this is a classical theravada thread. In this context, the external bases are the 4 great elements and form derived from them. Especially, the tangible object are the 3 following elements : earth, air, fire. Water is said to not be tangible.
Thanissaro seems to translate "tangible objects" with "tangible sensations" which according to classical theravada (and to buddhism in my view) is wrong. "Tangible sensations" are indeed mental objects, not tangible objects.