Music of Bach, entropy and information theory

[Cunamara]

I don't know if this has already been discussed here. Interesting.
Just a moment...

[pauln]

Interesting indeed; none of the four authors knows the difference between notes and pitches.

[Jonah]

I have a friend, in my opinion he is supposedly the greatest living composer (composer in the highest sense of this word, as Bach was). I supposedly only because I am not sure I heard every composer.
But he is also a deep think thinker on music, non-conventional analyst, non-conventional musicologist.
Some quite well-known perfomers even visite him to go through music they plan to play (he has defiitely also a teaching gift).

I write it only to give him some credits.

One of his topics always was the perception of music but of course first of all from point of the culture and musical semantics.

For me there is no doubt that the music has contents and meaning. The fact that people oftent connect meaning or contents with verbal expression is misleading (as well as the importance of visual perception in the European culture).
They often try to state that the music is 'abstract' to avoid too simplistic verbalization of musical contents (and therefore profanation). But music is not abstract, as actually any art (after all the art that is often called abstract got this name during rather socail process as an oppoistion to straightforward imagery of the academic art), otherewise we would not have been able to percieve a piece of art as something integral, something individual. Wether we verbalize and realize it conciously or not - once we recognize a piece of art we percieve its semantics, we percieve the meaning.

Of course in many cases (as with Bach) it can also have direct references coming from the cultural context but at the same time the greatest advantage of music is not that it is abstract but that its nature allos to express ambiguity and ambivalence in much more natural way than other arts (after all great poetry and literature and visual arts also do it).

My friend in his essay on Bach's music gave a few examples of Bach's themes that can be lplayed with very different phrasing (and of course it is not arbitry phrasings but they are quite solidly defined by the possible harmonizations in the same pisces by their placement in time space etc.), it also affects the meaning - but at the same time they still keep their integrity.


I use compasion with the diamon that has many sides but when we look at it we can see only one or two at a time.
It is like with analysis: when we analyze this music - we look at one side (so we should be aware it is not a final analysis of truth but just a coventional tool to help oour perception)
But when we really percieve music as listners or performers Bach gives us a possiblity to look at this diamond from all the sides simultaneously. (Obviously we cannot reproduce it analitically because for this we will have to return to the world where we operate with 3 dimensions only.)

I can of course in some cases even say the exact plot and events I hear in particular music pieces of Bach, but of course it will not be complete, and of course another person can hear the meaning differently and express it in another way.
However, the general background will stay the same, it is all there, and it is all explainable to certain degree.
One thing that is impossible to explaine is how it works all together.

My friend was once approached by the neurologists who did research on music perception and it was a very interesting collaboration too, they tried to do a scientific explanations of the things that he expressed as an aesthetic and musical concept.

I think we get more and more into the times when science begins to break its rational limitation (and 20th century oposition of scientific mentality to artistic or religious), I think it is becoming for and more synthetic.

As much as I can see this article is about the same topic but I am personally very far from it being purely humanitarian person.

[wolflen]

ohh dear...so this is how BB King did it....

As we listen to music, we form expectations . Upon hearing a particular note, we anticipate which notes might come next based on past transitions. The less likely the outcome, the more surprised we are upon hearing it.


and I thought Marshall McLuhan had too much time on his hands..

[supersoul]

I was just watching an interview with Wayne Shorter, and he told a story of when someone asked Tony Williams what he thought about when he was playing. Tony replied that if he was able to say what he was thinking while he was playing he wouldn't need to play it.

It seems that they took MIDI files of Bach pieces off the internet (Complete Bach Midi Index.) and applied big data techniques in an attempt to find the "information" in the piece. Which is cool, but MIDI files aren't actually the music. I didn't read that they did any analysis on an actual performance, which is where a written piece actually comes alive as music. So it's not really extracting information from music so much as analyzing Bach's various pieces, in written form, in terms of entropy, with entropy being a shorthand for how much a listener's expectation is met.

