It is a little-known fact that the material (quartz) that we describe as tiger-eye, that is chatoyant and a golden yellow color, was previously blue. Due to geological circumstances, the "blue" can leech-out, leaving the stone yellow.

Blue chatoyant quartz is called "phoenix-eye."

I'm inclined to suspect the stone we are discussing is probably naturally blue, and of a more-colorless or dull tone that resembles dark bluish-gray or "black."

By the way, red chatoyant quartz is called "dragon-eye.' Although this can be a natural coloration, it is a rare material, and (now) is often artificially colored.