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. |