I am going to go with turquoise. I have so many pieces with this stone, the color ranges from pale blue to deep dark green, with a lot of shades in between. Sometimes it can look translucent, and is often shot through with brown, black, or gray veins of other minerals. This is technically called turquoise matrix, I have some stones that have mica, some with gold in them, some with quartz. None of them look the same - unless you count that awful bright blue plastic looking stone that much of the mass produced factory jewelry has today.
The setting looks vintage, native american. Though NA jewelry can contain many different stones, turquoise was and is the most common. To be sure, take it to any jeweler who deals in a wide variety of stones. They will be able to tell you for sure.