As you explore more weave structures and dive deeper into sett, you will begin to hear the word “density” a lot. This can relate to how you calculate the sett or how you think about the relationships between structure and your materials.
Note: This blog post was updated in August 2023 to clarify the different kinds of repeats. I’ve changed what I was called a “threading” repeat to a “spacing” repeat to, perhaps, offer clarity on the two different kinds of repeats discussed here. In the earlier version of this post, the sett density in Fig 1 was miscalculated as 160%.
Spacing vs Structure Repeats
Achieving various threadings in the multi-heddle world involves spacing the ends a little differently than you may be used to. This may involve cramming the slots or skipping slots and holes. The crammed slotted ends allow you to thread a warp end through a hole in one heddle, then pass that end through the slot of another heddle(s), giving you control over each individual end. You can’t cram a hole and achieve control over each end. To calculate the sett of a multi-heddle threading, you need to take this spacing into account. To do this, it is important to understand the difference between a spacing repeat and a structure repeat.
A repeat is the smallest common repeating sequence.
The spacing repeat is how the warp ends are spread among the slots and holes to provide enough ends to thread any given weave structure. If you thread 3 ends in a slot and 1 end in a hole you have 4 ends spread out among 2 spaces, one space being a slot and the other space being a hole. Ends crammed in slot can be threaded through a hole or a slot in another heddle giving you agency over each end and the ability to place them in the order needed. You just can’t thread an end in a hole in another heddle hole.
The structure repeat is how the ends are ordered to achieve a specific structure. Each heddle has a different spacing repeat, but the structure repeat doesn’t change. The spacing is in service of arranging the ends so that you achieve a certain structure.
For instance, in Fig. 1, the back heddle spacing sequence repeated over and over again is 3 ends in a slot, 1 end in a hole, 1 end in a slot, 1 end in a hole, for a repeat of 6 ends over 4 spaces. These diagrams are oriented to be read from right to left, although you can thread them from either direction. See this blog post for more information about threading orientation.
Fig. 1 Point Twill on Three Heddles at 150% Density
For the shaft-loom weavers among us, think of this as how you would space your reed to achieve various setts. This is called “denting” because the slots in a shaft-loom reed are called “dents”. Rigid-heddle weavers, you don’t need to understand this to carry on.
This spacing repeat allows you to arrange the ends in a point twill order and have control over each individual end. Working from right to left the Heddle 1 Hole end (H1) is next to the Heddle 2 hole end (H2) end, which is next to the Heddle 3 Hole end (H3) which is next to a slot (S), then descend back through this sequence. Your structure repeat would be H1-H2-H3-S-H3-H2. This repeat is worked over 6 ends that are spaced differently in each heddle. If we assign numbers to these positions, it begins to look more like the sequences you see in shaft drafts, 1-2-3-4-3-2.
Sometimes spacing and structure repeats align in the front or back heddle and sometimes they don’t. This can be a function of if you are reading from right to left or left to right. I set up all these threading to be read right to left. Some repeats require a balance or a small portion of the spacing or structure repeat to evenly spread the structure repeat across the warp or to create the same interlacements at either edge. In the point-twill threadings I’ve provided as examples, I’ve included these balances, although we will save a discussion about balances for another blog post. I’ve also included slotted selvedges. (Hint, if there is a balance it is typically at the end of the threading so that gives you a clue to how the author set up the threading. This isn’t always the case as there are sometimes balances at the beginning and end.)
Calculating Sett Density Based on Spacing Repeats
What does this have to do with sett? Sett density is based on the spacing repeat and is expressed as a percentage of the heddle size. In a multi-heddle threading, the spacing sequence can be different for each heddle, so which one do you choose?
When determining sett, I look to the back heddle. The ends tend to be the most spread out over the back heddle, although this isn’t always the case. It is also the spacing I’ll need to use if working the direct warping method, so I can puzzle out two pieces at the same time. (If you are curious about warping, join our study group.)
In the point-twill spacing repeat in Fig. 1, you have more warp ends (6) than you have individual threading spaces (4), slots and holes, or 50% more threads than you do individual spaces to thread them. The formula to determine density is ends divided by spaces to get a decimal. Then change the decimal to a percent moving the decimal over two places to the right. In this case 6 ÷ 4 = 1.5. You would multiply your heddle size by the decimal, but the density is expressed as a percentage, which is achieved by moving the decimal over two places—1.5 = 150%. If using 12-dent heddles, your sett would be 18 e.p.i. (12 x 1.5).
Along the side of the threading in Fig. 1, you can see the various sett options on different heddle sizes. The dashed lines represent how the ends will spread when off the loom and washed.
If you look at the front heddle the spacing repeat is different, but the density is the same. The spacing repeat is 1 end in a hole, 5 ends in a slot, 0 ends in a hole, and 0 ends in a slots. This still gives us 6 ends over 4 spaces and the same sett density.
