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I can't understand how the transition from kappa-digamma to pi-pi happened in the transition from ekwos (same etymology as latin equus) to ippo.

I mean how did the prononciation change ? Because is it a matter of prononciation ?

The key is, there was never a digamma in hippos in the first place! (At least, not as far back as we have evidence for: there may have been one earlier than that.)

Early Greek, like Latin, had a set of labiovelar consonants. In other words, what the Romans wrote as qu and linguists write as /kʷ/ wasn't treated as a combination of /k/ and /w/ (kappa-digamma): it was a single phoneme in its own right.

(As a note, the tradition among Greek scholars is to write this single phoneme as q or /q/, based on how the Romans did it, even though this doesn't line up with the IPA. Confusing, but it's what we're stuck with now, so in this answer q always means a voiceless labiovelar stop. Some people even call it "qoppa", the name of an unrelated Greek letter, which is just outright a bad idea if you want people to understand you.)

In the oldest attested stages of Greek, the Linear B tablets from Crete, we can see that there was indeed a q: the word for "horse" is written 𐀂𐀦 i-qo, which represents hiqqos (h, double consonants, and final -s weren't represented in this writing system). It's not clear where the hi came from, since we don't see anything similar in Latin or other languages, but that's a separate question.

But the q sound was never completely comfortable in Greek. It's not one of the easier or more common sounds in the world, and requires you to do something with your lips and with your soft palate at the same time. So over the years, Greek disposed of it, replacing it with other sounds.

In Attic in particular, q could turn into either p (keeping only the lip part), k (keeping only the soft palate part), or t (averaging the two).

• Next to u, it became k (the "boukolos rule")


• Before e or i, it became t
  


• Elsewhere, it became p
  

This is why you see tin- "pay" next to poin- "fine", or thein- "kill (v)" next to phon- "slaughter (n)", or bou-kol- "cowherd" next to amphi-pol- "attendant", and so on. Note that these rules are only for Attic: this wasn't consistent across dialects. Compare Latin quis "who" and -que "and", Mycenaean (Linear B) qis, -qe, Attic tis, -te, Doric kis, -ke.

In the word for "horse", the q fell into the "otherwise" clause, so it changed from hiqqos to hippos.

P.S. While this sound change may look odd, it's not uncommon in the world. Both Proto-Italic and Proto-Celtic split into two branches each, one preserving q, the other turning it into p. And much later, Romanian did the same to all of Latin's qs.

If you analyze phonemes into components, /kw/ is velar+stop+labialized. Then if you remove "velar", then you have stop+labialized = /p/. So basically, the change /kw/ > /p(p)/ amounts to a weakening of velarization.