Etymology
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monotony (n.)

1706, originally in transferred sense of "wearisome sameness, tiresome uniformity or lack of variation," from French monotonie (1670s), from Greek monotonia "sameness of tone, monotony," from monotonos "of one and the same tone," from monos "single, alone" (from PIE root *men- (4) "small, isolated") + tonos "tone," from PIE root *ten- "to stretch." Literal sense of "sameness of tone or pitch" is attested in English from 1724.

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monotone (n.)

"unvarying tone in music or speaking, utterance at one unvaried pitch," 1640s; see monotony. OED says use of the word as a noun is peculiar to English.

Monotone is a natural device for increasing the sonority of the voice, so that it may readily fill a large space, and is also thought by some to have a peculiar solemnity of effect. It is much used as an element in chanting. [Century Dictionary]
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monotonous (adj.)

1750, of sound, "unvaried in tone, characterized by monotony, unvaried in tone," from Greek monotonos "of one tone" (see monotony). Transferred and figurative use, "lacking in variety, uninteresting, tiresomely uniform," is from 1783. Related: Monotonously; monotonousness.

The secondary sense of monotonous (same or tedious) has so nearly swallowed up its primary (of one pitch or tone) that it is well worth while to remember the existence of monotonic, which has the primary sense only. [Fowler]
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*men- (4)

Proto-Indo-European root meaning "small, isolated."

It forms all or part of: malmsey; manometer; monad; monarchy; monastery; monism; monist; monk; mono; mono-; monoceros; monochrome; monocle; monocular; monogamy; monogram; monolith; monologue; monomania; Monophysite; monopoly; monosyllable; monotony.

It is the hypothetical source of/evidence for its existence is provided by: Greek monos "single, alone," manos "rare, sparse;" Armenian manr "thin, slender, small."

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*ten- 
Proto-Indo-European root meaning "to stretch," with derivatives meaning "something stretched, a string; thin."

It forms all or part of: abstain; abstention; abstinence; abstinent; atelectasis; attend; attenuate; attenuation; baritone; catatonia; catatonic; contain; contend; continue; detain; detente; detention; diatonic; distend; entertain; extend; extenuate; hypotenuse; hypotonia; intend; intone (v.1) "to sing, chant;" isotonic; lieutenant; locum-tenens; maintain; monotony; neoteny; obtain; ostensible; peritoneum; pertain; pertinacious; portend; pretend; rein; retain; retinue; sitar; subtend; sustain; tantra; telangiectasia; temple (n.1) "building for worship;" temple (n.2) "flattened area on either side of the forehead;" temporal; tenable; tenacious; tenacity; tenant; tend (v.1) "to incline, to move in a certain direction;" tendency; tender (adj.) "soft, easily injured;" tender (v.) "to offer formally;" tendon; tendril; tenement; tenesmus; tenet; tennis; tenon; tenor; tense (adj.) "stretched tight;" tensile; tension; tensor; tent (n.) "portable shelter;" tenterhooks; tenuous; tenure; tetanus; thin; tone; tonic.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit tantram "loom," tanoti "stretches, lasts," tanuh "thin," literally "stretched out;" Persian tar "string;" Lithuanian tankus "compact," i.e. "tightened;" Greek teinein "to stretch," tasis "a stretching, tension," tenos "sinew," tetanos "stiff, rigid," tonos "string," hence "sound, pitch;" Latin tenere "to hold, grasp, keep, have possession, maintain," tendere "to stretch," tenuis "thin, rare, fine;" Old Church Slavonic tento "cord;" Old English þynne "thin."
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sameness (n.)

1580s, "oneness, unity, absence or negation of otherness," from same + -ness. From 1743 (Walpole's letters) as "want of variety, monotony."

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humdrum (adj.)
"routine, monotonous, dull, commonplace," 1550s, probably a reduplication of hum. As a noun, "monotony, tediousness," from 1727; earlier it meant "dull person" (1590s).
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variety (n.)

1530s, "change of fortunes," from French variété and directly from Latin varietatem (nominative varietas) "difference, diversity; a kind, variety, species, sort," from varius "various" (see vary). Meaning diversity, absence of monotony" is from 1540s; that of "collection of different things" is from 1550s; sense of "something different from others" is from 1610s. In reference to music hall or theatrical performances of a mixed nature, first recorded 1868, American English. The U.S. theater and entertainment industry magazine was founded in 1905 by Sime Silverman.

Variety's grammar is barbarous; its style is original and unique and completely independent of any other writing; its phraseology is wild and revolutionary and its diction is the result of miscegenation among shop talk, slang, Broadway colloquialisms, sporting neologisms and impatient short-cutting. [Hugh Kent, "Variety," American Mercury, December 1926] 
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