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Hierarchical clustering is a natural approach to discover ontologies from data. Yet, existing approaches are hampered by their inability to scale to large datasets and the discrete encoding of the hierarchy. We introduce scalable Hyperbolic Hierarchical Clustering (sHHC) which overcomes these limitations by learning continuous hierarchies in hyperbolic space. Our hierarchical clustering is of high quality and can be obtained in a fraction of the runtime. Additionally, we demonstrate the strength of sHHC on a downstream cross-modal self-supervision task. By using the discovered hierarchies from sound and vision to construct continuous hierarchical pseudo-labels we can efficiently optimize a network for activity recognition and obtain competitive performance compared to recent self-supervised learning models. Our findings demonstrate the strength of Hyperbolic Hierarchical Clustering and its potential for Self-Supervised Learning.