A broken twill is a twill that will cross the twill circle.  Many twills, e.g., straight draw, point draw, extended point, etc., revolve around the circumference of the twill circle . . . 1-2-3-4, 1-2-3-4-3-2-1, 1-2-3-4-1-2-3-4-3-2-1-4-3-2-1 . . . a broken twill may rotate around the circumference of the twill circle, but it will eventually cross it . . . 1-2-3-4-2-1-4-3 . . . in that sequence the twill circle is cross when the sequence goes from 4 to 2.

Many twills may be more than one thing.  For example, an advancing twill may also be a broken twill.  If a run of five and a step of one is used, the sequence goes 1-2-3-4-5-2-3-4-5-6-3-4-5-6-7...  The twill breaks when one run ends and the next one begins (e.g., 5-2, 6-3).  However, an advancing point twill with a run of five and a step of one would not be a broken twill if the sequence went 1-2-3-4-5-4-3-2-3-4-5-6-5-4-3-4-5-6-7-6-5-4...).  BTW - it's a lot easier to see this is graphic illustrations rather than in text.  If you have the January/February 2016 issue of Heddlecraft, you can see the images.

As far as Emery, it's not perfect . . . but, it is probably the best thing we have.  I believe weavers truly interested in rolling around in the mud on weave structures need to read it . . . and when I say read it, do more than look at the pictures.  When we can break down weave structures into plain weave, twill, and satin and then organize them by simple, compound elements, compound weaves . . . it helps distinguish what is going on in the weave and is a good place to start a discussion. This is when it becomes clear that a single two-tie threading woven as Summer & Winter is compound elements and Beiderwand is a compound weave.

Emery can be pushed to the point where it becomes muddy.  I often use as a particular four-shaft draft that can be interpreted as a simple weave or a compound weave depending on the yarns used and the sett.