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Chart:
Ltcas:
Diagram:
Landmarks:
Text:
Changes:
more
9abc
90ET
Chart extras:
Diagram tca:
Diagram course-POV-after:
Show 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Beats/minute now playing row bell |
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Name: |
Error message for name field
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On: |
Error message for moving bells field
Tenor Behind / Covers:
0
1
2
Error message for covers input
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☼% Place notation: |
Error message for place notation field
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Bob: |
Error message for bob masks field
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Single: |
Error message for single masks field
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Starting at: | ||||
Course bell: | ◉ | |||
Your bell: | ◉ | |||
After bell: | ◉ | |||
Moving: | bells | |||
Hunting: | ||||
Coursing: | ||||
Covering: | ||||
Coming to front: | ||||
Permutor: | ||||
· treble hunts · 2nds hunts · Plain Hunt · treble bobs · has prefix more | ||||
Lead and course: | rows/lead × leads/course = rows/course | |||
Permutations: | (ratio ) | |||
Palindromic PN: | ||||
Expanded PN: | ||||
Bob PN: | ||||
Single PN: | ||||
Bob permutor: | coursing(s): | |||
Single permutor: | coursing(s): more | |||
Follow string (PC): | ||||
Help for inferring the Single method from which a Double is derived: | ||||
Over the treble: | ||||
The treble: | ||||
Under the treble: | ||||
Under reversed: |
Table of Work |
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Table of Ltcas |
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Progress through Snowdon Diagrams 1998:
#
Progress through Snowdon Diagrams 2011:
p
methods/principles.
This page uses a Javascript program to analyze and display methods and principles. Please enable Javascript in order to use it.
(You do not need Java enabled to use this page, and to protect your computer you should keep Java disabled in your browser.)
This page has been tested on recent versions of Firefox, Safari, and Opera.
The help for this page is under construction.
If you are clicking the button to see a row at a time, the and buttons will be enabled whenever a bob or single respectively can be called.
Why use this program?
coursing order(s)
The methods and diagrams and their bobs and singles are primarily derived from Snowdon's Diagrams, 1998 edition.
The chart, diagram, and text show roughly the same information but in different forms. Each is visible if its checkbox is checked; you can show any combination of them but not none of them.
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 | |
11 | |
12 | |
13 | |
14 | |
15 | |
16 |
The chart lists the bells in each successive row, in the order in which they strike. Each row is preceded by its ordinal [1], [2], [3], etc. except for the initial row 0 of rounds. Handstrokes have a white background and backstrokes have a gray background. Lead end backstrokes are distinguished by a darker gray background.
Each lead end backstroke row is followed by the work number (② ③ ④ etc.) identifying the work done in the lead to come. The work number is the same as your bell's place at the lead end backstroke.
Each row at which a call was made
is followed by
a B for Bob
or an S for Single
.
The row two strokes later
at which the call takes effect
is followed by a ! (exclamation point).
Rounds and other rows in recognized patterns are marked as in the table below.
Row markers | |
---|---|
Rounds | • |
Back Rounds | ◦ |
Queens | Ⓠ |
Tittums | Ⓣ |
Whittingtons | Ⓦ |
To see all the markers, click on Plain Bob and look at a plain course (four leads, (Plain Course)). Other methods with this somewhat uncommon property are:
SaintBobs: St Martin's Bob , St Nicholas Bob , St Osmund Bob , St Remigius Bob , St Simon's Bob .
The diagram shows the path of each bell as it moves from place to place. As in the chart, backstrokes have a gray background and lead end backstrokes have a darker gray background. Each bell is indicated by a line of a different color (see table at right); the colors are chosen so that their names rhyme or chime with the bell number.
To the left of row [0.] are your course bell, your bell, and your after bell, shown as a bell character and a bell color.
To the right of row [0.] and every later lead end row is your bell's work, shown as the place number for that work, circled.
The name of the method is echoed above the diagram.
The landmarks list things an attentive ringer of your bell might notice and benefit from at each row.
The top row of the list gives your course bell, your bell, and your after bell as numbers and colors.
The Lead-treble-course-after (Ltca) display lists which bells you are over as the method/principle unrolls, not in terms of bell numbers but abstractly in terms of the treble, your course bell, your after bell, and when you Lead.
Knowing which way to look seems to be an important component of ropesight, and in learning Plain Bob an important step for me was learning the rhythm in which a ringer looks toward the treble. The Ltca sequence can be very helpful in this regard.
