Texts of polyphonic music MIDI files were analyzed using the set of symbols that produced the Fundamental Scale (a set of symbols leading to the Minimal Entropy Description). We created a space to represent music pieces by developing: (a) a method to adjust a description from its original scale of observation to a general scale, (b) the concept of higher order entropy as the entropy associated to the deviations of a frequency ranked symbol profile from a perfect Zipf profile. We called this diversity index the "2nd Order Entropy". Applying these methods to a variety of musical pieces showed how the space "symbolic specific diversity-entropy - 2nd order entropy" captures some of the essence of music types, styles, composers and genres. Some clustering around each musical category is shown. We also observed the historic trajectory of music across this space, from medieval to contemporary academic music. We show that description of musical structures using entropy allows to characterize traditional and popular expressions of music. These classification techniques promise to be useful in other disciplines for pattern recognition, machine learning, and automated experimental design for example.
['Gerardo Febres', 'Klaus Jaffe']
Music viewed by its Entropy content: A novel window for comparative analysis