Re: change ringing, was: dual loop technique?

["Dennis W. Leas" <dennis@mdbs.com>]

My apologies for the delayed response.  Hope this isn't too much info.

Change Ringing
--------------
(Most of this stuff is from "The New Grove Dictionary of Musical 
Instruments.")

Change ringing is traditionally performed by multiple ringers, one ringer 
per bell.  When a 
ringer sounds a bell during change ringing, he or she pulls the bell rope, 
the bell rings 
once and returns to a resting position.  Hence the bells are strictly 
controlled as to when 
they sound.

Given a set of bells, change ringing consists of sounding the bells in a 
predetermined 
order.  Various techniques are used to produce a sequence of ringing.  A 
"plain hunt" on a 
set of bells, named 1, 2 and 3 appears as:

 1 2 3
 -----
 2 1 3
 2 3 1
 3 2 1
 3 1 2
 1 3 2
 1 2 3

Three Bell Plain Hunt

This means that the pattern begins on the first row with ringer 1, then 
ringer 2, and then 
ringer 3.  Continuing with the second row ringer 2 sounds, then ringer 1, 
and then ringer 
3.  This continues until all the changes have been rung.

Draw a line through any given bell in the pattern above and you will see 
the bell wander 
through the pattern in a serpentine manner.  This is characteristic of the 
plain hunt.  A 
plain hunt is generated by flipping the order of adjacent pairs of bells 
and alternating 
which pairs are flipped.  With the set of three bells above, we have two 
transformations: 
1) (ABC->ACB) where the last pair is flipped and 2) (ABC->BAC) where the 
first pair is 
flipped.  We alternately apply transform 1 and 2.  The second row of the 
Three Bell Plain 
Hunt is generated by transform 1 from the first row, the third row is 
transform 2 from the 
second, and so forth.

With four bells, we flip the two outer pair and then the one inner pair:

 1 2 3 4
 -------
 2 1 4 3
 2 4 1 3
 4 2 3 1
 4 3 2 1
 3 4 1 2
 3 1 4 2
 1 3 2 4
 1 2 3 4

Four Bell Plain Hunt

Notice again, the path of any one bell through the pattern.  Bell four, 
for example:

 1 2 3 /
 -------
 2 1 / 3
 2 / 1 3
 / 2 3 1
 \ 3 2 1
 3 \ 1 2
 3 1 \ 2
 1 3 2 \
 1 2 3 /


However, with four bells a plain hunt produces only 8 combinations of the 
possible 24 (4! = 
24).  Many techniques can be used to produce all the combinations.  The 
Plain Bob is 
probably easiest to follow. (note: Bob has one o, not two.)  With the 
Plain Bob, the Plain 
Hunt pattern is used until a repetition would result, then a dodge occurs. 
 A dodge 
exchanges the order of the last pair.  Hence every eighth row of a Plain 
Hunt has a dodge 
inserted.  (Are you still with me on this?  Shheessh this is terse...wish 
I could make it 
clearer.)  A Four Bell Plain Bob looks like:

 1 2 3 4  (start Plain hunt)
 -------
 2 1 4 3
 2 4 1 3
 4 2 3 1
 4 3 2 1
 3 4 1 2
 3 1 4 2
 1 3 2 4  (Dodge 2 and 4, otherwise we'd get 1 2 3 4)
 1 3 4 2  (Plain hunt again)
 3 1 2 4
 3 2 1 4
 2 3 4 1
 2 4 3 1
 4 2 1 3
 4 1 2 3
 1 4 3 2  (Dodge 3 and 2, otherwise we'd get 1 3 4 2)
 1 4 2 3  (plain hunt again)
 4 1 3 2
 4 3 1 2
 3 4 2 1
 3 2 4 1
 2 3 1 4
 2 1 3 4
 1 2 4 3  (Dodge 3 and 4, completes the changes)
 1 2 3 4 

So I've been experiementing with this to generate looped patterns.  
Traditionally, each 
bell sounds the same duration (time-wise).  If you weren't using bells, 
say some stacato 
sound instead, the pattern might sound syncopated depending on the 
instruments, etc.

I find it fascinating because it is highly structured but, depending on 
the length of the 
changes, the mind has difficulty grasping the pattern.

- Dennis Leas
-- 
dennis@mdbs.com