Multiple String Casa Turksheads
Two String Casa Turksheads
The basic technique
If we start a knot defined as an even number of parts X an even number of bights which have a maximum common divisor of two, an interesting thing happens. At the exact midpoint of the knot the running end comes back to the standing end and brings things to a halt. However if we look closely at this partial knot we see that the bight progtession was two so there is a good place left to interweave the same partial knot into it, completing the original proposed knot with the second string. Further more there is a regularity to the pattern of both partial knots that makes the end result very easy to braid. In specifying the complete knot we must meet two criteria
First both numbers must be even.
Second they must have a common divisor no greater than two.
A 6 part X 8 bight knot
This is the first partial knot for this knot. At the left we have started a six part knot on an eight part mandrel with the usual bight increment.This will be a conventionaly coded knot. The first wrap is a free run since the bights are greater than the parts. The second wrap crosses the standing end in it's downward pass. Note the small white insert between the two pin bight progression. This is to show one of the nuances of braiding a knot by inspection. It shows the proper braid exit and entry for any knot with even parts (If this in not burned into your brain yet, see Lesson Two). Here we make the contrary crossing from an adjacent part to complete the casa pattern. In a minute you will see that this part was not really necessary but I wanted to throw it in any way.
In the center sketch we add the third wrap in green again with the existing part in red.
The right hand sketch completes our first partial knot. Observe that there is no place to tuck the running end to complete the not at this time. Just leave it hanging for now and this problem will go away after the interweave is in place.
Also see that each half wrap going up went over everything it crossed and each half wrap coming down went under. This will be true of all conventionally coded knots of this kind.
At the left is the first wrap of the "new" knot in the interweave. Here we go under every thing in the old knot as we go up and over everything in the old knot as we come back down. This pattern will continue throught the interweave.,br> In the second sketch we place the second wrap of the interweave. I am leaving the previous wrap green so you can readily see the "old" and "new" knots. In the second half of this second wrap the running end of the new knot crosses the standing end by going under. This is needed to "complete the braid". At this point the pattern becomes
going up - under the old - over the new
going down - over the old - under the new.
Two more wraps following these sequences completes a 6 part 8 bight casa turkshead and we now have places for the regular "tuck-ups" to complete the knot.
The two sketches show the knot tightened up and finished as a two color version and a single color knot. Notice that the two color is the barberpole color pattern.
Here is a small template of a 14 part X 4 bight version of the same knot.
Tools and Tips
The chart at the left shows the running sequence for both conventional and sobre coding for these knots.
The table at the right is a list of all the smaller possible knots with the proper common divisor. Of course it could be expanded by following the same pattern.
Because all turksheads are symetrical, you can start the second knot at the top of the first so the two finish on opposite sides so long as you observe the run sequence directions from the chart.
Nesting Bights
You might notice from the material so far that the second knot or interweave is placed by just making a contrarty crossing at each crossing of an existing part and observing braid entry and exit conventions. This also makes nesting bights with the interweave an easy process so that you can create casa coded "pineapples".
Also see where we took the final "tuck-up" in the foundation with the standing end.
Three String Casas
The Basics
The process for three string knots of this type is a little different in that they are simply three interwoven simple turksheads. Each of these will have 1/3rd The number of parts and bights of the finished knot.
This is a 6 part X 9 bight knot. With the interweaves being only 2 parts X 3 bights we need to pay particular attention to braid entry and exit here because the previously crossed parts are so few.
In all cases we start these knots on a pinned mandrel using the increments for the parts in the completed knot and not the interweave. (Do you have a 9 bight mandrel. I didn,t until I started using these 3 string knots.)
The color pattern in the bottom template was obviously obtained by using one color for two strings and another for the third. I have no idea what to call it but it is symetrical at least and useful for the customer who wants to see something new.
This knot done with with 1/8th goat lace and 33 bights makes a novel hatband for the average adult hat.
Here are two larger knots ( 9X12 and 15X9 ) so you can see the color pattern a bit better.
In truth there are not a great number of these knots, but when the math works out they give us something different to work with.
The Four String Knots
The Basics
Since we are back to even numbers the basic structure of our foundation is the same as for the two string knots. For this 12 X 8 knot it is a 3 part 2 bight with every thing going up crossing over and coming down crossing under.In the second template we lay in an identical run adjacent tp the first.
Again notice that we use the increment for the twelve part final knot. The contrary crossings of previously crossed parts is what establishes the casa coding.
The left template is the third interweave in the same manner. The easiest way to do these is just observe the contrary crossings thet maintain the casa coding.
The center template is the fourth interweave in place. Since we alternated the two colors in the braiding, we have another "barber pole" color pattern.
The third template is the color pattern from placing the two colors adjacent in braiding the same knot. This is what I call a "houndstooth or pinwheel" .
Nesting Bights
This is the start of what will finally be a 12 bight X 16 part type 3 pineapple knot. The first section is a 4 part X 3 bight structure placed on alternate pins of a 6 bight mandrel. The two sets of bight boundaries are marked in this first template so you can see how the structure will fit in the final knot. In nesting the bights the concept of bight intervals kind of gets lost. Just follow the template.
Now in the left template just parrallel the previous template from an inner bight boundary at the bottom to an outer bight boundaryat the top with the basic foundation knot- observing the contrary crossings as you go.
The last pass around the knot is a repeat of the second template at the new bight positions.
The final tuck-ups for this type of knot are always a little bit "fussy" and I just do what seems to work best at the time.
Copyright Sidney Wood 11/20/08
