Appendix A. Place Notation
Place Notation
2.
Place Notation can be used to describe:
- Conditional Changes
A.
Adjacent and 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.
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.
Example: 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.
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.
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 to save space, as follows:
- Where two sequences of Changes (represented by place notation) 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
2.
The notation required to describe a Jump Change, is as follows.
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.
Example: (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.
A contiguous set of Places enclosed in square brackets indicates how the bells in these Places are transposed from one Row to the next.
Example: [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.
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).
Example: 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.
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.
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.
Example: (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].
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.
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:
- Use standard place notation for all crosses and Places Made where other bell(s) are not jumping over these bells;
- Use round-bracketed notation in preference to square bracketed notation where possible; and
- Separate square bracketed notation into the smallest sets of contiguous Places.
Example: Use [432]7 rather than [432657];
Use (25) rather than [3452];
Use [432][765] rather than [432765];
Use (24)5[876] rather than [3425876].
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.
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.
C.
Conditional Changes
1.
Conditional Notation
A compact symbolic notation for a Change or a sequence of Changes that is applied only if a specified condition is met.
2.
Conditional notation is used to describe Dynamic Methods, and can also be used to represent some Static Methods or rule-based Compositions more concisely.
Conditional notation takes the form of a sequence of alternative clauses:
placenotation{condition}placenotation{condition}…Each clause consists of a Change or sequence of Changes as described in Section A and/or B above, followed by a condition enclosed in braces {}. The alternative clauses are applied in sequence. When an alternative is reached, its place notation is applied, generating one or more new Rows, and the final Row is then tested against its condition:
- If the condition is satisfied, the generated Rows are retained and the sequence restarts from the beginning of the first clause;
- If the condition is not satisfied, the Rows are discarded and the next alternative in the sequence is applied in the same way.
Example: Dixon's Minor:
-{h}12{1}14{2,4}16This means: cross (
-) at every handstroke (h); whenever the treble leads ({1}), make 12; whenever either the 2 or the 4 is leading ({2,4}), make 14; otherwise make 16. The sequence restarts from the first alternative after each Change that satisfies its condition.
4.
A condition consists of one or more masks that are tested against the final Row after the place notation is applied. A mask is a string of characters representing bells and wildcards, written in the order of the Places they occupy.
-
Each bell character in the mask requires that exact bell to be in that Place in the Row. The wildcard
x(lower-case) matches any bell in that Place.
Example:{1}is satisfied if the treble is leading;{xxxxx1}is satisfied if the treble is in 6th's Place (trailing).
-
More than one mask separated by commas can be included to represent an OR condition: the condition is satisfied if any one of the masks matches the Row.
- Trailing wildcards at the end of a mask may be omitted for brevity. For example,
{1}is equivalent to{1xxxxx}in a six-bell context and means "the treble is in first Place." The omitted trailing positions are assumed to match anything. -
A mask may be followed by
horbto require that the Row is at a handstroke or backstroke respectively. If no mask characters are given before the stroke indicator, the condition is satisfied at every matching stroke.
Example:{h}is satisfied at every handstroke;{b}is satisfied at every backstroke;{x1h}is satisfied when the treble is in 2nd's Place at a handstroke.
The alternative clauses are processed in the order written. When a later alternative would never be reached because an earlier one always satisfies its condition first, the later alternative is redundant. Conventionally, the most specific conditions should appear earliest in the sequence, with the least specific (or default) alternative last.
Each alternative's place notation may specify either a single Change or a dot-separated sequence of Changes, using the conventions described in Sections A or B.
Example: In Dixon's Minor
-{h}12{1}14{2,4}16, the alternatives are ordered most-specific to least-specific: the handstroke cross first; then 12 when the treble leads; then 14 when 2 or 4 lead; and finally 16 as the default. A different ordering would produce an incorrect Method because a more general alternative might match before a more specific one.Conditional Notation is designed primarily to define Dynamic Methods, where the choice of Change depends on the position of Bells in a preceding Row. However, the same mechanism can also express some Static Methods or rule-based Compositions more concisely when Blocks of Changes are repeated.
