Vilma Jää, a Finnish folk and pop singer, is bringing her eerie and affecting traditional music to the Metropolitan Opera.

Vilma Jää never expected to play a major role in one of the 21st century’s most acclaimed operas when she enrolled at the Sibelius Academy to study folk music.

The Italian composer Giacomo Puccini died of a heart attack on Nov. 29, 1924 without finishing his newest opera “Turandot.” ...