What confuses me on this is why isn't there a swath of 20K where the pattern reverses itself?
It's because usually the first and last numbers in the thread counts are meant to be "full pivots," meaning that they are not repeated when the pattern reverses itself.

Almost always today when you see a thread count given a full pivot is meant. However, you cannot always assume this. A lot of errors and variations in tartans have crept in when people misinterpreted whether a particular count gave a full or half pivot.

For a good example, take a look at the "Old Gordon" aka "Gordon of Esselmont" offered by various weavers. This is the Gordon tartan with three yellow lines. Sometimes they will all be equal in width (as they are supposed to be) but in some instances the center yellow line will be twice as wide as the other two, because a count was interpreted as giving a half pivot, so the size of that line was doubled in production.

Aye,
Matt