The conceptualization and implementation of a psychoacoustic sound field synthesis system for music is presented. Critical bands, the precedence effect, and integration times of the auditory system as well as the radiation characteristics of musical instruments are implemented in the signal processing. Interaural coherence, masking and auditory scene analysis principles are considered as well. The sound field synthesis system creates a natural, spatial sound impression and precise source localization for listeners in extended listening area, even with a low number of loudspeakers. Simulations and a listening test provide a proof of concept. The method is particularly robust for signals with impulsive attacks and quasi-stationary phases as in the case of many instrumental sounds. It is compatible with many loudspeaker setups, such as 5.1, ambisonics systems and loudspeaker arrays for wave front synthesis. The psychoacoustic sound field synthesis approach is an alternative to physically centered wave field synthesis concepts and conventional stereophonic sound and can benefit from both paradigms. Additional psychoacoustic quantities that have the potential to be implemented in the presented and other audio systems are discussed.