This verse form, in which two people speak alternately with each competing to cap the other, was used by Sappho and other Greek predecessors of Horace, and had already been adopted by Virgil in his pastoral poems, the Eclogues. The names are Greek: Thurii is a town in the south of Italy, and was also originally a Greek foundation. Ilia, to whom Lydia compares herself, was the mother who bore Romulus and Remus to the war God, Mars.
Horace admits elsewhere to having a quick temper, and commentators have wondered whether the reference to one in this piece was intended to associate him with the unnamed male speaker, but that is speculative: if there is such a reference, it could be jocular, autobiographical, both or neither.
Metre: (fourth) Asclepiad.
See the illustrated blog post here.
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