Was this in need of "proof"?
Read, for example http://www.ram.org/ramblings/books/the_eight.html
If only Neville had proof it would have been a much better novel.
Indeed.
Increasingly so is the New Scientist publication title.
Well there is that whole golden ratio thing, perhaps you've heard of it? While I personally find all of that a stretch, plenty of people find merit in it.
And so far as JS Bach is concerned, it's pretty clear he was a mathematical thinker even if it wasn't necessary deliberate in his composing. Maybe it was? I don't know and don't really care because a casual listen makes it obvious.
Western classical music at its core is built around Pythagorean temperament, so it stands to reason that some outgrowth of this system can be modeled using pure mathematics, does it not?
I realize there are people who have contempt for Western music for various reasons, but I'd tell them to hate the game, not the player... it's not the music's fault that crappy culture manifested.
Sure it was: read Gödel Escher Bach
First, the methods of the paper don’t have to be a Mendelssohn replacement to be useful. Second, if you don’t like that potential application, consider all the other predictive models that could benefit from these features.
Like I would totally agree that there’s value in predictive models. I just don’t think the work we’re commenting on is one of those, nor headed toward making one.
As for the paper, network entropy and node heterogeneity seem to be perfectly sensible statistical concepts, and encode useful information. They also dovetail conveniently with powerful tools in machine learning. Criticizing this paper for lack of potential applications feels unreasonable.
I’m also curious why you’re arguing with my tautologies!
Agreed! So what are you using them for?
> network entropy doesn’t need to identify the quality level of music on it’s own to be useful.
Okay. Another context-free tautology. So what are we even talking about then, what is your point? You offered above “you could eg. test the vast swaths of potentially overlooked composers to see if any of them merit closer listening.” Are you taking back that suggestion?
Feel free to offer something - anything - more specific on how the entropy can provide useful information about music. What uses are you envisioning? What other metrics in combination with entropy are you thinking of?
What I don’t see in your argument is a single specific reason the specific paper we’re commenting on has value, and what that value is. You’re suggesting that someone else doing something else might someday uncover usefulness or applications, and maybe it will build on this paper. That could happen, and yet measuring entropy is already a well known idea, and the applications to compression have been well explored already, and we can demonstrate that entropy of music has no correlation with quality, therefore the probability of what you suggest actually happening still seems rather low, and the discussion doesn’t seem to be improving the odds.
Anyhow, of course entropy correlates to music quality; maximum entropy music is white noise! I’ve even had luck finding interesting jazz musicians from the distribution of key signatures they use—- anything more entropic than the Real Book is a great indicator. Similarly, network entropy makes it easier to identify musicians with a flexible arsenal of riffs. You could adapt it to chord progressions to find unusual reharmonizations in live jazz to study and practice. It could be a helpful regularizer for neural network music generation. Entropic methods are among the most powerful in statistics.
As you point out, white noise is more entropic than the Real Book. Lots of uninteresting and bad music is also entropic. Why exactly is that a good indicator? I’m glad you finally have some examples, but this doesn’t demonstrate that entropy is a decent discriminator of anything.
> You did use tautologies...
You seem to think calling something a tautology is a way to dismiss it. Almost everything in mathematics is a tautology-- most of what I say is a tautology. Any rigorous argument is tautological; it's the aspiration of literally all formal reasoning.
> Lots of uninteresting and bad music is also entropic.
And here, you seem to think someone is claiming that entropy is equivalent to music quality, not just a useful correlate or eg. indicator of something that might be more likely to show up in good music than bad music. I don't know of anyone making that claim; all the examples I gave require mild correlation.