and 2 or 22 of 22/7. Maybe if that was all, we could say it was just another coincidence, but in the thirds sentence he referred to bar 7. Can you not visualize /7? Additionally in the second sentence Elgar points out the drop of the seventh in bars 3 and 4 which lead to finding 11 x 2/7 = 22/7. Elgar was confirming that Pi was the solution. Either we have a remarkable number of coincidences or the facts confirm Elgar's intentions.

12 - "In the first sentence he wrote of two quavers and two crotchets- at hint at "22" (of 22/7)." Hint's the word. Occam's razor suggests that, given two explanations for an event, we choose the simpler in the absence of a good reason to choose the other. I choose the simple explanation that Elgar was simply drawing attention to a basic rhythmic pattern he wished his listeners to observe throughout the variations. Since, so far, the only interesting thing you've observed is 3142, I suggest you haven't enough evidence to warrant anyone choosing any more exotic explanation.

a. The criticism ignores the other two hints a 22/7 which are contained in the other two sentences.

13 - "In the second sentence he referred to the drop of the seventh in 3rd and 4th bar." Here, I am confident that Elgar is only making a superficial remark. The seventh is the key interval in the work, it occurs more or less in the middle of the theme and, at moments of emotion later, such as in Nimrod, it is the sevenths that get developed.

a. It may appear to be a superficial remark on the surface. That is the genius of Elgar's enigma and the reason it was unsolved for over 100 years. Musicans heard about a Theme and thought only of melody. People heard about a "dark saying" and began looking for something serious and somber. People did not look for hints at Pi in his 1929 notes because they had not found the 3-1-4-2, decimal Pi, in the first four notes. They were not looking for these cleverly hidden hints.

14 - "In the third sentence he referred to "bar 7" which is a hint at "/7" of 22/7." Tendentious. English speakers do not use the word 'bar' to refer to the symbol '/'.

a. One needs a little imagination to solve and enigma. / can be said to look like a bar. Even without the bar, it is a hint at the number 7 which is cleverly obsured in his third sentence.

15 - "Elgar wrote that "The EV were begun in a spirit of humour."" What does that prove? On another thread I recently read of someone's surprise that the Bartok third piano concerto was so life affirming given that he was dying as he wrote it. There need be no correlation between a composer's mental state and the content of the music he or she is writing. See also Stravinsky Symphony in C.

a. This is just one more coincidence that was probably not a coincidence. Elgar was hinting that the enigma was related to something humorous. Remember the Indiana Pi Bill of the prior year. It was quite a joke and Elgar was know to enjoy such japes.

16 - "Elgar was known for his interest in puzzles and his love of japes (jokes)" Well, again, this is hardly proof that the overriding enigma is pi. It could just as easily be proof that there is no overriding enigmatic theme, and Elgar was having us all on.

a. Elgar's interests are consistent with the Enigma being Pi. We would not expect a humorous enigma from a person with no sense of humor and Elgar's biographers tell of his love of japes, puns and nursery rhymes.

17. "I think this is the enigma solution? What do YOU think?" I think you need to let go of your need to be right. If I may be flamboyant, I think you need to heed Thomas Cromwell, in his letter of 3 August 1650 to the General Assembly of the Kirk of Scotland, where he wrote: 'I beseech you, in the bowels of Christ, think it possible you may be mistaken.'

a. I asked for everyone's thoughts. I was criticized for being too certain after being criticized for being uncertain. Most confusing. Thomas Cromwell was a giant and he would probably enjoy the Pi solution. Ha Ha (more Pi humor)


----------



## MJTTOMB

My apologies for how harsh I was, it's certainly an interesting find, but you seemed to ignore his statements.

Thanks for the clarification. One way or the other, if polling were still open I would be a solid maybe.


----------



## Elgarian

nimrod3142 said:


> Again I am attacked for not being certain.


