In this paper an original system for the analysis of harmony and polyphonic music is introduced. The system is based on signal processing and machine learning. A new multi-resolution, fast analysis method is conceived to extract time-frequency energy spectrum at the signal processing stage, while support vector machine is used as machine learning technology. Aiming at the analysis of rather general audio content, experiments are made on a huge set of recorded samples, using 19 music instruments combined together or alone, with different polyphony. Experimental results show that fundamental frequencies are detected with a remarkable success ratio and that the method can provide excellent results in general cases.