I'm wondering how the tie-ups in Handwoven are determined. I've heard about "walking" tie-ups; what are those? And here's a different question, but maybe related. Why do we read threading drafts from right to left instead of left to right the way we read text?
First question first. The tie-up really only shows what shafts need to be moved by each treadle in order to produce the intended interlacement. So, for example, the tie-up for a 2/2 twill on four shafts would be 1-2, 2-3, 3-4, 1-4. (Usually, numbers indicate shafts that go up. If you interpreted them to mean shafts that go down, you'd get the same interlacement, but you'd be weaving the cloth face down.)
The marks in the treadling sequence tell you the order in which you use the treadles. For 2/2 straight twill, you'd use them in the order in which I listed them, treadle 1 (1-2), treadle 2 (2-3), treadle 3 (3-4), treadle 4 (1-4). When I weave using four treadles in sequential order that way, I usually start with the left foot and weave the first 2 picks with that foot, then shift to the right foot and continue with treadles 3 and 4.
A walking tie-up is one that allows you to alternate feet, the way you would if you were walking. For a walking tie-up with 2/2 twill, you'd tie the treadles: 1-2, 3-4, 1-4, 2-3, and weave left, right, left, right. We usually don't give walking tie-ups in the magazine because they can look confusing to the eye. Sometimes a reader is trying to identify the structure by looking at the tie-up, so we make the tie-up as logical as possible. If there are two treadles that produce tabby and several others that weave pattern, we usually put the two tabby treadles together and the pattern treadles together. When you tie up your own treadles, however, you can arrange them any way you wish, and tie, for example, the two tabby treadles on opposite sides to distribute the lifting to both feet.
As to your second question, here's why I THINK we read threading drafts from right to left: The threading draft intends to show the way the shafts are threaded if you are standing at the front of the loom. I think that the warping method of choice during the period when the drafting format became established was back to front. If you were right handed and sitting at the front of the loom to thread, you would want to thread the first warp thread on the right first and proceed from right to left. So, I think we write and read threading drafts from right to left because right-handed back-to-front warpers determined the format. In essence, it doesn't matter which side you thread from, so we could change our format (and the front-to-backers and the left-handed back-to-fronters might be happier). But such a change might not be welcome to all!