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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? $\endgroup$
    – Kyle Miller
    Oct 11, 2021 at 0:19
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    $\begingroup$ Obligatory counter example: John Cage, " 4' 33" " $\endgroup$
    – Carl Witthoft
    Oct 11, 2021 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. $\endgroup$
    – Camille Goudeseune
    Oct 11, 2021 at 19:48
  • $\begingroup$ @CamilleGoudeseune The question clearly speaks about recordings, not any kind of notation. I.e., you are supposed to work with the resulting sound wave. That's fair to any kind of music, or even other sounds. $\endgroup$
    – Emil Jeřábek
    Feb 13, 2022 at 8:19
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    $\begingroup$ @RodrigodeAzevedo But why would you want to convert music to music score? That's not natural at all, precisely because there is no universal notion of music score that could adequately represent all genres of music. The sound itself is a universal representation. By all means devise the complexity measure so that it is sensitive to the kind of sounds and structure that humans expect to make up music rather than other sound, but using a symbolic representation instead of the music itself is a backwards move. The question does it right. $\endgroup$
    – Emil Jeřábek
    Feb 13, 2022 at 9:16

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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. $\endgroup$
    – Timothy Chow
    Oct 11, 2021 at 12:42
  • $\begingroup$ @Timothy Chow - Yes, that's precisely what I meant. $\endgroup$
    – R W
    Oct 11, 2021 at 15:11
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    $\begingroup$ I found this paper very disappointing. They encode music as a midi file (that's reasonable), but this is then simply viewed as a bytestream without exploiting the actual meaning of that stream at all. For example, metadata is treated the same as musical data and redundancies in the midi stream aren't detected at all. It would be trivial to encode the exact same piece of music played in the exact same way twice, so that the variance in entropy between the two files is much larger than the variance they observe between genres. $\endgroup$
    – Martin Hairer
    Feb 13, 2022 at 11:52
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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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For those who can read Italian, there is this interesting book by the physicist Andrea Frova:

Frova, A. (2014). Armonia celeste e dodecafonia. Publisher: BUR.

The Preface is written by Giorgio Parisi and addresses pretty much the question asked by the OP.

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See for instance Normalized Compression Distance ( https://en.wikipedia.org/wiki/Normalized_compression_distance ) which is based on Kolmogorov Complexity and has been used to cluster music:

Cilibrasi, Vitanyi, 2003, Clustering by compression

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