The spectrum interpolation synthesis model has recently been applied in the high quality synthesis of harmonic musical sounds. In this work we investigate the performance of the model in the compression of music signals. Efficient methods for the automatic analysis, parameter extraction and synthesis of musical signals are presented. The system is tested on several examples of segments from wind and bowed string instruments. It is found that typically a perceived quality matching the original is obtained even when large portions of the waveform are generated by interpolation, implying that a high degree of compression is possible. Further, there is a graceful degradation in quality as the extent of interpolation is increased which makes the model well suited for use in a scalable audio coding framework.