Change ringing: extensions to place notation

I’ve experimented with method design at various times and place notation is a very useful tool, but it’s lacking in some situations. Here’s a few ideas for some bolt-ons.

A shortcut for rotational symmetry

Here’s the usual place notation for Bristol Surprise Major:

x58x14.58x58.36.14x14.58x14x18,18

The use of the comma , means we only have to write the first half of the full notation – it signifies palindromic symmetry.

However, Bristol also has double symmetry¹. This means we can half the amount of place notation needed, again, but there’s no standard way to express this. And that’s a shame.

Methods with both palindromic and double symmetry could be expressed very compactly by use of a new operator in the same vein as the comma. Here I describe a scheme for a new operator ; that does this.

Example: Bristol Surprise Major can be written using ; like this:

x58x14.58x58.36;18

This is exactly what is needed to generate Bristol Major, no more, no less.

You might notice that’s it’s just the first half of the traditional place notation for Bristol, and using ; instead of , – this is a pattern that applies to any well-formed² method with rotational symmetry.

Notation that uses ; cannot be edited in a way that makes it lose rotational symmetry. If you’re writing code to generate and experiment with rotational symmetry methods, that’s very handy.

Using ; also makes it much easier to compare similar double methods to see what is actually different about them.

For example, here’s DNCBM and Double Oxford side-by-side:

Double Norwich CBM   x14x36;18   
Double Oxford 8      x14x36;12   

You can very easily see it’s just the lead-end (and half-lead) which differs.

Examples of double methods using ‘;’ notation

Firstly, some simple things like plain hunt and Original (these are methods with rotational symmetry after all):

And some more traditional things:

How about the infamous Double Darrowby? Here’s the usual notation (with line breaks for sanity):

x36x34x36x56x36x34x36x56x36x34x36x14
x58x58x58x56x58x58x58x56x58x58x58x36
x14x14x14x34x14x14x14x34x14x14x14x58
x36x56x36x34x36x56x36x34x36x56x36x78,12

and the rotational symmetry version:

x36x34x36x56x36x34x36x56x36x34x36x14
x58x58x58x56x58x58x58x56x58x58x58x36;12

Working with notation that uses ‘;’

Expanding notation containing ; converts it into notation that contains the familiar , for palindromic symmetry.

Suppose you have some place notation of the form:

A;B

where A is a list of notates³ (e.g. 12x56.78) and B is a single notate (e.g. 12).

Here’s some Python pseudo-code for generating the corresponding , expression:

    palindrome_notation = A + A[:-1-s%2].doubled().reversed()
                            + B.doubled()
                            + ","
                            + B

where:

doubled() finds the double of notates (example: 12 -> 78 on stage 8)

reversed() is reversal of a list of notates

A[:-1-s%2] is removing the last item from the notate list A on even stages, and removing the last two items on odd stages

Rotation

It could be handy to specify rotation as part of place notation.

Example:

x16x16x16,12|1

That’s just the PN for plain bob minor with |1 added to the end, which means the PN is rotated to the right by one notate, resulting in this:

12x16x16x16x16x16x

This is anti-Bob Minor.⁴

And suppose we had |-2 at the end:

x16x16x16,12|-2

This rotates the fully-expanded PN two notates to the left, resulting in this:

x16x16x16x16x12x16

This variant of Bob Minor has the lead-end work two blows too early (which makes 3 the hunt bell).

Rotating a method’s place notation can change the music in the plain course, especially in more complex methods.

• Ringing