Etymology
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major-domo (n.)

also majordomo, "man employed to superintend a household, especially that of a sovereign or other dignitary," 1580s, via Italian maggiordomo or Spanish mayordomo, from Medieval Latin major domus "chief of the household," also "mayor of the palace" under the Merovingians, from Latin maior "greater" (see major (adj.)) + genitive of domus "house" (from PIE root *dem- "house, household").

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major (adj.)

c. 1300, majour, "greater, more important or effective, leading, principal," from Latin maior (earlier *magios), irregular comparative of magnus "large, great" (from PIE root *meg- "great"). From 1590s as "greater in quantity, number, or extent." Used in music (of modes, scales, or chords) since 1690s, on notion of an interval a half-tone "greater" than the minor; of modern modes, "characterized by the use of major tonality throughout," by 1811. Major league, in baseball, is attested by 1892.

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major (v.)

of a college or university student, "focus (one's) studies," 1910, American English, from major (n.) in sense of "subject of specialization" (by 1890). Related: Majored; majoring. Earlier as a verb, in Scottish, "to prance about, or walk backwards and forwards with a military air and step" [Jamieson, 1825] a sense derived from the military major.

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major (n.)

military rank above captain and below lieutenant colonel, 1640s, from French major, short for sergent-major, originally a higher rank than at present, from Medieval Latin major "chief officer, magnate, superior person," from Latin maior "an elder, adult," noun use of the adjective (see major (adj.)).

His chief duties consist in superintending the exercises of his regiment or battalion, and in putting in execution the commands of his superior officer. His ordinary position in the line is behind the left wing. [Century Dictionary, 1897]

The musical sense is attested by 1797.

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*meg- 
Proto-Indo-European root meaning "great."

It forms all or part of: acromegaly; Almagest; Charlemagne; maestro; magisterial; magistral; magistrate; Magna Carta; magnate; magnitude; magnum; magnanimity; magnanimous; magni-; Magnificat; magnificence; magnificent; magnify; magniloquence; magniloquent; Magnus; maharajah; maharishi; mahatma; Mahayana; Maia; majesty; major; major-domo; majority; majuscule; master; maxim; maximum; may (v.2) "to take part in May Day festivities;" May; mayor; mega-; megalo-; mickle; Mister; mistral; mistress; much; omega.

It is the hypothetical source of/evidence for its existence is provided by: Armenian mets "great;" Sanskrit mahat- "great, mazah- "greatness;" Avestan mazant- "great;" Hittite mekkish "great, large;" Greek megas "great, large;" Latin magnus "great, large, much, abundant," major "greater," maximus "greatest;" Middle Irish mag, maignech "great, large;" Middle Welsh meith "long, great."
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major-general (n.)

"military officer next in rank below a lieutenant-general," 1640s; see major (n.) + general (n.).

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*dem- 

Proto-Indo-European root meaning "house, household." It represents the usual Indo-European word for "house" (Italian, Spanish casa are from Latin casa "cottage, hut;" Germanic *hus is of obscure origin).

It forms all or part of: Anno Domini; belladonna; condominium; dame; damsel; dan "title of address to members of religious orders;" danger; dangerous; demesne; despot; Dom Perignon; domain; dome; domestic; domesticate; domicile; dominate; domination; dominion; domino; don (n.) "Spanish, Italian, and Portuguese title of respect;" Donna; dungeon; ma'am; madam; madame; mademoiselle; madonna; major-domo; predominant; predominate; timber; toft.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit damah "house;" Avestan demana- "house;" Greek domos "house," despotēs "master, lord;" Latin domus "house," dominus "master of a household;" Armenian tanu-ter "house-lord;" Old Church Slavonic domu, Russian dom "house;" Lithuanian dimstis "enclosed court, property;" Old Norse topt "homestead."

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parasympathetic (adj.)

in reference to major divisions of the nervous system, 1905, from para- (1) "beside" + sympathetic.

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majorly (adv.)
by 1887, from major (adj.) + -ly (2). Common in popular U.S. colloquial speech from c. 1995.
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big-league (adj.)
"prominent, important, first-rate," by 1925, a figurative use from baseball, where big league was used for "a major league" by 1891. See league (n.1).
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