Example:
- Plain Bob Sixteen can be expressed as
-{h}12{1}1D.Cross at every handstroke; Place Notation 12 when the treble leads; at all other rows, use Place Notation 1D. - The wrong-home-wrong calling for a 720 of Plain Bob Minor can be expressed as
-{h}1234{12xx56}14{1xxx6,1x5xx6}12{1}16.
7.
The condition mechanism is intended to be implementation-neutral. A computer-based ringing simulator implementing Conditional Notation should discard generated Rows when a condition fails and proceed to test the next alternative. In human-readable terms, the notation describes the rule by which the conductor or ringer would determine which Change(s) to ring by anticipating the final Row generated. In practice, Dynamic Methods need to be sufficiently simple and explained clearly to ringers — usually as a textual description — to make it easy to follow the logic represented by the Conditional Notation.
8.
It should be noted that the same Dynamic Method can be expressed in multiple ways using Conditional Notation, so it cannot be used as a test of uniqueness.
9.
The following table lists the Condition Place Notation for some Dynamic Methods that have been rung:
| Dynamic Method | Conditional Notation | Description |
|---|---|---|
| Dixon's Minor | -{h}12{1}14{2,4}16 | Plain Bob Minor with 14 being rung instead of 16 whenever 2 or 4 are leading. |
| Reverse Dixon's Minor | -{h}56{xxxxx1}36{xxxxx5,xxxxx6}16 | Reverse Bob Minor with 36 rung instead of 16 whenever 5 or 6 lie behind. |
| Oxford Badger Minor | -{h}12{1}1456{2xxxxx1,3xxxxx1}14{2,3}16 | Plain Bob Minor with 14 replacing 16 whenever 2 or 3 are leading, unless the treble is in 56 in which case 1456 replaces 16. |
| Monster Major | -{h}12{1}16{2,3,4}18 | Plain Bob Major with 16 rung instead of 18 whenever 2, 3 or 4 are leading. |
| Dixon's Doubles | 5{h}125{1}145{2,4}1 | Plain Bob Doubles with 145 rung instead of 1 whenever 2 or 4 are leading. |
10.
The following Dynamic Methods have been described in theory but have not yet been rung or formally named:
| Dynamic Method | Conditional Notation | Description |
|---|---|---|
| Dixon's Grandsire Minor | 36{x1h}-{h}14{2,4}16 | Grandsire with 14 rung instead of 16 whenever 2 or 4 are leading. |
| Dixon's Grandsire Doubles | 3{x1h}5{h}145{2,4}1 | Grandsire with 145 rung instead of 1 whenever 2 or 4 are leading. |
| Ander's Monster Major | -{h}12{1}14{2,4,6}16{7}18 | 12 made when 1 leads; 14 made when 2, 4 or 6 lead; 16 made when 7 leads. The plain course is 5580 changes. |
| Pseudo-double Dixon's Minor | -{h}36{xxxxx3-,xxxxx5-}56{xxxxx1-}14{2+,4+}12{1+}16 | Reverse Dixon's when negative; Dixon's when positive. Condition selects between the two patterns on the same Row-parity basis that distinguishes Reverse Dixon's from Dixon's. |
| Treble Bob Dixonoid Minor | -12-{xx1h,xxx1h}-34-{h}36{1xxxx6,x1xxx6,xx1xx6}14{5xx1,5xxx1,5xxxx1,6xx1,6xxx1,6xxxx1}16 | Treble treble-bob hunts. Places in 34 unless the treble is in 34 (then places in 12). If the treble is in 456, places in 14 when 5 or 6 is leading. If the treble is in 123, places in 36 when 6 is behind. Otherwise places in 16. |