# [r-t] Naremburn Treble Bob

Alexander Holroyd holroyd at math.ubc.ca
Fri Mar 1 18:35:44 UTC 2013

```Interesting.  If quarter-lead calls are necessary for the extent, it's not
very surprising that it hasn't been rung before.

I'm guessing an extent with only lead-end calls is not possible, although
this does not seem immediately obvious.

What TD minor methods are possible that admit an extent using lead-end
calls, but which are either asymmetric or violate the "usual parity rule"
(or both)?  There are lots that are simply lead-splicers with
symmetric methods not violating the rule.  But if we remove these then I
don't know of many examples.

One example I've talked about before is derived from two leads of Auryn
Differential: 34-34.1-25-1-34-1.34-34.1-25-1-34-4.  This is particularly
remarkable because the _standard calling_ (the equivalent of WHW) gives a
720.  (I believe Richard Smith claimed to have found some other methods
like this, but I haven't seen them).

If we restrict to in-course lead heads, there is a very fast algorithm for
determining whether a given method has a set of leads giving the
extent, as mentioned here:
http://bellringers.net/pipermail/ringing-theory_bellringers.net/2012-January/004090.html
So it would be easy enough to generate a list of all methods with that
property.  However, I don't know a good way to check if out-of-course lead
heads are allowed, and there seems no particular reason why such extents
might not be possible for some methods.

Ander

On Fri, 1 Mar 2013, Philip Earis wrote:

> I see Tom Perrins rang an extent on Naremburn Treble Bob yesterday
> (http://www.bb.ringingworld.co.uk/view.php?id=277767). Good work! The
> method is a very simple double treble-dodging construction, with a "Kent
> slow work" at both the front and back, and just a single dodge each time
> you go through 3-4. It could be a good training tool, and the line is so
> simple I'm very surprised it hasn't been rung before:
>
> Naremburn &x5x1x25x1x2x1, 1 = 152364
>
> ===
> 720 Naremburn Treble Bob Minor:
> 23456  1.75 4.25  5
> -------------------
> 26543    s    s
> 23564    s    s   -
> -------------------
> 3 Part.
> s = 12 for 1256 when treble is in 3-4.
> - = 14 at the lead end.
> ===
>
>
> There are I think 16 double treble-dodging minor methods with no more than two consecutive blows from which a 720 can be easily generated.  My favourite is the Bristol-esque Horton:
>
> &-34-4.5-2.3-34-1,1 142635 Cheddleton Surprise Minor
> &-34-4.5-2.3-34-5,2 135264 Hanley Surprise Minor
> &-3-4.5-2.3-4-1,1 134625 Stoke Double Surprise Minor
> &-3-4.5-2.3-4-5,2 136245 Stafford Double Surprise Minor
> &-5-4.5-2.3-2-1,1 156342 Horton Surprise Minor
> &-5-4.5-2.3-2-3,4 154263 Hartnell Surprise Minor
> &-5-4.5-2.3-2-5,2 142635 Milton Surprise Minor
> &34-3.4.5-2.3.4-34.5,2 165324 Audley Surprise Minor
> &34-5.4.5-2.3.2-34.1,1 134625 Alice Holt Forest Surprise Minor
> &34-5.4.5-2.3.2-34.5,2 136245 Longton Surprise Minor
> &3-3.4.5-2.3.4-4.5,2 156342 Biddulph Surprise Minor
> &3-5.4.5-2.3.2-4.3,4 135642 Troughton Surprise Minor
> &5-3.4.5-2.3.4-2.3,4 162534 W & P Surprise Minor
> &5-3.4.5-2.3.4-2.5,2 154632 Ash Surprise Minor
> &5-5.4.5-2.3.2-2.3,4 164235 Pertwee Surprise Minor
> &5-5.4.5-2.3.2-2.5,2 142563 Cheadle Surprise Minor
>
>
> And I think there are a further 39 double methods, of which Naremburn is one, which don't have the right parity structure to easily generate an extent.
>
> &-34-4-25-3-34-1,1 142635 Double Norwich Surprise Minor
> &-34-4-25-3-34-5,2 135264 New Superlative Surprise Minor
> &-34-45-25-23-34-1,1 134625 Untitled Surprise Minor
> &-34-45-25-23-34-5,2 136245 Beinn Laoigh Surprise Minor
> &-34-1-25-1-34-3,4 136524 Untitled Treble Bob Minor
> &-34.5.4-25-3.2.34-1,1 134625 Untitled Surprise Minor
> &-34.5.4.5-2.3.2.34-1,1 134625 Untitled Surprise Minor
> &-345-4-25-3-234-1,1 134625 Untitled Surprise Minor
> &-345-4.5-2.3-234-1,1 134625 Untitled Surprise Minor
> &-345-1-25-1-234-1,1 152364 Untitled Treble Bob Minor
> &-345-1-25-1-234-3,4 135642 Untitled Treble Bob Minor
> &-3-4-25-3-4-1,1 134625 Untitled Surprise Minor
> &-3-4-25-3-4-5,2 136245 Loch Cam Surprise Minor
> &-3-1-25-1-4-5,2 165324 Quharity Treble Bob Minor
> &-5-4-25-3-2-1,1 156342 Untitled Surprise Minor
> &-5-4-25-3-2-3,4 154263 Untitled Surprise Minor
> &-5-4-25-3-2-5,2 142635 Loch Yucal Surprise Minor
> &-5-45-25-23-2-3,4 164235 Untitled Surprise Minor
> &-5-45-25-23-2-5,2 142563 Goat Fell Surprise Minor
> &-5-1-25-1-2-1,1 152364 Naremburn Treble Bob Minor
> &-5-1-25-1-2-3,4 135642 Varragill Treble Bob Minor
> &-5.34.1-25-1.34.2-1,1 152364 Untitled Treble Bob Minor
> &-5.34.1-25-1.34.2-3,4 135642 Untitled Treble Bob Minor
> &34-3.4-25-3.4-34.5,2 165324 Loch Nevis Surprise Minor
> &34-5.4-25-3.2-34.1,1 134625 Untitled Surprise Minor
> &34-5.4-25-3.2-34.5,2 136245 Skiddaw Surprise Minor
> &34.5-4-25-3-2.34.1,1 134625 Untitled Surprise Minor
> &34.5-4.5-2.3-2.34.1,1 134625 Untitled Surprise Minor
> &34.5-1-25-1-2.34.1,1 152364 Untitled Treble Bob Minor
> &34.5.34.1-25-1.34.2.34.1,1 152364 Untitled Treble Bob Minor
> &3-34.1-25-1.34-4.5,2 135264 Sgor nam Fiannaidh Treble Bob Minor
> &3-3.4-25-3.4-4.5,2 156342 Glyder Fawr Surprise Minor
> &3-5.4-25-3.2-4.3,4 135642 Untitled Surprise Minor
> &5-34.1-25-1.34-2.3,4 135642 Untitled Treble Bob Minor
> &5-3.4-25-3.4-2.3,4 162534 Untitled Surprise Minor
> &5-3.4-25-3.4-2.5,2 154632 Basil Surprise Minor
> &5-5.4-25-3.2-2.3,4 164235 Untitled Surprise Minor
> &5-5.4-25-3.2-2.5,2 142563 Ben Clibrig Surprise Minor
> &5-5.4.5-2.3.2-2.5,2 142563 Cheadle Surprise Minor
>
> For what it's worth, I'm sure we rang a 1440 of the method listed as "Loch Cam" in Cambridge around 2001, and called it Double Cambridge Surprise.
>
>
> DISCLAIMER:
>