symmetry

A gift for a king must be absolutely perfect. And if this is impossible to achieve, the least important detail has to be sacrificed first. In this case being the social conventions on dealing with royalty. Which will not come as a surprise for those familiar to an artist’s impatience with anyone standing between him and perfection. And in the process we find in Bach’s dealings with Frederic the Great a strange parallel of RVW’s dealings with Edward the Conqueror: a nice gift, but showing in the creative process a little more respect for the beneficiary would have done no harm.

A second parallel is in the method of concealing completely unexpected information in an equally unexpected way: both applying numbers of bars that in musical respect do not even exist.

This is not entirely true; to celebrate the discovery, the complete Bach score has been performed by the Amsterdam based Combattimento Consort. Reason why I was informed on this dating method in the first place. 

In the case of Bach this resulted in a seemingly paradoxal behaviour. Yet another parallel with the partsongs; behaving paradoxal in the regrouping sequence that betrays them to be antedated. With Bach the paradox vanishes the moment the non-existent bars are taken into account. And because of the problematic character of paradoxes this makes it worth a try to establish the same with the music by Ralph Vaughan Williams.

A great help in making sense of the host of possible ways to calculate the overall number of bars, is the consistently applied imitative style. RVW even undertakes in SD the effort to copy in his alternative calculations of bars the completely invisible textreduction; invisibility included. Therefore we can trust him to copy the more evident features of the text as well. Of which the most striking ones are symmetry and unity. An unity hiding below a surface that is its very reversal.

And lo and behold; one out of 120 different calculations is perfectly symmetrical. And its result is the very reversion of unity, which in numbers is symbolized as ‘one’. And in three figure code 001:

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

This is not the only calculation to place Sweet Day opposite the united couple of Willow and Mistress. And it is rather remarkable that one amongst them reverses most of the words between brackets:

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

The other calculations are for the moment insignificant, as they contribute nothing to our efforts to repair the paradox in the evidence for antidating. Yet this does not implicate irrelevancy, we will return to them later. Meanwhile this couple suggest themselves as RVW’s tool to make the sequence work. The result this recount of bars was to achieve in the first place:

Sweet Day                                              50 bars
– – – – – – – – – –
The Willow Song                                  15 bars
O Mistress Mine                                   35 bars

But alas: logic objects strongly against the use of the amount of bars for both the first and third step of the sequence. And what is worse: in the process of repairing the paradox in the original sequence, we have learned that Sweet Day’s two bars in a deviating measure are too important to the calculations to be ignored. Which is exactly what the sequence is doing when their common 3/4 beat unites the songs. All reason therefore to dismiss the final step as erroneous. The discontinuity in measure, however, does appear exactly on the spot where the third step’s gap is expected to appear. So discontinuity readily presents itself as disconnection, and the sequence can be re-arranged accordingly:

Sweet Day                                              50 bars
– – – – – – – – – –
The Willow Song                                 33 bars
– – – – – – – – – –
O Mistress Mine                                   29 bars

***

Sweet Day                                            E-minor
The Willow Song                                E-minor
– – – – – – – – – –
O Mistress Mine                           E flat-major

***

Sweet Day                                 3/4 + 4/4 beat
– – – – – – – – – –
The Willow Song                                3/4 beat
O Mistress Mine                                 3/4 beat

As a result ‘unity’ has been removed from the regrouping, and needs to be replaced. To which purpose we have got a promising lead; the symmetry in the calculation that sets Sweet Day apart from the other songs. It is impossible to create symmetry without achieving unity. The former is just a special type of the latter; just one of its many shapes. All reason therefore look at the calculation more closely, and the first thing to catch our attention is the paradox:

