Other details that wouldn't fit: She has wings made of fire (similar to lapis') and her gem is on her back, and she can control fire (I know, she is a freak of nature). She is from the Beta Kindergarten, as she is a quartz, and that is where she met Jasper. Her cut of gem (what she is called by the diamonds, Peridot being facet 2f5l, cut 5xg) is facet 9, cut 9xh. Since she has such a severe defect (her wings and fire-control), she fought her way up the rankings that were set in the quartzes, and now she even has her own pearl.
Credit to @baconhat and Rebecca Sugar. Now includes pearl noises.