As discussed in a previous post, there is more than one way to thread any given structure in the rigid-heddle environment. You can reconfigure the threading, skipping more spaces to put more distance between the crammed areas to get closer to the sett you want. (This also applies to a single-heddle world.) In Fig. 2, you can achieve a 75% density. In this example, the spacing and structure repeats align.
Fig. 2 Point Twill on Three Heddles 75% Density
You can also thread this structure on two heddles achieving either 100% density or 150% density. Notice how in the threading on the right, the 1 is in a slot, and on the left, it is in a hole. As a rigid-heddle weaver, I have the freedom to assign threading positions to any number I like as long the ends are order how I need to achieve the weave structure I’m looking for. In the case on the right, I can place 1 on a heddle rod (R) and 4 on a pick-up stick (P). In the threading on the left, I would place 3 on a heddle rod and 4 on a pick-up stick. You could also adjust your materials to suit the sett in your preferred setup, which brings us to our next look at density.
Fig. 3 (Left) and 4 (Right) Point Twill on Two Heddles at Two Different Densities
Structure, Materials, and Hand
This could warrant an entirely separate blog post, but the subject is so closely related to determining these sett choices. I talk about sett in terms of open, balanced, and close. I prefer these terms rather than assigning a structural name to each density, although there is also logic in that thinking. Twills do perform well on a sett closer/denser than plain weave, but that doesn’t mean you can’t use a variety of densities and get the twill hand you are looking for. How firm or supple your fabric needs to be, your fiber type and size, and how the yarn is constructed, play a substantial role in making your ultimate sett decision. Any given yarn will have a maximum and minimum sett where it will perform well. To make these decisions, we often look to sett charts.
There is another way to look at determining sett developed by Thomas R. Ashenhurst, a nineteenth-century author who created a formula that is known as the Ashenhurst’s Rule. The basic formula is .9 of the square root of the yd/lb gives you your maximum density. It is popular among shaft loom weavers. Peggy Osterkamp, a beloved teacher, weaver, and creative thinker, summed up the method in this post. I encourage you to read Peggy’s post as she does a good job of comparing and contrasting the wraps per inch method vs. Ashenhurst’s method.
A new rigid-heddle resource, the Not So Rigid Weaver, has an Ashenhurst’s calculator on her site, which does all the square root calculations for you. The results of these calculations often contradict conventional sett charts, offering a wider range of setts. In Ashenhurst’s formula, the sett range for 8/4 cotton is 9.5-25, while on a conventional sett chart is 10-18.
The Ashenhurst calculation is based on shaft-loom performance. For the rigid-heddle weaver, I suggest avoiding exceeding 80% of the maximum density recommendations. The crammed slots can get too sticky and the crammed and spaced areas in the woven cloth may not even out in the wash, although you can use this as a feature. I also rarely find the lowest recommendation very viable. Peggy suggests, if you guesstimate your balanced sett based on your w.p.i., divide that number by .7 to get a number close to Ashenhurst’s maximum sett.
As a rigid-heddle weaver, I don’t use Ashenhurst’s method as much as I did as a shaft-loom weaver. Sett density in a rigid-heddle environment has a more limited range of setts than denting a shaft loom reed. This means I’m often choosing my yarn for my sett, not my sett for my yarn. Sett charts offer me a safety range and I know there is some wiggle room at either end of that spectrum.
To see what this looks like in practice, here are three 2/2 point twill samples woven on three heddles using the threading in Fig. 1 at three different densities, using a similar size and style yarn—unmercerized plied cotton, either 8/4 Brassard and/or 3/2 Beam.
2/2 Point Twill Swatches in Three Different Densities
The swatch on the far left is the most dense, woven on three 12-dent heddles for a sett of 18. It has a firm hand and lays flat, perfect for mats. When hung from the line, it doesn’t bend, while the other two have varying degrees of suppleness. The swatch in the middle is between firm and flexible, making it a nice hand for towels. It is woven on three 10-dent heddles for a sett of 15. The swatch on the far right is the most supple, woven on three 8-dent heddles with a sett of 12. This would be good for yarns that shrink a lot and wearables. I created a handout that breaks this down even farther. (Note: it is somewhat easier to weave a 2/2 twill on three heddles than two. Three heddles reduce the occurrence of split sheds. If you thread two, you can weave this same structure as a 1/3 twill, which decreases the split sheds, see handout.)
I think I’ll leave it there for now or I’ll be writing an entire book on the subject, oh, wait, I am! Thanks for your patience as I work through this material, and to the Yarnworker patrons for supporting the Yarnworker space. By giving you some of the theory sections in small doses, hopefully it will make it easier to absorb the whole and help me write better pages.
In April, the Yarnworker Patrons and I are going to begin to look at warping two and three heddles. Join us!