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Origin and history of duodecimal

duodecimal(adj.)

"reckoning by twelves and powers of twelve," 1714, from Latin in duodecimo (folded) "in a twelfth" of a sheet, from ablative of duodecimus "twelfth" (from duodecim "twelve;" see dozen) + -al (1).

Divisions based on 10s are convenient for arithmetical calculation and computation of numbers. Duodecimal reckoning (as in ounces, inches) is better suited to practical use in weights and measures for material substances (food, drink).

Thus English, like many other Germanic languages, retains a shadow number system based on 12. Eleven and twelve ought to be the first numbers of the "teens" series. Their Old English forms, enleofan and twel(eo)f(an), are more transparent: "leave one" and "leave two."

Old English also had hund endleofantig for "110" and hund twelftig for "120." "One hundred" was hund teantig. The -tig formation (see -ty (1)) ran through 12 cycles, and could have bequeathed Modern English *eleventy ("110") and *twelfty ("120"), but already in Anglo-Saxon times it was being obscured.

Old Norse used hundrað for "120" and þusend for "1,200." Tvauhundrað was "240" and þriuhundrað was "360." Older Germanic legal texts distinguished a "common hundred" (100) from a "great hundred" (120).

Among all its conveniences, the decimal division has the great disadvantage of being itself divisible only by the numbers two and five. The duodecimal division, divisible by two, three, four, and six, would offer so many advantages over it, that while the French theory was in contemplation, the question was discussed, ... whether the number twelve should not be substituted for ten, as the term of the periodical return to the unit. [John Quincy Adams, "Report of the Secretary of State Upon Weights and Measures," 1821]

also from 1714

Entries linking to duodecimal

dozen(n.)

c. 1300, doseine, "collection of twelve things or units," from Old French dozaine "a dozen, a number of twelve" in various usages, from doze (12c.) "twelve," from Latin duodecim "twelve," from duo "two" (from PIE root *dwo- "two") + decem "ten" (from PIE root *dekm- "ten"). The Old French fem. suffix -aine is characteristically added to cardinals to form collectives in a precise sense ("exactly 12," not "about 12").

The Latin word's descendants are widespread: Spanish docena, Dutch dozijn, German dutzend, Danish dusin, Russian duizhina, etc. The dozens "invective contest" (1928) originated in slave culture, the custom is probably African, the word probably from bulldoze (q.v.) in its original sense of "a whipping, a thrashing."

eleven(num.)

"1 more than ten; the number which is one more than ten; a symbol representing this number;" c. 1200, elleovene, from Old English enleofan, endleofan, literally "one left" (over ten), from Proto-Germanic *ainlif- (compare Old Saxon elleban, Old Frisian andlova, Dutch elf, Old High German einlif, German elf, Old Norse ellifu, Gothic ainlif), a compound of *ain "one" (see one) + from PIE root *leikw- "to leave."

FIREFLY: Give me a number from 1 to 10.

CHICOLINI: eleven!

FIREFLY: Right!

["Duck Soup"]

Viking survivors who escaped an Anglo-Saxon victory were daroþa laf "the leavings of spears," while hamora laf "the leavings of hammers" was an Old English kenning for "swords" (both from "The Battle of Brunanburh"). Twelve reflects the same formation. Outside Germanic the only instance of this formation is in Lithuanian, which uses -lika "left over" and continues the series to 19 (vienuo-lika "eleven," dvy-lika "twelve," try-lika "thirteen," keturio-lika "fourteen," etc.). Meaning "a team or side" in cricket or football is from 1743.