The Table of Ltcas presents this information horizontally.
The text gives virtually the same information as the chart, but in plain text form so you can copy and paste it easily to work with in a text editor or other program.
The changes show the place notation change that produced each row.
Click the button to start a second group of displays (chart, diagram, and/or text) for comparison, and the button to delete the first group of displays when you are done.
Open a new window in your browser and start a second session of this page, then arrange the windows side by side so you can compare the results.
(An earlier version of this page showed two or more on the same page, but as the page was expanded to show more information about each method/principle, it became difficult to arrange it helpfully. Possibly a future version will display more than one on the same page again.)
Singles | 3 |
Minimus | 4 |
Doubles | 5 |
Minor | 6 |
Triples | 7 |
Major | 8 |
Caters | 9 |
Royal | 10 |
Cinques | 11 |
Maximus | 12 |
Preset buttons are provided for an assortment of methods and principles. The methods and principles were selected to cover the ones ringers often start out with, and to include some in which the treble does not hunt (Bastow and Stedman), more than one bell hunts (Grandsire and Antelope), and the coursing order is not the order in which bells come to the front (Stedman). They are shown in two groups:
You can also customize the method/principle by entering parameters of your choice for:
When you make your customizations, the input fields and the button will be highlighted. Press your computer's Return, Enter, or Tab key if this doesn't happen spontaneously. Then click the button, to work with your custom settings.
To enter a mask for a bob or single, you must first check the the corresponding checkbox to enable it.
Place notation is a counterintuitive (from a mathematical point of view) but compact way of writing the changes between one row to the next in terms of which bells do not move. You can see examples by clicking any method/principle button.
For example, the place notation for Plain Hunt on 5 is 5.1.5.1.5.1.5.1.5.1. Each change is separated by a period; this place notation shows a sequence of 10 changes.
Place notation 5
(You might wonder if the bell in leads can exchange places with the bell at the end of the row. That is ruled out; it's too difficult. The bell in leads can only exchange places with the bell in 2nds; and the bell at the back in Nths can only exchange places with the bell in (N-1)ths.)
From rounds 12345, place notation 5 would produce 21435. You may want to work this out with pencil and paper if it is new to you.
Place notation 1
From 21435, place notation 1 would produce 24153.
To see how the rest of this list of changes works out, click Plain Hunt then either or (repeatedly) . The two simple changes 5 and 1 produce a variety of rows (sequences of bells).
Other features of place notation are illustrated by Plain Hunt . Its place notation is x.14.x.14.x.14.x.14.
Place notation x
From rounds 1234 place notation x produces 2143.
Place notation 14
From 2143, place notation 14 produces 2413.
To see how the rest of this list of changes works out, click Plain Hunt then either or (repeatedly) .
In summary:
You may have already realized that it is possible to write place notation that makes no sense. An example is the change 2, which specifies that the bell in 2nds stays put while every other bell exchanges places with another. But that can't work; who does the bell in leads exchange with?
Bell number |
Bell char. |
CCCBR char. |
---|---|---|
1 | 1 | 1 |
2 | 2 | 2 |
3 | 3 | 3 |
4 | 4 | 4 |
5 | 5 | 5 |
6 | 6 | 6 |
7 | 7 | 7 |
8 | 8 | 8 |
9 | 9 | 9 |
10 | a | 0 (zero) |
11 | b | E |
12 | c | T |
13 | d | A |
14 | e | B |
15 | f | C |
16 | g | D |
17 | h | F |
18 | i | G |
19 | j | H |
20 | k | J |
21 | l | K |
22 | m | L |
23 | n | N |
24 | o | P |
25 | p | Q |
26 | q | R |
27 | r | S |
28 | s | U |
29 | t | V |
30 | u | W |
31 | v | X |
32 | w | Y |
33 | x | Z |
34 | y | |
35 | z |
If there are 9 or more bells, the higher-numbered bells are represented here by lower-case letters, as is the usual computer science practice (see table at right). Up to "z" or 35 is accepted, but only up to "g" or 16 will be displayed in a diagram.
The CCCBR bell letters (see table at right) are accepted as well, and if the 90ET radio button is checked, they will be displayed instead of lower-case letters. This encoding uses 0 for 10, E for eleven, and T for twelve, then continues alphabetically from A for 13, skipping I and O to avoid confusion with 1 and 0, and E and T because they were already used, ending with Z for 33.
