Conventional changeringing is based around three fundamental axioms:
There are a succession of rows, which are permutations of the number of bells (in every row, each bell must appear once and only once).
The first row and last row are rounds, and no row must be repeated.
No bell may move more than one position between successive rows (no jumpchanges).
In cylindrical methods, there are no jumpchanges or repeated rows, but the definiton of a row as a permutation of the number of bells does not still apply. A row may contain one (and only one) bell twice, and one (and only one) bell not at all. This is easiest to see in cylindrical plainhunt, where bells 'lead' in thirds place, lie in seconds place, and consequently disappear off the back of a row and reappear at the front of the nextbutone row:
123456
213542
615324
165231
462513
642156
341265
431624
536142
356413
254631
524365
123456
Interestingly, in cylindrical plain hunt on an odd number of bells, all the oddnumbered bells can continuously hunt out, and all the evennumbered bells hunt in without any places ever being made:
12345
21432
54123
45214
32541
23452
14325
41234
52143
25412
34521
43254
12345
A triples method can be psuedomapped to a major method using the cylindrical construction. If the same bell rings in the first and last place of a given row, there is one constraint and so the number of places available for the remaining notation is reduced from 8 to 7. In alterate rows, the first bell of the row is constained to be the last bell of the lastbutone row, again reducing the possibilities to 7, and so allowing constructions like 'Stedman Major':
12345678
21354762
81537426
18354721
63857412
68375146
23871564
28317652
43816725
34187623
54816732
45861372
54816735
etc
