Etymology
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midwinter (n.)

also mid-winter, "the middle or depth of winter," Old English midwinter, also midde winter; see mid (adj.) + winter (n.). The middle of winter, traditionally the period around the winter solstice (Dec. 21, winter being reckoned from the first of November). As an adjective from mid-12c.

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New Year's Eve 

"evening before the first day of the new year," c. 1300; "þer þay dronken & dalten ... on nwe gerez euen." The Julian calendar began on January 1, but the Christian Church frowned on pagan celebrations of this event and chose the Feast of the Annunciation (March 25) as its New Year's Day. The civic year in England continued to begin January 1 until late 12c., and even though legal documents then shifted to March 25, popular calendars and almanacs continued to begin on January 1. The calendar reform of 1751 restored the Julian New Year in England. New Year's was the main midwinter festival in Scotland from 17c., when Protestant authorities banned Christmas, and continued so after England reverted to Christmas, hence the Scottish flavor ("Auld Lang Syne," etc.). New Year's gathering in public places began 1878 in London, after new bells were installed in St. Paul's.

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yule (n.)

Old English geol, geola "Christmas Day, Christmastide," which is cognate with Old Norse jol (plural), the name of a heathen feast, later taken over by Christianity; the Germanic word is of unknown origin. The Old English (Anglian) cognate giuli was the Anglo-Saxons' name for a two-month midwinter season corresponding to Roman December and January, a time of important feasts but not itself a festival.

After conversion to Christianity the word narrowed to mean "the 12-day feast of the Nativity" (which began Dec. 25), but was replaced by Christmas by 11c., except in the northeast (areas of Danish settlement), where it remained the usual word.

Revived 19c. by writers to mean "the Christmas of 'Merrie England.' " First direct reference to the Yule log is 17c. According to some sources, Old Norse jol was borrowed into Old French as jolif, hence Modern French joli "pretty, nice," originally "festive" (see jolly).

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