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Added 2011 March 17th
SOME VERY IMPORTANT CLARIFICATION ABOUT ENLARGEMENT
METHOD or PROCESS la Schaake

This is ignored by most knottyers.

When knottyer are speaking of 'enlarging a THK', say a  3L 4B enlarged to a  7L 10B
going on the RIGHT side of HP1 ( Spart vector ) in a METHOD I or PROCESS I
(so-called TYPE I) say " I made AN enlargement" " which is readily understood but is
an
abuse of language and logic.

IN FACT the knottyer's unique enlargement is for SCHAAKE TWO SUCCESSIVE
ENLARGEMENTS OF THE SAME METHOD.

A THK enlargement seen from the cordage route perspective establishing that indeed,
logically this use TWO successive enlargement PROCESS OF THE SAME  TYPE.


A THK enlargement seen from the basic knottyer's point of view.


When "pushing" the 3L 4B THK to a 7L 10B  THK (a COLUMN AND ROW coded
Regular Knot)  the first enlargement pushed the 3L 4B THK to a 5L 7B REGULAR
KNOT as far as the cordage route or shadow is concerned  and it is a 5L 7B Neither
COLumn NOR Row coded Regular Knot.
You need to get again a THK and this will  be done by the second enlargement.

Pray, realise, very clearly and sharply that when you say xL yB  you are SPEAKING
OF A CORDAGE ROUTE AND NOT  OF A PARTICULAR KNOT !

THIS IS VERY IMPORTANT because one may conceive of ENLARGING WITH
KEEPING THE CODING  and ENLARGING WITH A CHANGE OF CODING,
say from THK to GAUCHO Knot. 

Here you will realise that a THK MAY BE ENLARGED EITHER ONCE OR TWICE
and makes AN EVOLUTION TO ANOTHER CODING than the THK's.



This xl yB ( GDC=1) MAY BE ANY OF THE REGULAR KNOT .
Only by adding a particular coding on a 'generic' cordage route' will you get a particular knot.
Distinguish ENLARGING A CORDAGE ROUTE
and ENLARGING A PARTICULAR KNOT ( route + coding )


FIRST ENLARGEMENT  /  LAYING THE TRACKS
SECOND ENLARGEMENT SPLITTING THE TRACKS


Knottyers are obsessed with THE KNOT but they completely forget that a knot is a
cordage route AND a coding.

When reading Schaake you will do well to keep this topic in mind because it bears
on the formulas than Schaake gives for Column-coded Regular knots such as Gaucho
( Spanish Ring) , Head-Hunter, Fan....
If when Schaake write about two successive enlargement of the same type you
understand two of the abusive and illogical name used by knot tyers.
THIS IS A VERY IMPORTANT POINT THAT, ONCE AGAIN, HALL
MUDDLED WHEN HE EXPLAINED SCHAAKE's ENLARGEMENTS JUST AS
HE MUDDLED THE BIGHT ALGORITHM.




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Added 2011 March 17th
Here  is what I found yesterday
Illustration of the point made just above : HOW TO USE THE ENLARGEMENT
PROCESSES ON A THK TO MAKE IT EVOLVE TO A SPANISH RING KNOT or minimalist GAUCHO Knot.

Take a 3L 11 B THK and apply to it two successive (see topic just above ) TYPE II
ENLARGEMENT
processes (what knottyer mistakenly consider to be ONLY ONE
ENLARGEMENT) to GET THE7L 25B CORDAGE ROUTE
and make sure that
you DO NOT use the same crossings that you would use for making a larger THK but
apply a CODING THAT WILL YIELD A MINIMAL GAUCHO knot or SPANISH RING Knot.

Taking a 3L 13B THK and TYPE I processes you will get a 7L 31B Spanish Ring Knot if you are careful to put in the correct code.


To distinguish THIS from an ENLARGEMENT which KEEPS THE SAME CODING
will enlarging the cordage route I prefer to call that EVOLUTION as the coding MUTATE while the cordage route is made larger.


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Added 2011 June  21st

Making a better job than ASHLEY did on some of his knots.


DISMANTLING SOME KNOTS DIAGRAMS AND REBUILDING THEM
ABoK#2216   ;   #2217   ;   #2218   ;   #2219 (1391)   ;   #2222   ;  #2232
AS THEY SHOULD HAVE BEEN DRAWN (imo) IN THE FIRST PLACE :
AS CYLINDRICAL DIAGRAMS


23 pages Pdf - 4.92Mo

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RELATED TO THE TOPIC (MAY 17th)  JUST BEFORE THE ONE ABOVE

Added later August 1st 
Relating exploring made late July-early August 2011


What you need to understand, I stress again is that it is essential not confuse Enlargement of a knot and Enlargement of the Cordage Route (the knot without any crossing specified in its type).

 What should not be forgotten either is that the number of crossing in a row ( horizontal tool) is given by (Nb PARTS - 1).
It follows that a THK with an ODD number of PARTS has an EVEN number of crossings in a Row and can therefore be considered  as a minimalist GAUCHO 1-PASS.
In this case I cannot truly say that there has been a  MUTATION but rather an
EVOLUTION. 
A THK with an even number of PARTS would be a minimalist 1-PASS HEAD-HUNTER knot.

On an enlarged cordage route, expanded  from  9L 8B to 25L 22B it is possible, for example,
to make GAUCHO 2-PASS 3-PASS 4-PASS-PASS 6, 8-PASS  12-PASS 
but this is when starting with being completely free of our crossings, unfortunately before the enlargement there were crossings in the THK  and must live with them and try and accommodate the style of coding with the empty crossings places on the route while taking in account the existing crossings. In this case there is only one viable possibility : the 3-PASS.
Surely there are formulas to find which can predict the possible evolution but  I have not found them yet ;-)
The nomber of columns (horizontal tool) of crossings hence of crossings on a row is dependent on the number of  PARTS.
The number of Rows of crossings is dependent ont the number of BIGHTs ( 2*B)
So for a COLUMN CODED we need to 'tweak' the PARTS and for a ROW CODED we need to 'tweak' the BIGHTs.


Here is the example of a THK 4L 5B that becomes a HEADHUNTER Knot  3-PASS  
10L 13B


I think that now you have all the necessary and sufficient to have understood and to launch your own exploration without undue difficulties.






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Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2014 -(each year)

Url : http://charles.hamel.freeL .fr/knots-and-cordages/B