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In Indo-Iranian and Balto-Slavic languages (which are conveniently all Satem languages), there is a sibilant or affricate sound in places where Centum languages usually have a velar consonant. It seems reasonable for Centum languages to simply depalatalize, voice, lenite, or even glottalize the /ḱ/, remaining mostly in the rear/velar area, as opposed to Satem languages shifting all the way to /ʃ/ and /tʃ/. For example Quattuor in Latin is Chetiri in Slavic and Chatur in Sanskrit. How did this come about? Is there name for a rule of this sound change?

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    The name for it is palatalization. The Slavic branch had multiple waves of that, affecting sounds in different ways. Think of a short /j/ appearing after /k/ - it makes it sound close to a soft /tʃ/. See also the letters ќ and ћ which represent an intermediate sound.
    – ngn
    Mar 12 at 10:39
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    This is not limited to Satem languages in Indo-European. Palatalisation has happened at least once universally in Romance (and several times more in the individual languages), it’s extremely prevalent in Slavic (as @ngn mentions), Fennic languages have had several rounds of it, it’s happened in Swedish and Norwegian, Mandarin is steeped in it, Ethiopic has a significant tendency towards it, etc. It’s one of the most common sound changes there are. Mar 12 at 11:30

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The other answer focuses on the observation that it happens, and has a name; I address the "how" question. The starting point is having a difference between velar [k,g] and palatal [c,ɟ], the latter being a kind of fronted k,g. You can hear expert IPA demonstrations here. Although the articulatory difference between [k] and [c] is small, the acoustic effect is quite large. The palatals sound very much like linguals such as [ʃ, tʃ, ɕ]. This makes it easy to confuse true palatal sounds with postalveolars or alveolo-palatals, indeed the term "palatal" is used in many ways. As applied to IE reconstruction, the premise is that PIE started with [c, ɟ] (in IPA: /ḱ, ǵ/ in more traditional Indo-Europeanist orthography), then the satem languages simply followed a natural phonetic tendency of alveolarization to arrive at [ʃ] etc. Incidentally, North Saami historically also has a distinct palatal series of consonants spelled dj, which are similar to but still phonetically different from Hungarian dy, and in some dialects of North Saami, they have by this same alveolarizatin process merged with the alveopalatals [tʃ] spelled č.

The same [k] → [c] → [tʃ] path is attested in numerous languages that did not start with [c, ɟ] as PIE is assumed to have. As for terminology, the broadest term is "palatalization" which typically refers to any back of the mouth to front of the tongue shift. There are very many types of palatalization, and phonological studies there is a tendency to distinguish the alveolarization step, which is motivated by acoustics rather than articulation. The step where [ki] → [ci] is articulatory, involving an adjustment to the velar target into a fronted velar a.k.a. true palatal. Once there, the sound is susceptible to further perceptually-motivated reanalyses, based on the acoustic similarity of [c] and [tʃ].

The example of "four" actually does not relate to the Indo-European palatals, since the PIE root has [kʷ], not [ḱ]. A better example of a PIE palatal is the word "hundred", with [ç] in Sanskit, [s] in Slavic etc – the Sanskrit outcome is earlier in the historical chain than the Slavic outcome is. This just underscores the point that this shift is very common across languages, and can happen many times in the history of a language.

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  • Did you mean [ɕ] for Sanskrit ‘hundred’? At least I’ve never seen Sanskrit ś transcribed phonetically as [ç]. Mar 12 at 16:39
  • I've never seen ś transcribed as ɕ. The real question IMO is what basis an author would have for making a claim about modern IPA categories applied to the phonetics of a language spoken thousands of years ago. Do you have some basis in the Pratiśakhyas for choosing [ɕ] over [ç]. What about the stops and the nasal at the same place of articulation?
    – user6726
    Mar 12 at 17:01
  • Well, it’s how Wikipedia transcribes it, and also how every other description I’ve seen describes it (including Goldman 2002 and Cardona 2003 which Wikipedia also lists). The transcription ś and the modern reflexes, such as Hindi [ʃ], also very heavily imply that it is a sibilant, which [ç] isn’t. Mar 12 at 17:07
  • Compare Whitney's grammar. The historical change to lingual sibilant is explained in my answer. Phonetic properties change over time: the precursor of ś was a stop, but nobody claims that ś was a stop.
    – user6726
    Mar 12 at 17:15
  • Whitney uses a proprietary transcription scheme, not IPA. He does denote it ç in his transcription, but still describes it as a sibilant and a “sh-sound”. I don’t know offhand what contemporary grammarians say about the production of this particular sound, but is there any evidence that palatalisation had not yet led to an actual sibilant by the time of Classical (or even Vedic) Sanskrit? Mar 12 at 17:29
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As ngn says in a comment, this is palatalization.

It is a very common sound change. It happened in the descendents of the poster-boy centum language Latin:

Latin ''centum'' (/k/) -> Italian ''cento'' (/tʃ/), French ''cent'' (/s/), Spanish ''cien'' (/s/ in Latin America, /θ/ in Spain)

In Germanic it happened differently in different times and places: Danish ''kirke'' and Scots ''kirk'' have neither /k/ palatalized, German ''Kirche'' has only the second palatalized, Swedish ''kyrke'' has only the first palatalized, and English ''church'' has both.

Further afield, Arabic has no /g/ because where its relatives have that sound Arabic has /d͡ʒ/, for example Arabic جَمَل‎ (jamal) vs Hebrew גמל‎ (gamál) "camel".

And Beijing used to be written Peking because when Europeans first encountered the city the Chinese name had a /k/ in it, but over the last four hundred years the sound has been palatalized to /tɕ/.

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  • German never actually had palatalisation of /k/, but it did have the High German consonant shift which turned /ˈkirikaː/ into /ˈkxirixa/. The initial /kx/ was later undone back to /k/ in most of the German-speaking area, and syncope + vowel reduction turned /kirixa/ into /kirxə/, the current underlying form. And there is productive palatalisation for /x/ → [ç]. Also note that the Swedish word for ‘church’ still has the original final -a (kyrka, not kyrke), so it doesn’t have the context for palatalisation of the second k. Mar 12 at 12:58
  • Unlike the Swedish form, in Norwegian (where -a has often been reduced to -e or ), there are dialects, especially in more Nynorsk-adjacent areas, that have palatalised both k’s and now have kyrkje and similar forms. Mar 12 at 13:01

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