He is mainly remembered for his madrigals, which were influenced by Gesualdo, and for his polychoral sacred motets, posthumously published as Sacrae Hebdomadae Responsoria in 1622.
His father, Giovanni Battista Nenna, was a city official in Bari and was the author of "Il Nennio : nel quale si ragiona di nobiltà", a book about nobility and virtuous character, published in 1542.
A curious remark concerning his skilled participation in a chess game in Naples in 1606 is recorded in a manuscript book of discourses.
Nenna uses dissonance to build tensions that intimately reflect the passions expressed in the texts, and he employs imitative melodic and rhythmic patterns among the parts as they move towards points of conflict that then frequently resolve suddenly.
The chromatic structures are sometimes surprising, as in the beginning of "La mia doglia s'avanza", whose opening chords move from G minor to F-sharp major then D minor and finally C-sharp major, commencing a series of descending chromatic figures.
In "L'amoroso veleno", the voices use small, chromatic ascending scales to mimic the poison which slowly creeps up to the victim's heart.
He also wrote sacred choral music, including Tenebrae responsories for use during Easter and a psalm setting, all of which show a dignified and restrained approach, much in keeping with the Neapolitan style for liturgical music, and reflective of the work of the brothers Anerio and Gesualdo.
On the back of the frontispiece of a copy of the 1621 edition of the First Book of Madrigals, found in the collection of the Liceo Musicale di Bologna, composer Alessandro Grandi had written in 1623 a dedication wherein he begins, "Escono questi Madrigali del Signor Cauaglier Nenna dal sepolchro delle tenebre alla luce del sole", or "These madrigals of Signor Nenna exit from out the darkness of the grave to the light of the sun".