  Polyphonic music files were analyzed using the set of symbols that produced
the Minimal Entropy Description which we call the Fundamental Scale. This
allowed us to create a novel 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 of "symbolic
specific diversity-entropy" and that of "2nd order entropy" captures
characteristics that are unique to each music type, style, composer and genre.
Some clustering of these properties around each musical category is shown. This
method allows to visualize a historic trajectory of academic music across this
space, from medieval to contemporary academic music. We show that description
of musical structures using entropy and symbolic diversity allows to
characterize traditional and popular expressions of music. These classification
techniques promise to be useful in other disciplines for pattern recognition
and machine learning, for example.
