I am going out on a limb with a guess to the hallmark being Tommy & Rose Singer. Kind of doubtful as all pieces that belong to the hallmark always spell out Singer.
Also, are the stones sugilite?
Thank you in advance for looking. 
Have to agree as I have not seen the Singers use periods after the initials either. Then again, that’s just my unqualified opinion!
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Here is a little more on Tommy & Rose Singer jewelry mark… T&R Singer, T. Singer, T and a crescent moon, http://www.twodogssouthwestgallery.com/tommy-singer-jewelry.asp
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