Stedman is traditionally organized into
sixes
which are out of phase with its leads.
These are indicated in the place notation
by segments delimited with $s.
Stedman's bobs and singles are applied to segments rather than leads.
For methods and principles organized in segments
(at this writing Stedman is the only one I have found),
the simulation software offers the possibility of displaying
a segment
()
at a time
in addition to a row, lead, or plain course at a time;
and of displaying a bob segment or single segment
rather than a bob lead or single lead.
This page accepts the following place notation abbreviations and alternatives.
The CCCBR method libraries present place notation where possible as the initial sequence, the half end change, and the lead end change, though not in this textual form; the same information is presented tabularly. The downloadable XML form of these libraries denotes this using a comma only, as C.D.···.Q.R.S,T. The ringingmethods.co.uk site presents this comma-only form directly.
The ☼ button expands any abbreviations in the place notation to show the fully spelled out place notation.
You have several options.
Clicking the button starts over with the current method at the initial backstroke in rounds.
Clicking the button shows another row.
If the method or principle supports bobs or singles, and a call could be made, the and/or button(s) will un-grey so you can click.
Clicking the button shows a lead of the method/principle.
If the display was partway through a lead, clicking this button shows the rest of it. If you had clicked or , the lead will show the call; otherwise, it will be a plain lead.
If the method/principle is divided into segments shorter than a lead, then the button will be enabled. Clicking it shows a plain segment of the method/principle.
Stedman is the only common method/principle for which this applies.
Clicking the button clears all visible rows and shows a plain course of the method/principle. A plain course is a sequence of plain leads that brings the bells back into rounds.
The number of courses required is one of the inferred characteristics, displayed as leads/course.
If you step through the rows one at a time
using the
button,
and the method supports bobs,
the
button
will be enabled from time to time.
It is disabled except when
a Bob
call could be made.
When is is enabled,
you can click it
to make the call.
If the method/principle supports bobs, then the button will be enabled. Clicking it shows a lead of the method/principle with a bob called.
If the method/principle is divided into segments, then the button will be labelled instead. Stedman is the only common method/principle for which this applies.
If you step through the rows one at a time
using the
button,
and the method supports singles,
the
button
will be enabled from time to time.
It is disabled except when
a Single
call could be made at the next row.
When is is enabled,
you can click it
to make the call.
If the method/principle supports singles, then the button will be enabled. Clicking it shows a lead of the method/principle with a single called.
If the method/principle is divided into segments, then the button will be labelled instead. Stedman is the only common method/principle for which this applies.
If a call has been made on the current row,
the
button
(no call
)
is enabled.
Clicking it removes the call.
These buttons back up one row (), lead (), and segment () respectively. Each is enabled whenever its action can occur.
A second set of the , , , , , , , , and buttons float under the displays, so you can follow a long sequence more conveniently. They produce the same effects as the first set.
The button plays the last row in the display, in the pitches of the bells of the Miami tower.
To hear every displayed row, check the checkbox beside it.
To stop the rows being played, unclick the checkbox; playback should stop immediately.
For some reason, two strokes are consistently missing from the sounds for Plain Hunt on Three when a complete lead is played (the 1 in row 4 and the 2 in row 6). Other numbers of Plain Hunt work properly.
Many methods support calls that are used to ensure the band can ring all possible permutations. The most common calls are bobs and singles.
Each method/principle produces a finite number of different bell rows; the number of different rows is typically equal to the length of a lead times the number of coursing bells. Thus for example Plain Bob Minimus, with three coursing bells and a lead length of 8 produces 24 distinct rows. There are
(pronounced four factorial
) = 4×3×2 = 24
different rows of four bells, so that's all of them. However, Plain Bob Doubles, with 4 coursing bells and a lead length of 10, produces only 40 different rows out of the
5! = 5×4×3×2 = 120
different rows of five bells, leaving 80 rows that are not reachable in Plain Bob Doubles. An example is the row 12453.
To reach this other rows, ringers have introduced calls such as Bobs and Singles.
The common feature of bobs for most methods/principles I've looked at (and I've looked at a few) is that they do not change how many pairs of bells swap places (as a single does) but instead changes which pairs swap places. Most of those I've examined move the swap over one place either in or out, so that a bell that would have swapped keeps its place, the bell it would have swapped with swaps with the bell on the other side, and that bell which would have kept its place swaps instead.
