[r-t] Queens and Tittums

[Don Morrison]

On 2/15/07, Ted Steele <ted.steele at tesco.net> wrote:
> and may indeed have been covered elsewhere but in case not it may be
> worth observing that like the transpositions for Tittums and Queen's on
> higher numbers the major group also contains the reversal of the three
> main changes; or at least the changes with the interior  bells reversed.
> It is useful for three part compositions no doubt but perhaps slightly
> misleading to show the group as having just three members; in fact there
> are six.

I believe you've got two different groups here, one of which (the one
that is a cyclic group of order 3) is simply a subgroup of the other
(the cyclic group of order 6).

And I don't think there's anything misleading about talking about the
three element group at all. Both are, for example, themselves
subgroups of the fully symmetric S[8], that is the group whose
elements are the extent of major! If viewing the three element group
as distinct from the six element group is misleading, then logically
viewing either of them as distinct from S[8] would be misleading, too!
:-)

At least, I think that's right. I'm sure there's plenty of other folks
on this list to correct me if I'm mistaken.


-- 
Don Morrison <dfm at ringing.org>, <dfm2 at cmu.edu>
"Life is too short and Proust is too long"
      -- attributed to Anatole France by Russell
         Baker, "Crawling Up Everest"