Appendix A. Place Notation
Place notation is a compact way to describe a Change or a sequence of Changes when the Change(s) comprise Adjacent or Identity Changes.
A Change is represented in place notation by listing the Places made, starting from the earliest Place to the latest Place. All remaining pairs of adjacent bells swap.
Example: With 6 bells, the Change between the Row 214365 and the Row 241356 is written ‘14’.
Further explanation: The bells in 1st's Place and 4th's Place in the example above remain in the same Places in both Rows. The pairs of bells in Places 2 & 3 and Places 5 & 6 swap.
Places are represented by the same single characters as are used for bells, as described in 3.B.1.
Example: With 12 bells, the Change between the Row 2143658709TE and the Row 123456780T9E is written ‘9T’.
In an even-Stage Change only, all adjacent pairs of bells may swap, such that no Places are made. This is called the cross Change, and it is denoted in place notation with either ‘x’, ‘X’ or ‘-’.
Example: With 8 bells, the Change between the Row 12463857 and the Row 21648375 is the cross Change.
When a place notation includes external Place(s) (i.e. 1st's Place and/or the
highest-numbered Place of the Change) and internal Place(s),
this may be abbreviated to just the internal Place(s) because the external Place(s)
can be inferred.
When an even-Stage place notation comprises the two external Places only, this may be abbreviated to either just 1st’s Place or just the highest-numbered Place of the Change because the other external Place can be inferred.
Examples: With 6 bells, the Change 14 can be abbreviated to 4.
With 7 bells, the Change 147 can be abbreviated to 4.
With 8 bells, the Change 1458 can be abbreviated to 45.
With 12 bells, the Change 1T can be abbreviated to 1 or to T.
When using place notation to describe a sequence of Changes, a dot is inserted between the place notation for each change. However the dot is omitted on either side of a cross Change.
Examples: On 5 bells, an example sequence of 6 Changes is 184.108.40.206.1.3.
On 6 bells, an example sequence of 12 changes, including use of the cross Change, is 36x36.14x12x36.14x14.36.
In abbreviated form, this latter sequence might be written 3-3.4-2-3.4-4.3.
Many Methods have a sequence of Changes that takes the form A, B, ~A, C, where A is a sequence of Changes,
~A is the same sequence of Changes as A but in reverse order, and B and C are individual Changes.
There are various ways in which this can be represented in abbreviated form to avoid writing out the full place notation.
Further explanation: Consider Canterbury Little Bob Minor, which has a full place notation of 34.16x14x16.34.12.
This sequence takes the form A, B, ~A, C where A = 34.16x so ~A = x16.34. B = 14. C = 12.
This might be written &34.16x14+12. The & indicates that the string following it, up to the + symbol, should be expanded into A, B, ~A, where B is the last change in the sequence (i.e. 14), and A is the sequence excluding the last change. The + symbol indicates that the C change (12) is added at the end.
Another form is 34.16x14,12. Here any sequence of place notations greater than one Change in length is assumed to expand in the same form as the & operater above. An individual change, as shown after the comma, is appended to the end of the expanded sequence in the same way as the + operater above.
Technical comment: See 8. below for an additional consideration on how ~A applies when Jump Changes are used.
Extended place notation is required to describe Jump Changes. There is not yet a standard form of extended place notation though several forms have been proposed.
Example: The Change from Row 2143658709 to Row 2134586790 can be represented as 12(675)8.
Further explanation: A bracketed section can be included within a place notation that contains the transposition of an adjacent set of places within a Row. Places outside the brackets follow the normal place notation rules.
When a Method has the structure A, B, ~A, C as described in 7. above, there is an additional consideration when Jump Changes are involved. Adjacent Changes are self-inverse, meaning that the same Change applied twice in succession brings you back to the initial Row. However this may not apply to Jump Changes. Therefore if a Method with Jump Changes has a structure including ~A, not only are the Changes in ~A in reverse order, but any Jump Changes in A are inverted in ~A. For example, if A includes the Change 12(675)8, then in ~A that Change will be 12(756)8.