The music you are listening to is "Alme Luci Beate"
by Giulio Caccini. Caccini's music was modeled by Claudio Monteverdi ("Seconda
prattica"). This music was considered to be the beginning of modern opera,
as now poetry could be set to music with a new, Humanist theory of rhetoric
tacens, and not the old, inflexible, strictly hierarchical Scholastic view of
reality.
The singing of any syllable of text across several notes is called
melismatic music. When each syllable of sung text is associated with
one note, the music is syllabilic.