Introducing Twist into Yarn
So why might you introduce twist into either a commercially spun yarn or previously spun handspun yarn? Three main reasons: balance, appearance and structural enhancement.
I will go through the specifics of each of these and also discuss with what yarns and circumstances this could be appropriate. Most of this discussion will revolve around adding twist to commercially spun yarn but there are also some (occasional) reasons to do this with handspun yarns.
First is balance. We want a finished yarn, of course, to be balanced. And this can be difficult to achieve with certain hand spinning techniques if you introduce commercial yarn into the equation. Consider core spinning in which fibers are wrapped around a central "core" yarn/thread rather than being spun directly into a single strand. The wrapping fiber goes around the core and does not accumulate twist; the core, however, accumulates all the twist as you spin the yarn. If you decide to use a commercial yarn (that is already balanced) as your core, if you do not first introduce extra twist into the core yarn, it will be very hard to have a final corespun yarn that is balanced. So, what you first do is to run your commercial yarn through your spinning wheel in the opposite direction in which you will do your core spinning. Then you core spin in the other direction essentially counteracting the twist you put into your core (commercial yarn) so you can end up with an overall balanced corespun yarn. This technique of adding twist to a commercial yarn to achieve a final balanced yarn is helpful in many hand spinning techniques, not just corespinning; e.g. tailspinning, spiral plying, supercoils/coils.
Next, let’s discuss appearance. First, assume you have handspun a single and now decide to ply it with commercial yarn that is already balanced. A 45-degree angle is widely considered the perfect default starting point for a balanced, smooth, and durable 2-ply handspun yarn. This is the sweet spot for a well-balanced, round, and sturdy yarn; this angle lays flat, is great for general knitting/crocheting, and helps prevent pilling. Unless you spun your single with a lot of twist, if you ply the single with an already balanced commercial yarn, you will probably have a final 2 ply yarn with the angle more around 30 degrees - as you do not have as much twist to counteract when you ply. (Now, this is not necessarily bad as it can result in a softer and drapier but less durable yarn.) So, assuming you want to have that 45-degree angle in your 2-ply, first twist your commercial yarn in the same direction as your handspun single, and then ply the two together (in the opposite direction of course).
A technique that combines both balance and appearance (and involves hand-spun yarns) is to make a cable yarn using previously spun 2-ply yarns. Say you have made two 2-ply yarns that are both structurally similar (i.e. roughly the same gauge and the same fiber characteristics and about the same yardage) but you do not like the look of either. Consider making a cable yarn. A cable yarn is a highly durable, structured yarn made by twisting multiple already-plied yarns together in the opposite direction of their original twist. This "plying of plies" locks the fibers in place, creating an incredibly strong, rounded yarn with crisp stitch definition and excellent resistance to pilling.
Normally, if you wanted a cable yarn you would do this by making two singles and ply them with extra twist; and then make another two singles and again ply with extra twist. You would finally ply both 2-ply yarns together.
Here, though, you have two balanced 2 ply yarns already made. Twist each separately in the same direction and then ply both back together to make a cable yarn. (You get a different look if you twist them first in the S direction and then ply in the Z versus twisting both in the Z and then plying S; this is because the original 2-ply’s were (probably) made by spinning the singles in the Z direction and then plying in the S direction.) Experiment and see what you like.
One last reason for adding twist is structural enhancement, primarily done with commercial yarns but could also be done with handspun yarns. Introducing extra twist in a yarn can increase its strength, prevent splitting and/or alter the texture. (1) Extra twist forces individual fibers closer together, increasing friction and cohesion. This makes the yarn significantly stronger and less likely to snap under tension. (2) Extra twist also binds loose surface fibers tightly into the core of the strand. This prevents them from migrating and splitting, minimizing the fuzzy friction that causes pilling over time. And (3) adding twist compresses and alters the yarn structure. It packs more fibers into the same length, making the yarn denser, thinner, and smoother. Note that after adding extra twist to a yarn you will then have to consider the implications of the appearance and also how to achieve the final balance you want.
I have just hit a few main points of why you might consider introducing twist into commercial yarn or handspun yarn. Hopefully this provided you some ideas and thoughts of how either to achieve a balanced yarn with certain spinning techniques, alter the appearance of a yarn, and/or structurally change a yarn’s characteristics. I encourage you to experiment and see what you can create.
PS One bonus; using twist you can salvage a handspun yarn you are disappointed with because it doesn’t have the balance you want (usually too tightly spun). Take this unbalanced yarn and run it thru the spinning wheel in the opposite direction to either the plying, 2 ply yarn, or original spinning, single yarn. (Of course, you can add more twist in the same way if your yarn is not twisted tightly enough.) Do this carefully and check the yarn periodically as you do this to see if you are achieving a balanced yarn. Adding too much twist in the opposite direction can cause a 2-ply to come apart and a single to unravel - so check often and be careful!