Sett in numbers
Sett, in its essence, is the number of threads per unit of distance. You can pick the unit of distance of your choice; here we will stick with inches.
sett = # threads / inch
In its narrow sense, sett concerns the spacing of warp threads, or ends; we give it in ends per inch, or epi:
(warp) sett = # ends / inch
As weavers, we are also interested in the spacing of weft threads, or picks, so we also think about the weft sett; we give it in picks per inch, or ppi:
(weft) sett = # picks / inch
One can measure the setts of a piece of cloth with a magnifying glass (to see and count the threads) and a ruler (to measure distance), or a linen counter, a tool designed for the job.
Here is the view of a piece of cloth though a linen counter. Counting the warp (vertical) threads, one gets about 22 ends in 1 inch, or 22 epi. One can also determine the weft sett, by counting the horizontal (weft) threads, and get about 18 picks in 1 inch, or 18 ppi.
While so doing, one notices that each pick goes above 2 and below 1 end: this is a 2/1 twill. Furthermore, the twill diagonal starting from the top left corner is a little too steep to reach the bottom right corner, confirming that this cloth was beaten a little looser than square (ppi < epi).
Note that to get a more accurate measure of the sett, one would count the threads over a couple of inches or more.
If one doesn't want to count so many threads, one could figure out how many ends there are in one repeat of the cloth and measure the length of the repeat (in inches). With these measurements,
Sett = (# ends/repeat) / (length of 1 repeat)
On the picture above, the repeat has 3 threads. As indicated by the pink lines, it is 1/8 inch long. With these numbers, we get a sett of 24 epi, which is pretty close to the first sett measure (22 epi). With the first measure, we get the average sett over 1 inch of cloth. With the second measure, we get the sett over 3 threads.
For now, let's focus on sett in its narrow sense, the spacing of warp threads. This is the spacing we have to decide on as we dress the loom. The sett we pick depends on many factors (including what the weft spacing is going to be; see this graphic view of the relationship).
There is plenty of data out there to help a weaver decide on a sett, such as weavers' experience, one's own and the collective experience collated in tables and recommendations.
But what if I am designing a project with a yarn or a structure that are not in the tables at hand? How can I use the information I do have to make an educated guess?
There is a fair amount of variation between recommendations, something I think of as fuzz. Can we put a number on fuzz and make sense of it?
There are various means to achieve these goals. I will take a page from the industrial textile designers, and try to calculate the sett, for a given yarn and structure.
I will reinvent the classic sett calculating formula to show how it is put together. Bear with me, and you'll see that this sett formula did not fall from the sky.
Let's start with the latest sett formula above (sett = (# ends/repeat) / (length of 1 repeat)), and express the length of the repeat as
length of repeat in inches =
(length of repeat in # of yarn diameters) x (diameter of the yarn in inches)
Few of us have the equipment required to measure the diameter of yarn accurately. We can get to it indirectly by measuring how many yarn diameters fit in 1 inch (=diameters/inch, or dpi) and take the reciprocal. The sett formula becomes
Sett = (# ends/repeat) / (length of repeat in inches)
= (# ends/repeat) / [(length of repeat in # of yarn diameters) / (diameters/inch)]
Let's rearrange the above, and we end up with something a little more familiar:
Sett = (diameters/inch) x (# ends/repeat) / (length of repeat in # yarn diameters)
This formula is not particularly useful for measuring setts; it is, however, the basis for calculating setts. It neatly separates the size of the yarn, expressed as diameters per inch, or dpi, from characteristics of the woven structure (number of ends in the repeat, length of repeat expressed in number of yarn diameters). Let's call STR the number characterizing the woven structure:
STR = (# ends/repeat) / (length of repeat in # yarn diameters)
Standard sett calculating formula
Figuring out the number of ends per repeat is easy; we need only look at the draft. Finding out the denominator of STR is less obvious.
To start, we will assume:
the same yarn for warp and weft
the same sett for warp and weft (ppi=epi)
all picks travel the same path; all ends travel the same path, and it is the same as that of the picks.
Assumptions 1 and 2 indicate a balanced cloth, and assumption 3 indicates a regular structure, like plain weave or a straight twill.
