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Tdent, you wrote: I think that unfortunately, using these sloppy, untestable methods of 'proof', one can 'prove' almost anything. Elgar could have written "Circle of friends" - but he didn't. There are dozens of nursery rhymes and poems which have 'dark' things in them: what is special about blackbirds? What has 'four and twenty' got to do with pi? Has pi really been a universal part of primary school education for the last century?? Every piece of music abounds in numerical values, and with enough mathematical ingenuity these values can be rearranged into almost any form a person wants. The "derivation" of 22/7 is simply numerological mystification. Why exactly should one multiply 11 by 2 and then divide by 7, rather than any other set of operations on these three numbers? The decimal expansion that goes on for ever begins 3.14159, but the rounding is 3.142: you can't have it both ways, at least considering a melody where you have to choose either '1' or '2'. --Tdent (talk) 21:34, 4 February 2008 (UTC)
Additional "proof" (of the Pi solution)was provided by Elgar in 1929 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 , 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.
In 1929, Elgar was 72 years old and in ill health. His wife Alice had died as had his best friend August Jaeger. No one had solved his enigma in 30 years and he steadfastly refused to give up the answer. In the 1929 notes, he provided three strong hints to confirm that Pi was the solution. The first sentence refers to two quavers and two crotchets. This is a hint at 22 of 22/7, the common fractional approximation of Pi. (Remember, the first four notes are scale degree 3-1-4-2, a common decimal approximation of Pi.) In the second sentence, he points out the drop of the seventh in bars 3 and 4. These two sevenths (2/7) are preceded by the first eleven notes of the piece and 11 x 2/7 = 22/7. The third sentence contains a reference to bar 7. This is a hint at /7 of 22/7.
Could this possibly be a coincidence in a piece of music written the year after the humorous Indiana Pi Bill of 1897? Elgar loved japes and that piece of legislation regarding Pi was one of the best. "Four and twenty blackbirds (dark) baked in a (Pi) was just a pun. An enigma is only a puzzle or a riddle, and this obviously was one of the best. (it took over 110 years to solve).