## 2 Method  
The concept and design of the proposed radiation keyboard are illustrated in Figure 1. The sound field radiated by a harpsichord is analyzed by technical means. Then, this sound field is synthesized by the radiation keyboard. The radiation keyboard consists of a loudspeaker array whose driving signals are triggered by a MIDI keyboard. The superposition of the propagated loudspeaker driving signals creates the same sound field as a real harpsichord. To date, no sound field synthesis method is able to radiate all frequencies in the exact same way the harpsichord does. Therefore, we combine different sound field analysis and synthesis methods. This combination offers an optimal compromise: low frequencies f1 \(<\) 1500 Hz are synthesized with high precision in the complete half-space above the sound board, mid frequencies 1500 \(\leq\) f2 \(\leq\) 4000 Hz are synthesized with high precision within an extended listening region, and higher frequencies f3 \(>\) 4000 Hz are synthesized with high precision at discrete listening points within the listening region.  
To implement a radiation keyboard, four main steps are carried out. Figure 2 shows a flow diagram of the main steps: firstly, the sound radiation characteristics of the harpsichord are measured by means of microphone arrays. Secondly, an optimal constellation of loudspeaker placement and sound field sampling is derived from impulse these measurements. As the third step the impulse responses for the loudspeaker array are calculated. These serve as raw loudspeaker driving signals. Finally, loudspeaker driving signals are calculated by a convolution of harpsichord source signals with the array impulse responses. These driving signals are triggered by a MIDI keyboard and play in real-time. The superposition of the propagated driving signals synthesizes the complex harpsichord sound field.  
To synthesize the sound field, it is meaningful to divide the harpsichord signal into three frequency regions: frequency region f1 lies below 1.5 kHz, the Nyquist frequency of the proposed loudspeaker array. Frequency region f2 ranges from 1.5 kHz to 4 kHz, the Nyquist frequency of the microphone array. Frequency region f3 lies above these Nyquist frequencies. Different sound field measurement and synthesis methods are optimal for each region. They are treated separately in the following sections.  
Figure 1: Design and concept of the radiation keyboard (**right**). A MIDI keyboard triggers individual signals for 128 loudspeakers, which are arranged like a harpsichord. Replacing the real harpsichord (**left**) by the radiation keyboard creates only subtle audible differences. Unfortunately, the radiation keyboard cannot synthesizes the harpsichord sound in the complete space. Low frequencies f1 are synthesized with high precision in the complete half-space above the loudspeaker array (light blue zone). Mid frequencies are synthesized with high precision in the listening region (green zone) in which the instrumentalist is located. The sound field of very high frequencies is synthesized with a high precision at discrete listening points within the listening region (red dots).  
Figure 2: Flow diagram of the proposed method. First, harpsichord Impulse Responses (IR) are measured, then the distribution of loudspeakers and listening points is optimized, and finally, loudspeaker driving signals are calculated.