There are exceptions; see the list at right of some methods/principles whose bobs reduce by one the pairs swapping places.
Each bob is specified here as a list of masks that operate on the changes for a plain lead or segment.
A mask for the bob is applied to the changes at the end of the current lead, or (if the mask begins with a < as for Stedman Triples and higher) to the changes at the beginning of the next lead.
To see a bob, click the button or the / button. These buttons are disabled except when a bob is possible.
The common feature of singles for the methods/principles I've looked at (and I've looked at a few) is that they reduce by one the number of pairs of bells that swap places, making one of those pairs keep their places instead.
Each single is specified here as a list of masks that operate on the changes for a plain lead or segment.
A mask for the single is applied to the changes at the end of the current lead, or (if the mask begins with a < as for Stedman Triples or higher) to the changes at the beginning of the next lead.
To see a single, click the button or the / button. These buttons are disabled except when a single is possible.
Bobs and singles are specified here using a mask notation related to place notation. A bob or single is specified by a list of one or more masks, separated by periods. Each mask is an operator on a change, that produces a related change from it. Each mask is either:
=
and continuing with
the place notation that is to replace the masked change;
+
or
-
followed by one or more bell characters,
with
+BC…
indicating that B, C, etc. are to be added to the change's place notation
and
-BC…
indicating that B, C, etc. are to be elided from the change's place notation;
or
*
indicating that the change is to remain the same.
The character #
may be used in a
=
, +
, or -
list
to represent the highest-numbered bell abstractly,
as for example in Grandsire
where the masks for all even numbers of bells are the same,
as are the masks for all odd numbers of bells.
If the list begins with
then the masks are to be applied starting from the beginning of the change list;
otherwise,
the masks are to be applied ending at the end of the change list.
<
The majority of mask lists consist of a single mask applied at the end of the change list, as for example both the bob and the single of Plain Bob Minor.
Some mask lists affect more than one change, as for example:
A very few mask lists are applied at the beginning of the next lead or segment, as for example both the bob and single of Stedman Triples.
Stedman Doubles sixes | ||
---|---|---|
Which | Odd (1st, 3rd, …) | Even (2nd, 4th, …) |
Plain | 5.3.1.3.1.3 | 5.1.3.1.3.1 |
Single | 5.3.1.345.1.3 | 5.1.3.145.3.1 |
Why a mask notation for bobs and singles rather than just place notation? Blame it on Stedman Doubles, in which a single may be called for either kind of six. In both cases 45 is added to the fourth change of the six, but in one case that fourth change goes from 3 to 345 and in the other it goes from 1 to 145. Is that two kinds of single (145 and 345), making Stedman the only method/principle with a second kind of single, or one kind that depends on the context in which it is applied? I chose the second approach (after trying and discarding the first one).
Masks also support abstraction in the actions for bobs and singles so that some commonalitites across methods/principles and numbers of bells can be made evident; the identity operator on changes (mask *) which is convenient for Erin singles and Grandsire bobs; and the attribute of place deltas, the change in the number of placing bells caused by a call.
By default,
the method or principle begins at row 0 from rounds.
You can if you wish have it begin from
an arbitrary row number and/or row,
by entering them in the
Starting at
text inputs.
Plain Bob Singles
Each of these takes the current method or principle and transforms it into a related method or principle. They are presented in sequence from simplest to most complex. We use Plain Bob Singles (right) as an example.
The first two transformations do not in themselves produce another standard method or principle, but are combined to make more complex transformations. When applied one after the other (in either sequence) the result is the same as Reverse.
The remaining three transformations
produce recognized methods or principles with standard names.
If the original method's name is X
,
then the result of applying the Backward, Reverse, or Double transformation
is the method named
Backward X
,
Reverse X
,
or
Double X
respectively.
If X contains Plain
or Single
,
that part of the name is elided in the name of the transformed method.
If a tranform button is grayed out, that transformation is either not possible or would result in the same method or principle; hover the cursor over the button to find out which.
Because inversion is an operation that can also be applied to masks, the button inverts the bob and single mask lists along with the place notation. The other transformations do not apply to masks, so their transformation buttons reuse the original bob and single masks lists (if any) if the following conditions hold:
Otherwise, the transformed method is not provided with a bob or single.
