Bandgap of 'white' solids?

Under 'white visible light' illumination, my understanding is that colour is percieved as the combined effect of photons that are
reflected instead of absorbed. So an ideal matt black surface absorbes everything, whereas a matt white surface reflects everything. A transparent surface transmits most of the light, because the band gap is so large that only high-energy photons (UV range) have sufficient energy to excite electrons from the valance band to the conduction band for absorption. Conversely, the band gap of a 'black surface' is so small that virtually all photons have sufficient energy for absorption to occur. Therefore, what type of band gap does a 'white' surface have, or does it matter? Is it more of a specular surface phenomenon related to light scattering?
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