A sestina is a 39 line poem. It is structured as 6
sextet stanzas terminated by a tercet called the envoi or the tornada.
However there is more to the structure. The ending words (teleutons)
in each of the six lines of the first sextet are repeated
in the remaining 5 sextet stanzas, but are shuffled in
order. Furthermore, this shuffling follows the rules of
a mathematical structure called a "group". 1
In addition, as the group is cyclic Z6 (Abelian), it
has subgroups of the following sizes:
size 1 (the identity)
size 6 (Z6)
size 3 (Z3), and its corresponding coset
size 2 (Z2), and its two corresponding cosets
The subgroup Z3 is half of the group Z6.
As the group Z6 corresponds to each sextet stanza,
the Z3 subgroup corresponds to 6/3 or a couplet "envoi",
but using the Z2 subgroup, there will be a 6/2 = 3 line
envoi, and each envoi line will contain two of the terminal sextet
keywords. A example will make this clear (however a different
theory is used for the envoi).
The terminal keywords wil be labeled "A",
"B", "C",
"D", "E",
"F",
and they will be shuffled in a spiral form.
Click images or captions to view pages
Spiral order of terminal words in Sestina sextet
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Cyclic group Z6 associated with the sestina
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There are different theories as to how to structure the envoi. Why?
The reason is obvious: most poets are not Group Theory Mathematicians.
Use whatever theory that appeals. For example, use Z6/Z2
= 6/2 = 3. Instead of a 3-line envoi, each line containing two terminal words;
use a 2-line envoi each line containing 3 terminal words to get a modified
38-line Sestina.
Sestina by Caroline M. Davies
Writing a Sestina
is like the first time you tackle climbing a wall.
My god, you think, how on earth can I get up that
towering edifice that seems impossible to climb.
stuck at the bottom you shake and sweat
and hope that someone will haul you up.
Instead they call you a wimp.
So you start to climb, the cry 'wimp'
ringing in your ears, as along the wall
you make your way, inching up.
Searching for the next foothold you fear that
this is impossible. Tour sweat
runs into your eyes making it hard to climb.
And yet you must go on with the climb
or be forever classed a wimp
And terror is a small price to pay and sweat
for conquering the imposing wall.
Once you're half way you know that
there is only one way to go and that's up.
And you want to be the first up
You're not the only one making this climb.
After a while you decide that
this is a piece of cake. A wimp
could easily surmount this wall.
You can do it. No sweat.
Then you slip. Flailing, you sweat
until you mange to scramble up
to the next foothold on the wall.
Wishing you hadn't started this climb
but had watched the others like a wimp
Did they realy call you that?
They did all say that
But it just took blood, tears and sweat
and refusing the chance to wimp
out. And the only way to go was up
and you enjoyed the climb
you think, at the top of the wall.
You find that perfect moment, standing up
Your sweat cools, the climb over
You're not a wimp. You've beaten the wall.
Troubadour Arnaut Daniel invented the sestina form during the 12th century.
Much music has a mathematical structure (for examples, paindromes in movements
"ABA", or palindromic "ABAB"; palindromes in instrumentation (strings "S" and
wind instruments "W", thus SWS, SWWS, etc.), palindromic melody, and palindromic
harmony, etc. Arnaut Daniel and other troubadours and troubaritz may have borrowed
the mathemaical musical structure, with accompanying poetry in a Sestina group
form. Dante Alighieri and Petrarch both admired and used the Sestina form.
There are several variants of the Sestina form. One variant is the
Double Sestina. The Double Sestina is composed of:
six stanzas of six lines
six stanzas of six lines
one tercet envoy
75 lines
"Ye wasteful woods", an embeded sestina, Edmund Spenser, lines 151-189
Click to see.
"Ye Goatherd Gods", a rhyming double sestina, Philip Sidney
Click to see.
"Theodora", sestina, Handel
"Lagrime d'Amante al Sepolco dell'Amata", sestina, Monteverdi
A poetic form similar to the Sestina is the Pentina.
The Pentina is five stanzas of five lines followed by an envoy.
Each line in each five line stanza is terminated by a teleuton word.
Spiral order of terminal words in Pentina quintet
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Cyclic group Z5 associated with the pentina
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1
The theory of Groups and Galois Field was founded by
Évariste Galois. This theory was founded during
the early 19th century, later than the interest shown
in Sestinas by Dante and Petrarch.
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