The Grifter, the Poet & the Composer

____ The Grifter ____

The "Three Shell Game," close cousin of "Three Card Monte," ranks among history's oldest and simplest scams. Here I'm less interested in the sleight of hand aspects than the simple idea that there are only a limited number of ways for the grifter to rearrange the three shells. So let's fantasize a shell game run by Honest Grifter – no sleight of hand – every move is what it appears to be.

In such a game it would be possible, in principle, to locate the shell hiding the pea every time. If the original positions are labeled left to right (123) and the pea starts under #2, it doesn't take rocket science to see that there are only six final positions possible, (123), (132), (213), (231), (312), (321), and if you concentrate and follow where #2 goes (remember, there's no sleight of hand), you win.

But Honest Grifter has even fewer actions available to him in any single move than the six final positions would suggest. After all, he has only two hands, so he can only move two of the three shells at the same time. This means he has only three possible ways to rearrange the shells in any given move: (123)→(132); (123)→(321); (123)→(213). In cyclic notation this is: (1)(23); (2)(13); (3)(12) – reflecting whether the first, second, or third shell is left alone during the move. But wait. Honest can still win because the only change we made was to remove the possibility of a sleight of hand. Honest still has control because he can make as many moves (permutations) as he wants, and he can do this as fast as he is able, leaving you cross-eyed. And, in fact, even though he can only move two shells at once, he can still reach any of the six possible final positions even with this limitation. Here's one example:

____ The Poet ____

As any form becomes canonical,

it virtually invites

experiment, variation, violation, alteration.
(Anthony Hecht)

Apologies for repeating that quote from Anthony Hecht yet again. It's not just that I really want it to sink in as the only principle of evolution I know of in the arts, but this section is an example of at least one way that principle can work by shrinking a canonical form.

I've been writing about a family of permutations tentatively based on rearranging even-odd and left-right partitions of strings of elements (cards, pitches, words, whatever). In all of this I have tacitly assumed that the size of the string must be big enough to make it interesting, such as the "Hauptmann shuffle" which I am still pursuing. Examples have hovered around strings of 6 words (the sestina) or 7 notes (usual diatonic scale) or 8 computer processors. But something interesting actually does happen when you make these related permutations act on smaller and smaller strings: the patterns start to become indistinguishable from one another. Metaphorically, the geometry of the permutational moves "collapses" into just one or two elementary patterns.

Obviously, if you go all the way down to a one-element string (the only object in a "trivial geometry") you enter a sort of John Cage world. There are exactly no moves possible (other than identity), and once you don't make them, there isn't much else you can not-do.

A George Boole world with just two objects, on the other hand, has possibilities that will come in handy.  But my interest right now is in the Three World suggested by the shell game.

Fifteen years ago, Marie Ponsot (at age 77) won the Book Critics' Circle Award for her book of poetry, The Bird Catcher. Among the poems in that book was "Roundstone Cove"[1]

The wind rises. The sea snarls in the fog
far from the attentive beaches of childhood–
no picnic, no striped chairs, no sand, no sun.

Here even by day cliffs obstruct the sun;
moonlight miles out mocks this abyss of fog.
I walk big-bellied, lost in motherhood,

hunched in a shell of coat, a blindered hood.
Alone a long time, I remember sun–
poor magic effort to undo the fog.

Fog hoods me. But the hood of fog is sun.

– three verses of three lines each followed by a one-line envoi. Let a=fog, b=hood, c=sun. Then go to the end of each line before the envoi and note the familiar spiral pattern abc, cab, bca:

V1: fog – childhood – sun

V2: sun – fog – motherhood
V3: hood – sun – fog

this is capped by the inspired envoi that uses the form itself to turn the tables on the fog:

fog – hood – me[!] ... hood – fog – sun[2]

At this point, the sestina has de-generated into what Ponsot, and many other poets since she developed the form, call the tritina[3].  The characteristic sestina permutation (615243) has shrunk to the tritina permutation (312).

The forms create an almost bodily pleasure in a poet.

What you're doing is trying to discover.

They are not restrictive.

They pull things out of you.

They help you remember.

