Here's a quote (perhaps with a few typing errors) from
Peter Dallos, in the "Handbook of Physiology - The Nervous
System III". Sorry I don't have the complete reference.
This qoute is from pp 613-614:
"Within the pars tecta region of the membrane (between the
osseous spiral lamina and the foot of the outer pillar
wall) there is a single fibrous layer between the basement
membrane on the Organ of Corti side and a homogeneous layer
of ground substance on the scala tympani side. The lower
side of the basilar membrane is covered by a layer of
cells, the tympanic cover layer. The more peripheral
portion ... (pars pectinata) contains two fibrous layers
sandwiched between the basement membrane and two
homogeneous layers ... The strands run radially and are
formed of fine fibrils 50 Angstrom in diameter." In
another article, Peter says the fibers are collagen.