I have an impression that classical music pieces are more "structured" than white noise and more "complicated" than the soundtracks of the Billboard Hot 100 songs.

So assuming we are comparing recordings of similar duration I would expect in terms of Kolmogorov complexity C(soundtrack of a Billboard Hot 100 song)<C(classical music piece)<C(white noise). Maybe for a meaningful comparison we should also control for the number of instruments used.

Has anyone analyzed music from this perspective?

P.S. I ask here because it seems more likely that a mathematician would be somewhat familiar with both Kolmogorov complexity and music than a musician.

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    $\begingroup$ Knuth considered a simpler measure of complexity for song lyrics in The Complexity of Songs. Perhaps it's worth seeing what has cited this? $\endgroup$ Oct 11 at 0:19
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    $\begingroup$ Obligatory counter example: John Cage, " 4' 33" " $\endgroup$ Oct 11 at 11:26
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    $\begingroup$ To compare a Billboard 100 piece to a classical piece, the first problem is choosing a notation that's fair to both. Pop music has a lot of complexity in its recording, mixing, and mastering, and that lacks any notation as standard as the five line staff. $\endgroup$ Oct 11 at 19:48

See Music viewed by its entropy content: A novel window for comparative analysis by Febres - Jaffe and the references therein for the entropy based approach.

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    $\begingroup$ Entropy does indeed strike me as a more natural concept than Kolmogorov complexity in this context. $\endgroup$ Oct 11 at 12:42
  • $\begingroup$ @Timothy Chow - Yes, that's precisely what I meant. $\endgroup$
    – R W
    Oct 11 at 15:11

I would suggest that you contact David Meredith, from Aalborg University, author of this article :

Analysis by compression: Automatic generation of compact geometric encodings of musical objects


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