In Hausa, the word for "shoe, boot, sandal" is tà:kàlmí: (borrowed directly into the Songhay (Dendi) variety of Djougou as tàkăm). Within Hausa, this likewise corresponds to a verb tá:kà: "step on". The two-way similarity is striking, but if there was borrowing, which way did it go? A cognate set in Schuh (2008) casts some light on the question.
Hausa belongs to the West Chadic family, in which the best comparison to Hausa "shoe" seems to be Bole tàkà(:), with no obvious cognates within its own subgroup, Bole-Tangale (Ngamo tà:hò looks similar, but Ngamo h seems normally to correspond to Bole p, not k.) For "step on", however, Schuh points to a potential cognate set in a slightly more distantly related West Chadic subgroup, Bade. In this subgroup, we have Gashua Bade tà:gɗú, Western Bade tàgɗú, Ngizim tàkɗú which Schuh analyses as *tàk- plus an unproductive verbal extension -ɗu supported by Bade-internal evidence, eg tə̀nkùku "press" vs. tə̀nkwàkùɗu "massage". Within Bole-Tangale, one might speculate that Gera tàndə̀- is cognate, but Gera seems to be known only from short wordlists, so that would be difficult to show.
So the comparative evidence provides some support for the idea that Hausa tá:kà: "step on" goes back to proto-West Chadic. If tà:kàlmí: "shoe" could be regularly derived from this verb within Chadic, then the answer would appear clear: Songhay borrowed it from Chadic. However, while Hausa frequently forms deverbal nouns with a suffix -i: (Newman (2000:157), there seems to be no plausible language-internal explanation for the -lm-. In Songhay, on the other hand, a suffix -mi forming nouns from verbs (sometimes -m-ey with a former plural suffix stuck on) is reasonably well-attested: Gao (Heath 1999:97) dey "buy" vs. dey-mi "purchase (n.)", key "weave" vs. key-mi "weaving", Kikara (Heath 2005:97-98) kà:rù "go up" vs. kàr-mɛ̂y "going up", húná "live" vs. hùnà-mɛ̀y "long life". A shift *-mi to *-mu seems natural enough, especially since a few Songhay varieties actually have reflexes of "shoe" with a final -i in any case; so the Songhay form looks kind of like it could be **tàg "step on" plus deverbal -mí̀. To top it off, deverbal noun-forming suffixes in -r- are widely attested in Songhay, and Zarma attests a combined suffix -àr-mì: zànjì "break" vs. zànjàrmì "shard", bágú "break" vs. bàgàrmì "piece of debris" (Tersis 1981:244). If we treat the Hausa form as a borrowing from Songhay, we can then analyse it as **tàg "step on" plus deverbal -àr-mí. But before we get carried away, we should note that within Songhay there's no motivation for analysing the -mu / -mi in "shoe" as a suffix; the verb and the noun differ (if at all) only in the final vowel.
So what to make of all this? So far, the scenario that suggests itself is something like the following:
- Songhay borrows a verb *tàk "step on" from West Chadic (or vice versa?).
- Songhay internally forms a deverbal noun *tàk-mí "shoe" (there is no reconstructible contrast between *k and *g in coda position in proto-Songhay), alongside a variant *tàk-àr-mí.
- Hausa borrows this as tà:kàlmí:.
- Songhay replaces *tàk with a denominal verb formed from "shoe" (which becomes internally unanalysable): *tàgm-á. This step has possible internal motivations: in most of Songhay, final velar stops disappeared leaving behind only compensatory lengthening on the preceding vowel, and the resulting form tà: would have been homophonous with the much commoner verb "receive, take".
- Djougou Dendi, a heavily Hausa-influenced, somewhat creolized Songhay variety spoken in Benin, borrows the Hausa form as tàkăm.
Further Chadic comparative data may yet turn out to bear upon this etymology, but one thing seems clear: these two families have been affecting each other for a long time.