[r-t] Lots of asides (was Cyclic principles)

[Philip Earis]

Following a combination of a delayed flight, a delayed train and some 
flavoured vodka, I'm suffering a distinct lack of sleep focus here at the 
moment. So I thought I'd write an email.

It's interesting to see Tony's method, based on the first half-lead of an 
existing (double) method with a cyclic half-lead-end.  This is the same 
design-principle behind Orion maximus (*not* Orion surprise maximus), though 
Tony's method also has the added bonus of having music away from the 
division-ends.

When I was looking for decent cyclic methods a couple of years ago, one of 
the approaches I used was vaguely similar, in that using two different 
half-leads, both individually double, can produce a cyclic method which will 
have rotational symmetry.  This was done with the rung plain method Anglia 
cyclic (-1-2367-1-7-5-36-4-2 = 18234567), but can also be done with 
treble-dodging methods. Examples:

-5-4.5-5.36.4-4.5-4-7-6-5-4-1-5-4-3-2 = 13456782 (Bristol in first 
half-lead, 68 <4-runs> in plain course)
5-5.4-5-36-4-5.4-4.7-36.4.3-4-36-5-6.5.36-2 17823456 (Lancashire in first 
half-lead, 67 <4-runs> in plain course)

Neither of the second half-leads are particularly inspiring, though. As an 
aside, clearly if you use the same approach but take both your half-leads 
from regular double methods, you will get a regular rotationally symmetric 
method.  Leary mentions this in his book on composition, as an aside would 
you believe it. I also recently saw that this has been done with two 
existing methods: Diopside and Nimrod surprise major. These were first rung 
at Barrow Gurney - are they Cox methods too?! Diopside 
is -56-4-56-36-34-5-34-1-4-5.4-4.36.5-5.4-5-1, ie Derwent in the first 
half-lead and Bristol in the second.

As a (further (nested)) aside, I've just seen the notation for Selenium 
surprise for the first time:
-5-4.5-5.36-4-5-4-7.4-4.5.4-4.36.5-5.4-5-2 a. This has beautiful elegance 
without being symmetric. On a similar plan, perhaps it would be nice to have 
a ('asymmetric') method where the four quarter-leads each are able to 
generate a regular double method by themselves.  A quick play around gives 
something like -36-4-5-36.4-4.5-4-7.4-4.5.4-4.36-5-4-5.36.8 (mx) as an 
example (consisting of Superlative, Bristol, Lancashire, Cambridge Blue 
surpise major). It should be possible to do better in the sober light of 
day.

As a final aside, if you're after an incredibly neat cyclic 8-bell method 
(other than Anglia / Purple / Double Cambridge), have a look at this PABS' 
alliance offering.  It's got double offset symmetry, 82 <4-runs> in the 
plain course, and is the only decent method I've ever seen with 3rds made at 
a point of symmetry (I think this is nearly always a fundamental flaw in 
methods, eg Glasgow).  The notation of PABS' method is:
-4.5.36.4.5-6.5.6.5.6-5.4.36.5.4-3.4.3.4.3 = 15678234



----- Original Message ----- 
From: "Rebecca Cox" <r.j.cox at blueyonder.co.uk>
To: <ringing-theory at bellringers.net>
Sent: Friday, May 06, 2005 11:20 PM
Subject: [r-t] Cyclic principles


We've rung courses of a cyclic major principle at Backwell practices (and 
elsewhere) over the last year which, I think, meets all three of Graham's 
criteria. The method is
58-58.14-58-(36)-14-58.14-14 le 23456781, bob 38 for (36)
The method is a padded-out version of Winter and a lead is the first 15 rows 
of Lancashire S.

This is an excellent practice night method as it is a nice length (120), 
interesting, musical and different (odd number of changes per lead) but with 
a relatively simple structure. There's even an odd 87 in the plain course.

Musical peal compositions are available using just bobs, although to get all 
5678s, 6578s, 8765 and 8756s at the front and back a different start is 
needed (call at end of lead).

Tony Cox



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