Analysis of Bach's information-dense music
newscientist.com
newscientist.com
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.
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).
If you want a decent, comprehensive dive into music theory and composition you can pick up any old edition of Tonal Harmony.
Btw, that's a pretty modern thing and requires equal temperament to really work.
See https://en.wikipedia.org/wiki/Bach_Temperament for some speculation about what Bach might have used.
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).
I mostly reacted to this sentence.
Yes, I agree with the gist of what you are saying.
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.
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.
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.
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.
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:
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.
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.)
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).
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.
one could always decide to just not to (YAGNI).
"Notation Must Die" ... excellent deep-ish dive into music notation by the inimitable Tantacrul
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!
'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.'
Of course, if you can play it from a CD it has to be 'quantised' at some point.
However I agree that conventional music theory doesn't care about such fine degrees of quantisation.
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 impression is that it's not exactly mainstream. I'm also not sure to what extent it works for polyphonic 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
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.
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.
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