Hiding in plain sight- Elgar's Enigma Solution

[karlhenning]

Second, his paper was published in a credible academic journal, and should appropriately be viewed as a credible theory (his co-author is a music professor at a respected music school and I am sure can do as good an analysis as anyone on this site).

Thanks, it is nice to have it pointed out that we're not exactly dealing with a Newman here.

[Gurn Blanston]

First, Wiki is open to being edited by anyone and so much of what is there is suspect.  Second, his paper was published in a credible academic journal, and should appropriately be viewed as a credible theory (his co-author is a music professor at a respected music school and I am sure can do as good an analysis as anyone on this site).  Third, I doubt at this point that any solution will satisfy everyone and the enigma will remain unsolved in perpetuity.

I applaud his effort and found the article to be a worthwhile and entertaining read.  I doubt the authors had more ambitious goals.

Ditto

[(poco) Sforzando]

First, Wiki is open to being edited by anyone and so much of what is there is suspect.  Second, his paper was published in a credible academic journal, and should appropriately be viewed as a credible theory (his co-author is a music professor at a respected music school and I am sure can do as good an analysis as anyone on this site).  Third, I doubt at this point that any solution will satisfy everyone and the enigma will remain unsolved in perpetuity.

I applaud his effort and found the article to be a worthwhile and entertaining read.  I doubt the authors had more ambitious goals.

Well, if it were to turn out that his solution is air-tight, it would be a minor but definite coup towards solving one of the most famous musical mysteries of all time. I read the original article too and it sounds as if the author recognizes he is being speculative. It also shows he has done a great deal of sound research into the composer. But you gotta admit, as it seemed from the initial post, it appeared to have been presented as unassailable fact rather than "Here's a solution I have discovered and published; do you think it holds water?" And I think that raised some eyebrows here, mine included, especially as the poster has in no other way so far contributed to the forum. I absolutely agree it's clever and ingenious, but whether it's unassailable is something I can't say.

The reason I brought up Bernard Nightingale from Stoppard's "Arcadia," btw, is to call attention to the potential perils of historical judgment. If you know the play, you know that Bernard (in the early 1990s) puts together a theory, which he regards as unassailable, regarding Lord Byron's departure from England to Europe around 1810. Problem is (since the play alternates between 1990 and 1810), Bernard misreads all the clues and comes up with a conclusion that is completely erroneous. Evidence is a tricky thing, and the possibility of reaching conclusions that could be way off base can never be discounted. (OVOP enthusiasts, take note!)

[Scarpia]

I don't understand why there is so much blow-back aimed at nimrod for his theory.  I found it, while not totally convincing, a fine display of creative thinking and the pulling together of various pieces of evidence to come up with a credible guess.

Cut him some slack.

People on both sides of the rope have to give a little to create slack.

The fact that the first four notes of the theme are scale degrees 3-1-4-2 is interesting, I grant you.  The other clues?  The fact that there are 24 notes before Elgar placed a double-bar marking the end of the first strain of the theme means π?  Because we should ignore the obvious meaning of "dark saying" as "a mystery" and assume it refers to a particular nursery rhyme, "Sing a song of sixpence," which includes the phrase "four and twenty blackbirds baked in a pie, and a pie is π?   Because two intervals of a descending seventh  in the melody means 22/7?  (Did Elgar ever write a melody without at least two descending sevenths?)  Because there are 10 notes before the two descending sevenths and 10 can be miscounted as 11, and obviously this means 2 times 11 divided by 7?  Because, two years before, a legislature in a US state considered but never voted on a bill which contained an incorrect mathematical statement involving π (which was apparently not reported in England)? 

Finally, Elgar said (with no ambiguity) that he expected the puzzle to be solved at the initial performance, and no one at the initial performance had the score containing the double bar, which would have allowed them to count the 24 notes which supposedly are code for the 24 back birds baked in a pie, which are code for π.  Elgar also said "through and over the whole set another and larger theme 'goes', but is not played."  He said it goes "through and over" the entire set of variations, not that it is encoded in the first seven bars.  It requires no imagination to interpret the larger theme as a counter-melody which could have been played as a counterpoint to the main theme but was not.  Whenever a particular music  theme was suggested Elgar noted it was not the right answer, but he never suggested that the enigma was other than musical.

