This article presents a system to generate Arab music improvisation using machine translation (MT). To reach this goal, we developed a MT model to translate a vocal improvisation into an automatic instrumental oud (Arab lute) response. Given the melodic and non-metric musical form, it was necessary to develop efficient textual representations in order for classical MT models to be as successful as in common NLP applications. We experimented with Statistical and Neural MT to train our parallel corpus (Vocal → Instrument) of 6991 sentences. The best model was then used to generate improvisation by iteratively translating the translations of the most common patterns of each maqām (n-grams), producing elaborated variations conditioned to listener feedback. We constructed a dataset of 717 instrumental improvisations to extract their n-grams. Objective evaluation of MT was conducted at two levels: a sentence-level evaluation using the BLEU metric, and a higher level evaluation using musically informed metrics. Objective measures were consistent with one another. Subjective evaluations by experts from the maqām music tradition were promising, and a useful reference for understanding objective results.