|Conventional change-ringing 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 jump-changes).|
In cylindrical methods, there are no jump-changes 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 plain-hunt, 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 next-but-one row:
Interestingly, in cylindrical plain hunt on an odd number of bells, all the odd-numbered bells can continuously hunt out, and all the even-numbered bells hunt in without any places ever being made:
A triples method can be psuedo-mapped 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 last-but-one row, again reducing the possibilities to 7, and so allowing constructions like 'Stedman Major':