Carlos Gesualdo, image taken from wikipedia
Polyphonic songs (i.e. voices sing different melodies, but in such a way that they sound harmonious together) were a trendy thing during the Renaissance. In France for instance they had the chanson, and in Italy the madrigal.
A well known composer of the latter is Carlo Gesualdo (156?-1613), who wrote ground breaking madrigals and became a legend after murdering his wife Maria d’Avalos (and her lover).