Tensor tympani

The tensor tympani muscle originates from the cartilaginous wall of the Eustachian tube (also called the auditory tube) and the bony wall surrounding the tube. The muscle inserts onto the handle of the malleus. When tensed, the action of the muscle is to pull the malleus medially, tensing the tympanic membrane, damping vibration in the ear ossicles and thereby reducing the amplitude of sounds: compare the role of the stapedius muscle.

Innervation of the muscle is from branches of the mandibular division of the trigeminal nerve (V3), by way of the Otic ganglion.

Details from Gray's anatomy
The Tensor tympani, the larger of the two muscles of the tympanic cavity, is contained in the bony canal above the osseous portion of the auditory tube, from which it is separated by the septum canalis musculotubarii.

It arises from the cartilaginous portion of the auditory tube and the adjoining part of the great wing of the sphenoid, as well as from the osseous canal in which it is contained.

Passing backward through the canal, it ends in a slender tendon which enters the tympanic cavity, makes a sharp bend around the extremity of the septum, and is inserted into the manubrium of the malleus, near its root.

It is supplied by a branch of the mandibular nerve through the otic ganglion.

The Tensor tympani draws the tympanic membrane medialward, and thus increases its tension.