Starting from a personal experience in turning texts by poets into songs, I will show how mathematics might shed some new light on our understanding of the relation between poetry and music. After recalling the conflictual relations between poetry and chanson, I will focus on a geometric representation of the harmonic space-the Tonnetz-that enabled me to propose an original perspective on poetic song writing through the concept of 'Hamiltonian song'. Two musical examples will illustrate the flexibility of this formal approach in poetry-based song writing.