Edward Elgar's Enigma- Solution and Confirmation

Correction - Dan the bulldog falls into the Wye, not the Severn, in the variations.   Wagner's Rhine will have to be shifted a bit further west, too.

Sorry this has to be brief, and CR Santa will certainly not be satisfied.   First- the falling seventh is one of the key characteristics of Elgar's melodic style, especially for grand and public themes.   This does at first, superficially, make it rather odd he should draw attention to it here in his later note.   But it is a leading feature of his theme, which is going to be varied intensively, and any analyst would do the same.   Other characteristics are the inversions,  which might be argued to be constructivist, and, equally, improvisatory devices, and the rising scale in the cello part which is its root, and doesn't obviously relate to pi - or 24.  But the scale does suggest how the improvisation which Lady Elgar describes may have come about.  Both g minor and B flat tend to encourage composers to use melodies or themes constructed in thirds.   As for the numeric significance, if pi is the solution to the enigma, then only the first bar of the first six matters.   Now that falls well within the area in which chance and coincidence must be taken into account.  Six bars of 4/4 might well generate 24-note themes in any case.  Which might suggest the double bar has another, purely musical, significance.  Double bars occur in several of the variations and the finale, and none of these seem to relate to non-musical issues.  In at least one variation, the varied section of Elgar's theme following the double bar is repeated, representing, it would seem, a tricyclist.  I'm not going to suggest an enigmatic pun in that.

Is there any independent evidence at all that Elgar even knew about the Indiana Pi Bill?   Do he or his friends mention it in correspondence or memoirs?   

My line of thought is as follows.   If the role of pi is as you think it to be, the concept behind the work, then how did it get there?  The first bar of the theme, where the decimal value seems, either by accident or design, to be present, is the one that most needs explanation.   Your scenario would be more likely, I suggest, if Elgar had, when sketching what he had improvised, spotted what was probably a coincidence, and decided to work on it.   Though it's possible, I would suggest it's unlikely that he set out - even in a spirit of fun - to see if he could compose a theme, let alone an extended work, based on the decimal formula for pi followed by the fractional formula.   If Lady Elgar's account is right, he had almost immediately begun to treat his initial improvisation as a basis for musical character sketches of his friends.   But given his well known interest in ciphers, and puns, it might very well have amused him to find, if in fact he did, that his theme had twenty four notes and had arisen from a cell in which pi might have turned up.    However, he's not known for many musical ciphers, though, to be fair, his interest in ciphers as such seems not to have been a consistent theme throughout his life.   And most of the instances of it seem not to have been numerical.   I don't know the pianola roll notes, but presumably they don't consist just of three sentences, and what you quote is equally explicable in terms of musical analysis.   I could go further. The structure of the theme itself, I suggest, is against you. For example, the 2:2 pattern is present in his opening phrase, which is followed by a free mirror retrograde.  The first of the falling sevenths is on the octave, and it's a natural consequence and culmination of the rising scale underlying the opening four phrases.  The second seventh, a mirror phrase too, is on the next downward degree of the scale, and another two mirror phrases complete the first part of the theme, six bars long and constructed of three pairs.  The nature of song, which Samuel Langford apparently claimed was the only musical theory he had ever learned, is to go up and down. The key harmonic event, the B natural in the bass, does lie immediately after the sixth rising degree of the scale, but it occurs only once.  To suggest that this piece of composing is the result of a deliberate attempt to encode a complex mathematical reference might be seen as pushing it a bit.  Before Elgar, the best known musical ciphers are from his hero, Schumann.  Like BACH, they are alphabetical, and employ a single code.  If you are right, Elgar used not one but two code conventions inside six bars.  I'm not sure about the propriety of changing the code so soon in the message, but I'm not a cryptologist, and it may be quite OK.  But Elgar is said to have been quite convinced that the work's secrets would be decoded as soon as the Variations had been performed, and this was long before  computers.  You would have to be a pretty good listener to crack a numerical cipher from a twenty-eight second single exposure, (at the beginning of a new and brilliant half-hour work) of which half was coded in scale degrees and the other in intervals and numerical series.  On the other hand, he did once expect Dorabella to crack an Ogham-based message which hasn't yet been decoded in any plausible way.  (Did he ever decode it for her?) Some jape.  Some composer.   But my instinct is still that the solution, whatever it is, is musical.    Now if Elgar showed a documented interest in pi about this time, that might change things a bit.   Did he?

Sorry - I should have thanked you for quoting the 1929 Aeolian note sentences in full.   But with the best will in the world, I can't see that they mean anything other than what they appear, at first reading, to say.   Elgar is simply deconstructing his theme so that readers can follow what he does with it in the composition, and in a very formal and academic prose, since he knows what pedagogues will make of it if he isn't impersonal.  One of the endearing things about Vaughan Williams is that when he writes notes, they gently send up the whole programme note industry, but Elgar, for all his love of japes, wouldn't have risked it in this sort of context.  Interestingly (the Dorabella variation just won't go away) the first published arrangement for piano, which I think is still in print, doesn't accent the first note of the groups of four in the woodwind parts at the beginning of Dorabella, and throughout, at all, (it's usually held for a fraction longer than the other three) and which can prove, in the orchestral score, a minefield for conductors.   I wonder what happened on the piano roll.

Scepticism severely dented by the curse of the Elgar jape.   The melodic note immediately following 3.142 is D!  And, though this really is stretching things beyond breaking point, the old English notation for 'penny'. Now I wonder.  What is the best way to cook a hat?  And do you really need 22 over 7?  I don't think yet that pi can be the primary solution, but it is certainly worth a lot more thought.