From Wikipedia (Of Course!)
The Jew’s harp, also known as jaw harp, juice harp, or mouth harp,^{[nb 1]} is a lamellophone instrument, consisting of a flexible metal or bamboo tongue or reed attached to a frame. Despite the colloquial name, the Jew’s harp most likely originated in Siberia, specifically in or around the Altai Mountains, and is of Turkic origin. It has no relation to the Jewish people.^[2]

Jew’s harps may be categorized as idioglot or heteroglot (whether or not the frame and the tine are one piece); by the shape of the frame (rod or plaque); by the number of tines, and whether the tines are plucked, joint-tapped, or string-pulled.

The frame is held firmly against the performer’s parted teeth or lips (depending on the type), using the mouth (plus the throat and lungs when breathing freely) as a resonator, greatly increasing the volume of the instrument. The teeth must be parted sufficiently for the reed to vibrate freely, and the fleshy parts of the mouth should not come into contact with the reed to prevent damping of the vibrations and possible pain. The note or tone thus produced is constant in pitch, though by changing the shape of the mouth, and the amount of air contained in it (and in some traditions closing the glottis), the performer can cause different overtones to sound and thus create melodies.

According to the Encyclopædia Britannica Eleventh Edition, “The vibrations of the steel tongue produce a compound sound composed of a fundamental and its harmonics. By using the cavity of the mouth as a resonator, each harmonic in succession can be isolated and reinforced, giving the instrument the compass shown.”

“The lower harmonics of the series cannot be obtained, owing to the limited capacity of the resonating cavity. The black notes on the stave show the scale which may be produced by using two harps, one tuned a fourth above the other. The player on the Jew’s harp, in order to isolate the harmonics, frames his mouth as though intending to pronounce the various vowels.”^[3] See: bugle scale.

Jaw harps have been discovered in Shaanxi, China, dating back about 4000 years ago.^[4] The earliest depiction of somebody playing what seems to be a Jew’s harp is a Chinese drawing from the 3rd century BCE.^[5] Archaeological finds of surviving examples in Europe have been claimed to be almost as old, but those dates have been challenged both on the grounds of excavation techniques, and the lack of contemporary writing or pictures mentioning the instrument.

Although this instrument is used by lackeys and people of the lower class, this does not mean it is not worthy of consideration by better minds … The trump is grasped while its extremity is placed between the teeth in order to play it and make it sound … Now one may strike the tongue with the index finger in two ways, i.e., by lifting it or lowering it: but it is easier to strike it by raising it, which is why the extremity, C, is slightly curved, so that the finger is not injured … Many people play this instrument. When the tongue is made to vibrate, a buzzing is heard which imitates that of bees, wasps, and flies … [if one uses] several Jew’s harps of various sizes, a curious harmony is produced.

— Marin Mersenne, Harmonie Universelle(1636)^[6]

There are many theories for the origin of the name jew’s harp. The apparent reference to Jewish people is especially misleading since it “has nothing to do with the Jewish people; neither does it look like a harp in its structure and appearance”.^[7] In Sicilian it is translated as marranzanu or mariolu; both of which are derogatory terms for Jewish people also found in Italian^[8] and Spanish.^[9] In German, it is known as Maultrommel, which translates directly to ‘mouth drum’.^[7] The name “Jew’s Harp” first appears in 1481 in a customs account book under the name “Jue harpes”.^[10] The “jaw” variant is attested at least as early as 1774^[11] and 1809,^[12] the “juice” variant appearing only in the late 19th and 20th centuries.

It has also been suggested that the name derives from the French jeu-trompe meaning ‘toy trumpet’.^[13] The current French word for the instrument is guimbarde. English etymologist Hensleigh Wedgwood wrote in 1855 that the derivation from jeu harpeopposes the French idiom, where “if two substantives are joined together, the qualifying noun is invariably the last”.^[14] He refers to the jeu harpe derivation, but not to the jeu tromp derivation.

Both theories—that the name is a corruption of jaws or jeu—are described by the Oxford English Dictionary as “lacking any supporting evidence.”^[15] The OED says that, “more or less satisfactory reasons may be conjectured: e.g., that the instrument was actually made, sold, or imported to England by Jewish people, or purported to be so; or that it was attributed to Jewish people, suggesting the trumps and harps mentioned in the Bible, and hence considered a good commercial name.”^[16] Although the OED states that “the association of the instrument with Jewish people occurs, so far as is known, only in English”,^[15] the term jødeharpe is also used in Danish.^[17]