Abstract:Generative AI is radically changing the creative arts, by fundamentally transforming the way we create and interact with cultural artefacts. While offering unprecedented opportunities for artistic expression and commercialisation, this technology also raises ethical, societal, and legal concerns. Key among these are the potential displacement of human creativity, copyright infringement stemming from vast training datasets, and the lack of transparency, explainability, and fairness mechanisms. As generative systems become pervasive in this domain, responsible design is crucial. Whilst previous work has tackled isolated aspects of generative systems (e.g., transparency, evaluation, data), we take a comprehensive approach, grounding these efforts within the Ethics Guidelines for Trustworthy Artificial Intelligence produced by the High-Level Expert Group on AI appointed by the European Commission - a framework for designing responsible AI systems across seven macro requirements. Focusing on generative music AI, we illustrate how these requirements can be contextualised for the field, addressing trustworthiness across multiple dimensions and integrating insights from the existing literature. We further propose a roadmap for operationalising these contextualised requirements, emphasising interdisciplinary collaboration and stakeholder engagement. Our work provides a foundation for designing and evaluating responsible music generation systems, calling for collaboration among AI experts, ethicists, legal scholars, and artists. This manuscript is accompanied by a website: https://amresearchlab.github.io/raim-framework/.