Etymology
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incantation (n.)

"art or act of enchanting by uttering magical words, with ceremonies supposed to have magical power; the formula of words or the ceremony employed," late 14c., from Old French incantacion "spell, exorcism" (13c.), from Late Latin incantationem (nominative incantatio) "art of enchanting," noun of action from past-participle stem of incantare "to bewitch, charm, cast a spell upon, chant magic over, sing spells" (see enchantment).

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*kan- 

Proto-Indo-European root meaning "to sing."

It forms all or part of: accent; cant (n.1); cantabile; cantata; cantatrice; canticle; canto; cantor; canzone; Carmen; chanson; chant; chanter; chanteuse; chanty; chanticleer; charm; concent; descant; enchant; enchantment; hen; incantation; incentive; oscine; precentor; recant.

It is the hypothetical source of/evidence for its existence is provided by: Greek eikanos "cock," literally "bird who sings (for sunrise);" Latin cantare, canere "to sing;" Old Irish caniaid "sings," Welsh canu "sing;" Old English hana "cock."

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grimoire (n.)
magician's manual for invoking demons, 1849, from French grimoire, altered from grammaire "incantation; grammar" (see grammar). Also compare gramary, glamour.
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epode (n.)
1590s, a kind of lyric poem in which a short line follows a longer one (invented by Archilochus, also used by Horace), from Latin epodos, from Greek epodus "after-song, incantation," from epi "after" (see epi-) + odein "to sing" (see ode). Related: Epodic.
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Carmen (n.)
French opera by Georges Bizet (1838-1875), premiered in Paris March 3, 1875. As a proper name, it can represent (especially in Italian and Spanish) a diminutive of Carmel/Carmelo or Latin carmen "song, poem, incantation, oracle," from canere "to sing" (from PIE root *kan- "to sing").
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mantra (n.)

1808, "that part of the Vedas which contains hymns," from Sanskrit mantra-s "sacred message or text, charm, spell, counsel," literally "instrument of thought," related to manyate "thinks," from PIE root *men- (1) "to think." Meaning "sacred text used as a charm or incantation" is by 1900; sense of "special word used for yoga meditation" is recorded in English by 1956.

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conjuration (n.)

late 14c., coniuracioun, "conspiracy, a plot, act of plotting" (senses now obsolete), also "a calling upon something supernatural, act of invoking by a sacred name, invocation of spirits, magic spell or charm," from Old French conjuracion "spell, incantation, formula used in exorcism" and directly from Latin coniurationem (nominative coniuratio) "a swearing together, conspiracy," in Medieval Latin "enchantment," noun of action from past-participle stem of coniurare "to swear together; conspire," from assimilated form of com "with, together" (see con-) + iurare "to swear," from ius (genitive iuris) "law, an oath" (see jurist).

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charm (n.)

c. 1300, "incantation, magic charm," from Old French charme (12c.) "magic charm, magic spell incantation; song, lamentation," from Latin carmen "song, verse, enchantment, religious formula," from canere "to sing" (from PIE root *kan- "to sing"), with dissimilation of -n- to -r- before -m- in intermediate form *canmen (for a similar evolution, see Latin germen "germ," from *genmen). The notion is of chanting or reciting verses of magical power.

A yet stronger power than that of herb or stone lies in the spoken word, and all nations use it both for blessing and cursing. But these, to be effective, must be choice, well knit, rhythmic words (verba concepta), must have lilt and tune; hence all that is strong in the speech wielded by priest, physician, magician, is allied to the forms of poetry. [Jakob Grimm, "Teutonic Mythology" (transl. Stallybrass), 1883] 

Sense of "pleasing quality, irresistable power to please and attract" evolved by 17c. From 1590s as "any item worn to avert evil;" meaning "small trinket fastened to a watch-chain, etc." first recorded 1865. Quantum physics sense is from 1964. Charm-bracelet is from 1941; charm-school from 1919. To work like a charm (figuratively) is recorded by 1824.

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conjure (v.)

late 13c., "command on oath;" c. 1300, "summon by a sacred name, invoke by incantation or magic," from Old French conjurer "invoke, conjure" (12c.) and directly from Latin coniurare "to swear together; conspire," from assimilated form of com "with, together" (see con-) + iurare "to swear," from ius (genitive iuris) "law, an oath" (see jurist).

The magical sense is from the notion of "constraining by spell" a demon to do one's bidding. Related: Conjured; conjuring. Phrase conjure up "cause to appear in the mind" (as if by magic) attested from 1580s.

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song (n.)

Old English sang "voice, song, art of singing; metrical composition adapted for singing, psalm, poem," from Proto-Germanic *songwho- (source also of Old Norse söngr, Norwegian song, Swedish sång, Old Saxon, Danish, Old Frisian, Old High German, German sang, Middle Dutch sanc, Dutch zang, Gothic saggws), from PIE *songwh-o- "singing, song," from *sengwh- "to sing, make an incantation" (see sing (v.)).

Phrase for a song "for a trifle, for little or nothing" is from "All's Well" III.ii.9 (the identical image, por du son, is in Old French. With a song in (one's) heart "feeling joy" is first attested 1930 in Lorenz Hart's lyric. Song and dance as a form of vaudeville act is attested from 1872; figurative sense of "rigmarole" is from 1895.

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