I'm currently writing an essay on a mosaic in the British Museum, and am unsure about which stone the frame is constructed from (pictured). I would be most grateful for help identifying it.
Summarizing into an answer some information and a recommendation provided in my comments.
Onyx and Agate, both Silicates, can be differentiated based on bands as suggested in an earlier comment: they are parallel and almost always perfectly straight in the former, curved in the latter.
However, this frame could be made of Alabaster (Gypsum) as well. Gypsum is a much softer mineral, with a hardness of about 2 in the Mohs scale (shown in the figure below, from this site), whereas Onyx and Agate being Silicates, should have hardness around 7 like Quartz.
A scratch test with the steel nail or steel knife would allow to discriminate between Silicates and Gypsum: if the knife scratched the mineral, then it would likely be Gypsum / Alabaster, whereas if the mineral scratched the knife surface it would likely be a Silicate, in which case the bands would be the discriminant between Onyx and Agathe.
I realize this being a mosaic frame in a museum you may not be able to do a scratch test with the steel knife, so I recommend the safe nail approach: try to rub your fingernail against one of the corners or edges of the frame: if the mineral does not scratch your nail, then it must have a hardness lower than 2.5, hence excluding Silicates. You could then assume the frame is made of Gypsum/Alabaster; if it does scratch your nail, then it must be harder than Gypsum and you can assume it is a Silicate.
NB a further assumption made here is that the mineral is not Calcite or other Carbonate; this is based on aspect only, since it is unlikely a test with hydrochloric acid can be done.