The first 3-1-4-2 in the first four notes may be something.  The rest?  If you allow yourself such wide lattitude in finding "clues" you can find equally convincing "clues" in any piece of music.

[Scarpia]

All true - but riddles usually are based on clues which while making sense are not so iron-clad as to make the solution too straightforward.  Again, my point is that the Pi theory is interesting and entertaining to comtemplate and I am a bit mystified why the response from some quarters has been hostile, to a degree.

It is not like anything in the article wil change the Enigma Variations and how the music is percieved.  It is just an interesting diversion, imo.

I am put off by the fact that the "explanation" requires accepting false or misleading statements, such as the claim that the double-bar is unusual (it marks the beginning of the second strain of the melody and a shift from minor to major harmony) or that the 11 notes before the descending 7th is a clue, when by the most intuitive mode of counting there are 10.  I am also put off by the exaggerated and unjustified claims that this solution is convincing.  In the words of a famous physicist, this explanation is "not even wrong."

[Scarpia]

I just want to share this stunning discovery with you all.  Both Titner and Young have made recordings of Bruckner's original version of the 3rd symphony that come out to 71:22, exactly!  This led to a major discovery!   Notice the appearance of 22, 7 and 1 in the timing.  Clearly Bruckner intended this symphony to symbolize π since 22/(7x1) ≈ π.  This is obvious since two different recordings of the symphony came up to the same total time, which couldn't possibly be a coincidence.  This is also solves the mystery of the dedication, since Bruckner dedicated it to Wagner, who he believed was the most perfect composer, and the circle is the only perfect geometrical figure, and π is derived from the circle.  Thank god that the restoration of the original version restored the clues needed to solve this more than 100 year old mystery!  Nimrod, please send me the contact information for that music journal, since this astonishing result must be published before another Bruckner fan dies without knowing the truth!!!!  My colleague Sokal is editing the manuscript already.

[Scarpia]

I don't see the point in ridiculing anyone.

Then why are you ridiculing my idea, pray tell?

[Brahmsian]

I don't see the point in ridiculing anyone.

I agree, and I'm glad I wasn't the only one thinking this.  Especially ridiculing a fairly new GMG member.

[Brian]

I just want to share this stunning discovery with you all.  Both Titner and Young have made recordings of Bruckner's original version of the 3rd symphony that come out to 71:22, exactly!

The only person I feel like ridiculing at the moment is anyone who can spell it "Titner" without a hint of irony. 

[Gurn Blanston]

The only person I feel like ridiculing at the moment is anyone who can spell it "Titner" without a hint of irony. 

You mean misspell Tintner? 

[Scarpia]

The only person I feel like ridiculing at the moment is anyone who can spell it "Titner" without a hint of irony. 

You cannot imagine how crestfallen I am to find my thesis has a flaw.   

By the way, I just realized it was the second symphony that had the symbolic time.  Fortunately Bruckner offered to dedicate both the 2nd and the 3rd to Wagner, so the Wagner symbolism applies to both.   0:)

[jochanaan]

I am put off by the fact that the "explanation" requires accepting false or misleading statements, such as the claim that the double-bar is unusual...

Actually, that double bar IS unusual.  Most composers are very sparing with double bars, using them only at time or key changes or the end of major sections; certainly I cannot think of another case of a double bar at the mere end of the first phrase.  I make no judgment about nimrod's solution, but speaking as a performing musician, it's at least a possibility that Elgar meant the musicians at least to consider something in the first six bars...

[J.Z. Herrenberg]

You cannot imagine how crestfallen I am to find my thesis has a flaw.   

By the way, I just realized it was the second symphony that had the symbolic time.  Fortunately Bruckner offered to dedicate both the 2nd and the 3rd to Wagner, so the Wagner symbolism applies to both.

Yes, Bruckner brought both symphonies and Wagner - never one to eat humble Pi - chose the Third.


As for Nimrod's proffered solution - I simply don't know.

[Scarpia]

I my comments have given the impression of ridiculing the original poster, I apologize.  However I do not surrender the right to criticize the idea.  If I think about it, what irks me is not the assertions that I find unjustified, it is the fact that it ignores and depreciates what Elgar actually accomplished.    Let's look at Elgar's original remarks:

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.

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.

Where else do we get such tantilizing information from a composer about his own music?  There are two main points. 

