Appendix A. Place Notation

A.
Adjacent and Identity Changes
1.

Place notation is a compact way to describe a Change or a sequence of Changes when the Change(s) comprise Adjacent or Identity Changes.

2.

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.


3.

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’.


4.

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.


5.

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 T.


Further explanation: Note that, by convention, internal Places are never abbreviated, even when it would still be clear what the full Change is.
For example, the 7-bell Change 12347 could be abbreviated to 24, and 3rd's Place, as well as 1st's Place and 7th's Place, could all be inferred. However, by convention, this Change is only abbreviated to 234 -- internal Places are always specified.


6.

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 3.1.5.3.1.3.
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.


7.

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. These methods have Palindromic Symmetry (see Section 4.B.1).
As an alternative to notating the sequence in full, comma notation can be used as follows to save space:

Where two sequences of Changes are separated by a comma, this indicates that each of these sequences is to be interpreted as a palindrome and expanded as follows: When the last Change in the sequence is reached, the Changes are then repeated in the reverse order starting with the penultimate Change, if any.

Where there is only a single Change on either side of the comma, there is no penultimate change as described above, and therefore nothing to expand. The single Change is therefore incorporated without adjustment.

A method with a sequence of Changes of the form A, B, ~A, C can therefore be notated: AB,C


Example: Canterbury Little Bob Minor 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

Canterbury Little Bob Minor can therefore be notated: 34.16x14,12


Further explanation: In some Methods, the single Change is to the left of the comma, and the longer sequence is to the right.
For example, Grandsire Doubles can be notated: 3,1.5.1.5.1
This expands to: 3.1.5.1.5.1.5.1.5.1

If the sequences of Changes on both sides of the comma are greater than one Change in length, then both sides should be expanded.
For example, Carter Singles can be notated: 3.3.1,1.3.3.3
This expands to: 3.3.1.3.3.1.3.3.3.3.3.1


B.
Jump Changes
1.

Additional notation is required to describe Jump Changes, as follows.

2.

A pair of Places enclosed in round brackets indicates that the bell in the first of these Places jumps to the second of these Places in the next Row. The rest of the bells in the span of Places within the round brackets each move by one Place to accommodate the jump.


Examples: (14) indicates that the bell in 1st's Place jumps to 4th's Place in the next Row. The bells currently in 2nd's, 3rd's and 4th's Places each move down a Place in the next Row.
So, (14) would take Row 1234 to Row 2341.
Similarly, (41) would take Row 2143 to Row 3214.


Further explanation: The two Places enclosed in round brackets are at least two Places apart.


3.

A contiguous set of Places enclosed in square brackets indicates how the bells in these Places are transposed from one Row to the next.


Examples: [3412] indicates that the bells in the current Row are "read" in the order 3rd's Place, 4th's Place, 1st's Place, 2nd's Place in order to generate the next Row.
So, [3412] would take Row 2143 to Row 4321.
Similarly, [4321] would take Row 1324 to Row 4231.


Further explanation: The set of Places enclosed in square brackets comprises at least three Places, and these Places are contiguous -- i.e. they comprise a set of Places that form an adjacent set.


4.

Where the bracketed notations (round or square) don't account for all Places in a Change, standard place notation conventions apply. I.e. remaining pairs of bells cross, and there may be inferred external Place(s).


Examples: The Minor Change (24) specifies what happens to the bells in Places 2, 3 and 4. The remaining Places are therefore 1st's, 5th's and 6th's. Following standard place notation conventions, 1st's place is Made, and the bells in 5th's and 6th's Places cross.
So, Minor Change (24) would take Row 123456 to Row 134265.
Similarly, Caters Change [6543] would take Row 214365978 to Row 125634798.


Further explanation: If desired, the full Change may be specified in square brackets, even when external Places and/or crosses could be inferred. So, the Caters Change [6543] above could also be specified as [216543879]. However, this is considered less clear to the reader, and is discouraged in Section B.7 below.


5.

When needed, bracketed notation may be combined with each other and/or with standard place notation to define a Change.
Where more than one instance of bracketed and/or standard place notation are used to define a Change, there should be no overlap of Place ranges or individual Places. Furthermore, and following standard place notation convention, the various Place ranges and individual Places are ordered from lowest Place to highest Place.


Examples: (13)4(75) defines the Triples Change that takes Row 1234567 to Row 2314756. Note that there is no overlap of Places in the three sections of the notation.

(14)(53) should not be used since the range of Places in the second section (3-5) overlaps with the range of Places in the first section (1-4). This Change is more clearly described as [23514].

(24)[765]8 defines the Royal Change that takes Row 1234567890 to Row 1342765809. Again, there is no overlap of Place ranges or individual Places in the notation.

(24)8[765] and [765](24)8 are not correct notations because Place ranges and individual Places are not ordered from lowest Place to highest Place. This Change should be notated (24)[765]8.


6.

Dot notation is used to delineate separate Jump Changes in the same way as for standard place notation. Dots are only omitted before and after the cross Change.
Also, as with standard place notation, internal Places Made are always specified, even when these could be inferred.


Examples: (13)(64) defines a single Change, whereas (13).(64) defines two Changes.
(31)4[765] correctly defines a Triples Change. Convention is to include the 4 since it's an internal Place Made, even though it could be inferred.


7.

Where the same Change can be represented in more than one way, it is preferable for the simplest form to be used, as follows, in order to make the Change's operation most apparent to the reader:
(i) Use standard place notation for all crosses and Places Made where other bell(s) are not jumping over these bells;
(ii) Use round-bracketed notation in preference to square bracketed notation where possible; and
(iii) Separate square bracketed notation into the smallest sets of contiguous Places.


Examples: Use [432]7 rather than [432657];
Use (25) rather than [3452];
Use [432][765] rather than [432765];
Use (24)5[876] rather than [3425876].


8.

Adjacent and Identity Changes are self-inverse, meaning that the same Change applied twice in succession produces the starting Row. However this may not apply to Jump Changes. Therefore, when the comma notation described in Section A.7 above is used and Jump Changes are involved, not only are the Changes in ~A in reverse order, but any Jump Changes in A are inverted in ~A.


Example: Cambridge Treble Jump Minor has notation x3x(24)x2x(35)x4x5,2
Expanding the comma notation gives x3x(24)x2x(35)x4x5x4x(53)x2x(42)x3x2
Note that the Jump Changes are inverted in the second half of the Lead.


9.

The comma notation described in Section A.7 above should not be used if the last Change in the sequences on both sides of the comma are not self-inverse Changes. Such a Method would not have Palindromic Symmetry, and use of the comma notation would therefore be misleading. In this case, the sequence of Changes should be written in full, without the use of the comma notation.


Example: The Minimus Method with notation x14x(13)x14x12 appears to have the structure A, B, ~A, C, where A = x14x, B = (13) and C = 12.
However, (13) is not a self-inverse Change, and this Method is therefore not palindromic. The Method therefore should not be described using comma notation, and the full notation should be used.