Tanzanite 
Location: Tanzania, Africa
Variety of: Zoisite 
Chemical Composition: Ca2Al3(SiO4)3(OH), Calcium Aluminum Silicate Hydroxide
Hardness: 6.5 - 7

Tigereye
This is a combination of raw and tumbled tigereye. In the tumbled stones, there are yellow, blue, and red tigereye.
Variety of: Quartz
Chemical Composition: NaFe(SiO3)2 Sodium and iron with silicon dioxide (quartz)
Hardness: 6.5 - 7
 

Black Tourmaline
Alternate October Birthstone
General composition: (Na, Ca)(Li, Mg, Al)(Al, Fe, Mn)6(BO3)3(Si6O18)(OH)4 
Hardness: 7.0 - 7.5

Black Tourmaline on quartz
Alternate October Birthstone
General composition: (Na, Ca)(Li, Mg, Al)(Al, Fe, Mn)6(BO3)3(Si6O18)(OH)4 
Quartz is: SiO2
Hardness: 7.0 - 7.5

Tourmaline with quartz 
Alternate October Birthstone
Location: Brazil 
General composition: (Na, Ca)(Li, Mg, Al)(Al, Fe, Mn)6(BO3)3(Si6O18)(OH)4 
Quartz is: SiO2
Hardness: 7.0 - 7.5

Tourmaline Rubellite
Alternate October Birthstone
Location: Kunar, Afghanistan
General composition: (Na, Ca)(Li, Mg, Al)(Al, Fe, Mn)6(BO3)3(Si6O18)(OH)4 
Hardness: 7.0 - 7.5

Turquoise
Location: Arizona
Chemical Composition: CuAl6(PO4)4(OH)8*5(H2O), Hydrated Copper Aluminum Phosphate
Hardness: 5 - 6

Utah Picture Stone