1.  In the traditional "theme and variations" as practice by Bach, Mozart, Beethoven, Brahms, etc, the variations consist of elaboration of the structure of the theme.  The theme is played, it is varied with additional ornamentation, added counter-melodies, finally the melody itself may disappear or become dramatically transformed with only the harmonic progression and underlying structure of the theme remaining.  Elgar has told us here that he has done the opposite, he has freely varied the harmonic structure of the theme, and used the superficial aspects, the rising and falling thirds, the descending sevenths, the rhythmic motif of short-short-long-long long-long-short-short, as the unifying principal.  This is a novel way of constructing a "theme with variations" which points towards much music which was subsequently written.

2.  He has conceived his theme as the countermelody of a theme that he thought was familiar to his audience.  He wanted his audience to hear the underlying theme in their heads as a complement to what they actually heard.  He conceived the audience as actually being, in effect, a collaborative composer and performer of the music.  It would be as if Bach performed one of his choral preludes (think of Jesu, Joy of Man's Desiring, or the central Chorale from Wachet Auf) omitting the choral melody and inviting his audience to imagine the chorale in their heads.  I think this was a grand miscalculation on Elgar's part, because musical harmony is not nearly unambiguous enough for a person to infer a missing melodic line from a given counterpoint, no matter how brilliantly conceived.  But it is a wonderful idea, and would have been even more wonderful if he had later provided the theme (not to be played, but as a guide to the curious).

And this is to be depreciated in favor of Elgar expecting someone to sit there, "..21...22....23...24.  24 notes!  Eureka!  Those must be the 24 backbirds baked in the pie, I've heard tell of.  It's Pi, I tell you, Pi."  It is much more satifying to imagine Elgar writing those notes and imagining that the unheard counter-melody would be evoked in the minds of his audience.

And with that, my point is made, and I will offer no more criticism.

[Philoctetes]

[starrynight]

What about the enigmatic posts of Philoctetes in this thread?  Has anyone worked out THAT enigma yet?  Must be quite a puzzle...... 

[nimrod]

I my comments have given the impression of ridiculing the original poster, I apologize.  However I do not surrender the right to criticize the idea.  If I think about it, what irks me is not the assertions that I find unjustified, it is the fact that it ignores and depreciates what Elgar actually accomplished.    Let's look at Elgar's original remarks:

Where else do we get such tantilizing information from a composer about his own music?  There are two main points. 

1.  In the traditional "theme and variations" as practice by Bach, Mozart, Beethoven, Brahms, etc, the variations consist of elaboration of the structure of the theme.  The theme is played, it is varied with additional ornamentation, added counter-melodies, finally the melody itself may disappear or become dramatically transformed with only the harmonic progression and underlying structure of the theme remaining.  Elgar has told us here that he has done the opposite, he has freely varied the harmonic structure of the theme, and used the superficial aspects, the rising and falling thirds, the descending sevenths, the rhythmic motif of short-short-long-long long-long-short-short, as the unifying principal.  This is a novel way of constructing a "theme with variations" which points towards much music which was subsequently written.

2.  He has conceived his theme as the countermelody of a theme that he thought was familiar to his audience.  He wanted his audience to hear the underlying theme in their heads as a complement to what they actually heard.  He conceived the audience as actually being, in effect, a collaborative composer and performer of the music.  It would be as if Bach performed one of his choral preludes (think of Jesu, Joy of Man's Desiring, or the central Chorale from Wachet Auf) omitting the choral melody and inviting his audience to imagine the chorale in their heads.  I think this was a grand miscalculation on Elgar's part, because musical harmony is not nearly unambiguous enough for a person to infer a missing melodic line from a given counterpoint, no matter how brilliantly conceived.  But it is a wonderful idea, and would have been even more wonderful if he had later provided the theme (not to be played, but as a guide to the curious).

And this is to be depreciated in favor of Elgar expecting someone to sit there, "..21...22....23...24.  24 notes!  Eureka!  Those must be the 24 backbirds baked in the pie, I've heard tell of.  It's Pi, I tell you, Pi."  It is much more satifying to imagine Elgar writing those notes and imagining that the unheard counter-melody would be evoked in the minds of his audience.

And with that, my point is made, and I will offer no more criticism.

