Etymology
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waltz (v.)
1794, from waltz (n.). Meaning "to move nimbly" (as one does in dancing a waltz) is recorded from 1862. Related: Waltzed; waltzing.
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waltz (n.)

round dance performed to music in triple time, extraordinarily popular as a fashionable dance from late 18c. to late 19c., the dance itself probably of Bohemian origin, 1779 (walse, in a translation of "Die Leiden des jungen Werthers" from a French translation, which has walse), from German Waltzer, from walzen "to roll, dance," from Old High German walzan "to turn, roll," from Proto-Germanic *walt- (cognate with Old Norse velta), from PIE root *wel- (3) "to turn, revolve." Described in 1825 as "a riotous and indecent German dance" [Walter Hamilton, "A Hand-Book or Concise Dictionary of Terms Used in the Arts and Sciences"].

The music struck up a beautiful air, and the dancers advanced a few steps, when suddenly, to my no small horror and amazement, the gentlemen seized the ladies round the waist, and all, as if intoxicated by this novel juxtaposition, began to whirl about the room, like a company of Bacchanalians dancing round a statue of the jolly god. "A waltz!" exclaimed I, inexpressibly shocked, "have I lived to see Scotch women waltz?" [The Edinburgh Magazine, April 1820]
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*wel- (3)
Proto-Indo-European root meaning "to turn, revolve," with derivatives referring to curved, enclosing objects.

It forms all or part of: archivolt; circumvolve; convoluted; convolution; devolve; elytra; evolution; evolve; Helicon; helicopter; helix; helminth; lorimer; ileus; involve; revolt; revolution; revolve; valve; vault (v.1) "jump or leap over;" vault (n.1) "arched roof or ceiling;" volte-face; voluble; volume; voluminous; volute; volvox; volvulus; vulva; wale; walk; wallet; wallow; waltz; well (v.) "to spring, rise, gush;" welter; whelk; willow.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit valate "turns round," ulvam "womb, vulva;" Lithuanian valtis "twine, net," vilnis "wave," apvalus "round;" Old Church Slavonic valiti "roll, welter," vlŭna "wave;" Greek eluein "to roll round, wind, enwrap," eilein "twist, turn, squeeze; revolve, rotate," helix "spiral object;" Latin volvere "to turn, twist;" Gothic walwjan "to roll;" Old English wealwian "roll," weoloc "whelk, spiral-shelled mollusk;" Old High German walzan "to roll, waltz;" Old Irish fulumain "rolling;" Welsh olwyn "wheel."
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homoioteleuton (n.)

 in general, "the repetition of endings in words, rhyme and near rhyme," but also, in palaeography, a form of scribal error which occurs "when two words/phrases/lines end with the same sequence of letters. The scribe, having finished copying the first, skips to the second, omitting all intervening words" [Robert B. Waltz, "The Encyclopedia of New Testament Textual Criticism," 2013]; Greek, literally "same ending;" see homo- (1) "the same" + telos.

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two-step (n.)

dance style, 1893, from two + step (n.); so called for the time signature of the music (as distinguished from the three-step waltz). But as the positions taken by the dancers involved direct contact, it was highly scandalous in its day and enormously popular.

A certain Division of an Auxiliary gave a dance not long since. I went and looked on. What did they dance? Two-step, two-step and two-step. How did they dance? When we used to waltz, we clasped arms easily, took a nice, respectable position, and danced in a poetry of motion. Now, girls, how do you two-step? In nine cases out of ten the dear girl reposes her head on the young man's shoulder, or else their faces press each other. He presses her to his breast as closely as possible, and actually carries her around. Disgraceful? I should say so. Do you wonder at the ministers preaching on dancing as a sin, when it looks like this to a woman like myself who believes in dancing and has danced all her life? Mothers, as you love your girls, forbid them to dance after this manner. [letter in the ladies' section of Locomotive Engineers' Monthly Journal, March 1898]
To the Two Step may be accredited, serious injury to the Waltz, awkward and immodest positions assumed in round dancing, also as being a prominent factor in overcrowding the profession and causing a general depression in the business of the legitimate Master of Dancing. [The Director, March 1898]
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