This paper presents the Synthetic Polyphonic Ambient Sound Source (SPASS) dataset, a publicly available synthetic polyphonic audio dataset. SPASS was designed to train deep neural networks effectively for polyphonic sound event detection (PSED) in urban soundscapes. SPASS contains synthetic recordings from five virtual environments: park, square, street, market, and waterfront. The data collection process consisted of the curation of different monophonic sound sources following a hierarchical class taxonomy, the configuration of the virtual environments with the RAVEN software library, the generation of all stimuli, and the processing of this data to create synthetic recordings of polyphonic sound events with their associated metadata. The dataset contains 5000 audio clips per environment, i.e., 25,000 stimuli of 10 s each, virtually recorded at a sampling rate of 44.1 kHz. This effort is part of the project ``Integrated System for the Analysis of Environmental Sound Sources: FuSA System'' in the city of Valdivia, Chile, which aims to develop a system for detecting and classifying environmental sound sources through deep Artificial Neural Network (ANN) models.