## 1 Introduction  
Synthesizers tend to focus on timbral aspects of sound, which contains temporal and spectral features [1, 2]. This is even true for modern synthesizers that imitate musical instruments by means of physical modeling [3, 4]. Many samplers and electric pianos on the market use stereo recordings, or pseudostereo techniques [5, 6] to create some perceived spaciousness in terms of _apparent source width_ or _perceived source extent_, so that the sound appears more natural and vivid. However, such techniques do not capture the sound radiation characteristics of musical instruments, which may be essential for an authentic experience in music listening and musician-instrument-interaction. Most sound field synthesis approaches synthesize virtual monopole sources or plane waves by means of loudspeaker arrays [7, 8]. Methods to incorporate the sound radiation characteristics of musical instruments are based on sparse recordings of the sound radiation characteristics [5], like far field recordings from circular [9; 10] or spherical [11] microphone arrays with 24 to 128 microphones. In these studies, a nearfield mono recording is extrapolated from a virtual source point. However, instead of a monopole point source, the measured radiation characteristic is included in the extrapolation function, yielding a so-called _complex point source_[9; 12; 13]. Complex point sources are a drastic simplification of the actual physics of musical instruments. However, complex point sources were demonstrated to create plausible physical and perceptual fields [5; 14]. These sound natural in terms of source localization, perceived source extent and timbre, especially when listeners and/or sources move during the performance [5; 15; 16; 17; 18; 19; 20]. To date, sound field synthesis methods to reconstruct the sound radiation characteristics of musical instruments do not incorporate exact nearfield microphone array measurements of musical instruments, as described in [21; 22; 23; 24; 25]. This is most likely because the measurement setup and the digital signal processing for high-precision microphone array measurements are very complex on their own. The methods include optimization algorithms and solutions to inverse problems. The same is true for sound field synthesis approaches that incorporate complex source radiation patterns. In this paper we introduce the theoretic concept of a _radiation keyboard_. We describe on a theoretical basis, and with some practical considerations, which sound field measurement and synthesis methods should be combined, and how to combine them utilizing their individual strengths. All presented results are preparatory for the realization. In contrast to conventional samplers, electric pianos, etc., a radiation keyboard recreates not only the temporal and spectral aspects of the original instrument, but also its spatial attributes. The final radiation keyboard is basically a MIDI keyboard whose keys trigger different driving signals of a loudspeaker array in real-time. When playing the radiation keyboard, the superposition of the propagated loudspeaker driving signals should create the same sound field as the original harpsichord would do. Thus, the radiation keyboard will create a more realistic sound impression than conventional, stereophonic samplers. This is especially true for musical performance, where the instrumentalists moves their heads. The radiation keyboard can serve, for example,  
* as a means to produce authentic sounding replicas of historic musical instruments in the context of cultural heritage preservation [26; 27],
* as an authentic and immersive alternative to physical modeling synthesizers, conventional samplers, electrical pianos (or harpsichords, respectively) [3; 4; 28],
* as a research tool for instrument building [29], interactive psychoacoustics [30], and embodied music interaction [31]. The remainder of the paper is organized as follows. Section 2 describes all the steps that are carried out to measure and synthesize the sound radiation characteristics of a harpsichord.