Plain Bob Singles, swapped
The button swaps the first and second halves of the method or principle.
You'll notice that although the place notation is the original place notation with its halves swapped, the paths of the bells are not the original paths with their halves swapped.
For some methods, the standard Double transformation does not produce an interesting result, for example with Canterbury Place for which it produces Plain Hunt. The R/S Double transformation (Reverse over Single) takes the places
The swap-halves transformation is its own inverse, which means that swap-halves undoes itself.
The swap-halves transformation has no effect when applied to some methods, such as Plain Hunt: it produces the same method. The button is disabled for such methods.
Plain Bob Singles, inverted
The button inverts each change from top to bottom.
In terms of the place notation, with moving bells (3 in the example of Singles), each number in the place notation is subtracted from . If there are several numbers for a single change, as in the last change of Plain Bob Singles, then we would sort them back into sequence.
The invert transformation is its own inverse, which means that invert undoes itself.
The invert transformation has no effect when applied to some methods, such as Plain Hunt: it produces the same method. The button is disabled for such methods.
The button transforms a method to or from its Backward counterpart.
The Backward counterpart of a method is the method in reverse, from end to beginning. The changes are the same ones as the method's but they are listed beginning with the last change and continuing to the first.
The Backward transformation is its own inverse, which means that Backward undoes itself.
Reverse Bob Singles
The button transforms a method to or from its Reverse counterpart. It is the combination of and , in either sequence.
A Reverse method is produced by taking the original method, inverting every change top-to-bottom (as for ), and swapping the second half of the change list with the first half (as for ). The two transformations may be performed in either sequence; the result is the same.
The Reverse transformation is its own inverse, which means that Reverse undoes itself.
The Reverse transformation has no effect when applied to some methods, such as Plain Hunt: it produces the same method. The button is disabled for such methods.
Double Bob Singles
The button transforms a method to its Double counterpart.
The button is enabled for every method that begins from rounds and in which the treble Plain Hunts.
The Double counterpart of a method is produced from the method and its Reverse counterpart. For each change, the part of the Reverse method change that lies under the treble's place is joined with the part of the original method change that lies at or over the treble's place.
In terms of place notation, for each change, if the treble is in place P before the change, then all numbers in the place notation for that change of the Reverse method that are less than P are combined with all numbers in the place notation for that change of the original method that are greater than or equal to P.
The Double transformation is not its own inverse. In fact, since the Double transformation discards some information about the original method, it has no inverse transformation. For example, Snowden (1998) lists Double Norwich Court Bob (chart 79), place notation x.14.x.36.x.58.x:18/18, but the Single method Norwich Court Bob is nowhere to be found. 96 possible place notations for the hypothetical Norwich Court Bob would be transformed into Double Norwich Court Bob:
The Double transformation has no effect when applied to some methods, such as Plain Hunt: it produces the same method. The button is disabled for such methods.
The standard Double transformation produces no interesting result when applied to some methods, such as Canterbury Place for which it produces Plain Hunt. A variant in which the Reverse changes at or over the treble's place are combined with the Single changes under its place is often used for them. The button (Reverse over Single Double) produces this transformation.
These depend on which bell is Your bell. When the page loads, your bell defaults to . You can enter whichever bell you like for your bell, and then press the return or enter key which triggers recalculation of your course bell and after bell. If you enter a number other than the number of one of the bells, you'll get instead.
Your course bell is the bell doing the work that precedes yours in the coursing order. If your bell isn't a working bell (for example if you are trebling in most methods), then you are not in the coursing order and you have no course bell.
Your after bell is the bell doing the work that follows yours in the coursing order. If your bell isn't a working bell (for example if you are trebling in most methods), then you are not in the coursing order and you have no after bell.
Each plain lead moves each bell to the next work in the coursing order, so your course and after bells do not change though the work each of the bells is doing changes.
However, a call can send bells to do work that was not the next for them in the coursing order. When that happens, your course and/or after bells may change, whether because one or both of them has been sent to different work or because your bell has.
Each colored dot ◉ ◉ ◉ shows the color of that bell in the diagram.
The coursing diagram shows the coursing order in circular form. The large numbers are the places in the coursing order. The smaller pairs of numbers in the inner ring indicate where the bell in each passes the treble on the way to the next place.
