In this thesis, we present an articulated, empirical view on what human music making is, and on how this fundamentally relates to computation. The experimental evidence which we obtained seems to indicate that this view can be used as a tool, to systematically generate models, hypotheses and new technologies that enable an ever more complete answer to the fundamental question as to what forms of instrumental control of musical sound are possible to implement. This also entails the development of two novel transducer technologies for computed fingertip touch: The cyclotactor (CT) system, which provides fingerpad-orthogonal force output while tracking surface-orthogonal fingertip movement; and the kinetic surface friction transducer (KSFT) system, which provides fingerpad-parallel force output while tracking surface-parallel fingertip movement. In addition to the main research, the thesis also contains two research excursions, which are due to the nature of the Ph.D. position. The first excursion shows how repeated and varying pressing movements on the already held-down key of a computer keyboard can be used both to simplify existing user interactions and to implement new ones, that allow the rapid yet detailed navigation of multiple possible interaction outcomes. The second excursion shows that automated computational techniques can display shape specifically in the retinal afterimage, a well-known effect in the human visual system.