[r-t] Queens and Tittums
ted.steele at tesco.net
Thu Feb 15 19:12:05 UTC 2007
Richard Pullin wrote:
> May I remind and inform that Queens and Tittums are transpositions of
> each other.
> You can see that by looking at the below transpositions:
> Either Tittums came about because of this, otherwise it's plain but
> amazing coincidence.
> From Richard Pullin.
It is a tiny point in comparison to most of the others made about this,
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
Would group theorists regard this as being two separate groups or simply
as one group in which not all members transpose to produce all of the
The Plain Bob group of lead ends at the royal stage (shown below) is
another such instance that I have in mind and I have wondered whether
there is any theoretical reason why such cases arise.
Two lead ends give only three lead courses but all of the others give
the full nine; it seems odd that the other six don't form their own
Looking at Tittums and Queen's on higher numbers we see, obviously that
more rows are introduced.
1594837260 "Back" Tittums
1987654320 "Back" rounds
1864297530 "Back" Queen's
1E098765432T "Back" rounds
108642E9753T "Back" Queen's
154326 Back rounds
_1324 Tittums and Queen's and Back rounds (on the internal bells only,
Of course the "back" changes are only partial reversals since 1 and "n"
remain the same. However what I am wondering is whether or not these
extra rows, ie the reversals and, especially the unnamed rows are
regarded as having any particular musical qualities. It is possible to
see the queens and tittums sequences in these rows but with more
intermediate bells splitting them up, (as has been observed elsewhere)
and I guess that this may give rise to some interesting music but it
becomes increasingly subjective. The original question put by Richard
Pullin appears to be whether Tittums was originally recognised because
it was easily found as a transposition from rounds of the perhaps
marginally more obvious Queen's. I suspect that rather more than this
was probably understood. The musicality of the members of the larger
groups suggests to me that there is no coincidence here, rather the
basic rule of taking alternate bells from the rounds row and then each
third bell and each fourth etc. is a rule which by its nature produces
some pleasing sounds. The musicality is inherent within the rule and
therefore the groups that it produces will be musical to many people.
Queen's and Tittums are just the fundamental changes in these groups and
the most obviously musical. That they are fundamental is suggested by
the example of minimus where the three named changes are identical.
My knowledge of group theory is virtually non-existent and much of the
above may be nonsense (and will certainly be glaringly obvious to many)
but perhaps there may be some answers to the questions I have posed.
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