Etymology
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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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key (adj.)

"crucially important," 1913, from key (n.1). Perhaps from or reinforced by key move, in chess, "first move in a solution to a set problem" (1827), which to an experienced player opens the way to see how the solution will develop.

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key (v.)

mid-14c., "fasten with a wedge or key" (implied in keyed), from key (n.1). From 1630s as "regulate the pitch of a musical instrument by means of a key," also in the figurative sense "give a tone or intensity to." From 1963 as "do data entry or other work on a keyboard." Meaning "to scratch (a car's paint job) with a metal key" is recorded by 1986. Related: Keyed; keying.

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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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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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key (n.1)

"instrument for opening locks," Middle English keie, from Old English cæg "metal piece that works a lock, key" literal and figurative ("solution, explanation, one who or that which opens the way or explains"), a word of unknown origin, abnormal evolution, and no sure cognates other than Old Frisian kei.

Perhaps it is related to Middle Low German keie "lance, spear" on notion of "tool to cleave with," from Proto-Germanic *ki- "to cleave, split" (cognates: German Keil "wedge," Gothic us-kijans "come forth," said of seed sprouts, keinan "to germinate"). But Liberman writes, "The original meaning of *kaig-jo- was presumably '*pin with a twisted end.' Words with the root *kai- followed by a consonant meaning 'crooked, bent; twisted' are common only in the North Germanic languages." Compare also Sanskrit kuncika- "key," from kunc- "make crooked."

Modern pronunciation is a northern variant predominating from c. 1700; earlier and in Middle English it often was pronounced "kay." Meaning "that which holds together other parts" is from 1520s. Meaning "explanation of a solution" (to a set problem, code, etc.) is from c.1600.

The musical sense originally was "tone, note" (mid-15c.). In music theory, the sense developed 17c. to "sum of the melodic and harmonic relationships in the tones of a scale," also "melodic and harmonic relationships centering on a given tone." Probably this is based on a translation of Latin clavis "key," used by Guido for "lowest tone of a scale," or French clef (see clef; also see keynote). Sense of "mechanism on a musical instrument operated by the player's fingers" is from c. 1500, probably also suggested by uses of clavis. OED says this use "appears to be confined to Eng[lish]." First of organs and pianos, by 1765 of wind instruments; transferred to telegraphy by 1837 and later to typewriters (1876).

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key (n.2)

"low island," 1690s, from Spanish cayo "shoal, reef," from Taino (Arawakan) cayo "small island;" spelling influenced by Middle English key "wharf" (c. 1300; mid-13c. in place names), from Old French kai "sand bank" (see quay).

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low-key (adj.)

by 1895, perhaps 1847, from low key in some sense relating to deep musical tone or quiet sound; see low (adj.) + key (n.1). Low key in reference to a quiet voice is attested from 1837. Also compare undertone.

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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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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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