Place Notation

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Place Notation is a way of describing a Method in a concise textual form. It is uncommon, although possible, to learn to ring a method using this notation, however it is often used to communicate a new method to another person or, nowadays, to a computer.

There are many conventions for place notation, however they all share some common principles. These are best explained using an example; below is the place notation for Beverley Surprise Minor:

x3x4x2x3.4x34.5

Believe it or not, this small string of text describes the method almost entirely and will allow us to write out the blue line.

You can expect to see three things in this notation:

  • An x means that each pair of bells swaps position;
  • One or more numbers means that the specified bells remain in the same position (i.e. make a place) whilst any remaining pairs swap;
  • A . (dot) is just used to separate numbers if they follow each other.

Lets work through the notation for Beverley; the first character is a cross, so from rounds we get the following transposition:

1 2 3 4 5 6
 x   x   x
2 1 4 3 6 5

The next character is 3 which means that the bell currently at position 3 stays in the same place and all other bells cross:

1 2 3 4 5 6
2 1 4 3 6 5
 x  |  x  |
1 2 4 6 3 5

Notice that the bell at the back (the 5th) didn't have any bell to swap with so it also made a place. This is standard practice to condense the notation, only the internal places are mentioned.

Continuing on, the next character is another cross:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
 x   x   x
2 1 6 4 5 3

... followed by a 4:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
2 1 6 4 5 3
|  x  |  x
2 6 1 4 3 5

This time it is the bell at the front that makes an implicit place because there were an odd number of bells below the place.

The next characters are x2x3:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
2 1 6 4 5 3
2 6 1 4 3 5
 x   x   x   <-- x: Each pair swaps
6 2 4 1 5 3
| |  x   x   <-- 2: 2 makes a place, 4 and 1 swap, 5 and 3 swap, 6 is forced to make a place too
6 2 1 4 3 5
 x   x   x   <-- x: Each pair swaps
2 6 4 1 5 3
 x  |  x  |  <-- 3: 3 makes a place, 2 and 2 swap, 1 and 5 swap, 3 is forced to make a place too
6 2 4 5 1 3

The next character is a dot which we can ignore; it simply splits the 3 and 4 to make sure we read them as separate transpositions. Therefore the next characters are 4x:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
2 1 6 4 5 3
2 6 1 4 3 5
6 2 4 1 5 3
6 2 1 4 3 5
2 6 4 1 5 3
6 2 4 5 1 3
|  x  |  x
6 4 2 5 3 1
 x   x   x
4 6 5 2 1 3

Next we have two internal places; 3 and 4:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
2 1 6 4 5 3
2 6 1 4 3 5
6 2 4 1 5 3
6 2 1 4 3 5
2 6 4 1 5 3
6 2 4 5 1 3
6 4 2 5 3 1
4 6 5 2 1 3
 x  | |  x
6 4 5 2 3 1

And finally, ignoring the dot, is a 5:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
2 1 6 4 5 3
2 6 1 4 3 5
6 2 4 1 5 3
6 2 1 4 3 5
2 6 4 1 5 3
6 2 4 5 1 3
6 4 2 5 3 1
4 6 5 2 1 3
6 4 5 2 3 1
 x   x  | |
4 6 2 5 3 1

We're now half way through one lead (notice the treble at the back), but the notation has run out! This is another space saving convention: because most methods are symmetrical only the first half is given. To work out the second half of the method we simply work backwards through the notation, starting at the second-to-last transposition. In Beverley this is 34x4.3x2x4x3x:

1 2 3 4 5 6
2 1 4 3 6 5
1 2 4 6 3 5
2 1 6 4 5 3
2 6 1 4 3 5
6 2 4 1 5 3
6 2 1 4 3 5
2 6 4 1 5 3
6 2 4 5 1 3
6 4 2 5 3 1
4 6 5 2 1 3
6 4 5 2 3 1
4 6 2 5 3 1
 x  | |  x   <-- 34
6 4 2 5 1 3
 x   x   x   <-- x
4 6 5 2 3 1
|  x  |  x   <-- 4
4 5 6 2 1 3
 x  |  x  |  <-- 3
5 4 6 1 2 3
 x   x   x   <-- x
4 5 1 6 3 2
| |  x   x   <-- 2
4 5 6 1 2 3
 x   x   x   <-- x
5 4 1 6 3 2
|  x  |  x   <-- 4
5 1 4 6 2 3
 x   x   x   <-- x
1 5 6 4 3 2
 x  |  x  |  <-- 3
5 1 6 3 4 2
 x   x   x   <-- x
1 5 3 6 2 4

This nearly completes the lead, however we also need to know the lead end place notation for the method to finish it and start the next lead. This is often given with the place notation, for example x3x4x2x3.4x34.5,12. Therefore performing one more transposition, 12, we get 156324 to start the next lead. To generate the entire line, simply repeat these steps four more times (in this example) and you should get back to rounds.

Additional Syntax

It is quite common to use a - (hyphen) character to represent a cross. This is the case for the MicroSIRIL libraries.

You may also see an & (ampersand) or + (plus) character at the front of the place notation; this denotes whether or not the method is symmetrical. If the notation starts with an ampersand, you will have to run through the notation backwards at the half way point; if it starts with a plus it is not symmetrical and the notation given will provide you with an entire lead.

Uses for Place Notation

It is possible to ring a method by place notation - you just apply the rules on this page to your bell and either cross or make a place as appropriate. Once mastered, it will allow you to learn a method in minutes!

More common uses for place notation are for communicating methods, and today this is often via computers. You will see place notation inside the Abel and Excalibur software packages, and also take a look at the URL's used in Visual Method Archive and methods.ringing.org: it should look familiar!


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