[r-t] Plain Bob lead heads/ends (was ringing-theory Digest, Vol 89, Issue 9)

[edward martin]

On 9 February 2012 16:52, Matthew Frye <matthew at frye.org.uk> wrote:
>
> On 9 Feb 2012, at 15:49, edward martin wrote:
>> In even bell methods, if the lead block is symmetrical about the
>> treble then the lead heads and lead ends must be in plain bob group
>
> Not what you mean, surely? eg King Edward S Minor (Cambridge with 36 half lead) is perfectly symmetrical but first lead end is 156423. What you say is only true if the correct pairs of bells you then identify actually *do* swap, but this is certainly not required.

Perhaps you actually didn't read what I said: (It was poorly phrased
but I DID say "because of the half-lead pivot bell  and its specific
conjugate pairs " ie
"In even bell methods, if the lead block is symmetrical about the
treble then the lead heads and lead ends must be in plain bob group
(ie the 2-3-4-5-6 etc will be in a plain hunt relationship because of
the half-lead pivot bell  and its specific conjugate pairs )
On 8 bells these are
2 ; 3x4 5x6 7x8
4 : 2x6 3x8 5x7  etc"

>
> I'm not sure what your later point is about twin-hunt triples methods. What you describe certainly is a way of looking at *some* methods with the correct lead ends, but it probably only covers quite a small minority of them.

Please be assured that out of the 66 Twin-hunt Triples methods with
five leads to a plain course, 24 of them are palindromic ;and in each
of these, because the correct pivot has its specific conjugate pairs,
11 of them have Grandsire type leads
For this to happen the pivots and conj. pairs must be
3; 4x5; 6x7 or
4; 6x3; 7x5 or
6; 7x4; 5x3 or
7; 5x6; 3x4 or
5; 3x7; 4x6
These 11 pallindromic methods have PN:
3.1.5.1.7.1.  7.   1.7.1.7.1.  5.1. 275634  = Single Oxford Bob
3.1.5.1.7.3.  7.   1.7.3.7.1.  5.1. 267453  = Hereward Bob	
3.1.5.1.7.3.  7.   5.7.3.7.1.  5.1. 246375  = Double Oxford Bob	
3.1.7.1.7.1.  7.   1.7.1.7.1.  7.1. 253746  = Grandsire	
3.1.7.1.7.1.  7.   5.7.1.7.1.  7.1. 275634  = Double Grandsire	
3.1.7.1.7.3.  7.   3.7.3.7.1.  7.1. 246375 = St. Clement’s College Bob 	
7.1.5.1.7.1.  7.   1.7.1.7.1.  5.1. 253746  = Single Court Bob	
7.1.5.1.7.3.  7.   1.7.3.7.1.  5.1. 275634  = Double Court	Bob
7.1.5.1.7.3.  7.   5.7.3.7.1.  5.1. 267453 = London Bob	
7.1.7.1.7.1.  7.   5.7.1.7.1.  7.1. 253746 = Reverse Grandsire	
7.1.7.1.7.3.  7.   3.7.3.7.1.  7.1. 267453  = College Bob	

Of the remaining 42 non-pallindromic Twin Hunt Triples methods, 10 of
them have this same set of leads

3.1.5.1.7.3.  7.   1.7.1.7.1.  7.1. 275634 =	(Yorkshire Court? Not yet named)
3.1.5.1.7.3.  7.   5.7.1.7.1.  7.1. 267453 = 	Not yet named
3.1.7.1.7.1.  7.   1.7.3.7.1.  5.1. 275634 = 	Calvary Bob
3.1.7.1.7.1.  7.   5.7.3.7.1.  5.1. 267453 = 	Not yet named
5.1.5.1.7.3.  7.   1.7.1.7.1.  5.1. 275634 = 	Not yet named
5.1.7.1.7.1.  7.   5.7.1.7.1.  5.1. 275634 = 	Not yet named
7.1.5.1.7.3.  7.   1.7.1.7.1.  7.1. 253746 = 	Not yet named
7.1.5.1.7.3.  7.   5.7.1.7.1.  7.1. 275634 = 	Not yet named
7.1.7.1.7.1.  7.   1.7.3.7.1.  5.1. 253746 = 	Not yet named
7.1.7.1.7.1.  7.   5.7.3.7.1.  5.1. 275634 = 	Not yet named

Eddie