No apology is need.  I wanted knowledgeable people to consider and discuss what my research had found.  IMHO there is a large amount of evidence to indicate that Elgar did indeed create his melody as a puzzle incorporating three forms of Pi.  It could be coincidence but it is hard for me to look at the 3-1-4-2 first four notes, the 11 notes followed by 2 (drops of the seventh in the third and fourth bar), and the coincidence of there being 24 black notes before the double bar when Elgar tells us their is a "dark saying."   I agree that no one would count 24 black notes on first hearing but I did notice the 3-1-4-2 on first hearing when I considered that it was written about his CIRCLE of friends.  I thought, "could "CIRCLE be a clue?"  Then I vocalized the 3-1-4-2 and was shocked.  I believe Elgar believed someone in the audience would have that same thought process.  The other findings of Pi came much later for me as I was looking for some confirmation.  People challenged me about how would Pi relate to the "drop of the seventh" and they challenged me about what relevance does Pi have to a "dark saying?"  I looked for two years and talked to many people in the US and in UK and worked with their ideas and challenges.  When I read the 1929 notes written by Elgar near the end of his life, I found each of the three sentences contained something that could be a hint at Pi (as I described separately.)   

As far as the theme being a melodic counterpoint, that has been the established thinking for 111 years but Elgar said no to every melody that was ever presented to him over his lifetime.  And there were many melodies offered.  A theme can also be a concept or main idea of a work.  In that context it is easy to see how Elgar would write that the "theme was not played" and the enigma was "offstage."

I apologize to those I offended by not emphasizing that my statements were my belief and not widely known.  It is a new explanation of the enigma people obviously want to hold on to their old beliefs.  I wanted to share the new information with you and get your feedback.  I am disappointed that some readers have repeated claimed that my counting of 11 notes before the drop is false.  I am also disappointed that the minor point about the double bar after measure six has been misstated by several people even though the melody clearly extends through bar seven.

Additionally, Wiki would not publish my information when first suggested in 2007, unless and until it had been published in a peer reviewed Journal.  That is why I researched for 2-3 years before the information was published by Columbia University, "Current Musicology."  I do not agree with the criticism of Wikipedia that my post has created.

[(poco) Sforzando]

It is a new explanation of the enigma people obviously want to hold on to their old beliefs.

Not necessarily, but they want to feel confident that the new theory is adequately supported.

I am disappointed that some readers have repeated claimed that my counting of 11 notes before the drop is false.

11 if you count the top G, 10 if you do not.

I am also disappointed that the minor point about the double bar after measure six has been misstated by several people even though the melody clearly extends through bar seven.

I don't see that anyone has "misstated" anything about the double bar. The important musical point is that, after the first 6-bar phrase, a second 4-bar phrase starts at bar 7. If bar 6 sounds unresolved, that's because it's a subdominant harmony (or a II 7 if you want to count the first violin A as a chord tone), and the major tonic at 7 resolves that harmony. But the melody does not "clearly" extend through bar seven. Elgar has indicated in numerous ways that the material starting at 7 is a new period (change of mode from minor to major, new melodic motif, change in orchestral texture including the addition of wind instruments, change of phrasing from the detached style in 1-6 to a more legato style in 7-10, etc.)

I'm afraid at this point that the only "circle" we can all agree to is the one this thread is now going in a . . . .

[nimrod]

Two other examples of "Hiding in plain sight" are the recent Bin Ladin in the middle of a Pakistani city, and the older "Purloined Letter" short story by Edgar Allen Poe. 

[eyeresist]

Again, my point is that the Pi theory is interesting and entertaining to comtemplate and I am a bit mystified why the response from some quarters has been hostile, to a degree.

It is not like anything in the article wil change the Enigma Variations and how the music is percieved.  It is just an interesting diversion, imo.

The reason that some of us are reacting strongly is that we have learned that obsessive conspiratorial thinking is not to be trusted (as the "silent" Philoctetes has pointed out). The problem with the "people are entitled to their opinion" argument is that you end up giving credence to people for whom fact is irrelevant. Luckily we have not yet reached the stage of teaching the "turtles all the way down" theory of cosmology in schools, but it is a slippery slope which we should take reasonable precautions to stop from sliding down. Precautions such as insisting on verifiable fact and logical argument. Note that the various strong refutations of his premises and argument have simply been ignored by the theorist.

BTW, if you google ' +"four and twenty blackbirds" +pi ', you'll find this person has been pumping his theory all over the interwebs, so there are obviously some heavy ego issues involved.