|Symmetry||Ringing Homepage Email me|
|The different symmetries possible in change-ringing methods|
|I became interested in method-symmetries when looking at cyclic methods, which cannot have conventional symmetry. Martin Bright has written the definitive article on method-symmetry, which can be found on his homepage.|
As Martin's article explains, a method with an even length can have one of eleven possible symmetry types; however, only nine are possible for valid, true methods. The following is a list of the nine, with details and an example grid for each type.
This is by far the most common type of symmetry in methods.
The notation is palindromic (reads the same forwards or backwards) about the mid-point (the half-lead), with the exception of the leadhead change.
First used in 1752, it has become popular recently due to its use in cyclic methods. Methods with this symmetry have no distinct reverse.
After the half-lead, the notation from the first half is used from the beginning in the same order, but reversed.
This has also been used recently in cyclic methods. The grid is the same when rotated through 180 degrees.
Moving out both ways from either quarter-lead (here the 123678 and the 36), the notations are the reverses of each other.
A method with only this type of symmetry has never been rung. Methods must be twin-hunt with this symmetry.
Only horizontally symmetric notations are allowed. On eight bells, this means only x,18,1278,1458,123678 & 36 are allowed.
This is horizontal symmetry, with conventional (palindromic) symmetry as well. Again. methods must be twin-hunt with this symmetry.
Again, only horizontally symmetric notations are allowed.
This is conventional (palindromic) symmetry as well, with rotational symmetry about each quarter-lead.
The notation can be thought of as conventional symmetry with quarter-lead rotations.
This is only one valid method possible with this symmetry.
The method is symmetrically very pure.
There is no symmetry present in these methods.