This note is an accompaniment to the proposed Central Council Decision (G), the Decision on Method extension. It explains the details of the Decision and illustrates its application with an example. The proposed Decision does not aim to change the status quo, it just brings together the 1953 Report on Extension and later amendments.

There is an obvious similarity between the methods that we call Plain Bob Minor and Plain Bob Major, or between Kent Treble Bob Royal and Maximus. For many other methods, it is less clear how to relate a method at one stage (number of bells) to a higher stage. Decision (G) formalises this relationship between methods on different stages and provides the definition of a Method Extension. This means that it provides us with rules to tell us whether two methods, let's call them X Major and Y Royal, are related closely enough to count as "the same method" or not. If they are then we say that our Royal method is an extension of the Major. We sometimes refer to X as the parent and Y as its extension.

Another Decision - (E) D.4 - states that two methods at different stages (numbers of bells) and of the same class (Surprise, Delight etc.) can only be given the same name if they are Extensions (as defined by Decision (G)).

The Decision also states that methods that are extensions, like Y and X above, then they must have the same name. Unfortunately, as we shall see later, Decision (G) allows some parent methods to have more than one extension, so there could be a Z Royal also contending to be the extension of X. In this case the Decision requires you to consider extension (or contraction) to further stages to see which "extension path" fits best.

The Decision is expressed as a "formula" or set of rules which you follow in order to produce an extension of a parent method by adding two more bells. For some parent methods, the formula will produce only one extension, for some it will produce more than one, while for many it will produce none at all. The Decision covers all plain and treble dodging methods, as well as some alliance and treble place methods.

For the rest of this note we will deal with treble dodging methods.

Adding two extra bells alters a method in three ways:

- There are two extra bells in each row and change.
- The treble's path extends adding 4 extra rows to each halflead.
- The plain course requires 2 more leads

The formula deals with the first two points as follows:

An additional pair of crossing bells is added to each change.

Leading and lying places are maintained, internal places may stay where they are or "expand" that is move two positions up from lead. So place notation 36 in a Minor parent could become 38 or 58 in the Major.

Four rows' worth of work from the parent is repeated somewhere in the halflead.

When you have built the place notation of the new method you must then work out its lead head. If it does not give the required number of leads in the plain course it is clearly no good. If the parent has "Plain Bob lead heads" then the Decision requires that the extension does too. This will eliminate more possibilities.

To apply the formula, we start by breaking up the parent method into sections:

36 | 123456 214365 124635 216453 | B | The work when the treble is in 1-2 up (sometimes called the 1-2 section) we refer to as the B section. For Cambridge Surprise Minor this consists of the changes - 36 - |

14 | C | ||

12 | 261435 624153 621435 264153 | D | The work when the treble is in 2-3 (in this case the change 14) we refer to as the C section and so on through D E F etc. till the half lead. |

The letter A is used in the Decision to refer to the work at the treble's lead.

The formula divides a method into work above and below the treble. Except in the case where the parent is a Double method, where there is a special requirement that its extension be Double also, the Decision states that you apply the extension formulae to the work above and below completely independently.

To produce extensions of work above the treble we proceed as follows-

First we break the place notation into sections B, C, D ... as described above, ignoring any places made below the treble. So for Cambridge Surprise Minor we get

B | C | D | E | F | |

Parent | - 36 - | 4 | - - - | 6 | - - - |

We extend the B and C sections by keeping the internal places the same giving

B | C | |

Extension | - 38 - | 4 |

The formula now allows us some choice about how to produce the remaining sections. We choose a point at which we want to "start the extension". At this point we repeat the work of the previous two sections, but with internal places expanded. If we were to choose to start the extension after C this would give

B | C | B2 | C2 | |

Extension | - 38 - | 4 | - 58 - | 6 |

We have used B2 to mean "B with internal places expanded by 2".

From this point on the extension must be made up of the remaining sections from the parent, all expanded. In the case of Cambridge Surprise Minor D E and F are trivial, so we get

B | C | B2 | C2 | D2 | E2 | F2 | |

Ext BC | - 38 - | 4 | - 58 - | 6 | - - - | 8 | - - - |

This is familiar as the backwork of Cambridge Surprise Major. It is referred as extension type BC for obvious reasons.

Note that the formula allows other extension start points, for example

B | C | D | E | D2 | E2 | F2 | |

Ext DE | - 38 - | 4 | - - - | 8 | - - - | 8 | - - - |

This is the extension used by York Surprise Major.

We follow a similar approach to produce extensions of work below the treble. Section B and C are of no interest and for Cambridge Surprise Minor D - G are

D | E | F | G | |

Parent | - 12 - | 3 | - 14 - | 5 |

There are two types of extension permitted below the treble

__Expanding__

This type of extension is similar to the process of extending above the treble. We pick an extension start, repeat the two preceding sections, this time expanding internal places, and copy the remaining sections from the parent expanding them as well.

D | E | D2 | E2 | F2 | G2 | |

Ext EDE | - 12 - | 3 | - 14 - | 5 | - 16 - | 7 |

This should be familiar!

There is a restriction imposed on Expanding Extensions. If seconds place is made in the parent, this must be retained in the extension. In practice this means that we must look through the place notation, and not start the extension until we have passed the last 12. This rather limits the choice for Kent Treble Bob.

__Static__

In this type of extension we choose an extension start, repeat the two sections prior to that point and then copy the remaining sections across from the parent. No internal places are expanded. Thus we might try

D | E | D | E | F | G | |

Ext SDE | - 12 - | 3 | - 12 - | 3 | - 14 - | 5 |

In fact this choice of start point is not allowed, as there is a restriction imposed on static extensions. Any place made immediately below the treble's path has to be preserved in the extension. In practice this means that we must look through the place notation of the parent and not start the extension till we have passed the last such place.

Examining Cambridge Minor shows that there is a place made immediately below the treble has in every section D, E, F and G - so that static extension is not a good thing to try for Cambridge! You will notice, though, that it is well suited to Kent Treble Bob. In fact the position for Cambridge is not this bad. If the parent has a place made immediately below the treble at the half-lead we are allowed to break from a strict static extension, and expand just this place to keep it immediately below the treble. This allows extensions like the following.

D | E | F | G | F | G | |

Ext SEF | - 12 - | 3 | - 14 - | 3 | - 14 - | 7 |

Cambridge Minor has 3 possible extensions above the treble

Ext BC | - 3 - | 4 | - 5 - | 6 | - - - | 8 | - - - |

Ext CD | - 3 - | 4 | - - - | 6 | - - - | 8 | - - - |

Ext DE | - 3 - | 4 | - - - | 8 | - - - | 8 | - - - |

There are 4 possible extensions below

Ext SEF | - 2 - | 3 | - 4 - | 3 | - 4 - | 7 | (Half-lead expanded) |

Ext SFG | - 2 - | 3 | - 4 - | 5 | - 4 - | 5 | |

Ext SFG | - 2 - | 3 | - 4 - | 5 | - 4 - | 7 | (Half-lead expanded) |

Ext EDE | - 2 - | 3 | - 4 - | 5 | - 6 - | 7 |

We can work out the lead ends produce by the 12 possible combinations. Only one turns out to be satisfactory; the only allowable extension is BC/EDE.

*Prepared by Peter Niblett on behalf of the Methods Committee.*

*The Ringing World*, June 16, 1989, page 563