Square Knots
I am going to call all casa coded turksheads that differ in parts X bights by one as being square. All of these will evaluate by P/b=N+r as N=1 or for one crossing of the standing end and r=1 or r=-1 for a bight progression of +1 cw or -1 ccw. These knots are not only very easy to braid , but the technique involved can be used to create a variety of more complex knots with equal ease.
5 Parts X 4 Bights
This is the simplest case to illustrate the points I want to make. Observe that wrap by wrap, each half wrap ends at a braid exit at the edge of the knot. The result of this is that the knot builds from the edges upward in the first half and down in the second half. Consequently we are building the fundamental braid sequence for a path across the knot of U1-O1-U1-O1 in the reverse order as we braid. In the first wrap we go up clear and O1 coming down. The second wrap is O1 up and U1-O1 down. Wrap three is U1-O1 up and O1-U1-O1 down. The last wrap is O1-U1 O1 up and U1-O1-U1-O1 to finish. This working with the fundamental coding makes these knots exceptionally easy to braid. I have seen this referrred to as braiding to the pattern or weave.
6 Parts X 5 Bights
This is the same basic pattern in a knot with even parts. The coding here is U1-O1-U1-O1-U1 going up and O1-U1-O1-U1-O1 coming down. The two different ones are because this knot has an even humber of parts. They are the same in both directions for knots with an odd number of parts.
Another 6 Part X 5 Bight Knot
Since we are working directly with the coding pattern as we braid these knots, we can make it anything we want. If we change one row of the code pattern as in this panel at the arrows we can create a different knot almost effortlessly. This makes the coding U1-O3-U1 going up and O1-U3-O1 coming down.
The sketch on the left is the regular 6 X 5 and the one on the right is the one from the panel just above. This particular braid is shown in "Advanced Leatherwork - Interesting Braids and Flat Plaits" by Ron Edwards on page 100 as "Snake Belly 6 strand" and by Robert Black in the Sept. Oct issue of the Leather Crafters & Saddlers Journal as a hat band. I think I first saw it about 60 years ago at Teec Nos Pos or Atarque as a headstall for a bridle.
Some 9 x 8 knots
In the first sketch we have a complete template for a 9 X 8 casa knot. The little chart is a comparison betwen that coding and a 1-3-3-1 coding to see where they differ. You should see that we only change the two rows of coding marked in red to make a different knot. The numbers at the bottom of the templates are the termination of the wraps. Notice in the next drawing that we don,t deviate from the casa coding till near the end of the third wrap.
In the rest of the wraps we just build the new code kind of backward as we go.
Here are a sketch and photo of the U1-O3-U3-O1 coded knot. the photo is done with 1/8th 'roo scrap. This knot looks a lot like a three pass ring knot with a single pass edge
, but is a single pass throughout so far as the braiding goes.
The semantics of single and multi-pass knots tends to confuse me a little. Basically I consider any knot done with a single string to be a single pass braid.
A 9 part 10 bight example
There are only two things different about this one.
First the bight progression is CCw.
Second I have chosen to use "sobre" coding to place the over crossings at the braid entry as we braid.
Also notice the finish is done with the standing end.
About This Topic
In this discussion I have tried to make two main points. The first being the ease with which this particular type of knot can be braided.
The second is that, since the knot builds from the edges, we can run in any coding sequence we want by visual inspection. It is best to use an odd number of parts so the code pattern is symetrical and use a single crossing at each edge for stability in the finished knot.
Copyright Sidney Wood 11/30/2007