(Marie Ponsot)

____ Entr'acte ____

So let's review what we have so far by referring to the following diagram (see A Few Notes about Notations about cyclic notation vs Cauchy one-line notation, the latter of which relates to the red arrows).

In the yellow square at the upper left is the identity permutation. Like the Cagean one-element world, taken by itself the identity permutation just sits there. If this were the only permutation allowed, it would describe a valid but trivial system, useful perhaps for navel-gazing. I think of the identity as mathematics' glue – without it, no groups, no geometries, the world itself falls apart. Still, a tube of glue just sitting on a shelf is not very interesting. So we look further.

The three gray squares on the right side represent the three valid moves available to Honest Grifter in the shell game. They are related because each of them has a fixed point, i.e., each move leaves one shell untouched, while the other two shells are reversed. Notice that the shell game arrows (which represent the Cauchy notation) do not all share the same arrow pattern in two dimensions. The shell game path at the top, 3-2-1, like the identity, is a wave. But the arrow paths for the other two shell game permutations both form spirals 1-3-2 and 2-1-3.

If we now create a mirror image of all the shell game paths on the right, we not only get the identity which we noted above, we also get two new permutations. This will then account for all of the six possible permutations of three elements.[4] One of these is the tritina. The other we have not come across before. I will label this hypothetical poetic form "Itritina" for inverse-of-tritina.[5] As far as I know, no one has every written a poem using the Itritina as a form, however composers have made good use of it.

Notice that all three shell game permutations (as well as the identity) are their own inverse. And this is where the identity stops sitting around twiddling its thumbs and begins to come into play. "Inverse" essentially means that if you apply the permutation for two iterations you end up back where you started. E.g., as in the lower right (shell), 1-2-3 → 2-1-3 → 1-2-3. If we call the identity permutation I and any one of the shell permutations S, then S repeated twice has the same result as I, or: SS=I (S²=I).

The tritina and Itritina, on the other hand, are each other's inverse. If you stick to the tritina permutation T, as we saw in the tritina form, it takes three iterations to return: 1-2-3 → 3-1-2 → 2-3-1 → 1-2-3. So TTT=I (T³=I). But after arriving at 3-1-2 from 1-2-3 by a tritina permutation, you can immediately return to 1-2-3 by applying an Itritina (inverse tritina) permutation T*. Another way of looking at this is that the order of the permutations generated by iterating the sestina is the reverse of that for Itritina, and vice versa. So we also have TT*=T*T=I.

And this now gives us a hook for making an unlikely connection between a poetry form and a well known musical chord progression.

____ The Composer ____

First, another reminder that mathematics, being what it is, means that the real world "objects" it may or may not represent need not be noun-like entities, but may also be verb-like entities. We came across this first in this series of posts with the essay on parallel processing where the objects being shuffled were instructions. The example used there came from a paper by Harold S. Stone, "Parallel Processing with the Perfect Shuffle." In that paper, Stone summarizes the process in a nutshell:

          1) shuffle;
          2) multiply–add;
          3) transfer results back to input of shuffle network.

Let's adapt this iterative procedure as Stone stated it, with a musical chord as the initial input. (Those with some background in neo-Riemannian music theory will recognize the result and wonder what's gained here. A more complete comparison of the two procedures will have to wait for now.) The procedure will stop when an iteration returns the initial chord. Here we go.

• The shuffle, performed on the masks, will be the T* (Itritina) permutation described above: (123) in cyclic notation, (123)→(231) in Cauchy notation.
• The "multiply" operation will be to multiply all three elements of the shuffled mask by (2mod3)[6] 
• The "add" operation will be to add the new mask to the previous triad.

It's easier to "watch" this happening than it is to describe it. The initial input for this example will be a C-major triad in root position. I will use integer notation with parallel letter notation for root-position triads, e.g., 0,4,7 with the corresponding traditional notation CeG. The initial "mask" (or "sieve") will be the triple (0,0,2).

