[r-t] 8 spliced atw 7com

[Mark Davies]

Rob writes,

> I've seen it sent up as 113 or 112 com and
> this gives a handy indication of who's chickened out and called the split tenors
> section at the start rather than the end.

Surely there are other starting points which, when counted via the 
"conductor's method", would muddy your conclusions! I guess it's 
unlikely anything else would be rung in practice (although I might just 
organise that peal... :-)

Anyway, to me, this adds to the argument. It's the same composition no 
matter whether you have the split-tenors section first or last. (No one 
would consider they had called anything other than Holt's original just 
because they had rung the S--S section first not last!) Hence, it ought 
to have the same COM.

Also, to follow up an earlier comment Don made:

> Not all properties of a composition are invariant under rotation. Yes,
> truth and length are. But lots of interesting ones aren't: musical
> rows a composition contains, ease of calling, whether or not it's
> tenors together, whether it's particularly easy for handbells.

I think that all stable properties of a composition are either (a) 
invariant under rotation, or (b) variant, but dependent only on the 
transposition from rounds to the starting row you have chosen. For 
instance, if you start a round-block from a course end marked as 
14235678, the music, ease of calling, tenors-togetherness, and 
suitability for handbells, are all determined by the transposition 
12345678->14235678. In this example, we can immediately see that 5678 
music will be unaffected; the tenors will be together if they were in 
the original, and not if not; and that the 5-6 handbell pair will be as 
before (and the 3-4 pair too, if this is a course end).

This means that composition properties partition into two nice sets, one 
set independent of rotation, the other only dependent on the starting 
transposition of the rotation. "Conductor's COM" fails to appear in 
either set, therefore it is not a stable property of a composition. QED!

MBD