Etymology
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muse (v.)

"to reflect, ponder, meditate; to be absorbed in thought," mid-14c., from Old French muser (12c.) "to ponder, dream, wonder; loiter, waste time," which is of uncertain origin; the explanation in Diez and Skeat is literally "to stand with one's nose in the air" (or, possibly, "to sniff about" like a dog who has lost the scent), from muse "muzzle," from Gallo-Roman *musa "snout," itself a word of unknown origin. The modern word probably has been influenced in sense by muse (n.). Related: Mused; musing.

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Muse (n.)

late 14c., "one of the nine Muses of classical mythology," daughters of Zeus and Mnemosyne, protectors of the arts; from Old French Muse and directly from Latin Musa, from Greek Mousa, "the Muse," also "music, song," ultimately from PIE root *men- (1) "to think." Meaning "inspiring goddess of a particular poet" (with a lower-case m-) is from late 14c.

The traditional names and specialties of the nine Muses are: Calliope (epic poetry), Clio (history), Erato (love poetry, lyric art), Euterpe (music, especially flute), Melpomene (tragedy), Polymnia (hymns), Terpsichore (dance), Thalia (comedy), Urania (astronomy).

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musing (n.)

late 14c., "act of pondering, meditation, thought," verbal noun from muse (v.). Related: Musingly; musings.

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museum (n.)

1610s, "the university building in Alexandria," from Latin museum "library, study," from Greek mouseion "place of study, library or museum, school of art or poetry," originally "a temple or shrine of the Muses," from Mousa "Muse" (see muse (n.)). The earliest use in reference to English institutions was of libraries for scholarly study (1640s); the sense of "building or part of a building set aside as a repository and display place for objects relating to art, literature, or science" is recorded by 1680s.

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amuse (v.)

late 15c., "to divert the attention, beguile, delude," from Old French amuser "fool, tease, hoax, entrap; make fun of," literally "cause to muse" (as a distraction), from a "at, to" (from Latin ad, but here probably a causal prefix) + muser "ponder, stare fixedly" (see muse (v.)).

Original English senses obsolete; meaning "divert from serious business, tickle the fancy of" is recorded from 1630s, but through 18c. the primary meaning was "deceive, cheat" by first occupying the attention. "The word was not in reg. use bef. 1600, and was not used by Shakespere" [OED]. Bemuse retains more of the original meaning. Greek amousos meant "without Muses," hence "uneducated."

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mosaic (n.)

c. 1400, "process of making patterns of inlaid work in hard materials," from Old French mosaicq "mosaic work," from Italian mosaico, from Medieval Latin musaicum "mosaic work, work of the Muses," noun use of neuter of musaicus "of the Muses," from Latin Musa (see Muse). Medieval mosaics often were dedicated to the Muses.

The word was formed in Medieval Latin as though from Greek, but the (late) Greek word for "mosaic work" was mouseion (and Klein says this sense in Greek was borrowed from Latin). Meaning "a piece of mosaic work" is from 1690s. Figurative meaning "anything resembling a mosaic work in composition" is by 1640s. As an adjective in English, "made of small pieces inlaid to form a pattern," from 1580s. Related: Mosaicist.

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music (n.)

mid-13c., musike, "a pleasing succession of sounds or combinations of sounds; the science of combining sounds in rhythmic, melodic, and (later) harmonic order," from Old French musique (12c.) and directly from Latin musica "the art of music," also including poetry (also source of Spanish musica, Italian musica, Old High German mosica, German Musik, Dutch muziek, Danish musik), from Greek mousikē (technē) "(art) of the Muses," from fem. of mousikos "pertaining to the Muses; musical; educated," from Mousa "Muse" (see muse (n.)). Modern spelling from 1630s. In classical Greece, any art in which the Muses presided, but especially music and lyric poetry.

The use of letters to denote music pitch probably is at least as old as ancient Greece, as their numbering system was ill-suited to the job. Natural scales begin at C (not A) because in ancient times the minor mode was more often used than the major one, and the natural minor scale begins at A.

Meaning "the written or printed score of a composition" is from 1650s. Music box is from 1773, originally "barrel organ," by 1845 in reference to the wind-up mechanical device; music hall is by 1842 as "interior space used for musical performances," especially "public hall licensed for musical entertainment" (1857). To face the music "accept the consequences" is from 1850; the exact image is uncertain, one theory ties it to stage performers, another to cavalry horses having to be taught to stay calm while the regimental band plays. To make (beautiful) music with someone "have sexual intercourse" is from 1967.

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*men- (1)

Proto-Indo-European root meaning "to think," with derivatives referring to qualities and states of mind or thought.

It forms all or part of: admonish; Ahura Mazda; ament; amentia; amnesia; amnesty; anamnesis; anamnestic; automatic; automaton; balletomane; comment; compos mentis; dement; demonstrate; Eumenides; idiomatic; maenad; -mancy; mandarin; mania; maniac; manic; mantic; mantis; mantra; memento; mens rea; mental; mention; mentor; mind; Minerva; minnesinger; mnemonic; Mnemosyne; money; monition; monitor; monster; monument; mosaic; Muse; museum; music; muster; premonition; reminiscence; reminiscent; summon.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit manas- "mind, spirit," matih "thought," munih "sage, seer;" Avestan manah- "mind, spirit;" Greek memona "I yearn," mania "madness," mantis "one who divines, prophet, seer;" Latin mens "mind, understanding, reason," memini "I remember," mentio "remembrance;" Lithuanian mintis "thought, idea," Old Church Slavonic mineti "to believe, think," Russian pamjat "memory;" Gothic gamunds, Old English gemynd "memory, remembrance; conscious mind, intellect."

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bemuse (v.)
"to make utterly confused, put into muse or reverie, muddle, stupefy," from be- + muse (compare amuse); attested from 1735 but probably older, as Pope (1705) punned on it as "devoted utterly to the Muses."
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Clio 
"muse of history, muse who sings of glorious actions," usually represented with a scroll and manuscript case, from Latin Clio, from Greek Kleio, literally "the proclaimer," from kleiein "to tell of, celebrate, make famous," from kleos "rumor, report, news; good report, fame, glory," from PIE *klew-yo-, suffixed form of root *kleu- "to hear."
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