If we call the procedure described for this example X (which starts with chord 0,4,7 and mask (0,0,2)) we see that it returns the initial chord after 24 iterations of the same procedure X, or, X²⁴=I

In music notation, it looks like this:

. . . and it sounds like this:



Pretty boring, eh? So let's jazz it up just a bit by adding a simple repeating rhythm:

Starting to sound familiar? Still, what composer in his or her right mind would seriously try something like this at any length? Hmmm, let's try not using the whole cycle, but using, say, 19 chords (18 iterations). It's an unusual way of getting from C major to A major – it "works" but it's still pretty dull. So let's break it up with a couple of pauses. Then mess around with that too-perfect voice-leading. Then we might get something like this:

This is a piano reduction of bars 143–76 from the second movement (scherzo) of Beethoven's Ninth Symphony.

It's tempting to say that only a master grifter like Beethoven could have pulled off a trick like this – turning theory's lock-step march in a circle into an exciting race to the edge of a cliff.[7]

Now, with a tip-o-the-hat to Richard Cohn who first brought those 19 chords to the music theory community's attention in 1991[8] (more to come on Neo-Riemannian theory's potential, including turning its dead ends into back doors, in future posts), here is a performance of the 19 chords in context. It took me a while searching YouTube to find a couple of good performances that take all the scherzo  repeats marked in the score, which I consider essential, especially here. (More another time on the subject of repeats, a favorite topic of another friend of mine, Mark Doran.) Measures 142-76 of the Scherzo movement can be heard starting at approximately 18:53 and (the repeat) at 21:00 in this recording of the entire Beethoven Ninth Symphony performed by Mariss Jansons and the Symphonieorchester des Bayerischen Rundfunks. Go ahead and listen to the whole thing for the 250th time in your life. When did you ever regret hearing it again?

I'll be back shortly with a few more brief comments on these measures. The question is still open: even given that the analysis above is "true" (which it is), is that what Beethoven heard? – Or the more accessible: Is that what  I  hear?

_____________________

[1] Image with the Ponsot poem reproduced here was found on the web site of the Poetry Society of America:

"Launched in 1992 by the Poetry Society of America and the Metropolitan Transportation Authority, Poetry in Motion® is today one of the most popular public literary programs in American history. Poetry in Motion® places poetry in the transit systems of cities throughout the country, helping to create a national readership for both emerging and established poets."

[2] Maybe this is a little far fetched, but I read c'=me; then in the envoi we have abc'→bac, one of the grifter moves but not one of Honest Grifter's since it reintroduces a sleight of hand. In one brief line Ponsot has flipped fog and hood & discovered me as the sun. The poem (to me) presents a Russian doll effect: Sun(fog(coat(mother(child)))), a prison, but one whose walls are dissolved by the identification sun↔me.

[3] A quick web search will turn up numerous examples, both professional and amateur, showing that the form was quickly added to the poet's tool kit of forms. One nice example is "Tritina for Susannah" by David Yezzi.

[4] Since we only have three objects to permute here, an equivalent way of viewing the family of permutations of (123) in Cauchy 1-line

123   321

312   213

231   132

with up-down as simple rotations, and left-right as mirrors. 

[5] I was tempted to call this permutation "Son of Tritina" but, as you will see in the next couple paragraphs, this would set up a situation where the son is also the father of his mother – an intriguing  possibility I would rather leave to be sorted out by an expert such as one of my favorite mathematician-pianist-magicians,  Raymond Smullyan.

[6] Reminder: (0×2)mod3=0; (1×2)mod3=2; (2×2)mod3=4mod3=1.
[7] It's difficult to leave this passage so abruptly. We need to hear what comes next after the example ends up in the air – no matter how often we've heard this old war horse before. In mere words, what my ear hears next is: That A-major triad collapses into a single note, A#, and then on to a solitary B, a false summit. No. Better: that B leaves an open question. Is it a root? a third? a fifth? And, given what just went before, there is no way to figure out what it's "function" might turn out to be until the bassoons start up and we (O.K., _I_) "hear" [?? – what's the aural equivalent of hindsight?] the context-less B as the dominant for the real destination of the past 34 bars: E minor. Then begins a fugato which Beethoven (not given to fully trusting conductors who are not him) marks in the score "Ritmo di tre battute"which signals that  the previous four-square "Über-rhythm" is now a three-beat "Über-rhythm."  (This is the equivalent, in this case, of going from time signature 12/4 to 9/4 keeping the quarter note constant – an early and tamer version of metric modulation.) The effect, to my ears, is (due to a horizontal superposition of 3 in 4), a piling up of the head of the opening theme that resembles the effect of an actual stretto. This, especially when we reach the call-response of the timpani "solos" with the woodwinds' replies, propels the music even faster and prepares for the still far-off presto trio. At least, that's how I hear it.

