Many TurksHead Knots (THK) can be produced by first tying one of  three basic foundation knots, which are the 2pX3b, 3pX2b, and the 3pX4b THK. Adding additional turns or  AB crossovers will increase the number of bights and  by using a method called laying the tracks and using a "mule" the  THK can be EXPANDED to produce a variety of larger knots. Once you gain experience in tying THK the need to use the mule can be eliminated.

All of the larger knots (in this tutorial) which have an EVEN number of parts will begin with the 2pX3b THK as a foundation knot and all the larger knots that have and ODD number of parts will have a foundation knot that is either 3pX2b or 3pX4b.

The number of times the foundation has to be raised depends ONLY upon the number of parts!  Subtract the number of parts in the foundation knot  from the number of parts in the desired knot and divide that result  by 2 and the answer is the number of times you need to increase the foundation knot. 

 As to the number of extra turns or AB crossovers needed to get to a specific number of bights, that number is the bightsdesired minus the  bightsStart plus the parts in the foundation knot take all of that and divide it by the partsDesired  and then subtract one. 

All that information is to remaind me about the mathmatics involved but I have generated a table that allows you to EASILY choose the final topology and see what the required foundation knot is and to determine how many extra turns or AB crossovers are needed and how many times the foundation knot has to be raised. The table is presented below and covers many of the knots that are tied in hand.

                                                                  PARTS

Following the blue line diagonally from right to left you see that you  encounter the 3pX2b foundation  three (3) times before you reach the far right side.  This is the number of times the knot will have to be raised. 

Continuing to follow the blue line upward you move only once (1) time before reaching the top most occurance of the 3pX2b foundation.  This is the number of AB crossovers that will be needed. 

To summarize the 3pX2b foundation is first given an AB crossover which increases the knot to a 3pX5b. Next using the "mule" the knot is raised from the 3pX5b to a 5pX9b,  the process is repeated again and the knot becomes a 7pX13b and finally the process is repeated for the final time which raises the knot to a 9pX17b THK

There are some good sites that discuss the use of the mule and increasing the dimensions of THs.   Until I have added the photos and discusssions of those techniques here I would direct you to the following websites for some good examples of how to increase THs.

The Alaska Museum of Fancy Knots website  has a good tutorial on how to make  Nantucket Sailor's Bracelets which demeonstrates the use of the mule on both odd and even part THs and a discussion of AB crossovers. 
   
A tutorial by Bud Brewer on the KHWW website called Nantucket Mat    demonstrates how to increase a TH by performing an AB crossover  and without using the mule.

Since there is a signifigant amount of information on the table above which contains ALL of the information about "EVEN" and "ODD" part THs on the same chart , I have made a separate table for each type .  

The color of the diagonal lines indicates which side of the Standing Part (SP) that the Working End (WE) should take when starting to lay down the tracks.  The mule will split the tracks and will assist you to determine whether to pass over or under the next bight.   Of course the WE changes to the other side of the SP as it makes the down pass and then reverts back to the original side on the next up pass if applicable. 

The diagonal lines represent the INCREASES in the number of leads from a 2 lead  to a 10 lead for the EVEN part TH knots and from a 3 lead to a 9 lead for the ODD part TH knots.

The column to the left of column2 for EVEN PART THs and vertical column3 for ODD PART THs  shows how many initial bights (loops) have to be tied before doing any expansion.    Each time the same foundations typ2 is encounterd  as you move up in column 2 or 3   represents another loop for 2pX3b THs or another AB crossover for the 3part THs..

The table below is for EVEN PART THs and the starting point for these expansions will be the  2pX3b TH  which is a simple overhand knot where the WE is brought up next to the SP. 

NOTICE:  If the 2pX3b is expanded by taking the WE to the left of the SP, a 4pX5b TH will result, however if you expand by taking the WE to the right of the SP the resulting TH will be 4pX7b !!!!!!!

For ODD PART THs  the starting point for the expansions will be either the  3pX2b TH  or the 3pX4b TH.  The diagrams below show the 3pX2b and 3pX4b starting  knot topologies as wll as a diagram of how to perform an AB crossover.

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Turks Head Knots using Pins and a Former

If you set two rows of pins into and at the sides of a  board or at the sides of a  tubular form and assign the pins numbers such that the pin numbers are same on the left as they are on the right, then all you have to do is to determine the number of BIGHTS you want and you will have to insert the same number of pins on each side  of the form as there are bights.  To determine how to tie the Turkshead you will start at Pin 1 and attach the end of the cord to pin 1.  In order to determine which pin the cord should go around will be determined from the number of leads or parts. 

 THE RULE :  is to take the number of LEADS and subtract 2, then divide that answer in half and that is the number of pins to skip over. 

                        P= (Leads -2)*(1/2)

 What to do if the number does not come out a WHOLE NUMBER (you know it has a remainder)???           (This WILL happen for all ODD part TH's !!!)
That is easy just forget about the remainder and skip the WHOLE NUMBER of pins on the leftthand side BUT on the righthand side you will skip the WHOLE NUMBER PLUS ONE more. Thats all there is to it. 

