rhyme.
APPENDIX
Arnaut’s Algorithm
The line-ends of the first stanza (A, B, C, D, E and F) are chosen for the second and subsequent stanzas according to a ‘spiral’ algorithm illustrated in Figure 1. It can be seen that the position and relative order of the line ending alters in a complex manner from stanza to stanza.
Figure 1: The ‘spiral’ algorithm
Consider line-end A: it moves down one line for the second stanza and then down two lines for the third stanza, down one line again for the fourth stanza and so on. The algorithm can therefore be considered as the sequence of displacements from the starting position, namely, +1; +2; +1,–2; +3;–5. The last displacement returns the first line-end (A) from the last line of the last stanza to the starting position.
Defining the sequence of translations as
How do the other line-ends behave after six iterations? Well, consider the situation after the first iteration; line-end A now occupies the position previously occupied by line-end B. Now carry out six iterations, namely +2; +1;–2; +3;–5 and finally the first of the next cycle: +1. This sequence also sums to zero, meaning that the line-end returns to where it was. In general therefore we can say for all line ends in the first stanza corresponding to the position of line-end A after interation
which proves that the entire set of line-ends returns to the original position and order after a full cycle of six iterations, or in other words a seventh stanza would be identical (in respect of line-ends) to the first.
Acknowledgements
My thanks, as always, go to JO CROCKER for running my life with such efficiency, understanding and good humour while I have been engaged upon this book. My publisher SUE FREESTONE has shown her usual blend of patience, kindness, enthusiasm and accommodation, as have ANTHONY GOFF and LORRAINE HAMILTON, my literary and dramatic agents. Thanks to JO LAURIE for her game guinea-piggery in reading early sections on metre and trying out some of the exercises, and to my father for his baffling but beautiful sestina algorithm. Especial gratitude must go to IAN PATTERSON, poet, Fellow and Director of Studies in English at Queens’ College, Cambridge, for casting his learned and benevolent eye over the manuscript–all errors are mine, not his. I thank him also for allowing me to include his excellent centos and sestina. My thanks to his predecessors at Queens’, Professors A. C. SPEARING and IAN WRIGHT, and to PETER HOLLAND of Trinity Hall, who between them did their doomed best to make a scholar of me during my time there. Aside from my mother, the person who most awoke me to poetry was RORY STUART, a remarkable teacher who has now retired to Italy. I send him my eternal thanks. If every schoolchild had been lucky enough to have a teacher like him, the world would be a better and happier place.
The author and publisher acknowledge use of lines from the following works:
Simon Armitage, ‘Poem’,
Carolyn Beard Whitlow, ‘Rockin’ a Man Stone Blind’,
John Betjeman, ‘Death in Leamington’,
Elizabeth Bishop, ‘Sestina’,
Jorge Luis Borges, Haikus and Tanaka from
Anthony Brode, ‘Breakfast with Gerard Manley Hopkins’,
Anne Carson, ‘Eros The Bittersweet’, Dalkey Archive Press, 1998
G. K. Chesterton, ‘The Ballade of Suicide’,
Wendy Cope, ‘Valentine’,
–––‘Engineer’s Corner’,
Frances Cornford, ‘Fat Lady Seen From A Train’,
Cummings, E. E., ‘1 (a’, ‘r-p-o-p-h-e-s-s-a-g-r’,