[8] Richard Cohn: 1991, "Properties and Generability of Transpositionally Invariant Sets," Journal of Music Theory 35(1-2) and 1992, "Dramatization of Hypermetric Conflicts in the Scherzo of Beethoven's Ninth Symphony," 19-th Century Music 15(3).

Jeu de Cartes

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged.

 ––Poincaré

The idea that someone with a bit of natural dexterity and a lot of practice can trace any card's path as it travels through several riffle shuffles of a deck is amazing to most of us (and a good reason we amateurs should stay away from Blackjack tables and Poker games). The above video by Kevin Houston gives an excellent demonstration of how card tracking is possible using a "perfect shuffle" and then goes on to explain the math behind why this particular shuffle works as it does. In passing, musicians will recognize one of the techniques since it's based on modular arithmetic––the same elementary principle as the one at work behind the "octave equivalence" and "pitch class" concepts. But what we're interested in here is still mostly the "geometries of permutations."

Another interesting card shuffle is often associated with the mathematician Gaspard Monge (1746-1818), a colorful character active during and after the French Revolution and usually thought of as the inventor of descriptive geometry. What is often called the "Mongean shuffle" works like this. . . .

We'll select only six cards from the deck to make the principle clear, keeping in mind that, once understood, it can be applied to the entire deck of 52 cards. Let's say we have, arranged from top to bottom, the Ace, 2, 3, 4, 5, and 6 of clubs. Now, ignoring the mechanics of how this shuffle might be performed in practice by a dealer or magician (it's rather clumsy compared to the riffle illustrated in the video), we lay out a single Mongean shuffle of these six cards face up. Begin by laying down the top card, the Ace, then place the next card, a deuce, on the table to the left of the Ace, then the three to the right of the Ace, the four to the left of the deuce, the five to the right, and finally the six to the left. The result is the re-ordering 6, 4, 2, Ace, 3, 5:

Flipping this map diagonally and repeating the procedure, we can follow any card through six shuffles until it returns to its original position.

Why does this map look familiar? (As if you haven't guessed already.) But "looks familiar" isn't enough. Let's try applying a procedure that, once again, will be familiar to most musicians – or at least to those who have played/looked at Bach's Musical Offering.[1]

Here again is the basic Mongean shuffle:

Let's get the cards out of the way to follow the moves more easily. This gives us a sort of placeless map .... (sorry) ...

Start by flipping this map over horizontally, resulting in a retrograde map.

Then flip that result over vertically, resulting in an inversion of the retrograde.

Then lay the cards back on the table using the new map to see what this retrograde-inversion shuffle results in.

The retrograde-inversion of the Mongean shuffle produces precisely the same map we encountered in the sestina.

But we're not finished quite yet. Trying to visualize the Mongean shuffle as a transformed version of a spiral (the way we initially described the sestina) is a bit of a stretch. Still, following a curvy path, it almost makes sense to see how the spiral:

might be seen as a tangled/untangled version of Monge, which itself can be seen to resemble a snake twisting back on itself or the action of a wave rebounding from the side of a pool:

If we want to get away from continuous "curving actions" but still stay with some sort of helpful visualization that gives the same results, we might think of these two procedures as things to do with two three-pronged combs. Making one comb out of the left side and one out of the right, we reverse one of them, stretch them both a bit, and then interleave the result. Then the spiraling looks like this in the corresponding comb version:

Starting back at the consecutive numbers once more, this time dividing the positions into odd and even, we separate them again, turn one of them backward again, and then recombine by concatenation.  So the wave in its corresponding comb version looks like this:

