The middle ear is the portion of the ear internal to the eardrum, and external to the oval window of the inner ear. The mammalian middle ear contains three ossicles, which transfer the vibrations of the eardrum into waves in the fluid and membranes of the inner ear. The hollow space of the middle ear is also known as the tympanic cavity and is surrounded by the tympani bone. The auditory tube (also known as the Eustachian tube or the pharyngotympanic tube) joins the tympanic cavity with the nasal cavity (nasopharynx), allowing pressure to equalize between the middle ear and throat. The middle ear is the portion of the ear internal to the eardrum, and external to the oval window of the inner ear. The mammalian middle ear contains three ossicles, which transfer the vibrations of the eardrum into waves in the fluid and membranes of the inner ear. The hollow space of the middle ear is also known as the tympanic cavity and is surrounded by the tympani bone. The auditory tube (also known as the Eustachian tube or the pharyngotympanic tube) joins the tympanic cavity with the nasal cavity (nasopharynx), allowing pressure to equalize between the middle ear and throat. The primary function of the middle ear is to efficiently transfer acoustic energy from compression waves in air to fluid–membrane waves within the cochlea. The middle ear contains three tiny bones known as the ossicles: malleus, incus, and stapes. The ossicles were given their Latin names for their distinctive shapes; they are also referred to as the hammer, anvil, and stirrup, respectively. The ossicles directly couple sound energy from the ear drum to the oval window of the cochlea. While the stapes is present in all tetrapods, the malleus and incus evolved from lower and upper jaw bones present in reptiles. The ossicles are classically supposed to mechanically convert the vibrations of the eardrum, into amplified pressure waves in the fluid of the cochlea (or inner ear) with a lever arm factor of 1.3. Since the effective vibratory area of the eardrum is about 14 fold larger than that of the oval window, the sound pressure is concentrated, leading to a pressure gain of at least 18.1. The eardrum is merged to the malleus, which connects to the incus, which in turn connects to the stapes. Vibrations of the stapes footplate introduce pressure waves in the inner ear. There is a steadily increasing body of evidence that shows that the lever arm ratio is actually variable, depending on frequency. Between 0.1 and 1 kHz it is approximately 2, it then rises to around 5 at 2 kHz and then falls off steadily above this frequency. The measurement of this lever arm ratio is also somewhat complicated by the fact that the ratio is generally given in relation to the tip of the malleus (also known as the umbo) and the level of the middle of the stapes. The eardrum is actually attached to the malleus handle over about a 0.5 cm distance. In addition the eardrum itself moves in a very chaotic fashion at frequencies >3 kHz. The linear attachment of the eardrum to the malleus actually smooths out this chaotic motion and allows the ear to respond linearly over a wider frequency range than a point attachment. The auditory ossicles can also reduce sound pressure (the inner ear is very sensitive to overstimulation), by uncoupling each other through particular muscles. The middle ear efficiency peaks at a frequency of around 1 kHz. The combined transfer function of the outer ear and middle ear gives humans a peak sensitivity to frequencies between 1 kHz and 3 kHz. The movement of the ossicles may be stiffened by two muscles. The stapedius muscle, the smallest skeletal muscle in the body, connects to the stapes and is controlled by the facial nerve; the tensor tympani muscle connects to the base of the malleus and is under the control of the medial pterygoid nerve which is a branch of the mandibular nerve of the trigeminal nerve. These muscles contract in response to loud sounds, thereby reducing the transmission of sound to the inner ear. This is called the acoustic reflex. Of surgical importance are two branches of the facial nerve that also pass through the middle ear space. These are the horizontal portion of the facial nerve and the chorda tympani. Damage to the horizontal branch during ear surgery can lead to paralysis of the face (same side of the face as the ear). The chorda tympani is the branch of the facial nerve that carries taste from the ipsilateral half (same side) of the tongue. Ordinarily, when sound waves in air strike liquid, most of the energy is reflected off the surface of the liquid. The middle ear allows the impedance matching of sound traveling in air to acoustic waves traveling in a system of fluids and membranes in the inner ear. This system should not be confused, however, with the propagation of sound as compression waves in liquid. The middle ear couples sound from air to the fluid via the oval window, using the principle of 'mechanical advantage' in the form of the 'hydraulic principle' and the 'lever principle'. The vibratory portion of the tympanic membrane (eardrum) is many times the surface area of the footplate of the stapes (the third ossicular bone which attaches to the oval window); furthermore, the shape of the articulated ossicular chain is like a lever, the long arm being the long process of the malleus, the fulcrum being the body of the incus, and the short arm being the lenticular process of the incus. The collected pressure of sound vibration that strikes the tympanic membrane is therefore concentrated down to this much smaller area of the footplate, increasing the force but reducing the velocity and displacement, and thereby coupling the acoustic energy.