# Separation Anxiety

How far apart do they get? That's often considered a factor in estimating the difficulty of a particular pair in a method. It explains the experience that ringing the slow work is the most difficult aspect of Kent on the tenors. Following on from Tina's recent article about the features that make a method handbell-friendly, we can look at the handbell-friendliness of each pair in standard methods, as measured by average separation. What do I mean by average separation? The separation of a pair (e.g. 7-8) in a change is the number of bells between them: 0 if they are in adjacent positions, 1 if they are in 2nd and 4th place (say), and so on. Adding up the separation of the pair in every change in the plain course, and then dividing by the length of the course, gives the average separation. Here are the results for the standard eight Surprise Major methods.

### Average separation for each pair: Standard 8 Surprise Major

Method |
1-2 |
3-4 |
5-6 |
7-8 |

Cambridge | 2.00 | 2.11 | 2.27 | 1.63 |

Yorkshire | 2.00 | 2.09 | 2.68 | 1.23 |

Lincolnshire | 2.00 | 2.20 | 2.27 | 1.54 |

Rutland | 2.00 | 2.21 | 2.27 | 1.52 |

Pudsey | 2.00 | 2.05 | 2.57 | 1.38 |

Superlative | 2.00 | 1.89 | 2.75 | 1.36 |

London | 2.00 | 1.98 | 2.59 | 1.43 |

Bristol | 2.00 | 2.21 | 2.82 | 0.96 |

The first interesting thing about this table is that the average separation of 1-2 is always 2. The second interesting thing is that for each method, adding up the average separations of all the pairs always gives a total of 8 (apart from rounding inaccuracies). In the comments I explain why this is.

For each method, the tenors stay closest together, then 3-4, then 5-6. This supports the usual perception that the tenors are the easiest inside pair, followed by 3-4, and 5-6 are the most difficult.

The smallest number in the table is 0.96 for the tenors in Bristol, but I'm not going to claim that Bristol on the tenors is easier than Yorkshire. However, if we look at the right-place methods, the smallest average separation for the tenors is in Yorkshire, and this supports the common approach of regarding the tenors to Yorkshire as the best starting point for Surprise Major.

The fact that the total of the average separations, for a given method, is always 8, means that if a method has one pair that stays close together, there must be other pairs that are further apart. For example, the very low 0.96 for 7-8 in Bristol is balanced by the high 2.82 for 5-6.

It's interesting to have some quantitative data to feed into the discussion about handbell-friendliness.

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