h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

After 107 Years, We Finally Have The Solution to Elgar's Enigma

On June 19, 1899, Sir Edward Elgar's Enigma Variations, Opus 36, was introduced to the public for the first time. The piece was an immediate success and it is still very popular today. An interesting side note to his music is the fact that Sir Edward told the world that there were two enigmas contained in this music. The first enigma involved determining which of his friends each variation represented. This enigma was quickly solved as Sir Edward provided initials on each section of the score to help identify each friend/variation. The second enigma though has never been solved. Many solutions were offered to Sir Edward during his lifetime but he always insisted that they were not correct. Before his death in 1935, he said he was surprised that no one had found the correct solution because it was "so simple."
Sir Edward wrote a dedication on the score, "To My Friends Pictured Within". As the entire piece is about variations, he could have written, "To My Circle of Friends." This variation includes the word "circle." In math, characteristics of all circles are related by a universal constant, Pi. A common approximation of Pi is 22/7 which equals 3.142857. When the first four numbers 3-1-4-2 are played on a musical scale with 1 being the root, 3 being the third, etc., we hear the opening Theme of his Enigma Variations.
A story is told that Sir Edward at one time, had numbered the keys of his piano to help a friend play a tune. His "student" gave up in confusion when he noticed the same numbers repeated in other octaves. Sir Edward laughed so hard that he rolled on the floor. This shows that he was very familiar with the note/number relationship and he had a great sense of humor.
In order to confirm that the Pi solution is correct, it must be shown to answer all of the clues which Sir Edward gave us during his lifetime. None of the previously suggested solutions has been able to answer these clues which is proof that they are not the correct solution.
Sir Edward gave his first two direct clues when he wrote this note for the first performance, "The Enigma I will not explain- its 'dark saying' must be left unguessed, and I warn you that the connexion between the Variations and the Theme is often of the slightest texture; further, through and over the whole set (of variations) 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."
This note actually contains two clues, the "dark saying" and "the chief character (who) is never on the stage". Pi could be described as the chief character as it never appears on stage and this theme is the basis for all of the variations. The second clue, the "dark saying" could be a clever reference to the line from the very familiar English nursery rhyme "Four and twenty BLACKbirds baked in a pie/Pi."
In 1929, Sir Edward wrote, "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 the 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." Actually, there are two drops of the seventh after the first eleven notes. Sir Edward again hinted at Pi, 11 notes times two sevenths = 11 x 2/7 = 22/7, the common approximation of Pi.
Dora Penny Powell said in November of 1899 that Sir Edward, speaking of the Enigma, told her, "It is so well known that it is extraordinary that no one has spotted it." Later, when Troyte Griffith suggested, "God Save the King" was the answer, Elgar responded, "Of course not…but it is extraordinary that no one has found it." Shortly before he died, Sir Edward again said that he was surprised that no one had correctly solved the enigma because it was so simple. Pi is universally taught as part of primary education.
Dora said that Sir Edward told her privately, "I thought that you of all people would guess it." Why would he say that? There are two very good reasons. Two years before composing the Enigma Variations, Sir Edward had written a code puzzle for Dora Penny which is still unsolved. "The Dorabella Cipher" is famous in its own right, and it has become one of cryptography's most intriguing puzzles. This hinted at the solution being a cipher. Additionally, in two separate letters to Dora written in 1901, Sir Edward used the first measure of the Enigma Variations as his signature. (The falling third, rising fourth, the 3-1-4-2). That is why he thought that Dora, of all people, would guess it.
What do you think about this solution and its confirmation in the clues?

Dick Santa
[Personal details removed by Moderator]USA
Revised June 13, 2007
[email protected]

I figured out that the first five notes of the Enigma theme were the same as Pi about twenty years ago, but dismissed it, as the rest of the theme just doesn't match. Given that Pi was popularly known to about 8 decimal places, Elgar could easily have used more than just five notes. So I don't find this at all convincing.

The rest of this "solution" as presented here is very far-fetched.

In particular, the story of Elgar attaching numbers to the keys of the piano and getting his friend to play the theme is revealing. The friend was an engineer but tone-deaf. If the theme was in fact based on Pi, then he as an engineer would have spotted it. If the theme was a popular tune, then being tone-deaf, he would not have recognised it, which is the normal interpretation.

