Etymology
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medley (n.)

c. 1300, "hand-to-hand combat, war, battle," a sense now obsolete, from Old French medlee, variant of meslee, from mesler "to mix, mingle, meddle" (see meddle). From mid-14c. as "cloth made of wools dyed and mingled before being spun," whether of one color or many, but especially pied cloth. The general meaning "a combination, a mixture" is from c. 1400; that of "musical composition or entertainment consisting of diverse parts from different sources" is from 1620s.

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melee (n.)

"confused conflict among many persons," 1640s, from French mêlée, from Old French meslee "brawl, confused fight; mixture, blend" (12c.), noun use of fem. past participle of mesler "to mix, mingle" (see meddle). See also medley. Borrowed in Middle English as melle but it was lost and then reborrowed 17c.

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*meik- 

also *meig-, Proto-Indo-European root meaning "to mix." 

It forms all or part of: admix; admixture; immiscible; mash; meddle; medley; melange; melee; mestizo; metis; miscegenation; miscellaneous; miscible; mix; mixo-; mixture; mustang; pell-mell; promiscuous.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit misrah "mixed;" Greek misgein, mignynai "to mix, mix up, mingle; to join, bring together; join (battle); make acquainted with;" Old Church Slavonic mešo, mesiti "to mix," Russian meshat, Lithuanian maišau, maišyti "to mix, mingle," Welsh mysgu "to mix." 

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olio (n.)

savory medley dish of Iberian origin, 1640s, from Spanish olla, Portuguese olha, both from Vulgar Latin *olla "pot, jar." With the common mistake of -o for -a in English words from Spanish. The sense was transferred from the pot to what went into it. Extended sense of "any mixture or medley, a collection of various pieces" is from 1640s in English.

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satirical (adj.)
1520s, from Late Latin satiricus, from Latin satira "satire, poetic medley" (see satire (n.)) + -al (1). Related: Satirically.
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pastiche (n.)
"a medley made up of fragments from different works," 1878, from French pastiche (18c.), from Italian pasticcio "medley, pastry cake," from Vulgar Latin *pasticium "composed of paste," from Late Latin pasta "paste, pastry cake" (see pasta). Borrowed earlier (1752) in the Italian form.
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melange (n.)

"a mixture, a medley," usually "an uncombined mingling on elements, objects, or individuals," 1650s, from French mélange (15c.), from mêler "to mix, mingle," from Old French mesler "to mix, meddle, mingle" (see meddle).

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farrago (n.)

"hodgepodge, a confused mix," 1630s, from Latin farrago "medley, mixed fodder, mix of grains for animal feed," from far "grain" (see farina).

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gallimaufry (n.)
"a medley, hash, hodge-podge," 1550s, from French galimafrée "hash, ragout, dish made of odds and ends," from Old French galimafree, calimafree "sauce made of mustard, ginger, and vinegar; a stew of carp" (14c.), which is of unknown origin. Perhaps from Old French galer "to make merry, live well" (see gallant) + Old North French mafrer "to eat much," from Middle Dutch maffelen [Klein]. Weekley sees in the second element the proper name Maufré. Hence, figuratively, "any inconsistent or absurd medley."
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pie (n.3)

printers' slang for "a mass of type jumbled together" (also pi, pye), 1650s, perhaps from pie (n.1) on notion of a "medley," or pie (n.2); but compare pica (n.1). As a verb from 1870. Related: Pied.

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