Re: VERY Basic Footwork Question
I teach new students to walk with a natural step; that is what runners refer to as a, "heel-toe pushoff." Essentially, natural walking mechanics begin with pressure on the heel, then rock to the "ball" of the foot underneath the big toe, the step is completed with pressure continuing to transfer on the big toe and eventually transferred off the foot through the big toe. I would hestitate to say that walking/running/turning on your toes is "natural," and I would support that by simply inviting you to stand on your toes for a period of time. Eventually, your calf muscles would tire and you would be inable to continue to stand on your toes. Conversely, it would not be difficult to stand on your heels for a long period of time as no muscle use (except balanceing) is required to perform the action.
Similarly, I have choosen to teach new students that the pivot should not interfere with that step, and to pivot on the heel and "grip" the floor with their toes. This is similar to some karate styles. I consider pivoting on the heel to be a basic step and very neutral in movement. It may not be the "best" choice, but then again that choice is for my students to decide for themselves.
I have noticed that when students become familar with the movement, they can incorporate pivoting on the toes. I have seen many weapons arts that include a weight distribution over the toes and pivoting on the toes. In any case, as a point of balance, the pivot should take play directly under your center of balance; a gyroscope will not stand unless its center of mass is over the pivot point.
I ultimately have choosen to use my heel to pivot in my circular movements. I made this choice because I was regulary separating and breaking my toes due to a "sticky" mat surface.