*

Ideomorphically, of course, the two worlds can't be mixed––playing cards are not words and card shuffling is not poetry. And neither, again ideomorphically, is a snake or a spiral a card trick or a poem. And that's just the point, because we are searching for sub-surface isomorphic actions–beyond metaphor and analogy–that connect otherwise unrelatable worlds. In the isomorphic underworld, not only can a hair comb be a metaphorically useful object-symbol within a poem, it can also provide a translucent structural basis for the poem. In fact, the first of the two "comb moves" above is precisely the way the sestina was often described, rather than the spiral description I chose to begin with. The technique in medieval times was known as retrogradatio cruciata–"backward crossing."[2]

Next: Just what is multi-tasking parallel processing, anyway? ––––>

______________________

[1] I mention Bach in this passing reference rather than Schoenberg, whom many would prefer to focus on as the more obvious culprit. I did this to keep my background emphasis that all these tricks are ancient & didn't just spring into being starting in the early 20th century. It's relatively easy to identify the inventor of the steam engine, but not so easy to identify the inventor of the wheel. By the time JS Bach came on the scene, many of these tricks/transformations had already long been in use. For a fun time with the Bach canons in the Musical Offering, there are two interesting web sites – one in a math version and one in a non-math version.

[2] Treated as religious symbolism, this term might also suggest anything from dark word play to heresy to outright satanism. But I have never read any suggestion of this elsewhere, so this must remain my personal fantasy. (Still, an interesting potential plot twist for a novelist or playwright, though?)

A Proper Sestina

. . . how much time is lost in invention, internal arrangement, and combination! for which nobody thanks us, even supposing our work happily accomplished.

––Goethe, Conversations with Eckermann

The sestina is a poetic form that I, at least, don't hear much about these days. Its invention is commonly attributed to Arnaut Daniel (fl. c.1180-c.1210), a Provençal troubadour of the 12th century. It pre-dates the invention of the initial canonic form of the sonnet, attributed to Giacomo da Lentini (fl. c.1233-c.1248). In contrast to the sonnet which has had a relatively unbroken history, the sestina keeps dropping out of sight and being rediscovered (by poets, at least), a discontinuity that appeals to me and fits in nicely with what's yet to come in this thread.  But now we need an example.

Dante Alighieri was a big admirer of the poetry of Arnaut Daniel, famously paying tribute to him in Purgatorio XXVI.139-48. Dante also occasionally used the sestina form himself.  One of the better known of these sestinas is "Al poco giorno, ed al gran cerchio d'ombra" which, for those fluent enough in Italian to appreciate fully, can be found >here<.  Later, one of Dante Alighieri's great admirers, Dante Gabriel Rossetti (1828-1882), translated this sestina into English, adding his own title.[1] This translation is where I will jump back into my story–––

Rossetti, Madonna Pietra

Sestina of the Lady Pietra degli Scrovigni

To the dim light and the large circle of shade

I have clomb, and to the whitening of the hills,
There where we see no colour in the grass.
Nathless my longing loses not its green,
It has so taken root in the hard stone
Which talk and hears as though it were a lady.

Utterly frozen is this youthful lady,
Even as the snow that lies within the shade;
For she is no more moved than is the stone
By the sweet season which makes warm the hills
And alter them afresh from white to green,
Covering their sides again with flowers and grass.

When on her hair she sets a crown of grass
The thought has no more room for other lady;
Because she weaves the yellow with the green
So well that Love sits down there in the shade,––
Love who has shut me in among low hills
Faster than between walls of granite-stone.

She is more bright than is a precious stone;
The wound she gives may not be healed with grass;
I therefore have fled far o'er plains and hills
For refuge from so dangerous a lady;
But from her sunshine nothing can give shade,––
Not any hill, nor wall, nor summer-green.

A while ago, I saw her dressed in green,––
So fair, she might have wakened in a stone
This love which I do feel even for her shade;
And therefore, as one woos a graceful lady,
I wooed her in a field that was all grass
Girdled about with very lofty hills.

Yet shall the streams turn back and climb the hills
Before Love's flame in this damp wood and green
Burn, as it burns within a youthful lady,
For my sake, who would sleep away in stone
My life, or feed like beasts upon the grass,
Only to see her garments cast a shade.

How dark soe'er the hills throw out their shade,
Under her summer-green the beautiful lady
Covers it, like a stone covered in grass.

