Etymology
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arise (v.)
Old English arisan "to get up from sitting, kneeling, or lying; have a beginning, come into being or action, spring from, originate; spring up, ascend" (cognate with Old Saxon arisan, Gothic urreisan), from a- (1) "of" + rise (v.). Mostly replaced by rise except in reference to circumstances; formerly the choice between the two often was made merely for the sake of rhythm.
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rumba (n.)

type of Afro-Cuban dance, also a ballroom dance based on it, the rhythm of it, and the music suitable for it; 1914 ("La Rumba" was the name of a popular tango melody from 1913), from Cuban Spanish rumba, originally "spree, carousal," derived from Spanish rumbo "spree, party," earlier "ostentation, pomp, leadership," perhaps originally "the course of a ship," from rombo "rhombus," in reference to the compass, which is marked with a rhombus. The verb is recorded from 1932. Related: Rumbaed; rumbaing.

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modal (adj.)

"pertaining to or affected by a mode," 1560s, originally a term in logic, from French modal and directly from Medieval Latin modalis "of or pertaining to a mode," from Latin modus "measure, extent, quantity; proper measure, rhythm, song; a way, manner, fashion, style" (in Late Latin also "mood" in grammar and logic), from PIE root *med- "take appropriate measures." Musical sense is from 1590s; In grammar from 1798.

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signature (n.)

1530s, a kind of document in Scottish law, from French signature (16c.) or directly from Medieval Latin signatura "signature, a rescript," in classical Latin "the matrix of a seal," from signatus, past participle of signare "to mark with a stamp, sign" (see sign (v.)).

Meaning "one's own name written in one's own hand" is from 1570s, replacing sign-manual (early 15c.) in this sense. Musical sense of "signs placed it the beginning of a staff to indicate the key and rhythm" is from 1806. Meaning "a distinguishing mark of any kind" is from 1620s.

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swing (n.)
Old English swinge "stroke, blow; chastisement," from swing (v.). Meaning "suspended seat on ropes" is from 1680s. Meaning "shift of public opinion" is from 1899. The meaning "variety of big dance-band music with a swinging rhythm" is first recorded 1933, though the sense has been traced back to 1888; its heyday was from mid-30s to mid-40s. Phrase in full swing "in total effect or operation" (1560s) perhaps is from bell-ringing. The backyard or playground swing-set is from 1951.
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mode (n.1)

"manner;" late 14c., "melodies, strains of music" (a sense now obsolete; see musical senses below), from Old French mode and directly from Latin modus "measure, extent, quantity; proper measure, rhythm, song; a way, manner, fashion, style" (in Late Latin also "mood" in grammar and logic), from PIE root *med- "take appropriate measures."

Meaning "manner of acting or doing, was in which a thing is done" is by 1660s. Sense of "inflectional category in conjugation" is mid-15c. In music, 1670s as "method of dividing the intervals of the octave for melodic purposes" in reference to ancient Greek music; by 1721 in reference to modern music.

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scan (v.)
late 14c., "mark off verse in metric feet," from Late Latin scandere "to scan verse," originally, in classical Latin, "to climb, rise, mount" (the connecting notion is of the rising and falling rhythm of poetry), from PIE *skand- "to spring, leap, climb" (source also of Sanskrit skandati "hastens, leaps, jumps;" Greek skandalon "stumbling block;" Middle Irish sescaind "he sprang, jumped," sceinm "a bound, jump").

Missing -d in English is probably from confusion with suffix -ed (see lawn (n.1)). Sense of "look at closely, examine minutely (as one does when counting metrical feet in poetry)" first recorded 1540s. The (opposite) sense of "look over quickly, skim" is first attested 1926. Related: Scanned; scanning.
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cadence (n.)

late 14c., "flow of rhythm in prose or verse," from French cadence, from Old Italian cadenza "conclusion of a movement in music," literally "a falling," from Vulgar Latin *cadentia, from neuter plural of Latin cadens, present participle of cadere "to fall" (from PIE root *kad- "to fall"). A doublet of chance (n.).

The notion is of a "fall" in the voice in reading aloud or speaking, as at the end of a sentence, also the rising and falling in modulation of tones in reciting. Later (1590s) extended to music, in reference to a sequence of chords expressing conclusion at the end of a phrase and resolving to the key in which the piece was written. Also the measure or beat of any rhythmic movement (c. 1600). In 16c., sometimes used literally for "an act of falling." Related: Cadential.

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rhyme (n.)

"agreement in terminal sounds of words or metrical lines," a 16c. attempt to restore a classical spelling to Middle English ryme, rime (c. 1200) "measure, meter, rhythm," later "rhymed verse" (mid-13c.), from Old French rime (fem.), which is related to Old Provençal rim (masc.), earlier *ritme, from Latin rithmus, from Greek rhythmos "measured flow or movement, rhythm; proportion, symmetry; arrangement, order; form, shape, wise, manner; soul, disposition," related to rhein "to flow" (from PIE root *sreu- "to flow").

The persistence of rime, the older form of the word, perhaps is due to popular association with Old English rim "number" (from PIE root *re- "to reason, count"). The intermediate form rhime was frequent until late 18c.

In Medieval Latin, rithmus was used for accentual, as opposed to quantitative, verse, and accentual verse usually was rhymed, hence the sense shift. In prosody, specifically the quality of agreement in end-sounds such that the last stressed vowel, and any sounds after it, are the same, and preceding sounds differ. 

Verse was invented as an aid to memory. Later it was preserved to increase pleasure by the spectacle of difficulty overcome. That it should still survive in dramatic art is a vestige of barbarism. [Stendhal "de l'Amour," 1822]

The sense of "a piece of poetry in which consonance of end-sounds is observed" is from 1610s. From 1650s as "word that rhymes with another." The phrase rhyme or reason "good sense" (chiefly used in the negative) is from late 15c. (see reason (n.)). Rhyme scheme "ordered pattern of end-rhymes in metrical composition" is attested from 1931. Rhyme royal (1841) is a stanza of seven 10-syllable lines rhymed a-b-a-b-b-c-c.

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square (adj.)

early 14c., "containing four equal sides and right angles," from square (n.), or from Old French esquarre, past participle of esquarrer. Meaning "honest, fair," is first attested 1560s; that of "straight, direct" is from 1804. Of meals, from 1868.

Sense of "old-fashioned" is 1944, U.S. jazz slang, said to be from shape of a conductor's hand gestures in a regular four-beat rhythm. Square-toes meant nearly the same thing late 18c.: "precise, formal, old-fashioned person," from the style of men's shoes worn early 18c. and then fallen from fashion. Squaresville is attested from 1956. Square dance attested by 1831; originally one in which the couples faced inward from four sides; later of country dances generally.

[T]he old square dance is an abortive attempt at conversation while engaged in walking certain mathematical figures over a limited area. [The Mask, March 1868]
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