Diagonal, checkered rainbow

Seems very Native American, no?

It's the most compact, yet perhaps the most unusable of all the designs. Not only does one loses month ordering, but the color diagonals seem to "coil" around the square in an unintuitive, difficult-to-follow way. The next designs mostly tried to "unfold" it.

Example: What day does August 7 fall on? First, find 7. Now follow its violet diagonal until it crosses with the AUG row and from that cell go up to find the dayname: Tuesday in this case.