Do you mean ratio as in measurement for the whole itomaki or in relation to the amount of wood being used (equal parts ? ) .
I'd say it depends on the kind of shamisen you're having/making, the kind of wood you are using and the complexity of design.
Use rather hard kinds of wood, instead of softer ones, if you are working with two different materials.
Ratio depends on the joinery of the 2 woods, unless you have a low angle plane, never glue end grain to end grain.
Ratio also depends on the desired effect.
I would ask what are the itomaki blank dimensions quanity * thickness * width * length you're going for.
Like 3 blanks t"*w"*l" in inches. That will allow you to know how much material than measure the length and width you want the pieces of wood to run with on the sketch. You should have an idea before making the banks, but make them at least an 1/16th to 1/8th thicker then you plans.