“very widely-distributed” – must be indo-european. Sounds Indian to me. I guess Hindi.

Definitely not Hindi. The phonology does not at all support it. If Indian at all, it might have been Tamil, but I doubt it. Besides the Dravidian languages are not widely distributed.
My guess is Kiswahili. It is part of the widely distributed Niger-Congo language family.

It’s a west-African tonal language of the Xhosa family, perhaps Xhosa itself.

d.m.f.

….Now having heard it and thought about it….I’m in the mood for some cora music… ;)

d.m.f.

I think I’ve heard a bilabial “f” sound in the recording. That makes me believe it’s an African language, but one that can do without a final vowel in every word. Maybe Wolof?

Wolof is a possibility, and it is a member of the Xhosa family (as is Yoruba and a few others).

d.m.f.

The answer is Malagasy, the main language of Madagascar. The recording comes from this site.

Well, the Austronesian family is very widely-distributed.

I knew it was an austronesian language when I heard it but I was going to guess Tagalog.