[r-t] Definitions so far

[Richard Smith]

Thanks for these comments, Don.

Don Morrison wrote:

> On Sat, Jan 17, 2015 at 1:19 PM, Richard Smith <richard at ex-parrot.com> wrote:
>
>> 3.  Bells are conventionally numbered with '1' denoting the
>> highest pitched bell being used at the time, '2' denoting the
>> second highest pitched bell, and so on.
>
> Given the complex psychoacoustic phenomena around bells are we sure
> that "highest pitched bell" is uniquely defined? Also, do we want to
> worry about the possibility of towers with two bells pitched the same?

Personally I'm not too concerned about this.  Is anyone 
else?

>> 1.  A /row/ is a sequence of one or more blow.
>
> I presume this is a minor typo and is intended to be "blows".
> I believe it should explicitly state "a finite sequence".

Both good points.  Now corrected.

>> 4.  Rows are conventionally denoted by writing in sequence the
>> number of the bells sounding each of its constituent blows.
>
> Is this really true? Is it not the symbol representing that bell,
> avoiding two digit numbers?

Good point.  I've replaced 'number' with 'bell symbols'.

>> 7.  When one or more bells sound in the same order the last
>> blows of each row for an extended period, these bell are said
>> to be /covering/.  When a covering bell is present, it is most
>> commonly the tenor.
>
> I'm having trouble parsing "sound in the same order the last blows of
> each row". Is this a typo, or am I missing something?

I think I missed a word out:

7.  When one or more bells sound in the same order *as* the last
blows of each row for an extended period, these bell are said
to be /covering/.  When a covering bell is present, it is most
commonly the tenor.

> I presume "an extended period" is deliberately vague? The difference
> between a covering bell and the 4 in Cheeky Little Place Minimus
> would seem to be an entirely social construct. Perhaps any definition
> of covering needs to make the distinction between covering and currently
> unusual methods explicit?

Yes, it's intentionally vague because I don't believe it can 
be defined rigorously for the reason you say.  A touch of 
Plain Bob Minor could be considered variable cover doubles, 
but my use of the phrase "for an extended period" was 
supposed to suggest that this was somewhat against the 
spirit of the rule.  Similarly, in my view Itram Little 
Place Minimus is somewhat against its spirit, as it's really 
a Singles method with cover.  But I don't think its feasible 
or desirable to make either interpretation illegal. 
Perhaps we say this explicitly?  "These definitions do not 
attempt to define how many consecutive blows constitute an 
extended period."

>> 8.  A /working row/ is the representation of a row once any
>> covering bells have been removed.  An /ordinary working row/
>> is a working row which is also an ordinary row.  In casual
>> speech, it is normal to refer to an ordinary working row as a
>> "row", or even as a "change".  The latter use is discouraged.
>
> It is not clear whether "latter" refers to "after ordinary working
> row" or "after row". Perhaps it would be better to replace "the latter
> use is discouraged" by something like "use of 'change' to refer to a
> row is discouraged."?

Agreed.

>>   (d) Any higher odd stages, 2n+1, is named using
>>   Latin-derived name for an n-tuple names: 13 is /Sextuples/
>>   from the Latin /sex/ meaning six, 15 is /Septuples/ from
>>   /septem/ meaning seven, etc.
>
> Minor typo(s) here, should be "any higher odd stage" or "are named",
> etc.

I've gone with "any higher odd stage".  The "names" after 
n-tuple was also superfluous and is now gone.

>>   (c)  An /ordinary change/ is any change that combines the
>>   effect of one or more plain changes, each of which affects
>>   different bells.  The null change is excluded from this
>>   definition by convention.
>
> The last sentence is redundant. I presume this is intentional.

It doesn't add anything to the definition, but I felt it 
helped explain it: the null change is excluded not for any 
good technical reason, but because it would be unpopular to 
include it.

> I fear "each of which affects different bells" is ambigous.
> I can imagine someone reading this thinking "1-2" and "2-3" are
> "different bells" since they are different pairs of bells.

What about:

    (c)  An /ordinary change/ is any change that combines the
    effect of one or more plain changes, each of which
    exchanges non-overlapping pairs of bells.  By convention
    the null change is excluded from this definition.

(I did have 'disjoint', but I think I prefer 
'non-overlapping' as less technical.)

> It's a little surprising that changes are defined in terms of
> positions, but kinds of changes are defined in terms of bells.
> I don't think it causes any trouble, but does set me to
> scratching my head.

I'm happy to rephrase if you can think of a better wording.

>>   (d)  A /jump change/ is any progression between ordinary
>>   rows that is not an ordinary change, nor the null change.
>
> It might better to phrase this as "any progression between ordinary
> rows that cannot be described by an ordinary change, nor the null
> change". While no ringer would do this, I could imagine a naive
> non-ringer coming to these definitions, and starting to think in terms
> of swapping around pairs of bells. And coming up with the "change"
> that consists of apply swaps of positions 1-2, 2-3, 4-5, then 2-3
> again, and concluding that results in a jump change. This potential
> issue may afflict some of the earlier kinds of changes.

I see what you mean.  I've adopted your wording, except that 
I've replaced "nor" with "or".

>>   (b) The /cross change/ is the ordinary change in which every
>>   bell swaps places with an adjacent bell.
>
> Shouldn't this be "a cross change"? I don't think "the cross change"
> is unique. Isn't there a different one for each even stage?

Good point.  Much the same applies to null changes.

