I looked at the article.

I don't agree with Outo that "The writers themselves understand the limitations of the results." It would be better if they did. I don't find any suggestion that they did.

Granting that I don't understand much of the inner detail and didn't much try to, which will give an easy dismissal of this to anyone who is half inclined to do that, I have to say that the article fails by a very wide margin to overcome the natural resistance to a seemingly absurd finding -- and that it's not hard to surmise what's the problem in the method.

And, as near as I can tell, the article does not deal at all with the central wonderment that comes out of any critical reading of it, which is, what exactly they mean by "novelty," and how and why they decided on seeing it how they did, whatever that was. It talks in general terms about the issue but doesn't get around to really letting us know how they were operating, or even if they grasped the fact that it involved choices, that any choices that would be made toward such a complex end would necessarily be highly sophisticated, and that they would be debatable. I would say that any credible attempt at such a project would need to deal head-on with this -- first of all to show the awareness, secondly to show in plain English how and what they decided on, and, importantly, to explain their choices. The article is full of formulas which I imagine contain some (but not all) of the answers. But that's not enough. I'm left with no confidence that they grasped the complexity and debatability of what would be involved.

(An aside: A thing that makes the result less bizarre than it might seem is that they didn't consider a real high number of composers -- just 19. However, it

was enough that the result still is odd. Their method was such that the 'winner' was almost certain to be a later composer than an earlier one.)

BTW, does anyone else here who has looked at the article (or will look at it) have any greater confidence about that? Or do you even see or understand how they defined anything?

They talk about it in general terms, and they do give some seeming specifics, like this, which I'm going to quote at length because it exemplifies how they don't really address this issue; they give vague generalities together with isolated specifics that don't help, together with some jargon which, granted, it wouldn't hurt if I understood it but which has the strong appearance of failing to deal with the fundamental issues that I talked about.

(BTW you may notice some grammatical errors too, which also appear elsewhere in the article. Pardon if this sounds elitist

but such things in themselves make it hard for me to have a high regard for the journal.)

".....we model a musical composition as a temporally ordered set of simultaneously played nodes or codewords. For the actual element we take the codeword transition, the bigram (2-gram) of codewords. They are shown in Fig. 2(A) with the beginning of one of Chopin’s preludes as an example. While our methodology can be applied in a clear and straightforward manner to analysing musical compositions, we note that other aspects of music such as structure, tempo, instrumentation, etc. are also important in music. Our primary focus on codeword transitions here are based on the importance of harmony and melody in the Western classical music tradition [29] and the fact that for this paper we will be studying the piano, but for a more complete and useful modeling of music those elements will need to be incorporated in the future, and later we discuss some recent developments therein."In case you're interested in some specifics about the math -- which IMO more than anything else show how they start running with this thing before they've established their feet or the ground that they're running on:

"Since each codeword transition is a directed dyad, they can be collectively visualised as a network whose backbone is shown in Fig. 2(B). The cumulative distribution of the number of occurrences of the codewords is shown in Fig. 2(C), and approximates a power law with exponent ρ = 2.13 ± 0.02, indi- cating significant disparities in popularity between codeword transitions. Although such a pattern is established early in history (Fig. S1), the number of unique codeword transi- tions ever used also constantly increases in time (inset of Fig. 2(C)), with the highest rate of increase observed during the Romantic period.

We now compute the novelty and influence of musical compositions. Writing a composition ζ as a sequence of codewords ζ = {γ1,γ2,...,γm} the generation probability of ζ is given by the first-order Markov chain

ΠΩ(ζ)=πΩ(γ1)πΩ(γ1 →γ2)···πΩ(γm–1 →γm), (5) For πΩ we employ the Maximum A Priori (MAP) estimator [31] commonly used in

Markov chains, given as

πΩ(γi →γj)= z(γi →γj)+α0(γi →γj) , (6)

γ∈Γ (z(γi →γ)+α0(γi →γ))

where z(γi → γj) is the number of the γi → γj transition in the conventional pool Ω and α0(γi → γj) is the prior representing the novel pool in our scheme...."BTW, to me, phrases like "We now compute the novelty and influence of musical compositions" could in themselves raise other questions and provoke laughter in some minds, like the thing in

Dead Poets Society about it become a simple matter to calculate the greatness of a poem.

For fun, I'll quote this other line, which has another grammar error (but never mind about that) and which would further decrease most people's expectation of goodness in the article's method:

"Beethoven, for instance, stand among the lower half in computed novelty."BTW, I can easily imagine how they got that -- and at the same time, from it I can easily see some of what was missing in the method.

Similarly, there's also this, which isn't as outrageous as the Beethoven example but would provoke similar head-shaking in many -- not even mainly in the basic point but in the flat-out-ness of it:

"....Beethoven, Schubert, and Liszt were less novel than Mendelssohn and Schumann...." Worst of all (IMO), they don't recognize the weakness of what they did, and apparently they don't know what they don't know -- what they don't know about music, and what they don't know about the complexity of such a subject. Look at this confidence that they indicate about this work, toward the end of the article:

"Higher-order Markov modeling shows a broad agreement with our main findings using first-order Markov, showing further robustness of our model and analysis." As I said before, I do find it of interest that there's some method (any method, even a bad one) that shows this Rachmaninoff result -- because it's so opposite from any usual notion. But, the natural immediate takeaway, without looking at the article, is that the method probably was nuts. And it looks like indeed it was.