When you are counting up you will have to stay in  modulo(BIGHTS) arithmatic but that will not be a problem because you will only have the same number of pins as there are bights so you will automatically have to go back to pin 1 when you reach the last bight.  We will show how this works with an example.

EXAMPLE  7pX6b TH 
Begin by finding the number of pins to be skipped
 (7-2)/2 =2.5  then WHOLE NUMBER is  2  
and so the number of pins to SKIP on the left will be Pl = 2
and  the number of pins to SKIP on the right will be Pr= Pl+1 = 2+1 =3 

Starting with the lower pin1 (our righthand side) we skip two so we have
1 + 2 +1 = 4  so this is pin4 on the lefthand side (our topside)  from there we go to 4+3+1 =8 - 6 =2.  This pin2 on the bottom side.  Notice since we went higher than the number of bights we sutracted that number from our total to bring us to the proper location. Continuing on we start with pin 2  so
2+2+1 =         pin5  top                  5+3+1=9-6=   pin3  bottom               
3+2+1=          pin6  top                  6+3+1=10-6= pin4  bottom                    
4+2+1= 7-6= pin1  top                  1+3+1=           pin5  bottom               
5+2+1= 8-6= pin2  top                  2+3+1 =          pin6  bottom                 
6+2+1=9-6=  pin3  top                  3+3+1 =7-6=  pin1  bottom               


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Flat TH  Mats Cordage Length Calculator

The Flat TH Cordage Calculator computes the cordage lengths for  Turks head and Multistrand circular mats  and also generates a KNOT TEMPLATE  which can be followed when tying the knot and a MAT TEMPLATE (that  can be printed).   Below is a picture of the calculator



Shown below is a view of one of the templates the Mat Template can generate.


The calculator may be  borrowed for evaluation   (like checking a book out of the library).  

                              Simply click  Mat Calculator    

To purchase your own registered calculator visit Knotworkn Market       

After the file  downloads to your computer press RUN then RUN again and when the registration page  comes up then press the START button.

I have not personally tested this calculator against  many of the mats that are possible. since I personally prefer the cyclindrical form but I developed this calculator as a tool for the many folks that do tie TH mats  at the request of Gordon Perry. 
I put it here for people to use and to evaluate it.  I have a feedback form on my home page and would appreciate any comments that you are willing to provide especially if they could be used to improve the calculator.
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 Single Strand  8 plait braiding

An example of single strand 8 plait braiding is shown in the picture below. 

 To braid a single strand eight plait grommet obtain at least seven feet (210 cm) of cordage and locate the center.  At the center form a circle of roughly 3 inches (7.5cm) diameter taking cordage from both halves equally.  Begin to form a grommet by making four turns around the starting loop with each of the free ends being sure to keep the lay of the grommet correct.


The pictures above show the first two strands of the grommet. 

Shown below  are the third and fourth strands of the grommet laid up




The next steps show how to interlock the cordage and to start the interweave of the grommet. 

The strand coming from the right passes to the left of the leftmost strand and then turns back towards the right crossing in front of the leftmost strand and over ONE additional strand and then passes UNDER itself and the additional strand.  

The leftmost strand after passing to the right of the rightmost strand then turns towards the left passing OVER the rightmost strand and then immediately passing UNDER the TWO strands that were not passed under by the rightmost strand.  This is the same as passing OVER the same two strands that the rightmost strand passed under.

The picture on the left below shows this process clearly .    The photo on the right below shows the same information as the photo to the left but additionally shows how to interweave the strands in order to make the plait.



Each cordage end is woven over TWO then under TWO.  The weaving should pass over and then under the SAME two strands each time. Continue the weaving on around until the area where the cordage first interlocked.


The figure above shows the weaving pattern as the strands pass through the initial interlock for the first time.  The weaving sequence is always the same over 2 then under two.




In the photos above the over 2 under 2 can easily be seen. The awl is pushed under the two strands that need to be passed under and the two strands between the awl  and the working end  are  the two strands that are to be passed over. The interweaving tends to spiral around the grommets as the weaving progresses.


The lobes of the interweaving are apparent in the photo above with three sets of  lobes then a space  followed by another set of three lobes a space and so on .  At this point  all but the last sequence of weaving has been completed.  The rightmost strand has made  two complete rotations of interweaving and so must the leftmost strand so that with the four strands from the grommet and the four fron the interweave we get an eight strand plait.



The photo above shows the end of the interweave and the strands meet at the same location passing under two strands.  All that is required is to go back through and adjust the tension and remove any slack from the plait.


At this point the ends can be lashed and clipped or they can be fed up through the plait and tied into a two strand Matthew Walker knot or a diamond knot.

Below are some  examples of single strand eight plait knots.



This is a collection of the first three knots of the Periodic Table of Knots formed using single strand 8 plaiting.  The knots are connected together using Spanish Ring knots. 

The Periodic Table of Knots is shown below and is one of those items that I do not know from whom I received the photo.


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