[r-t] Undifferentials

Mark Davies mark at snowtiger.net
Wed Jul 13 21:23:43 UTC 2011

I am quite inspired by Graham's example! It is *not* possible to 
construct it from a three-bell principle of the same lead length, by 
doubling up pairs of bells.

To summarise, in the first two examples we saw:

Ander's: -123458-1238-1678-145678
Frank Blagrove's: -1678-1678-18-18

Neither method can be considered as a principle with half the lead 
length, but both are in some sense related to a four-bell principle with 
the same lead length. Pairs of bells follow each other around closely, 
never getting more than one blow apart, and then only to let another 
pair through in a "super cross".

However, Graham's example is different:

GACJ: 34-16-16-36-16-16-16-16-16-14-16-16-

Here there are two groups of three bells, but if you try and form pairs 
between the groups, you find that they do not come near each other at 
all. In fact, the method works the opposite way round: bells in the same 
place-bell group course next to each other all the time!

So the examples we have form two types. Either you can find pairs of 
bells which stick together, one from each the place-bell group, as in 
Ander and Frank's methods, or you find that the place-bell groups 
themselves stick together, always coursing or working with each other.

Neither of these properties is necessarily bad, since coursing bells are 
often the signal of a musical method. But it does seem to imply some 
kind of restriction on what method construction types are possible.

Or does it? I've been looking for further examples, and I have to say 
unless I'm doing it wrong they appear to be very few on the ground. 
There aren't many unprinciples! (Great name by the way Ander). However I 
have found one which I think is quite interesting:

MBD: -14-36-14-14-56-14-14-56-14-14-36-14

This example is unfortunately trivially false in the plain course 
(within the lead, in fact!). So it is not a very good method. But I 
think it is an unprinciple - just like Graham's example, there are two 
separate groups of place bells, but the bluelines for the two groups are 
in fact identical, up to "slidyness". However unlike any of the previous 
examples, in my method there is no close coursing relationship within 
any set of bells.

So unless I have missed something, or the falseness is an unavoidable 
aspect of this construction, it means that a close, one-blow apart 
relationship between bells is absolutely not a requirement for an 

I'm quite surprised by this.


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