1760, in musical sense "placement of the mouth on a wind instrument," from French embouchure "river mouth, mouth of a wind instrument," from assimilated form of en- "in" (see en- (1)) + bouche "mouth" (see bouche).
word-forming element meaning "in; into," from French and Old French en-, from Latin in- "in, into" (from PIE root *en "in"). Typically assimilated before -p-, -b-, -m-, -l-, and -r-. Latin in- became en- in French, Spanish, Portuguese, but remained in- in Italian.
Also used with native and imported elements to form verbs from nouns and adjectives, with a sense "put in or on" (encircle), also "cause to be, make into" (endear), and used as an intensive (enclose). Spelling variants in French that were brought over into Middle English account for parallels such as ensure/insure, and most en- words in English had at one time or another a variant in in-, and vice versa.
French, literally "mouth" (Old French boche, 11c.), from Latin bucca "cheek," which in Late Latin replaced os (see oral) as the word for "mouth" (and also is the source of Italian bocca, Spanish boca). De Vaan writes that "The meaning 'mouth' is secondary, and was originally used in a derogatory way." It is perhaps from Celtic, Germanic, or a non-IE substrate language. Borrowed in English in various senses, such as "king's allowance of food for his retinue" (mid-15c.); "mouth" (1580s); "metal plug for a cannon's vent" (1862; verb in this sense from 1781).
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<a href="https://www.etymonline.com/word/embouchure">Etymology of embouchure by etymonline</a>
Harper, D. (n.d.). Etymology of embouchure. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/embouchure