              (35        +      15)  –     ——-       15———-+—-       35—–      =      100

This symmetry adds up to the reversal of unity (001). And as it is a real challenge to compose purposedly music in a way that enables this equation to emerge, we have arrived back at the very first result of this analysis in Part One: this cycle contradicts itself in an extremely difficult way on the matter of unity. It seems RVW has written the same message simultaneously in different languages. And this enables us to figure out what the differences in copyrights for his songs are telling;  if symmetry equals unity, and unity equals one, then a symmetrical calculation to add up to one hundred informs us that the reversion of unity equals unity:

if                                       symmetry    =    unity
and                                   symmetry    =    ytinu
then                                           unity    =    ytinu

The paradox has dissolved; the reversion of unity now expresses symmetry in text. And even if this solution depends on just one calculation out of 120, this calculation has arrived at a high order of organisation by means of intelligent design. Which allows us to regard this as a purposed creation, rather than as the result of blind chance. Untill spontaneous evolution of increasingly high levels of order out of chaos will become the dominant theory for the origins of art, that is.

Untill that theory takes over, this calculation demonstrates that RVW has composed his ‘Three Elizabethan Part Songs’ as an unity, even if it doesn’t show very well. And without any musical links between songs, he must have done it by means of symmetry. Real existing symmetry of composition, not symmetry in one out of 119 non-existing ways to count bars.

As RVW’s music is expressing the text in every way one can think of, its symmetry is likely to express that of the text. A reproduction of that feature in numbers of lines, words, or syllables, however, hasn’t come forward during this investigation. Therefore all symmetry I was able to make out of the available data is in the text expression. But, though plausible, this symmetry is rather far-fetched, as it is produced by yet another reversion:

To recognize this one, we must keep in mind that SD is designed to be combined with TWS into a copy of any given triplet of OMM (Part One). By which means three stand alone texts are forged into unity. And within this unity OMM replaces the omitted final quatrain of TWS:

Let nobody blame him, his scorn I approve.
I call’d my love false love, but what said he then?
——-Sing, willow, willow, willow,
If I court moe women, you’ll couch with moe men.

This is an exact representation of OMM’s third layer (see Part Two), but seen from her point of view. Providing us with a sound argument to identify this poor soul as ‘True Love’s roaming mistress. Furthermore, this testifies of a close connection between TWS and the third layer of OMM, and of course this is not the first time that TWS gets connected to porn. For the innuendo of its inserted dialogue I refer to Part Two. An innuendo that is tale telling about the song’s real character, of which even SD lifts a tip of the veil:

The ‘dew’ shall weep thy fall tonight

Judged by the innuendo, it is apparently possible to weep in company, which in itself is enough to make the Willow song as ambiguous as the others, for there is no word on the poor soul to weep in solitude. An omission that robs this song of all its innocence:

The fresh streams ran by her, and murmur’d her moans

As if it is not enough for the poor soul to sigh and moan by world’s oldest phallus symbol (dating back to Genesis 3 ; 7), she causes her company to tune in: “The fresh streams ran by her”. And her moans are the very last sounds genuinly murmuring streams are able to reproduce. In combination with ‘Poor Soul’s identification as ‘Mistress” this results in TWS to answer the opening question of OMM:

She is at the sycamore, notice her sighing and moaning

O mistress mine! where are you roaming?
O! stay and hear; your true love’s coming,

This phrasing clearly shows the congeniality of songs, but the current order makes no sense at all. The sooner OMM is therefore relocated to the cycle’s centre position, the better. To the textual symmetry this may be devastating, but the music will take over: in both SD and TWS it will express the decent surface, and in the centre the ambiguous depths. And that is not the only symmetry music will achieve:

text                     Sweet Day           –          O mistress mine           –       The willow song
expression              high                   –                      low                          –                    high
music                       slow                  –                      fast                          –                    slow
– – – – – – (andantino tranquilo)                 (allegretto)                                      (lento)
key                        E minor               –               E-flat major                  –                 E minor

Interestingly, in this scheme the new centerpiece shows all the hallmarks of its deeper layers. Even the cycle’s key is for its durance turned to tasteless fun. And who hears the Holst Singers perform the cycle (in this very order) on their 1995 recording, will also notice that the centre piece has the higher sound.