Originally I hypothesized that the Javascript software could infer the work for each place, but now I believe that is not possible, primarily because the names used for the work in various methods/principles show little regularity and indeed vary geographically and over time. The Javascript software instead infers what I call the landmarks, such as where your bell passes the treble, dodges, and similar well-defined phenomena. Instead, I have gone through and manually assigned work names for some of the methods and principles on some numbers of bells, as an experiment.
If the method or principle is one for which I have manually set up names for each place's work, based primarily on Adams Ringing Circles (2000), then each place's work is shown in the ring of arrows, with the place circled just before it, but keep in mind these are my abbreviations for what Adams says, divided as necessary to give each place some work, and may not match what you are used to. Otherwise, the place numbers are shown in the ring of arrows.
Various facts can be inferred about each method/principle, some directly and others indirectly.
Where numbers are listed for Hunting, Coursing, and Coming to front, they represent not bells but places at the lead end backstroke.
The tenor behind / covers, if any, are not moving.
In Plain Hunt, all the moving bells hunt, of course. In many methods only the treble hunts, but in Grandsire two bells hunt, the treble and the bell in 2nds at the lead end.
Note: in Grandsire the other bell that hunts changes with each Single call, but the fact that the bell in 2nds at the lead end backstroke hunts does not change.
These bells cover (in the mathematical sense) all the working places, from the front to the back, and a lead of the method/principle sends each one to a different place than it started in.
They are listed in the coursing order, an abbreviated representation of the permutor. The coursing order begins with the lowest-numbered place that is permuted to a different place, continues with the place the bell in that place is sent to, continues with the place the bell in that place is sent to, and so on until stopping when the first-listed place would be reached again.
For many (but not all) methods and principles, the coursing order is evens up, odds down: 2 4 … 5 3.
If you specified a tenor behind or two or more covers, the bells performing that function are listed.
This is related to the coursing order but usually not the same.
The permutor of the method/principle is a vector that shows where each bell is sent by a plain lead of the method/principle.
As an example, look at the permutor calculated for Plain Bob Minimus (4). It is [1423].
You can confirm this by comparing successive lead end rows separated by plain leads.
Successive lead end backstrokes for Plain Bob Minimus |
|||||
---|---|---|---|---|---|
Row num. |
Row | Leads to leads |
2nds to 4ths |
3rds to 2nds |
4ths to 3rds |
0. | 1234 | 1 | 2 | 3 | 4 |
8. | 1342 | 1 | 3 | 4 | 2 |
16. | 1423 | 1 | 4 | 2 | 3 |
24. | 1234 | 1 | 2 | 3 | 4 |
1 | 1 |
2 | 2 |
3 | 6 |
4 | 24 |
5 | 120 |
6 | 720 |
7 | 5,040 |
8 | 40,320 |
Each lead is the same number of rows long. The number of leads listed is how many plain leads are required to take the bells from rounds to rounds.
The number of permutations of moving bells is
(pronounced M factorial
);
its value is
.
The factorial of 1 through 8 is given in the table at right.
It increases very rapidly,
faster than any polynomial.
The inferred characteristics include the number of permutations of the moving bells and the ratio between the number of permutations and the number of rows in a plain course.
These indicators show:
Plain Hunt, Antelope, Erin, and Stedman are examples of principles. Most other change ringing patterns are methods.
Exceptions:
Each indicator is normal text if true, or grayed and struck through if false.
A method/principle's place notation is palindromic if its changes are symmetric about the half end change in the middle, with the exception of the. lead end change at the end. For example, C.D.···.Q.R.S.R.Q.···.D.C.T is symmetrical about half end change S, except for lead end change T; all the changes preceding S are reflected following it, in mirror-image fashion. See the discussion of the palindromic abbreviated form.
Many but not all methods/principles are palindromic in this sense; see the list at right for some examples of non-palindromic methods and principles. If the method or principle is palindromic, its place notation is presented in palindromic form.
The expanded place notations present the method or principle's place notation with all abbreviations expanded.
If the method/principle is divided into segments (as is Stedman), the place notation for each non-prefix segment is presented in sequence, separated by $s. Otherwise a single place notation is presented.
For methods and principles that support bobs or singles, these are the place notation(s) for a lead in which a call is made.
If the method/principle is defined with two or more segments, like Stedman, then the place notation for a call in each segment is presented, separated by semicolons. Otherwise a single place notation is presented for bobs (if defined) and singles (again if defined).
coursing order(s)
For methods and principles that support bobs or singles, these are the permutor(s) and the coursing order(s) for a lead in which a call is made.
