Complexity Engineering

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.





Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

1 comment on “Measuring the Complexity of Sounds and Music

  1. alexander599

    Can we do Sound of Music and correlate to Austrian innovation leadership please ?


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