qgis - Interpolation of contours (from one "main-contour-shapefile")

I calculated, that the best and smallest possible äquidistance (equidistant) for my map is 30m. After I generalized my DHM, I extracted contours of a interval of 30m and smoothed them. Now I have my "main-contours".

But I also want contours with 10m äquidistance (equidistant), and I need to interpolate it from my main-contours (because my DHM is not accurate enough to extract 10m-contours directly).

EDIT: The 10m-contours are just for optical reasons (counting) and don't have to be accurate. The accuracy of the 30 m-contours is fine enough!

Is that possible with Grass, Saga or Qgis?

EDIT: The 30m-contours are accurate, (vertical error less then 15m), the 10m-contours have errors so I don't want them! :)