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Do "charm" and "чары" share a common etymological root?

(NB: "чары" is a Russian plural noun meaning "magic" or "charm." Also note that the English noun "charms" has historically meant magic or enchantment.)

According to the OED, "charm" originates (through French) from Latin carmen ("song"), which is believed to originate from the Proto-Indo-European verb *keh₂n- ("to sing").

And according Wiktionary, "чары" is from "Proto-Slavic *čarъ, from Proto-Balto-Slavic *ker- *kēr-, from Proto-Indo-European *kʷer-.

Despite this, the similarities in sound and meaning of the two words seems too great to just be a coincidence...does anyone have any other info about their origin and possible etymological links?

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    You've basically answered your own question: they're unrelated. Chance similarities like this between languages are actually a lot more common than one would think -- this kind of question comes up here all the time. – TKR Oct 27 '18 at 17:32
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    @Ajagar "Charm" comes from Latin car-men "song", from can- "sing"; the "ch" came in when it was transmitted through French. "Miracle" comes from Latin mira-culum, from mir- "wonder at". The roots look nothing alike, and there's no "proto-language" involved here: we have ample records of Latin and French from every stage of this process. You say there's no historical record of language, but there absolutely is, dating back thousands of years. – Draconis Feb 2 at 4:42
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    @Ajagar Also, if you want to compare to the Hebrew, you should use the root š-y-r, not an inflected form. It also looks totally different from Latin can- and mir-. Now, you could argue that English "charm" was affected by šiyrim somewhere in the process, but it's just unnecessary: we already see Latin c- turning into ch- before a vowel in French, and Occam's razor tells us not to make random connections with Hebrew when we don't need to. – Draconis Feb 2 at 4:45
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As it was mentioned in the comments, you have already given an answer. But let us make it more obvious.

Russian чары has a convincing Proto-Slavic reconstruction *čarъ (this word has many Slavic cognates) and also seems to have the same root as Avestan kǝrǝnaoiti 'means', Lithuanian kẽras 'magic', etc. (Чары 'charm' was taken as a means of reaching one's aim.) So, there should have been something like *kʷēr-: *kʷer- in PIE.

English charm is derived eventually from Latin canere 'to sing' ('with dissimilation of -n- to -r- before -m- in intermediate form *canmen (for a similar evolution, see Latin germen "germ," from *genmen),' www.etymonline.com), which does not correspond to PIE *kʷēr-: *kʷer-, look: there are IE cognates such as Greek ήι-κανός 'cock' (it sings early in the morning), Breton cana 'to sing' (it is easy to see that there is no /r/), etc. which give us grounds to reconstruct something like *k(h₂)n-e- in PIE. The precise reconstruction is not important as much as the fact that it includes no /r/.

Well, there are no 'great similarities in sound and meaning' between charm and чары as you probably can see. These words do not share the same root.

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