The most evident characteristic of these six results is their average being one-hundred. A remarkable round figure to derive by mere chance from a group of 120 that averages 103.6333etc. But the original group of 160 arrives at a modest 100.925. Which is a challenge to some mathematician (with too much spare time) to explain. Why does adding superfluous data increase the chance for the higher five out of six closely related calculations (3 x 100 & 2 x 101), selected from this group on unrelated grounds, to arrive with their average of 100.4 at point blank distance from the overall average?
This question answered, this same mathematician is very welcome to examine what is my real concern: none of these six calculation uses the complete Willow Song. The amount of relevant calculations is therefore further reduced to 6 x 4 x 4 = 96, with an average score of 100.333etc. Which is only .067 below the average of these five out of six calculations. But this difference, little as it is, is not quite the last word in precision:
The selected calculations are arranged in three pairs, of which two produce identical results, in spite of a small difference in terms. Mathematic logic learns the difference is therefore irrelevant, and this group of five out of six different calculations is at the same time a group of only three different calculations; producing two times 100 and one time 101. Results going far beyond anything I am prepared to believe Dame Fortune can accomplish on her own: unto ∞ figures behind the point this trio’s average equals that of the group of 96 it is in the end derived from. Dismissing chance as cause for such amazing precision, this procedure must be an essential part of the design of the partsongs. And the one out of six calculations to stay clear from any average, happens to produce 98;
the exact number of words in both Virtue and the full Song of Willow
A short glance at the data now reveals that the total of bars for TWS not incorporated in previous six calculations, equals the number of words not incorporated in these bars; RVW did set his music to 65 words. If this set of calculations is purposedly designed by or for RVW – and this chapter is about to present even more evidence to support this thesis – this sample of text expression should earn its creator a statue at the centre of Trafalgar Square (to express the reason for this honour, it should of course be placed inside that pillar already occupying the spot).
In fact RVW deleted some more than 33 words, but with the inserted prose this is such a natural thing to do, that nobody notices. And that’s a pity; by the time TWS has ended, this same inserted prose has turned 65 words into 74; bringing the song up to size with OMM (even raising the pronounced syllables to her level: for maximal precision depending on the pronounciation of ‘every’ in line six as ev’ry).
74 is also the score for Reduced Virtue as Herbert wrote it down: in line three RVW replaced the original ‘to night’ by ‘tonight’. With Herbert’s original written spelling of 95 syllables to equal OMM’s pronounced ones (with every replacing ev’ry), and Sweet Day’s pronounced syllables to surpass reduced TWS’s by a mere three, it only stands to reason to discover that Vertue’s original 99 words equal the unreduced Song of Willow as George Herbert knew it: the 1623 folio edition of Shakespeare’s works spells the word ‘nobody’ in line eleven as ‘no body’.
Apparently RVW copied a more recent edition of Othello. But thanks to George Herbert his composition is still linked to the 1623 folio. The prose inserted in the full Song of Willow consists of 21 words. This makes the original Song of Willow to cover 120 words in its sixteen lines. Bringing us back at the reduction that caused RVW’s 120 / 160 different calculations.
In case this introduction is not enough to assure RVW posthumously the next Nobel prize for mathematics, we will now proceed towards the benefit of this exercise. These calculations do of course not copy a text-with-a-purpose for nothing.
To recognize this benefit we must reconsider the way the six calculations are paired. In the first couple one calculation combines symmetry and unity in isolating SD from the others, the other just isolates SD, so their common feature is isolation. In both the other couples one calculation adds up to unity, and the other to symmetry. Allowing to regard one of these couples as superfluous. But which one to delete? no matter which couple is combined with the first one, in four calculations no alternative is used twice. And on top of this problem of choice comes the problem with balance. Though one calculation in the first couple combines symmetry and unity, the couple itself serves the single purpose of isolating SD. The other couples just combine symmetry and unity. While lacking a clear purpose.
Lacking any method to find out which couple is the superfluous one, it stands to reason to regard both their combinations with the first couple, as alternatives. To make sense of such an approach these alternatives should differ in some respect. This requires the redistribution of the final four calculations. A procedure also bringing their couples in line with the first one. All couples will now serve a single purpose; in following scheme the second couple produces unity, while the third one brings symmetry. And all problems are delt with effortlessly:
Sweet Day (bruto) = The Willow Song (story) + O Mistress Mine (netto)
verses (1 + 2) + 3 (short alternative) (long alternative)
– – – – – 35 + (13 + 2) = (33 – 18) + (27 + 8)
– – – – – 35 + 15 + 15 + 35 = 100
Sweet Day (netto size) = The Willow Song (story) + O Mistress Mine (bruto)
verses (1 + 2) + 3 (long alternative) (short alternative)
– – – – – 34 + (13 + 2) = (33 – 13) + (29 + 0)
– – – – – 34 + 15 + 20 + 29 = 98
Sweet Day (netto) + The Willow Song (refrain) + O Mistress Mine (netto)
verses (1 + 2) + 3 (short alternative) (short alternative)
– – – – – 34 + (13 x 2) + (33 – 20) + (27 + 0)
– – – – – 34 + 26 + 13 + 27 = 100
Sweet Day (netto) + The Willow Song (refrain) + O Mistress Mine (bruto)
verses (1 + 2) + 3 (long alternative) (long alternative)
– – – – – 34 + (13 – 2) + (33 – 15) + (29 + 8)
– – – – – 34 + 11 + 18 + 37 = 100
Overall result 398
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The second option produces an only slightly different total:
Sweet Day (bruto size) = The Willow Song (story) + O Mistress Mine (netto)
verses (1 + 2) + 3 (short alternative) (long alternative)
– – – – – 35 + (13 + 2) = (33 – 18) + (27 + 8)
– – – – – 35 + 15 + 15 + 35 = 100
Sweet Day (netto size) = The Willow Song (story) + O Mistress Mine (bruto)
verses (1 + 2) + 3 (long alternative) (short alternative)
– – – – – 34 + (13 + 2) = (33 – 13) + (29 + 0)
– – – – – 34 + 15 + 20 + 29 = 98
Sweet Day (bruto) + The Willow Song (refrain) + O Mistress Mine (bruto)
verses (1 + 2) + 3 (long alternative) (long alternative)
– – – – – 35 + (13 – 2) + (33 – 15) + (29 + 8)
– – – – – 35 + 11 + 18 + 37 = 101
Sweet Day (bruto) + The Willow Song (refrain) + O Mistress Mine (netto)
verses (1 + 2) + 3 (short alternative) (short alternative)
– – – – – 35 + (13 x 2) + (33 – 20) + (27 + 0)
– – – – – 35 + 26 + 13 + 27 = 101
Overall result 400
At this point the reduction of five different calculations to three, reveals why it is an essential part of the partsong’s design. The superfluous 100-101 pair is now divided over two alternative sets of four calculations. Therefore each set of four is at the same time a set of three. And it doesn’t matter which calculation from each set’s second couple will be deleted. The choise has no influence on the overall results, being respectively reduced to 298 and 299.
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SUMMARY
Mathematical logic has in the end derived from the Edwardian music for three Elizabethan Part Songs, both alternative intervals in time between the reigns of Elizabeth I (1533 – 1603), and Edward VII (1841 – 1910; succession 1901, coronation = formal installment 1902).
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