Just a point about modes of expression, really. Jeremy Marchant hasn't _attacked_ you personally. On the contrary, he's taken your hypothesis and subjected it to exactly the kind of sceptical scrutiny that any proposed hypothesis needs to be subjected to if it's to be taken seriously. He's gone to a great deal of trouble to consider every one of the points you made, and if anyone were to give such detailed and constructive consideration to a hypothesis that _I'd_ proposed, I'd feel well-treated (albeit disappointed), even if they disagreed with my conclusions at the end. In fact, when I've published papers myself in my own fields of research, some of the most valuable improvements have been brought about by the constructive criticism of colleagues and/or referees. That's how the peer review process works. It's not about Jack being right and Jill being wrong. It's about Jack and Jill working together (sometimes heatedly, because they're human) to establish something that they can both agree bears the best resemblance possible to the truth.


----------



## nimrod3142

Thank you for your comments. I certainly appreciate constructive criticism. Although I discovered the 3-1-4-2 scale degree in the first four notes, much of the rest came from collaborative thinking and discussing. A gentleman in the UK was first to recognize the significance of the Pi finding. He made many suggestions and asked many questions that completely left me blank at first. He suggested that the dark saying may have been related to the Baker family (friends of Elgar) through Four and twenty blackbirds "baked" in a pie. He also suggested that the 1929 notes about the "two quavers and two crotchets may have something to do with 22 of 22/7. He also suggested my reading Julian Rushton's book about the Enigma Variations. My son, and co-author, noted the twenty four black notes in the first six bars. Another enigma enthusiast, explaining his own hypothesis, remarked about the double bar after bar 6 which I had previously overlooked. Because Wikipedia would not include my hypothesis unless it had been published in a peer reviewed journal so I was forced to write a research paper. In my search for a good definition of Pi, I came across the Indiana Pi Bill of 1897. Imagine my surprise and delight. After 18 months of research another 18 months to publication, I wanted to share my findings with other people and ask for their opinions.

I guess I did not value criticism based against my strong conviction or because I referred to some hints using the word "probably." I would have thought the totality of evidence was overwhelming. I guess that is what happens when one works on a project for 3+ years and then freely shares the results.

I welcome constructive criticism and difference of opinion. I would prefer that reviewers consider the many pieces of evidence as a whole rather than try to pick each one apart.


----------



## SirPadgett

*Elgar's Enigma Theme Unmasked*

The unstated Principal Theme to Elgar's Enigma Variations has been discovered. It is "Ein feste Burg" (A Might Fortress) by Martin Luther as realized by J.S. Bach and Felix Mendelssohn. To learn more about this historic discovery, visit*
*http://enigmathemeunmasked.blogspot.com/p/elgars-enigmas-exposed.html


----------



## Romantic Geek

SirPadgett said:


> The unstated Principal Theme to Elgar's Enigma Variations has been discovered. It is "Ein feste Burg" (A Might Fortress) by Martin Luther as realized by J.S. Bach and Felix Mendelssohn. To learn more about this historic discovery, visit*
> *http://enigmathemeunmasked.blogspot.com/p/elgars-enigmas-exposed.html


I like the Pi idea better than this one...


----------



## jimread

Pi in the sky lol

A radio 4 programme, apparently Ed said to one of his lady friends, you of all people should know where the theme came from.

She rode her bike from Shropshire to meet him, the programme presenter, a musician himself, re-traced her route on a bike and saw that the shape of the Malvern hills looking at them from the North West formed the notes of the theme.

Considering his love for Worcs and the English countryside in general it's not really surprising. Go there play it in your car and you can see the place in music.

Jim


----------



## nimrod3142

Hi Jim,

Thanks for considering the Pi solution. 

The shape of the Malvern Hills has been suggested by others in the past and that fact is amazing, however, how does it answer the clue that Elgar gave regarding "dark saying"? It is also widely reported that Elgar said the theme was "well-known" and he expected someone to guess his enigma on first hearing. I guessed "Pi" after my first hearing. Is the shape of the Malvern Hills from that direction something one would be expected to guess at first hearing? Elgar's lady friend, Dora Penny, was most likely to guess Pi because she recently completed her schooling but his other friends were in the 40s and 50s. He also sent Dora Penny two letters signed with a staff of 3-1-4-2 scale degree (opening four notes of the Enigma Variations.


