[r-t] Queens and Tittums
edward.w.martin at gmail.com
Wed Feb 14 13:01:41 UTC 2007
When I first looked at composition of 21 part peals of Stedman Triples
I saw the need for me to identify row types
If PEs were rotations of rounds queens & tittums I had noticed that in
triples there are only 3 positinal relationships (As in plain
hunt,on handbells, excluding the 7-8, these positions are a coursing
pair; a coursing bell with one bell between and a coursing pair with
two bells between)
Applied to 21 part format:-
'A' is 12, 23, 34, 45, 56, 67, 71
'B' is 13, 24, 35, 46, 57, 61, 72
'C' is 15, 26, 37, 41, 52, 63, 74
then allowing for each pair to be reversed ( eg 12 = A and 21 = A* )
each of the 5040 rows can be expressed in 21 equal parts using these 3
letters or their reverses.
The 21 PEs can be seen to be AAAAAA, BBBBBB, CCCCCC
Each potential bobbed block can be set out in abstract form and its
potential variations and possibilities explored.
Mathematicians may mock my naivity but although it was painfully long,
this approach worked for me & if only I had a clue how to programme a
computer I might have turned out more than the half dozen or so that
it took me some 2 years to produce !
I am in compleat agreement with RAS whenhe says
"I not sure tittums came about because of this per se, or
that it's simply a coincidence. Rather, the things that
make certain changes (rounds, tittums, back rounds, etc.)
sound particularly pleasant, are precisely the things that
result in them being transpositions of each other."
and, being interested in history, I have tried in vain to find some
written record of when Queens & Tittums were first named.
In Stedman's book(1677), the pairs 13, 57, 24, 68 are simply referred
to as being in 3rds, and the pairs 15, 26, 37, 48 as fifths. Together
they were known as 'concords' One idea that he had was have these
concords rung as if by 4 bells, thus they might plain hunt on 4 with
each pair striking as one bell!
But the full rows produced by these concords are noit given the
titles Queens & Tittums. and I have not yet found these names in any
other early book though I feel that these set changes were known, &
practiced from earliest times. I have theories but this is probably
getting off topic for this list
On 14/02/07, Richard Smith <richard at ex-parrot.com> wrote:
> Richard Pullin wrote:
> > May I remind and inform that Queens and Tittums are transpositions of each
> > other. [...]
> > Either Tittums came about because of this, otherwise it's plain but amazing
> > coincidence.
> I not sure tittums came about because of this per se, or
> that it's simply a coincidence. Rather, the things that
> make certain changes (rounds, tittums, back rounds, etc.)
> sound particularly pleasant, are precisely the things that
> result in them being transpositions of each other.
> Why is queens pleasing to listen to? Because it runs down
> the scale of odd bells, then through the even bells. I.e.
> it takes every second note from the scale. What about
> tittums? On eight, 15263748, it takes every fourth note
> from a scale. If you take every second note from something
> that is already taking every second note, it's equivalent to
> taking every fourth note.
> But that description is slightly disingenious: Queens
> doesn't take precisely every second note as it jumps from 7
> to 2; likewise every other jump in tittums doesn't fit. It
> also doesn't explain why there isn't (on eight bells) a
> third example where every sixth bell is chosen.
> A slightly more accurate would be to consider them as seven
> bell changes, rung with tenor covering. Now rounds is
> 1234567; queens is 1357246 -- which is precisely every
> second bell (if you wrap round to the beginning of the row).
> Repeating -- i.e. taking every second bell from queens --
> gives 1526374. And once more goes back to rounds, 1234567.
> Why? Because queens is every second bell from rounds;
> tittums is every fourth (2x2) and the next step would be
> every eighth bell (2x2x2), but taking every eighth bell and
> evrey bbell is the same thing.
> On ten bells, every fourth bell isn't tittums -- every fifth
> bell is; neither does taking every eighth bell bring rounds
> again -- we need every tenth bell for that. This means we
> get some extra rows on ten bells:
> 123456789(0) Rounds
> 135792468(0) Queens
> 159483726(0) 'Reverse tittums'
> 198765432(0) 'Reverse rounds'
> 186429753(0) 'Reverse queens'
> 162738495(0) Tittums
> 123456789(0) Rounds
> Queens is every second bell; 'reverse tittums', every
> fourth; 'reverse rounds', every eight -- which is
> equivalent to counting backwards through the sequence.
> Then 'reverse queens' is every second bell counting
> backwards'; tittums, every fourth bell counting backwards
> (or every fifth bell counting forwards); and taking every
> eight bell backwards is the same as taking every bell
> forwards and gives rounds again.
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