Cylindrical Constructions Ringing Homepage      Email me

   By imaging the blue-lines of conventional methods as being wrapped round a cylinder, a new class of method can be created if a cut is made in the cylinder. cylinder
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:

    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 odd-numbered bells can continuously hunt out, and all the even-numbered 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 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':
    12345678
    21354762
    81537426
    18354721
    63857412
    68375146
    23871564
    28317652
    43816725
    34187623
    54816732
    45861372
    54816735
    etc