–––Dante Alighieri

         (Tr., Dante Gabriel Rossetti)

Taking up now where my previous sestina entry, "On the Advice," left off, let's try to do this mostly without reference to any spirals. Go to the first stanza in Dante's poem, note the order of the final word in each line, and assign a letter or number:

                                                shade    hills    grass    green    stone    lady

                                                   A         B          C           D           E           F

                                                   1          2           3          4            5           6

Now, using the same letters or numbers, do the same with the second stanza: 

                                                lady    shade    stone    hills    green    grass

                                                   F         A           E          B          D         C

                                                   6         1            5          2           4         3

Going through six complete stanzas in this way, stopping before the final three-line envoi[2], the linear "rhyme" scheme[3] for Dante's poem emerges whether you know the spiral trick or not. Using alphabetic notation for now:

ABCDEF  FAEBDC  CFDABE  ECBFAD  DEACFB  BDFECA

If you follow the pattern by connecting the dots (words) through six verses, you come up with a "map" that looks like this:

This is one possibly helpful way of representing "what happens" structurally in the background just barely below the surface, not only for the poet making a sestina, but also––in some way––for the poet's audience hearing or reading it.

We don't have to squint very hard to see that the paths between successive verses are not drawn at random.  There is a repeating pattern here whether or not the reader is aware of it in-time.  And this leads to the more usual descriptions of "how to" compose a sestina.

The repetition scheme above read, say, in this way:

ABCDEFF AEB    DCCFD ABEE       CB FA DD    EACFB        BDFEC           A

is how the reader/listener experiences the form in time.  (Spaces indicate one possible reading –– an "interpretation" which is outside the poet's control and further helps to mask the structure.)  It is doubtful, to me at least, that anyone, especially those unfamiliar with the sestina form, upon hearing a sestina for the first time, would "cognize" (entrap by the conscious) the form that produced this string of repeated words.  That there were repeated words, yes, of course; but not a/the compositional pattern.

But the question at this point is not the analytically easy factual question, "What is happening structurally in this or any sestina?" but: How does one "experience" the defining structure of a sestina?––the thing that makes it a sestina and not a sonnet or rap[4] or prose.  At the risk of drawing opprobrium from a sphere of poesy experts and amateurs, here is what I believe is happening (maybe even meant to happen in some sense) and not happening, experientially . . .

First of all, here's what doesn't happen in experiencing the poem.  Remember the initial, and surely the simplest, explanation for the spiral algorithm is to think first of a string of things in one dimension. Then to rearrange them by going into two dimensions and applying a spiral to select the things into a new order. And then carrying that newly ordered string back into one dimension.  That works fine for the carpenter building a sestina, the poet. But no way on earth does anyone experience a sestina by following the changing positions of the terminal words from one stanza to the next as a spiral. So what possibly does happen then?

Each of the six repeated words (A through F) carries some subjective (first-person) "weight" for the reader[5] that interacts with the poet's "narrative" beginning in the first stanza.  This may be at a conscious or subconscious level, but the main point is that the reader takes a word––like taking a card from a deck offered by a magician (NB!)––and is drawn in to follow it from verse to verse through the sestina's contrapuntal (NB!) maze.  The next time through, the reader might take a different word leading to a different path through the exact same surface narrative.  [Why am I reminded of Bach?!] And at any point in the middle of a reading, there is the possibility that attention might be drawn from the initially chosen word to a different one, subverting a consistent "correct" path; so instead of following, say, (D-D-D-D-D-D), the poem's structure and the reader's "attention status" might encourage a reading that reflects the path (D-D-D-D-E-E) or (D-D-F-D-C-D)––an uncountable number of ways to experience (interpret?? analyze???) the poem.