I like the premise, I'm a bit of a sucker for strange mathematics being applied to music, I just think it's not even scratching the surface of what music actually is. For instance, I'd like to see a study in how small variations in rhythm and dynamics can be analyzed. Notes are never just played exactly on the beat, exactly on tempo, at one of seven volume levels, a good performance will have a lot of detail that is barely quantifiable, but those sonic details are part of what makes music come alive, at least to me.

[wolflen]

I was just watching an interview with Wayne Shorter, and he told a story of when someone asked Tony Williams what he thought about when he was playing. Tony replied that if he was able to say what he was thinking while he was playing he wouldn't need to play it.

It seems that they took MIDI files of Bach pieces off the internet (Complete Bach Midi Index.) and applied big data techniques in an attempt to find the "information" in the piece. Which is cool, but MIDI files aren't actually the music. I didn't read that they did any analysis on an actual performance, which is where a written piece actually comes alive as music. So it's not really extracting information from music so much as analyzing Bach's various pieces, in written form, in terms of entropy, with entropy being a shorthand for how much a listener's expectation is met.

I like the premise, I'm a bit of a sucker for strange mathematics being applied to music, I just think it's not even scratching the surface of what music actually is. For instance, I'd like to see a study in how small variations in rhythm and dynamics can be analyzed. Notes are never just played exactly on the beat, exactly on tempo, at one of seven volume levels, a good performance will have a lot of detail that is barely quantifiable, but those sonic details are part of what makes music come alive, at least to me.

The midi file .. I have a remastered CD of Glen Gould playing the Goldberg Variations..I have heard other people play them..perhaps it was the recording studio or the piano or the day of the week..Goulds' version is the best I have found..even his singing along on some tracks. The midi files to me sound mechanical..it is the
time to wonder if AI is the performer-lord have mercy.

Your wanting to see a study of dynamics brings to mind the micro analysis of musicians abilities and sounds that the Steely Dan sessions were subject to by Fagen and Becker. It drove some of the players nuts.

[Litterick]

I wish the mathematicians would leave Bach alone.

[ragman1]

'Music has a complex structure that expresses emotion and conveys information. Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality. How can we quantify the information contained in a piece of music? Further, what is the information inferred by a human, and how does that relate to (and differ from) the true structure of a piece? To tackle these questions quantitatively, we present a framework to study the information conveyed in a musical piece by constructing and analyzing networks formed by notes (nodes) and their transitions (edges). Using this framework, we analyze music composed by J. S. Bach through the lens of network science, information theory, and statistical physics. Regarded as one of the greatest composers in the Western music tradition, Bach's work is highly mathematically structured and spans a wide range of compositional forms, such as fugues and choral pieces. Conceptualizing each composition as a network of note transitions, we quantify the information contained in each piece and find that different kinds of compositions can be grouped together according to their information content and network structure. Moreover, using a model for how humans infer networks of information, we find that the music networks communicate large amounts of information while maintaining small deviations of the inferred network from the true network, suggesting that they are structured for efficient communication of information. We probe the network structures that enable this rapid and efficient communication of information—namely, high heterogeneity and strong clustering. Taken together, our findings shed light on the information and network properties of Bach's compositions. More generally, our simple framework serves as a stepping stone for exploring further musical complexities, creativity, and questions therein.'

Welcome to Loonyville.

[Christian Miller]

I wish the mathematicians would leave Bach alone.

Me too

[Christian Miller]

There is very much a cult of Bach isn't there? It's not like the nerds spend all this time mathematically analysing Mozart or Schubert.

I think it comes from a misguided notion - common among yer STEM types who read a bit of Hofenstader or whatever - that back is some sort of 'universal music' that exists somehow outside humanity in an objective quasi-platonic sort of space.

I think this does Bach and his music a tremendous disservice.

