3 and 1 broken twill
3/1 Broken Twill is an advanced tablet weaving technique that follows similar principles to the basic double face weave technique. The name describes the different aspects of the technique.
The finished band has a twill pattern on the band - which are lines of floats across the band at a 45 degree angle (in either direction, depending on the initial threading direction of the tablets).
The 3/1 part of the name refers to the fact that the floats are built up by the top thread floating over the top of the band for three rows, then under for one.
The combination of these causes a double-faced weave that allows for nice, crisp 45-degree pattern lines. The draw-back being that lines orthogonal to the band (ie across the width of it) can never be crisp and straight.
For a full discussion of the teachnioque, refer to Phiala's 3/1 twill tutorial: http://www.stringpage.com/old/twill.html