I realize that "uncountable" may seem like an overstatement, but remember that, if you wish to defeat this claim by actually calculating the number of possible paths as a fun exercise in combinatorics, you must include "attention flagging" moments––paths which leave a hole in the structural fabric. E.g. (still concentrating only on the word repetition scheme), we must include paths such as (A-B-B-x-A-C), (C-C-e-k-F-x), (p-q-E-q-E-E), and so on, where the lower case letters indicate undefinable variables ("stray thoughts") that happen to pop into the mind during a reading and that may or may not have anything to do with the poem but nevertheless do have something to do with the reader's experience.[6] One possible reading in this view––and maybe the most common and "human" one––might be, for example, (a-b-c-d-x-f) which might mostly follow the surface narrative but doesn't (can't or won't) follow the sestina's characteristic word repetition pattern at all.  (This is a version of what might be called the just-let-it-wash-over-you experience––an approach not to be scoffed at in approaching a new work.) Being quasi-engaged in something while remaining oblivious to how or why it works is not uncommon.

And now for a pop quiz.

You may not have noticed anything unusual about the fact that I chose, as an example to work from, an English translation of a sestina by Dante Alighieri rather than finding a sestina originally written in English.  Finding this Rossetti translation was a bit of serendipity, because it now allows me to ask you all a question that, if you answer it honestly to yourself, may prove a wee bit embarrassing... (It was embarrassing for me when I made the discovery.) –– Now that you know the sestina's defining form,  whether you think of it as spiral or linear, did you notice, when reading this poem, that the form was violated?  It wasn't Dante, but the translator Rossetti, who made a "mistake." The "mistake" occurs in verse 5 where Rossetti has reversed Dante's (proper sestina) terminal word order for lines 4 and 5.  We might try to "correct" the mistake by naively reversing lines 4 and 5 of the translation:

"Corrected" verse:

A while ago, I saw her dressed in green,––
So fair, she might have wakened in a stone
This love which I do feel even for her shade;
I wooed her in a field that was all grass
And therefore, as one woos a graceful lady,
Girdled about with very lofty hills.

This would technically fix the form, but now we have a real conundrum about what the verse says, or is supposed to say––how it scans between two poets––one poetizing directly in Italian and the other translating poetically into English.  Here is the original for comparison:

• Io l'ho veduta già vestita a verde
• Sì fatta, ch'ella avrebbe messo in pietra
• L'amor, ch'io porto pure alla sua ombra;
• Ond'io l'ho chiesta in un bel prato d'erba
• Innamorata, come anco fu donna,
• E chiusa intorno d'altissimi colli.

Even to attempt to discuss this form-content anomaly (I certainly hesitate to accuse Rossetti of making a mistake!), let alone resolve it, is well beyond my abilities in both poetry and translation. But that isn't the point here at any rate. My point is to demonstrate that if you disrupt the highly complex rhythm below the surface set up by a rigid structural scheme such as the spiral algorithm, it may or may not affect the content or message at the surface––that is, the experience.

This idea of sub-surface structure vs surface perception will return in a more violent form when I discuss music applications later. But for now I want to explore not mistakes and violations in the form, but surprising logical extensions.

Next: Jeu de Cartes –––>

(By the way, how did you do on the pop quiz?

Did you spot the mistake before I told you about it? 

And if so, did you discover it by hearing it

or analyzing your way into it?)

_______________________________
[1] This is not meant to be a full, or even fully accurate, tracing of a small piece of poetry's history, nor to give the sestina undue importance in that history. But in setting it up I did realize that it illustrates nicely how poets, possibly more than other artists, seem to talk with one another across centuries.
[2] I am purposely leaving out the envoi to make this demonstration more clear. I am aware that the envoi as a culmination or destination or turn may even be the point of a given sestina, so leaving it out of the discussion misses the full "poetry." However, I have noted that there are many variant "acceptable" patterns for the envoi that would better be discussed in light of the pattern found in those first six stanzas which are my focus here.  In other words: another time, maybe.
[3] More properly called a repetition scheme.
[4] . . . but rapping within the confines of the canonical sestina form would be an interesting challenge, wouldn't it.
[5] "Weight" is meant to convey more than "meaning" and refers not only to acceptable dictionary definitions, but to incorrect understandings, past associations, contexts, and even the subjectivized sound or "flavor" of the word.  Also, "read" may also be read as "hear" or "listen to."
[6] My contention (better: my guess), which I doubt I could ever adequately defend, is that a "perfect attention"-reading is either impossible or rarely achieved.  But as far as I know, either to demonstrate or disprove my contention would take defeating the first-person avowal problem––or worse, asking the reader to pay attention to what she is paying attention to, and then accurately report back.  (This is also not a good strategy for making love, but I digress (or perhaps it wouldn't be a digression––this particular sestina, after all, is about . . . . ) . . . . )

Sestina On the Advice of Anthony Hecht

Poet:

As any form becomes canonical,

it virtually invites

experiment, variation, violation, alteration.
(A.H.)

