Here is a picture of a robe , diffuse color white 0.8 , specular dark gray 0.1

lights 2 , 3 no shadows and 40% intensity

light 1 60% intensity

all lights white or slight gray, the default colors mess up colors.

this gives a little sheen in highlighted areas. Too much light makes things harder.

rendered to get the attached picture. 

an image file attached to the texture helps a lot , or the weave node

edited for picture arrachment