Unlike plain leads, which always have one coursing order, bob or single leads may have two or more disjoint coursing orders. For example, in Plain Bob Minor, a lead for which a single is called has two coursing orders: one for 2nds and 3rds, which exchange places, and another for 4ths, 5ths, and 6ths, which cycle among themselves.
Stedman is one of the oldest methods or principles
and was created before they were well understood.
Thus it has some distinctive features not found in
any other method or principle.
One of these is that it has two plain segments in each lead
(called sixes
),
each with a different permutor.
A single produces different permutors (and thus coursers)
when applied to the first kind of six
than to the second kind of six.
The follow string lists the sequence of bells that the point-of-view bell follows (rings over) during a plain course, with "L" interspersed for each blow in leads. If the method or principle has more than one lead in its plain course, the divisions between them are marked with dots (⋅).
The follow string can be quite long, and for anything above 5 or 6 bells is too long to fit in the table. By default only the part that can fit is displayed. If you wish to see the whole string, click it; if you wish to hide the overflow again, click it again.
A Double method is created from an original method by a specific transformation in which the parts of the original method lying above the treble are combined with the parts of the Reverse of the original method lying below the treble.
To aid in inferring the Single method from which a Double method was created, for appropriate methods (those in which the treble hunts) this page displays:
The place notation for the Single method must include all of the places over the treble and all the under-reversed places. You will have to guess the other places, as the Double transformation discards some information about the Single method.
These methods are present in Snowdon only in Double form; inferred Single precursors are given here, confirmed by reference to other definitions if available.
The table of work summarizes what each working bell does as it moves through the method/principle.
The From column lists the places a bell can find itself in at a lead end backstroke. Each row summarizes what happens for a bell in that place. The rows are listed in coursing order.
The Pass the Treble columns name the places in which such a bell passes the treble, first going in and then going out. The places in which such a bell rings over the treble are emphasized.
The Work column names the work such a bell performs. The names of the work in different methods appear to be arbitrary enough that this is set on a method-by-method basis, which so far I've only set up for a few common methods/principles. For all others, except for bells that hunt, treble bob, or hunt to a place and back (which can be automatically identified), the work is blank.
The To column gives the place such a bell finds itself in at the end of the lead, assuming of course no call was made.
As long as no calls are made, each working bell cycles through the table row by row.
If a call is made, some working bells will find themselves in another place at the lead end backstroke. Such a bell then continues on the row whose From place is that place.
The table of Ltcas lists who a bell follows as it moves through the method/principle, not in terms of bell numbers but abstractly in terms of
The From column lists the places a bell can find itself in at a lead end backstroke. Each row summarizes what happens for a bell in that place. The rows are listed in coursing order.
The Call column
lists the calls that can affect a bell starting from that place.
Only calls
that affect the bell's
Ltcas or To
place
are listed.
The Follows column lists the bells followed by a bell starting from that place, in terms of Leads, treble, course, and after. The bells starting from some places, namely the treble in methods and in some methods like Grandsire another hunting bell, have no course or after bells and so neither c nor a appear in the list of bells they follow.
If the bell is affected by a call, its Ltca list is presented for the call too.
The To gives the place the bell finds itself in at the end of the lead.
I learned when to look for the treble in Plain Bob this way.
The software that runs this page is larded with runtime checks for unexpected errors and internal inconsistency. The error signal indicates when any of these checks find a problem.
There are already programs and tables and charts out there — why bother to write my own?
Which are the handstrokes and which are the backstrokes?and
What (ordinal) number is that row?, questions whose answers I suppose knowledgeable ringers already know or don't need to know; but I kept getting mixed up about the strokes and I wanted to be able to know which row I was looking at (the 5th one, or the 125th one, or …) so I could refer back to it later. So I started writing programs that addressed the issues that were puzzling me. You'll note that this page produces charts and diagrams in which backstrokes have distinctive backgrounds, and in which every row is numbered.
convenienterrors that fitted how I thought things should be turning out. Writing a program to do it for me eliminated the second concern and reduced the first one.
And why not just use the CCCBR method libraries to define all the methods and principles?
what(what chart, what diagram, what permutor, what calls, …) but also why. I give explanations for everything, at least to the limit of my understanding. If you are code-minded, you can look at the code, too, and see what's happening in detail and specifically.