Since 2023, generative AI has rapidly advanced in the music domain. Despite significant technological advancements, music-generative models raise critical ethical challenges, including a lack of transparency and accountability, along with risks such as the replication of artists' works, which highlights the importance of fostering openness. With upcoming regulations such as the EU AI Act encouraging open models, many generative models are being released labelled as 'open'. However, the definition of an open model remains widely debated. In this article, we adapt a recently proposed evidence-based framework for assessing openness in LLMs to the music domain. Using feedback from a survey of 110 participants from the Music Information Retrieval (MIR) community, we refine the framework into MusGO (Music-Generative Open AI), which comprises 13 openness categories: 8 essential and 5 desirable. We evaluate 16 state-of-the-art generative models and provide an openness leaderboard that is fully open to public scrutiny and community contributions. Through this work, we aim to clarify the concept of openness in music-generative AI and promote its transparent and responsible development.