The other clues, such as four and twenty blackbirds, are so vague as to be meaningless.

"The drop of a seventh should be noted". And yes it does happen at note 11. But that only gives us 7th @ 11. There's another 7th @ 13. Getting from these to 22/7 is rather contrived.

Saying that Dora of all people should have solved it is not really explained by the fact that Elgar frequently wrote to her in ciphers. Because the proposed solution is not a cipher at all.

So no, I don't buy it.

Thank you for your comments, I really do appreciate them.

Why do you not consider the solution to be a cipher?

Elgar, in 1929, directed attention to the drop of the seventh in bars 3 and 4, which shows that he intended that 2 7ths to be part of the solution. 2/7 x 11 = 22/7. What other solution addresses the drop of the seventh?

Why do you not think that "The Four and twenty Blackbirds baked in a Pi" is a direct reference to "Pi"?

Elgar signed two letters to Dora with the opening notes to his Enigma, the 3-1-4-2 cipher, and then told her he thought she, of all people, would have guessed it. Don't you think that is a pretty big hint to Dora, of all people?

>>Why do you not think that "The Four and twenty Blackbirds baked in a Pi" is a direct reference to "Pi"?

Because there is mention of four and twenty blackbirds.

>>Elgar signed two letters to Dora with the opening notes to his Enigma, the 3-1-4-2 cipher, and then told her he thought she, of all people, would have guessed it. Don't you think that is a pretty big hint to Dora, of all people?

He signed it with the notes of the Enigma, but everybody considering the problem knew the notes of the Enigma, so he hadn't in this way given Dora an extra clue. If "she of all people should have guessed it", there must be some other reason.

Could the reference to BLACKbirds be the dark in "Dark saying?"

Not likely. There's no direct link between "Dark Saying" and "Pi". You've speculated that:

Dark Saying could mean Black
Black could be short for Blackbird
Blackbird could refer to the common nursery rhyme "Four and Twenty Blackbirds baked in a pie"
and pie could be Pi.

That's just too many steps to make a reasonable connection.

Thanks for your explanation.

Can you explain how the van Houten theory ties into "the drop of the seventh in bars 3 and 4", which Elgar hinted at in 1929?

No I can't. I'd never heard of Elgar pointing them out, until you mentioned it.

I meant to tell you that your initial posting was quite well written.

The criteria of the "drop of a seventh" is discussed on page 67 in Julian Rushton's 1999 book entitled, "Elgar: Enigma Variations."

He states that it is one of five criteria that must be satisfied by the correct solution of the Enigma. The other four are also covered in my intial posting.

Do you have any ideas about how I might get my theory reviewed by a larger audience. I would sure benefit from feedback from as many people as possible to help me in further research. Two heads are better than one.

There is an Elgar society, but in general they are not interested in proposed solutions. They decided long ago that there is not enough information available to solve the puzzle, so any proposed solutions are just speculation.

Let's look at your first posting in detail.

1st Paragraph - OK, except that one of the friends is sometimes disputed.

2nd Paragraph:

- "he could have written "to my circle of friends", but he didn't, so it's false logic to link the dedication to Pi.
- 3.142 is only Pi to 3 decimal places. The third digit after the decimal point is actually 1, as Elgar would have known.
- "When the first four numbers 3-1-4-2 are played on a musical scale with 1 being the root, 3 being the third, etc" -- only when you treat is as a minor scale. The Enigma theme is in a minor key.
- "We here the opening Theme of his Enigma Variations" - no, we hear the first four notes of the theme. Since Pi is much longer than 4 digits, it is
surprising Elgar didn't use more of it in his theme.

3rd paragraph:

The story of Elgar getting his friend to play a tune appears to have been garbled, and I in my comments earlier misremembered it. It was a friend, (Troyte Griffith), not a student. Elgar says:

"I marked with sticky paper certain keys on the piano, and on each paper I put a number, showing the sequence in which they were to be played. I asked Troyete to play in the order they were marked. WHen he had finished, I removed the sticky paper and tol him, 'Troyte, you now know the Enigma!'

