In this paper, we propose a theoretical framework for the design of tangible interfaces for musical expression. The main insight for the proposed approach is the importance and utility of familiar sensorimotor experiences for the creation of engaging and playable new musical instruments. In particular, we suggest exploiting the commonalities between different natural interactions by varying the auditory response or tactile details of the instrument within certain limits. Using this principle, devices for classes of sounds such as coarse grain collision interactions or friction interactions can be designed. The designs we propose retain the familiar tactile aspect of the interaction so that the performer can take advantage of tacit knowledge gained through experiences with such phenomena in the real world.