I’m admittedly baffled by this article, and I’ve also skimmed the arxiv paper. I’ve formally studied music theory and Bach more than the average person.
First, I’m not sure why the author has chosen to represent music as a graph showing the relationship between individual notes. Usually we analyze Bach in terms of harmony and the relationship between each chord. In fact, we don’t even care about chord names, we just care about the relative differences, which is why we use Roman numerals to analyze instead of note names.
I think there is something interesting in using a graph to model voicings, but the example here seems to ignore the very methods Bach used to compose.
To that end, we very much already know what Bach does to create tension and release or surpass the listener. It’s in the name, “deceptive cadence”.
So I would have loved for this to have confirmed - or refuted! - something we already know. For example, to quantify for us why a V-vi cadence feels deceptive. But we never get there. We have a set of graph techniques applied to Bach’s music without much discussion of why we believe that way of modeling makes sense.
> I’m not sure why the author has chosen to represent music as a graph showing the relationship between individual notes.
I think this can easily explainted: You only get notes from the data. Chords, etc are "cultural" constructs: Names for certain sets of relationships between individual notes.
So as you said: We should assume that their technique of analysis should reproduce our notions. For example I would assume that the note transitions primarliy happen inside the key of a piece or that comparing the note transitions between different voices follows certain patterns ("contrapoint"). And it would be interesting to connect their data space to our existing framework.
But that's a lot of additional work that might not be necessary for certain goals: If the goal is to see if their technique is able to answer certain questions (such as differentiating styles of composition), that's already good enough.
My general assumption would be: If their data space or technique of representation is rich enough to reconstruct the original data, it is just as good in terms of what we can answer. The question is then: How convenienty can we answer our questions using their representation.
I'd disagree with your first sentence, which is that the data only contains notes. The original score - the data - also includes note duration, which notes are voiced simultaneously, and a starting and terminal note of the composition. With the model in their paper, all of that information is lost (or ignored.)
That is, I do not believe that your assumption is true, that the original data could be reconstructed from their representation.
I am theoretically open to the idea that perhaps we don't need all of the original information from the score in order to answer certain questions about the music. But I am skeptical that this particular analysis will yield anything fruitful.
After reading Section A.1 (Data Collection and Network Construction), I wonder to what degree their analysis depends on MIDI encoding practices. For example, for a keyboard fugue, you could use one channel for the entire piece, one channel per voice, or one channel for each hand, with the voices moving between the two as a human player would play them. Apart from rare corner cases (especially in the WTCs), they would sound exactly the same, but I think their method generates very different networks for them.
And MIDI files might be a recording of an actual performance (with all ornamentals played out, chords arpeggiated to varying degrees, etc.), or try to capture an urtext edition as accurately as possible (leaving much to interpretation).
You've - accidentally - hit on one of the biggest challenges I've been struggling with for pianojacq, the input of which is MIDI files, but MIDI files are quite lossy with respect to the original text as written, especially when it comes to ornaments. I'd like to recover those automatically to show them 'properly' but so far I haven't found a really good and reliable way to do this. Any ideas to get me unstuck would be most appreciated.
Bach is exactly on the cusp between linear counterpoint, which didn't use functional harmony, and later classical music, which did.
Bach did not agree with Rameau's take on harmony. You can see this in CPE Bach's Essay on the True Art of Playing Keyboard Instruments, which was written by his son and is a decent distillation of Bach Sr's approach.
There are vertical arrangements that can be recognised as chords and modulations, but there's also a lot of horizontal shaping in the lines between them.
This is how you get fugues, canons, linear inversions, retrogrades, and so on - none of which can be analysed using simple chord theory.
There is far, far more going on than the occasional use of what we'd now call a deceptive cadence.
> In fact, we don’t even care about chord names, we just care about the relative differences, which is why we use Roman numerals to analyze instead of note names.
Btw, that's a pretty modern thing and requires equal temperament to really work.
Roman numerals can describe scale degrees and harmonic function in any temperament. They do not require equal temperament to "work"; they work just as well in just temperament.
The numerals describe the degree/chord's relationship to the tonic. The difference is that in just temperament, you cannot switch which degree/chord is tonic (Roman numeral I) without re-tuning, while in equal temperament you can switch freely.