With these assumptions, we can reasonably say that the space needed for a pick to travel from face to back (or vice-versa) of the cloth is 1 thickness of yarn, or 1 yarn diameter. By counting how many times the pick travels between face and back, or intersects with the cloth, within a repeat, we can calculate the length of the repeat in yarn diameters: it is the number of ends per repeat plus the number of intersections. This is the standard cloth setting formula
Sett = (diameters/inch) x (# ends/repeat) /
[(# ends/repeat) + (# intersections/repeat)]
For future use, let's have R = number of ends per repeat and I = number of intersections in one repeat. We can write:
STR = R / (R + I)
Can we make sense of this formula?
Let's represent a yarn with 10 diameters per inch, or 10 dpi.
Let's weave plain weave with this yarn, with black yarn in the warp and orange yarn in the weft.
Let's take a cross section of 1 inch of the cloth through the exact middle of a weft thread.
Warp threads will appear as 1/10 inch black circles and the weft thread will appear as a 1/10 inch wide orange ribbon.
There are 2 ends in a repeat for plain weave. On the diagram above, it is easy to see that a repeat occupies 4 diameters: 2 diameters for the warp threads, and 2 diameters for the weft thread interlacing with the warp.
STR = R / (R + C)
= 2 / 4
STR = 0.5
Let's make a similar diagram for a straight 2/2 twill.
There are now 4 ends in a repeat for 2/2 twill, and a repeat occupies 6 diameters: 4 diameters for the warp threads, and 2 diameters for the weft thread interlacing with the warp.
STR = R / (R + C)
= 4 / 6
= 0.67
Are these diagrams realistic?
These calculations make good sense when the cloth is represented as above, with the stiff warp treads and the weft thread doing all the bending.
However, in balanced cloth—which this is supposed to be, as per the starting assumptions—one would expect warp and weft to be equally flexible.
Here is a more realistic representation of the plain weave cross section:
With this representation, it is less obvious why a repeat would have to occupy 4 diameters.
In particular, could the warp threads be packed tighter? Well, yes! Let's calculate the maximum sett.
On this diagram, the top cross section shows the maximum packing with stiff warp threads.
The bottom cross section shows flexible warp threads spaced to allow only the thickness of the weft thread between them.
What sett is represented on the bottom cross section? Let's count how wide is a repeat, measured in yarn diameters. Eyeballing the grey circles, it's about 3.5 diameters.
Can we calculate this number?
The pink triangle indicates the geometric relationship between the threads.
By construction, the short side of the right angle, a, is 1 diameter, the hypotenuse, c, is 2 diameters, so we can calculate b, the length of the third side (thank you Pythagoras):
a^2 + b^2 = c^2;
b= √(2^2 - 1^1 )
=√3
The width of a repeat in the bottom cross section is thus 2 x b = 2√3 = 3.46 diameters.
STR = R / (length of repeat in yarn diameters)
= 2 / 3.46
STR = 0.577
The same construction could be used to calculate the maximum sett for other woven structures.
What the standard sett calculating formula does not do
The sett formula does not take into account the possibility of threads moving once the cloth is off the loom and finished. There is not much movement in plain weave, but as soon as floats get longer, threads shift around.
Different structures can have the calculated sett (e.g., 2/2 twill, basket weave, and
The sett formula only contributes some information to the designer; it does not replace the designer in determining the sett.
In conclusion
The standard sett formula has the virtue of being simple. It It does not give the maximum sett, but it does put a number on the weaver's intuition that plain weave (STR=0.5) is sett looser than 2/2 twill (STR=0.67), that is sett looser than 4/4 twill (STR= 8/(8+2)=0.8).
Where to from here…
How does the calculated sett compare with the actual sett? (calculated sett as a tool)
What if picks and ends have a different path through the cloth? (calculated ppi is different from calculated epi)
What if the picks that form a repeat follow different paths (e.g., lace weaves, waffle, pinwheels, etc.) (average sett)
Can we calculate a sett for compound weaves (e.g., Summer & Winter)
THIS COULD BE OUR FOOTER…