Music education has historically relied on individualized mentorship, yet the increasing demand for accessible and inclusive pedagogical tools calls for new approaches. While generative artificial intelligence (AI) has shown promise in adaptive learning for mathematics, language studies, and computer science, its potential in music education remains underexplored. The complexity of music notation, combined with the need for rhythmically and melodically coherent materials, poses unique challenges for AI-driven pedagogy. This paper presents HarmonyHub, a platform that leverages generative AI to support adaptive music learning. We created HarmonyHub as an open-source research project, developed collaboratively by contributors, and this paper reports on its design, implementation, and initial results. Building on research about how people learn music and how technology can enrich teaching, HarmonyHub aims to empower students and educators by providing dynamically generated, personalized practice exercises. The project situates itself within the broader theme of inclusivity in music education, exploring how technological innovation can bridge gaps in access, diversity, and pedagogical adaptability. The platform integrates modern web technologies (Ionic and Angular) with large language models (LLMs) to generate exercises tailored to user-defined parameters such as instrument, difficulty level, key, time signature, exercise duration, and practice focus. Exercises can be delivered in various musical and digital formats, ensuring flexibility across diverse learning environments. A web-based interface, accessible from any browser, further enhances accessibility by allowing students, educators, and self-directed learners to select parameters and generate exercises instantly. The results from the initial implementation demonstrate the feasibility of creating rhythmically precise, melodically coherent, and pedagogically meaningful exercises within seconds. This marks a significant advancement in the use of AI for complex creative domains like music. By integrating music pedagogy with adaptive technologies, HarmonyHub not only supports more effective practice strategies but also contributes to a broader vision of inclusivity in music education, fostering unity and building bridges across diverse learners and communities. The implications of this work extend beyond music education, offering a model for how generative AI can be applied to other domains that require nuanced engagement with symbolic and creative data. For music educators, HarmonyHub represents a practical, scalable, and open-source resource that enhances adaptability, fosters engagement, and supports diversity in the classroom.