[Christian Miller]

The midi file .. I have a remastered CD of Glen Gould playing the Goldberg Variations..I have heard other people play them..perhaps it was the recording studio or the piano or the day of the week..Goulds' version is the best I have found..even his singing along on some tracks. The midi files to me sound mechanical..it is the
time to wonder if AI is the performer-lord have mercy.

Your wanting to see a study of dynamics brings to mind the micro analysis of musicians abilities and sounds that the Steely Dan sessions were subject to by Fagen and Becker. It drove some of the players nuts.

Gould is perhaps the most jazz of classical pianists. His identity dominates the music sometimes.

Andras Schiff is good if you want someone more transparent.

[RLetson]

I suspect that some mathematico-theoreticalists are drawn to Bach because of his use of various schemas--mirror fugues, inverted lines, and such--that hint at some kind of magic decoder ring that will explain how the art was generated. As if you could somehow account for Shakespeare's sonnets by looking at how the 14-line/4+4+4+2 layout, rhyme scheme, and iambic pentameter interoperate. There's a whole lot more going on there, and it ain't quantifiable, and I suspect that no AI is going to adequately reproduce it.

[Christian Miller]

I suspect that some mathematico-theoreticalists are drawn to Bach because of his use of various schemas--mirror fugues, inverted lines, and such--that hint at some kind of magic decoder ring that will explain how the art was generated. As if you could somehow account for Shakespeare's sonnets by looking at how the 14-line/4+4+4+2 layout, rhyme scheme, and iambic pentameter interoperate. There's a whole lot more going on there, and it ain't quantifiable, and I suspect that no AI is going to adequately reproduce it.

Yeah, of course. I mean I read Godel, Esher, Bach years and years ago, and no-one has done it better since.

[Jonah]

His identity dominates the music sometimes.

I think it does not dominate.
He just does what should be done in my opinion.

I cannot separate the music from performance. To me the written composition does not fully exist until it is being performed (every time it is being performed it begins to exist again).

And in that sense I cannot also separate the personality of the performer from... hm .. the music. Obviously because music is only there for me when it is being performed.

I also do not accept the conception 'it is not Bach, it is Gould' etc. As I do not get where the line is drawn, it is very synthetic for me.

Conventionally I understand why Schiff can be 'more transparent' in concern of Bach's music than Gould, but if I have to speak about my real perception of music I do not really understand it.
Even more I think this conception of perception is misleading.
At the end it just makes no sense.

It does not exclude the analysis of musical language of course and work with musical text.

But we should remember that it is exactly what it is: it is the text - a conventional form of recording the music which structure is often different from the structure formed by the music when it sounds.

just one specific example is the theme from G minor fugue from WTK II.
You cannot make a phrasing of this theme without interpretation, you will have to chose. And Bach is in both possible phrasings at a time.
Both variants are supported harmonically and both can be identified later in the harmonization of the material of the fugue, so there is no 'objective' marker which one to choose.
But when you play you will have to choose. And also the most common phrasing is totally connected with the influence of text.
But if you get rid of visual representation of text, you can immediately hear totally different phrasing.

[BWV]

The control should be a random sample of forgotten 18th century composers

i suspect all the algorithms did is recreate music theory in a much more obtuse and confusing manner

like feeding Faulkner novels into a some machine learning algorithm and reinventing what everyone learned in 7th grade grammar

[Christian Miller]

The control should be a random sample of forgotten 18th century composers

i suspect all the algorithms did is recreate music theory in a much more obtuse and confusing manner

like feeding Faulkner novels into a some machine learning algorithm and reinventing what everyone learned in 7th grade grammar

You've clearly been watching the same YouTube channels I have...

[CliffR]

Yeah, of course. I mean I read Godel, Esher, Bach years and years ago, and no-one has done it better since.

I got about two thirds through before I gave up. I was pretty taken with it at the time, but now think that comparing program recursion with self reflection is a little weak.