Music, an intrinsic part of human culture, has long been recognized for its ability to evoke emotions, memories and physiological responses. From the rhythmic beats that make us dance to the soothing melodies that provide solace in times of distress, music's impact on the human psyche is undeniable. Timely, in the wake of the COVID-19 pandemic, the world has witnessed a subsequent and equally concerning mental health "pandemic.” As societies grapple with the repercussions of prolonged isolation, economic downturns, and the collective trauma of a global health emergency, the search for therapeutic interventions has never been more pressing. Among the myriad of potential solutions, one timeless human experience stands out: the power of music. Our study aims to understand how music’s benefits for well-being can be harnessed to combat the rising levels of neurodegenerative diseases and depression. By exploring the neural manifolds and latent neural dynamics of music listening and emotional experience, we aim to uncover the therapeutic potential of music through topology. Our findings not only shed light on music’s role in mental well-being through emotional synchrony across subjects, but also offer hope in times of crisis. Alongside shared neural dynamics across subjects, we also find one subject in which a major difference in emotional experience leads to a drastically different manifold shape, clustering and coloring. These results are the first to pain music listening, emotional experience and well-being in a topological light. We see our results positioned as a backdrop for future research in computational neuroscience on music and well-being, our study being the first to approach mental well-being and music listening with topology. We also outline next steps that would extend our preliminary results immediately to neurodegenerative diseases, depression and more. In a world where mental health issues are on the rise, this topological approach to music and well-being can provide deeper understanding to music therapy’s non-invasive, accessible and enjoyable avenue for improving the well-being of countless individuals; by accounting for inter-subject variability with topologically-inspired computational neuroscience, we can finally put a name to how music helps heal.