To date electric pianos and samplers tend to concentrate on authenticity in terms of temporal and spectral aspects of sound. However, they barely recreate the original sound radiation characteristics, which contribute to the perception of width and depth, vividness and voice separation, especially for instrumentalists, who are located near the instrument. To achieve this, a number of sound field measurement and synthesis techniques need to be applied and adequately combined. In this paper we present the theoretic foundation to combine so far isolated and fragmented sound field analysis and synthesis methods to realize a radiation keyboard, an electric harpsichord that approximates the sound of a real harpsichord precisely in time, frequency, and space domain. Potential applications for such a radiation keyboard are conservation of historic musical instruments, music performance, and psychoacoustic measurements for instrument and synthesizer building and for studies of music perception, cognition, and embodiment.