As technologies and interfaces for the instrumental control of musical sound get ever better at tracking aspects of human position and motion in space, a fundamental problem emerges: Unintended or even counter-intentional control may result when humans themselves become a source of positional noise. A clear case of what is meant by this is the "stillness movement" of a body part occurring despite the simultaneous explicit intention for that body part to remain still. In this paper, we present the results of a randomized, controlled experiment investigating this phenomenon along a vertical axis relative to the human fingertip. The results include characterizations of both the spatial distribution and frequency distribution of the stillness movement observed. Also included are results indicating a possible role for constant forces and viscosities in reducing stillness movement amplitude, thereby potentially enabling the implementation of more positional control of musical sound within the same available spatial range. Importantly, the above is summarized in a form that is directly interpretable for anyone designing technologies, interactions, or performances that involve fingertip control of musical sound. Also, a complete data set of the experimental results is included in the separate Appendices to this paper, again in a format that is directly interpretable.