The Roman numeral notation did come a little while after Bach, but I believe the concepts the notation represents are older (though some of the concepts may have been more implicit in the past).
> In fact, we don’t even care about chord names, we just care about the relative differences, which is why we use Roman numerals to analyze instead of note names.
I mostly reacted to this sentence.
Yes, I agree with the gist of what you are saying.
Agreed. In the very first example (fig 1), a G-B chord going to A-C has the network showing edges from G to A and C (B to A and C), whereas in music we look at G going to A and B going to C (just two moves). I.e., it makes more sense to consider this as just two edges, not four.
While neat and interesting, I think using information theory to analyze music can very easily fall flat especially when comparing across very different musical traditions.
A relevant story for this:
When Europeans came to Senegal they perceived the drumming as being irregular and chaotic. Through taking a class on this drumming I have been able to appreciate how much subtle time differences not represented by western music notation play a role in this music, and also how complex the rhythms are (even when just approximated via western music notation)
Very often there is an implicit discretization that happens before these analyses of music are run and it’s easy to choose a wrong one or for there to not be an easy and human interpretable way of defining the domain of your probability distributions required for such an analysis.
Another example: in pop music timbre plays a much bigger role than in classical music as artists have experimented with vocal styles, synthesizers, and many other ways of shaping sound which cannot be represented by classical music notation.
Truly distilling quality of music down to metrics that would have predictive power… I mean that seems like an advancement beyond AGI given that humans can’t reliably do it by examining or listening to source material alone.
We have this today! Roman numeral analysis and the study of western music theory will give you the tools to be able to compose a piece of music, without listening to it, and know what will sound good or bad or new and surprising to the listener.
The metrics we have are Roman numeral analysis. We know the four chords to use that will make music sound familiar. We know the harmonies to use that will make music sound like jazz.
This makes sense since it’s possible to create music that sounds like a certain genre without trial and error.
This is to say nothing of non western music, and I’d be interested in an effort, like Chomsky, to define a universal grammar. But we have a lot of material to start with!
It's worth noting that GP's example was about non-quantized rhythmic patterns, which are poorly understand by music theory.
'There are two reasons why my fellow academics should be engaging closely with J Dilla’s music. The first is just cultural literacy; Dilla was influential and is more widely imitated with every passing year. The second is maybe more important: there are not widely used analytical tools for studying this music, and there is a whole world of microrhythm and groove out there that the music academy has been neglecting. Right now, “music theory” classes are mostly harmony and voice-leading classes, and that harmony is too often limited to the historical practices of the Western European aristocracy. But rhythm is at least as important as harmony, and in some musics, significantly more so. There is a persistent belief that rhythm is “less intellectual” or “more instinctive” than harmony and therefore less worthy of serious study. That is pure atavistic racist nonsense, but it also means that it’s hard to do better, because we don’t have the vocabulary or the methods to study rhythm in the depth that it deserves. If we can figure out how to talk about Dilla time, then that will open up a lot of other kinds of time as well.'
But rather than only what sounds good, it should be possible in principle to analyze a given piece of music and say, this is on par with the masters, this is not, etc.
Even more tangible if to determine what music is “great” that transcends time and culture. This is less subjective because a small body of work turns out to be great, yet it must have some intrinsic qualities that drive its longevity and universal appeal.
My point is general it’s better to do a deep dive into individual musicians and styles to look for findings than to take a framework of analysis developed for one style of music and use it to compare across very different styles of music.
For an interesting analysis of rhythmic variations not represented by classical notation, this is one of the best articles I e seen so far
Not just on the temporal dimension. I find that what is called "pitch bend" is highly relevant to the "quality" of most music (even western popular music).
no one's trying to compare across different traditions and your story is uncharitably critical of Europeans, could you pleases use a more ethnically neutral example in the future?
> no one's trying to compare across different traditions
Except that this is precisely what 18th century European musical theorists did, a practice that continues to the present day in some (not all) music education institutions.
While you can certainly hear jokes made in Africa, India and Asia about various deficencies of European music, what you will not find on those continents is a dominant cultural practice of explaining the inherent superiority of their own musicking.
