Measuring the Complexity of Sounds and Music

Abstract music backgroundHave you ever wondered how complex a sound is? Our brain is fairly good at recognizing sounds or pieces of music, even from incomplete information. It is also able to hint if a sound or piece of music is simple or elaborate. However, because the brain is essentially an analogue device, it is not good at measuring things. When it comes to complexity the situation is particularly difficult. Yes, of course, it is clear that rap is far simpler (and easier to compose) than classical music but the question is just how much simpler. How complex is a given sound or a piece of music? How do you actually measure the complexity of a sound with a given durations. This is how we do it:

  • Transform a sound/music file, for example in “.wav” format into a sampled data file.
  • Transform the 1-D data file into an N-dimensional array using a shifting technique.
  • Process the generated N-dimensional data file with our QCM Engine OntoNet using a moving-window technique.

Skipping all the technicalities, here is an example. The sound in question is that of a firing laser. The data file contains over 4000 points and looks as follows.


The corresponding entropy evolution is this:

Laser_EntropyThe complexity evolution (orange curve) is illustrated below:

Laser_ComplexityAn example of relationship between two channels of the N-dimensional array is depicted below.


The laser sound file in “wav” format may be downloaded here.

Is Verdi more complex than Tchaikovsky? Found out soon.





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