Biosensing technologies are increasingly available as off-the-shelf products, yet for many designers, artists and non-engineers, these technologies remain difficult to design with. Through a soma design stance, we devised a novel approach for exploring qualities in biodata. Our explorative process culminated in the design of three artefacts, coupling biosignals to tangible actuation formats. By making biodata perceivable as sound, in tangible form or directly on the skin, it became possible to link qualities of the measurements to our own somatics - our felt experience of our bodily bioprocesses - as they dynamically unfold, spurring somatically-grounded design discoveries of novel possible interactions. We show that making biodata attainable for a felt experience - or as we frame it: turning biodata into somadata - enables not only first-person encounters, but also supports collaborative design processes as the somadata can be shared and experienced dynamically, right at the moment when we explore design ideas.