|Abstract||The aim of this work is to present the concept of a multi-faceted music complexity descriptor set. The complexity of music is one of the less intensively researched areas in music information retrieval. Especially an automated estimation based on the audio material itself has not been addressed by many researchers. However, it is not only a very interesting and challenging topic, it also allows for very practical and relevant applications in music information retrieval. After giving some background information about the motivation for this research, we will discuss examples of practical applications, such as collection visualization, playlist generation, and music recommendation. In a review of former work we will see existing models for melodic, rhythmic, and harmonic complexity facets. Since these are not directly applicable for our needs, we will then give a set of operational defnitions for the author's approach to the problem. Preliminary results for rhythmic and acoustic complexity are reported and discussed. From these we sketch the steps for future work within and beyond the scope of a PhD thesis.