Etymology
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la-di-da (interj.)
mocking affected gentility, 1874, a derisive imitation of the "swell" way of talking. Compare lardy-dardy (1859).
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di- (2)

word-forming element of Latin origin meaning "apart, asunder," the form of dis- before certain voiced consonants. As des- was a form of dis- in Old French, some Middle English words have forms in both de- and di-; compare devise, which really belongs to di- and is related to divide.

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di- (1)

word-forming element of Greek origin meaning "two, double, twice, twofold," from Greek di-, shortened form of dis "twice," which is related to duo "two" and cognate with bi-, from PIE root *dwo- "two." In chemistry it indicates a compound containing two units of the element or radical to which it is prefixed.

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da (n.)

"father," by 1851, a nursery or provincial abbreviation of dad.

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la-la 
syllables used to make nonsense refrains in songs; compare Old English la, a common exclamation; but la-la is imitative of babbling speech in many languages: Greek lalage "babble, prattle," Sanskrit lalalla as an imitation of stammering, Latin lallare "to sing to sleep, lull," German lallen "to stammer," Lithuanian laluoti "to stammer."
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a la 
from French à la, literally "to the," hence "in the manner of, according to," from à, from Latin ad "to" (see ad-) + la, fem. of definite article le "the," from Latin ille (fem. illa; see le). Attested in English in French terms from fashion or cookery since late 16c.; since c. 1800 used in native formations with English words or names.
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di- (3)

word-forming element of Greek origin meaning "through; in different directions; between," also often merely intensive, "thoroughly;" the form of dia- before vowels.

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*da- 

*dā-, Proto-Indo-European root meaning "to divide."

It forms all or part of: betide; daimon; Damocles; deal (v.); deal (n.1) "part, portion;" demagogue; demiurge; democracy; demography; demon; demotic; dole; endemic; epidemic; eudaemonic; geodesic; geodesy; ordeal; pandemic; pandemonium; tidal; tide (n.) "rise and fall of the sea;" tidings; tidy; time; zeitgeist.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dati "cuts, divides;" Greek dēmos "people, land," perhaps literally "division of society," daiesthai "to divide;" Old Irish dam "troop, company;" Old English tid "point or portion of time," German Zeit "time."

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la (2)
fem. form of the French definite article, used in English in certain phrases and sometimes added ironically to a woman's name with a suggestion of "prima donna" (OED examples begin 1860s). See le.
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la (1)
musical note (sixth note of the diatonic scale), early 14c., see gamut. It represents the initial syllable of Latin labii "of the lips." In French and Italian it became the name of the musical note A, which is the sixth of the natural scale (C major).
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