I spent last Thursday and Friday at a workshop on error analysis, and Thursday evening there there was a Corsican banquet, with a concert by the musical group Sarocchi. The banquet and concert were in honor of Joseph Mariani, who is originally from Corsica. Here's a video of part of an a capella duet, which I took with my cell phone:
The language of the performance is of course Corsican, and the Wikipedia article on Corsican says that
Ferdinand Gregorovius, 19th century traveller and enthusiast of Corsican culture, reports that the preferred form of the literary tradition of his time was the vocero, a type of polyphonic ballad originating from funeral obsequies. These laments were similar in form to the chorales of Greek drama except that the leader could improvise. Some performers were noted at this, such as the 18th century Mariola della Piazzole and Clorinda Franseschi.
The Wikipedia article on Corsican music says that
Polyphonic songs (pulifunie) in Corsica are a cappella, and can be either spiritual or secular. Hymns, motets, and funereal songs (lamentu) are an example of the former, while the nanna (lullaby) and the paghjella are examples of the latter. Traditionally, 4 to 6-voice improvised polyphony was sung only by men, with the exception of the voceru (sung only by women) and cuntrastu (usually 2-voice) and nanne often sung by women. Brotherhoods of polyphonic singers (cunfraternita) remain, some dating back to the 12th century. Corsica's actual tradition of improvised vocal polyphony is more recent, dating to 15th century. It is traced to renaissance practice of falsobordone and the Genoese tradition of Trallalero.
At Thursday's performance, M. Sarocchi gave an explanatory introduction before each song, but I can no longer recall which the details of this one, which was the last of the evening's offerings. Perhaps someone who knows Corsican, or a Corsican-like language, can transcribe it for us.
N.B. The business of cupping a hand over one ear is apparently traditional in this sort of singing. I don't know how widespread this practice is, or what it's called by those who use it. If you try it, you'll see that it enhances lower-frequency sounds, especially your own voice, which is presumably the motivation.