Logic is an arrow––to the point, singular, literal . . . no detours. 

Metaphor is a map, full of blind alleys, irrelevancies, absurdities, ambiguities, multiple meanings, choices . . . interesting things. It lets you begin your story where you please––middle, end, wherever, it doesn't matter.

Taking you to the edge and convincing you not to jump, logic keeps you safely within the world you are given.

Subverting reality, distracting you to a world that may never exist, metaphor takes you to the edge, tells you to fly, and pushes you off.

Logic is a necessary connection.

Metaphor is an imaginary bridge.

Premise and consequence: metaphor and logic are inseparable––together they create art and science.

Internal Critic:

OK, then.  You know quite well that a proper sestina consists of 6 verses of 6 lines each, followed by a closing 3-line envoi. "On the Advice of Anthony Hecht" either is a single 6-line verse followed by a 1-line envoi, or it is six 1-line verses followed by a 1-line envoi. Or is it just prose –– notes for a future poem perhaps? Another W.I.P.-mask you so like to hide behind to avoid completing anything. In any case, it fails as a sestina.

Furthermore, each verse of a proper sestina must contain six distinct words that are repeated from one verse to the next; also, these repeated words must appear as the terminal word of each line. "On the Advice" has only 2 repeated words, and these never appear at the end of a line/verse.

Here's a suggestion: Let's generously accept "On the Advice" as a bizarre 2-verse "binary sestina." If we label "logic"=0 and "metaphor"=1, then the 6-line stanza begins this obviously unfinished poem with the word repetition order 010101.  This might be the beginning of a more reasonable structure getting back to something more closely resembling the sestina form we have come to expect.  So we keep what you have as verse A and work out the word repetitions as the structural basis for five more verses B through F.  Then you will only have to compose out from this scheme:

A   010101

B   100110

C   011010

D   001101

E   100011

F   111000

Poet:

That's very helpful of you, but that's a lot more 0's and 1's than I had planned.  I'm not sure I have that much to say about logic and metaphor.


Internal Critic:

Well . . .

Poet:

And seriously––... didn't you catch the recap of all six key words in the envoi?

Internal Critic:

Well, no. I really didn't hear the six key words you think you "repeated" in the envoi.  But still I'd certainly have to pan any attempt to keep my attention through 36 lines with 18 logics and 18 metaphors, plus another three of each for a proper envoi.  But I have another suggestion for you.  Why not try actual, proper rhyming?  Leave the first stanza as it is, then in stanza B use, oh, I don't know, 0="pedagogic" and 1="petits-fours."  Then maybe verse C could use, let's see ... how about 0="trick" and 1="door."  And since we now have six distinct words in the pattern, why not go back and change verse A so it uses all six of these words––label them 1 through 6––one in each of verse A's six lines? Then we, I mean you, could riff on this pattern:

A   123456

B   615243

C   364125

D   532614

E   451362

F   246531

"New" and "different" are so overrated. You're brilliant. You can do this! Trust me.

Poet:

Uh-huh.

Internal Critic:

And it would be a nice touch––a tribute, if you will––if you could try iambic pentameter rather than the frankly quite ugly prose you seem to like. The public, after all, has come to expect the beauty of stacked iambs.  After all, they are the feet we've come to love.

Poet:

Uh-huh.

So you'll finally be happy if I write a poem using the exact formula concocted by a troubadour to win a poetry slam in some tavern in Provence 800 years ago?

Internal Critic:

Well . . .  But it will be your own voice, of course.  There's still plenty of good poetry to be written in ....

Poet:

. . .

Thanks for all this. Really. But I sort of like it just the way it is. Whatever it is.

Internal Critic:

OK. Your call. But one last thing–––.

It's not all that important, but . . .

       what were you trying to say about logic and metaphor?

So this is going . . . . . where? –––>