To me this suggest that "the Enigma" is a tune. Certainly, if it is a number, then this story makes no sense, as the numbers on the sticky paper were 1, 2, 3, 4, etc. showing the order to play the notes, not their position in the scale.

Sixth paragraph: I've already dealt the the blackbirds.

7th paragraph: Elgar points out the quaver quaver crotchet crotchet pattern followed by crotchet crotchet quaver quaver as being important, but it doesn't seem to be addressed by your theory

Good with your searching!

Excellent feedback. As you might have expected, I did not consider the comments from the editor of the Elgar Journal to be constructive.

Could you recommend some reference materials that you found useful?

I have a book of musical anecdotes, and there were a few anecdotes in it relating to Elgar and the Enigma. That's where I got the story of the sticky paper, and his comments to Dora Penny. Other than that, the most important thing is to have the theme written down in front of you.

I consider that only the first six bars are important.

I really wish people would recognize finally, once and for all, that the enigma is BACH. Elgar chose the only key in which the name BACH can be played. He says that it "goes but is not played" and this is true - just listen, at

http://www2.eng.cam.ac.uk/~hemh/enigma.htm

Bach was German, and in German notation "B" means Bb and "H" means B natural, so BACH is Bb - A - C - B .

Elgar was hugely in awe of Bach and it is not conceivable that he wrote the variations accidentally in the right key and accidentally managed to fit B-A-C-H into the texture - not once, but dozens of times. Not only does it appear twice in the first 8 bars but the proof is so poignantly made in movement XII (B.G.N.) Andante - when a solo cello (the only time any solo instrument is played) quietly and slowly states (in the correct key) the notes "B-A-C-" but the "H" is swallowed up rather rudely by the clarinet starting the next movement. It is as if Elgar is saying "here it is" but he pulls it out of our reach at the last minute.

OK, deny it. But it is the elephant in the room. The 3.142 is not bad. Rule Britannia is OK. Auld Lang Syne is fair. But B-A-C-H is perfection and purity.

Happy listening. Once heard and understood it is impossible to hear it any other way.

Hugh Hunt
Trinity College
Cambridge

I've givrn my opinion on the Bach suggestion in a separate conversation. I'd don't consider it to be the solution.

I have recently found a few more pieces of information that support Pi as the enigma.

1. The year before Elgar wrote the EV, there was a huge jape/joke about Pi. The Indiana House of Representatives passed a law which tried to specify a method for calculating Pi. The effort was based on a charlatan telling them that Pi was difficult to determine. Actually Pi had been calculated to more than 150 decimal places, and the method he was suggesting, squaring the circle, had been rigorously disproven a few years earlier by a real mathmatician.

2. There are exactly "Four and twenty blackbirds" (black notes with wings- as ties or slurs) in the first six bars of Elgars Pi melody. They are "baked in a Pi".

3. Most importantly, each of Elgar's three sentences written in 1929 when he was 72 years old and in ill-health, contains a hint at 22/7, fractional Pi. The first sentence refers to two quavers and two crotchets, a hint at 22. The second sentence draws attention to the two drops of a seventh which none of the other "solutions" can relate to. These two sevenths come after the first 11 notes giving us 11 x 2/7 = 22/7. The third sentence refers to a repeat in bar 7. This is a hint at /7 of "22/7".

How many coincidences does it take to show Elgar's intention was to construct a melody based on Pi? That is the new enigma!!!!!!!!

I've heard that the Enigma was simply Ein Feste Burg ist Unser Gott, a Lutheran hymn which was known to everybody in the society of the time, and which is a perfect match in every note with the Enigma theme, over the entire length of the piece. I haven't checked it, though.

Going through Santa's points:

1. The State of Indiana did not pass a law on the subject of Pi. That's a myth. A crackpot came to them asking them to pass the a piece of legislation; they looked into it and found it was rubbish.

2. There are exactly "Four and twenty blackbirds" (black notes with wings- as ties or slurs) in an arbitrary number of bars you've chosen from the melody.

3. Most importantly, each of Elgar's three sentences written in 1929 when he was 72 years old and in ill-health, contains a hint at 22/7. But 22/7 is not Pi, and Elgar presumably knew this.

It's much more likely to be a musical variation than a numeric puzzle, because experience shows that any number will fit any theory.