Which is not evident from the score, because RVW lowers the top note by the piece. In a gradual descent over a minor third from g in SD, via f in OMM, to e in TWS. —————————— But having achieved all this, the Holst Singers ignore in OMM’s first line the musical accents and sticks to the meter of the surface text. And in order to enhance musical unity, they sing OMM rather slow for its tempo indication. ————————— Slow – Fast – Slow, meanwhile, is the standard lay out for a three-part piece of music known as ‘French Overture’. Which is perhaps not exactly the way to define this cycle of songs, but perfect as an eufemism for any dealings along the lines of these poems.

A major drawback of this construction is the impossibility to establish both musical and textual symmetry at the same time. The only thing I can make of it, is this: if in this cycle the reversal of unity equals unity, than a reversal of symmetry may very well stand for symmetry. After undoing the symmetry of text, it is the center of the cycle that by textexpression exposes the textual unity. At the same time the resulting musical symmetry establishes the musical unity that completes the regrouping sequence. And we don’t even need to reverse songs: symmetry demands planning in advance. Which automatically results in a common time of composition to al parts of the cycle, and establishing unity is now simply a matter of dating:

Sweet Day                             Edwardian music
The Willow Song                 Edwardian music
O Mistress Mine                  Edwardian music

Nobody would consider this music Victorian anyway. Not with its expression of ‘coming’ in its lowest meaning. And in this regrouping sequence the paradox has vanished, so there is no reason to distrust the result. But to relocate this music with absolute certainty to the early twentieth century, we have to continue this highly important mathematical exercise. Granting OMM a key of her own, RVW backs my opinion that OMM is a key in her own right. A further exploration of this topic goes beyond the limits of this article, but a key the song certainly is; only a few lines ago we have seen it turned to ‘tasteless fun’. All reason therefore to try its choice of positions.

Two of OMM’s totals have untill now be combined with the story of  TWS; the key that in turn deciphers OMM’s true love story, and both place SD opposite the other songs:

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)                =    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

Both the other totals of OMM go very well together with TWS’s refrain, especially when the remaining standard procedures of SD’s third verse are to be explored:

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 (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

In this choice of four calculations no alternative is used repeatedly. And half of them show a satisfying (reversal of) unity. Furthermore the third calculation’s lack of symmetry is well compensated by the result of the fourth one. Making this couple complementary in confirming unity. As it happens, these very same calculations will arrive at the very same results if SD’s remaining pair of alternatives is applied, instead of the ones shown above:

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

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

SUMMARY

The three musical scores imitate their texts in regrouping from independent pieces to both combinations of two against one. Calculations based on the numbers of bars in the partsongs imitate the reduction of these texts from sixteen to twelve lines. These calculations also reproduce the symmetry and unity of the songtexts. In the words of the songtexts these features reveal the necessity to make TWS and OMM to swap positions. This replaces the symmetry in text by symmetry in music. In symmetry of textexpression actually. The musical composition follows the regrouping from three stand alone songtexts to an unity at pitch. Which proves the antedating of a twentieth century composition to the 1890’s.

Sweet Day                                              50 bars
– – – – – – – – – –
The Willow Song                                 33 bars
– – – – – – – – – –
O Mistress Mine                                   29 bars

***

Sweet Day                                            E-minor
The Willow Song                                E-minor
– – – – – – – – – –
O Mistress Mine                           E flat-major

***

Sweet Day                                 3/4 + 4/4 beat
– – – – – – – – – –
The Willow Song                                3/4 beat
O Mistress Mine                                 3/4 beat

***

Sweet Day                             Edwardian music
The Willow Song                 Edwardian music
O Mistress Mine                  Edwardian music

go to next chapter – – – – – – – – – – – – – – – – – – – – – back to the previous chapter