What theatre type is a highly ceremonial musical and dance drama, of which the 240 texts produced today were written by members of a single family five hundred years ago, and whose lines were designed to be sung rather than spoken?

Noh theatre.

Explanation:

Noh (Nō) theatre is a Japanese performance art which became especially popular from the 14th century CE and which is still performed today. Noh actors, who were always male in the medieval period, famously move and make gestures in a very slow and highly stylised manner while they wear masks of particular designs which show the characters they are playing such as youths, aristocratic women, warriors, and demons.

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answer; approx,300,000 ;