>> 5.  A /stage change/ is a change that progresses from a row of
>> one stage to a row of a different stage.
>>
>> 6.  A /cover change/ is change other than a stage change which
>> either alters the choice of covering bell or bells, or alters
>> the order in which they strike.
>
> It may be a failure of my imagination, but I'm having trouble
> reconciling these non-working changes with the definition of change. A
> "transposition" doesn't seem to have any room for bells appearing and
> disappearing, does it?

No, but it probably should: think 12345 to 21432, a possible 
first change in cylindrical.  And, to be honest, "A /change/ 
is the transposition that effects the progression from one 
row to the next" is rather wordy.  How about defining change 
simply as "A /change/ is the progression from one row to 
the next"?

But even when we restrict ourselves to ordinary rows, 132546 
is a six-bell row.  It could be a row of Minor, in which 
case the working row is 132546; or it could be Doubles with 
the tenor covering, in which case the working row is 13254; 
or it could be Minimus with 46 covering and 1325 as the 
working row.

Let's suppose it's Doubles, and it is followed by a 12 
(six-bell) place notation to the cover while still ringing 
Doubles.  The next row is therefore 135264, but the next 
working row is 13526.  The change is an ordinary change 
because changes are defined by their actions on rows, not on 
working rows.  It's also a double change as two pairs cross 
in the row.  It's not a stage change because the changes 
before and after are both Doubles, but it is a cover change 
as 6 was covering before and 4 is afterwards.  And because 
it is a cover change, it is not a working change, nor is it 
an ordinary working change.

Has that helped explain what I mean?

The reason for the definition of a working change is that I 
plan to define a method in terms of a sequence of working 
changes.  That is, a method cannot include a change of cover 
or of stage in its plain course.

>> 8.  Ordinary working changes (and the null change) are
>> conventionally denoted by writing in order the places made.
>> For example, in Minimus the single change that swaps the bells
>> in seconds and thirds place is denoted '14', as places are
>> made in first and fourths place.  Bell symbols are used for
>> places above ninths place.  The cross change is variously
>> denoted 'X', 'x' or '-'.  This representation of a change is
>> called its /place notation/.
>
> This representation is the heart of place notation, but place notation
> requires a little bit more, doesn't it? A convention for
> disambiguating adjacent non-cross changes, and the convention for
> (optionally) eliding some unneeded places.

The place notation of a block needs separators, but here I'm 
defining the place notation of a change.  Your point about 
optionally eliding external places is valid, though.  How 
about adding: "Where a place is made leading or lying, it 
may optionally be elided, providing not all the places are 
elided."

>> 1.  A /block/ is a sequence of rows where the progression
>> between rows is defined by changes.  A /sub-block/ of some
>> block is a sequence of contiguous rows from that block.  It
>> too is a block.
>
> Must a block be finite? Must it be of non-zero length? Must
> a sub-block be of non-zero length?

Good point.  "A /block/ is a finite sequence of one or more 
rwos ..."  I don't think I need to explicitly state that 
sub-block must have non-zero length as I state that it is a 
block.

>> 2.  When a block is a sub-block of some larger block and does
>> not include the last row of the larger block, it additionally
>> has a /block-end change/.
>
> While I suppose one could argue it is really 1+2 that defines
> sub-block, it does seem kind of contradictory. Should
> (1) say something like "A sub-block of some block is a
> sequence of contiguous rows, possibly plus a change, plus
> a citation of its parent block"?

No.  A sub-block is just a block.  A block is sequence of 
contiguous rows, possibly together with a block-end change. 
Neither a block nor a sub-block need a citation to their 
parent block.

> All in all this whole sub-block thing seems confusing. It is a more
> complex entity than just a sub-sequence, but how much more complex
> depends upon its parent block. Perhaps there needs to be another
> entity defined which is a block plus a change, and that then is, under
> appropriate circumstances, a sub-entity of a block? I dunno, maybe I'm
> completely missing something, but it is making my brain itch.
>
>> A block without a block-end change is
>> called a /terminal block/, and a block with one, a
>> /non-terminal block/.
>
> The same block can be a terminal block and a non-terminal block,
> since its terminality depends upon the identity of a parent block.
> Or am I missing something?

No.  A block is either terminal or non-terminal because it 
cannot simultaneously have a block-end change and not have 
one.

Let me have a go at reformulating these two definitions.

1.  A /block/ is a finite sequence of one or more rows, listed
in the order they are to rung, together optionally with a
change referred to as its /block-end change/.

2.  A block may be divided into /sub-blocks/ whose rows are a
sequence of contiguous rows from the parent block.  A
sub-block is a block.  If the sub-block's rows do not include
the last row of the parent block, then its block-end change is
the change describing the progression from the last row of the
sub-block to the first row not included in the block.
Otherwise the sub-block's block-end change is the block-end
change of the parent block, if it has one.

3.  A block without a block-end change is called a /terminal
block/, and a block with one, a /non-terminal block/.

Is that an improvement?

I also need to state that a performance is a 
terminal block, and as I'd like to keep 4 (defining change 
ringing) as simple as possible, I'll put it in 5:

5.  A performance is a terminal block consisting of up to 
three sub-blocks.  In order they are: [...]

>> Usually the opening block and closing block constists of just
>> rounds, and referred to as the /opening rounds/ and /closing
>> rounds/, respectively.
>
> Needs the verb "are", I believe.

Thanks.  Fixed.

RAS