----------



## KJohnson

The music itself is way more interesting and remarkable than the enigma within it. The orchestration is so colorful and creative that you lose even the slightest interest you may have had in the title.


----------



## nimrod3142

Good point! Maybe that is why his puzzle was unsolved for over 111 years.


----------



## Chris

Please indulge this irrelevant addition to the discussion  

A classical geometrician, a mathematician, and an engineer, are asked to define pi.
Geometrician: 'It is the ratio of the circumference of a circle to its diameter'.
Mathematician: 'It is an irrational and transcendant constant defined as twice the smallest positive x, x being in radians, for which cos(x) equals zero'.
Engineer: 'It's about 3'.


----------



## nimrod3142

That's good! I am obviously not a mathematician but I can relate to the other two. 

If you asked a composer (Edward Elgar) he would tell you it that Pi is 3.142, 22/7, or a dark saying (a pun inside a nursery rhyme, "Four and twenty blackbirds baked in a "Pi".)


----------



## PetrB

I loathe all the mathematicians who are constantly trying to fit their numbers to art in general. There is something so horribly and plainly wrong about the need to quantify everything, especially the arts. It is almost pathological.

This is a case of where numbers Always Lie, because they can be so fit to anything along with a little rationale.

If art could be quantified, there would be a tidy list of who actually were / are the best composers: those lists would not at all vary if the 'system' used to quantify them was 'at the truth of it.'

You can't reduce everything to numbers, any more than you can reduce it all to musical notes.

Never cared about these literal - associative things attached to music. Don't care of whom those 'musical portraits' are. 
I don't even find Elgar at all palatable.


----------



## PetrB

A piano teacher somehow got off on her own tangent when I was in a lesson and working on a Chopin piece. The digression had to do with all the suggested motivations behind the piece, what he was thinking, feeling, of which there are myriad and all insupportable by any directly attributable documentation whatsoever.

As she wound it down, she came to a very dry and matter of fact dismissal of it all, "Me, I don't care if he had a toothache when he wrote it."

This is your kind of pleasure, a kind of pleasure, frankly, that I think has nothing to do with the music and more with a true compulsion -- bordering on a clinical obsession -- to define anything you might sense as 'ordered' in your own terms and on your own turf - with math.

Even if it were provable (many here have been in their posts, while polite, quietly but hysterically funny about dismissing your theorem) I believe the whole procedure and preoccupation on your part is 100% obstructive to your meeting this piece head-on, unarmed, and letting it really work on you. The Art Of Music, when presented, should be received in complete openness, and trust, so the music itself can do its work on you. That requires a giving up of self and real trust in, after all, what is nothing but bent air.

ADD: But I omitted the key thing. Artists primarily think within the modes of their craft and medium: that mode of thinking is their first impulse. 

Math, or an orange peel next to a cup and saucer with tea dregs in it, and the supposed random placement of those objects on the table, and perhaps the crease in the table cloth at just that place... can trigger and catalyze a purely musical thought, and without any steps to account for in transliterating thought, immediately suggest musical events or a structure.

You see all from a math perspective, compelled, evidently, to do so. Thus the artist has all other manner of things and objects from other disciplines as their catalysts, but are too, compelled to think as artists - if Elgar had been thinking math, I can guarantee you it would not have guaranteed his choice of pitches if they did not first suit his ear.

To think otherwise, to parse this most abstract and plastic of the arts out with math or the literal rhetoric of verbal logic, is to fail to get anywhere near what an artist does, and that keeps you, I think, sadly, at a far remove from directly receiving what they did do. It keeps forever on the 'outside of music,' and it will never be in you. That makes me want to offer you commiseration more than anything, because its pull on you must nonetheless be great.

"I chose to paint water lilies, but it could have been anything." ~ Claude Monet


----------



## jalex

PetrB said:


> I loathe all the mathematicians who are constantly trying to fit their numbers to art in general.


Not sure there are any actual mathematicians who do that. You seem to have your sights aimed at the wrong people. In my experience it seems to be over-enthusiastic musicologists.


----------



## Vaneyes

Gimme a second, I'll figure it out.

View attachment 3674


----------

