[r-t] Cyclic methods

[Andrew Johnson]

Also try this:

7.3.7.3.7.1.5.1.5.1

The idea is that plain hunt for n rows on n bells reverses those bells. 
Reversing the first x and last n-x of n bells gives a reverse rotation of 
rounds.
Reversing and rotating a reverse rotation gives a rotation of rounds.

5 rows of plain hunt on the back 5 bells reverses 34567 while 1&2 dodge 
and end up reversed, giving
2176543
5 rows of plain hunt on the front 5 bells reverses 21765 while 4&3 dodge 
and end up reversed, giving
5671234
as the lead-end.

This gives a double principle of 70 changes in the plain course, and 32 
4-runs.

It extends straightforwardly:

9.3.9.3.9.3.9.1.7.1.7.1.7.1
126 changes, 72 4-runs
E.3.E.3.E.3.E.3.E.1.9.1.9.1.9.1.9.1
198 changes, 128 4-runs

All these runs come from the forward or reverse rotations of rounds in 
each block of n-1 rows, so I don't think the idea works quite as well on 
higher numbers. 

A variation:
Starting with internal rather than external places so creating wrong 
rather than right hunting gives
3.7.3.7.3.5.1.5.1.5
and starting at a different point gives right hunting again
5.1.5.1.5.3.7.3.7.3
This variation has triple dodges rather than double, and 3rds/5ths/3rds 
rather than 3rds/5ths court places, so is more static.

An alternative is to fully reverse the half-way row using plain hunt on 7. 
This can give variations similar in feel to College Bob.
7.3.7.3.7.1.7.1.7.1.7.1
7.1.7.1.7.1.7.3.7.3.7.3
7.1.7.1.7.1.7.1.5.1.5.1
5.1.5.1.5.1.7.1.7.1.7.1


Andrew Johnson
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