And yes, it is also true that the culture that engages in this is but a single subset of European musical culture, but it also happens to be the dominant one, embraced by both the educational establishment and the elites across the continent. They may look down on certain Basque folk traditions as well as Gamelan and Carnatic traditions, but looking down is precisely what this European phenomena does whenever other traditions are under discussion.
> [...] what you will not find on those continents is a dominant cultural practice of explaining the inherent superiority of their own musicking.
Citation needed. Africa and Asia (including India) are fairly big places, and they also have some peoples with very high opinions of themselves and their cultural legacy. I don't know enough, but my null hypothesis would be that until proven otherwise, I would expect that to extent to music as well (and not just literature or cuisine etc, where I definitely know it's happening.)
It's not about whether there are individuals who feel that way. It's about whether that opinion/attitude has become baked into institutions that play key gatekeeping roles in those societies. One big difference in those countries is that music tends to be(not exclusively anymore, but historically) learned via apprenticeship, a social structure that reduces the scale and scope of "music school" type institutions.
I would have if I could think of one. Also anyone would think those rhythms were chaotic if they had no cultural familiarity with them (including myself!), so I don’t see it as a criticism?
Here’s an example of someone with a lot of twitter followers in the tech world using information theory to compare across different types of music:
Thank heavens I can now listen to Bach without fearing he may not be great. Now if "maths" can prove da Vinci was a great artist and Michelangelo a great sculptor and Shakespeare a great writer!
> Now if "maths" can prove da Vinci was a great artist
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.
> 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?
You might be missing the point somewhat. With these methods, you could eg. test the vast swaths of potentially overlooked composers to see if any of them merit closer listening.
Very highly unlikely. The method in the paper isn’t measuring quality or novelty or authenticity or listenability or anything useful for evaluating composers without listening to them. It’s measuring the compressibility of MIDI files. We already know that Bach is less compressible than Philip Glass, and more compressible that Charles Ives. The methods in this paper cannot tell you if a composer is boring or derivative, nor whether they’re fresh and innovative for their time. They also can’t tell you anything about a performance. I mean go ahead and try, I’m all for experimenting, but I predict that trying to apply this paper to looking for overlooked composers will be an exercise in sifting through noise, more effort than searching manually, and spending time writing code instead of listening to good music.
I think (have never tried) that analyzing the harmony and rhythm (can you quantify syncopation?) you’d have a good start at determining if a song is worth listening to.
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.
And likewise, you might be missing the point. This paper doesn’t really seem to add any useful knowledge to the corpus, and its methods are extremely unlikely to be useful at all for any of the purposes you are suggesting or imagining. We’ve already had gzip for a long time, and we already know it does not make a good predictive model for anything except storage space.
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.
My point is just that proving known facts can be useful and interesting.
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.
You’re totally right in the abstract, those statements in your comment about concepts and tools are true if not tautological. What’s missing is that this paper provides no useful information about music or composers, and not does not prove anything nor demonstrate anything not already known and/or proven. It’s not a viable path to discriminating the quality of musical compositions, and I think we can prove that (I already suggested known counter-examples).
I didn’t argue with your information-free tautologies about tools, I’m pointing out that they are straw man when it comes to using entropy to identify the quality level of music.
> 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.
You said I was using tautologies as straw men, which is incoherent and suggests you’re not arguing in good faith.
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.
It looks like we've hit a reply depth limit, which is maybe for the best, because I don't think we're making any progress here.
> 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.
You did use tautologies, and they are right there above and still irrelevant, and thus straw man arguments in the context of the question what useful information is this specific paper contributing to the corpus of knowledge. The irony of flinging bad faith accusations and ad-hominem when trying to distract from the failure to have a relevant argument isn’t lost on me though.
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.
The paper definitely doesn't "prove that Bach was a great composer". It's about something completely different. The title of the referenced article is BS.
The headline of the referenced NewScientist article has little to do with the paper and the findings. It's just a way to represent music (not even shure if it's new since I've seen such representations in the past). Finding appropriate representations is important to make progress with deep learning and DNNs to understand and generate music; today's approaches based on NLP and word embeddings are not able to properly represent music and its multidimensional complexities. But I don't assume that the model presented in the paper can represent this complexity, or the measured information is the most relevant one.
unles you have decades of domain expertise, chances are you are going to fail at analysing music in a meaningful way. stop thinking you can just waltz into this subject
