Information Theory and Music.

Information theory and music has actually proven to be a quite useful and accurate way to deal with the analysis of music.

What if I told you that someone with no music theory knowledge at all successfully did an analysis of a couple of Mozart's Sonatas?

The idea is pretty simple. According to Zipf's law, in an extending amount of text, certain words will appear more often than others and there exist an inverse relationship between the most common words and least common words. Thanks to H. Simon, Zipf's law was later applied to the musical compositions.

Information Theory

The initial uses of information theory in music was used to view patterns within Classical composers and atonal composers. What we have is that regardless of the style, composer, or whatever, the same type of patterns and relationships occurred. This is to say, that since all the composers analyzed used the 12 notes, that certain patterns had to occur.

After it was confirmed that for the most part our music contains recognized patterns, a technique from information theory called segmentation was used. Essentially segmentation takes a look at musical sections where patterns changes and calls the points where the patterns change as new sections. Thusly, any musical form can actively be analyzed by the segmentation algorithm. However, as with most statistical methods, as the pieces become longer, and longer, and longer, the algorithm breaks down because the appearance of the symbols become statistically insignificant.

Application

Essentially Applications for this so far has been used to determine traits within composers, traits within musical eras, determine how much influence another composer had on another piece, or determine if one composer truly wrote a piece they claim to have written. It has also been used to help organize musical databases.

Anyways, thought I'll just introduce this topic.

interesting. :D

But hard to talk about without really knowing anything about it. Any links to these analyses or studies?

To be brief:

I don't think this is really anything particularly surprising or shocking, since a lot of the musicology analysis work is simply statistics, pattern recognition, etc etc. You're checking for patterns and checking if these patterns are statistically significant or not, then why not.

What really makes the whole analysis actually difficult is not getting the facts right, or recognizing tendencies in different epochs, it's trying to find what it meant musically or what the purpose of patterns and so on were.

So you need to actually look beyond the music itself to find answers. For example, it's a fact that the late romantic period tended against harmonic clarity. This isn't because the patterns just mean that, patterns are patterns.

What makes that statement an actual fact is various reasons such as the composers themselves writing or saying things, critiques of the music, etc etc. All this historical evidence gives the patterns and so on an actual decipherable meaning.

So, I'd say you can extrapolate a lot of fields such as statistics and, hell, even stuff like game theory and end up with something useful if applied to music. Thing is, I think this is all stuff that's been already done/is being done all the time.

Just I guess this is one way of looking at it.

I agree with SSC. Getting such data is one thing (and can be extremely useful), but it still needs to be interpreted. For the lack of a more detailed explanation I don't know how far this approach goes, but I highly doubt the raw results of such an analysis will be very enlightening/interesting to a person who can't draw conclusions from them, taking a wide range of musical knowledge (and creativity) in consideration.

Yes, I think good musical analysis has a lot to do with creativity. I prefer a somewhat subjective, yet original and clever analysis to an "inventory" that simply lists data about a piece any time. And the ability to communicate ones findings in words also shouldn't be underestimated. The cleverest analysis is useless if you can't find the words to describe your ideas. (And this is unfortunately where many analyses fail.)

But this approach may be very interesting to get information about a piece regardless, the above description of the method is just a bit too vague to be able to tell.

I agree with SSC. Getting such data is one thing (and can be extremely useful), but it still needs to be interpreted. For the lack of a more detailed explanation I don't know how far this approach goes, but I highly doubt the raw results of such an analysis will be very enlightening/interesting to a person who can't draw conclusions from them, taking a wide range of musical knowledge (and creativity) in consideration.

Yes, I think good musical analysis has a lot to do with creativity. I prefer a somewhat subjective, yet original and clever analysis to an "inventory" that simply lists data about a piece any time.

But this approach may be very interesting to get information about a piece regardless, the above description of the method is just a bit too vague to be able to tell.

Come on you're getting no scraggy statements. Of course raw data is useless that is why it's called ... and get this "Information theory." In other words, interpretation of raw data.

What information theory and music allows you to do is to take out subjective ideas what is and what isn't and then regroup objects based on their patterns . For example, just to use a trivial example, it's often as by people, "Was Beethoven romantic or classical?" Well, you could simply do a segmentation analysis on all his work and being to pinpoint where shifts being in his work that would provide an objective answer rather than "it's in my opinion that _____"

Another purpose is that it can be helpful for new composers. Often times we hear pieces and say, "That note sounds out of place." and the composer retorts, "I wanted it that way." Well you could just so a segmentation analysis of the work and see if the young buck really wanted that note there or if it was just an error. And Yes, segmentation takes into account deviation that are thrown in to change patterns while at the same time highlighting possible anomalies.

what it meant musically or what the purpose of patterns and so on were.

For example, just to use a trivial example, it's often as by people, "Was Beethoven romantic or classical?" Well, you could simply do a segmentation analysis on all his work and being to pinpoint where shifts being in his work that would provide an objective answer rather than "it's in my opinion that _____"

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Another purpose is that it can be helpful for new composers. Often times we hear pieces and say, "That note sounds out of place." and the composer retorts, "I wanted it that way." Well you could just so a segmentation analysis of the work and see if the young buck really wanted that note there or if it was just an error. And Yes, segmentation takes into account deviation that are thrown in to change patterns while at the same time highlighting possible anomalies.

1: Totally good example. This is precisely what musicology is about when it comes to analysis, organization, epoch distinctions, bla bla bla. History and theory in general.

2: The second point MAY be valid, of course, if we consider the result of the pattern research and statistics to be something that can change our minds. Who knows, maybe the kid's telling the truth, despite the probability being low given the evidence accumulated.

But that's obvious stuff. :x

Come on you're getting no scraggy statements. Of course raw data is useless that is why it's called ... and get this "Information theory." In other words, interpretation of raw data.

What information theory and music allows you to do is to take out subjective ideas what is and what isn't and then regroup objects based on their patterns . For example, just to use a trivial example, it's often as by people, "Was Beethoven romantic or classical?" Well, you could simply do a segmentation analysis on all his work and being to pinpoint where shifts being in his work that would provide an objective answer rather than "it's in my opinion that _____"

Another purpose is that it can be helpful for new composers. Often times we hear pieces and say, "That note sounds out of place." and the composer retorts, "I wanted it that way." Well you could just so a segmentation analysis of the work and see if the young buck really wanted that note there or if it was just an error. And Yes, segmentation takes into account deviation that are thrown in to change patterns while at the same time highlighting possible anomalies.

I'm not criticising this approach. I'm just saying that there are different levels of data interpretation and the more fundamental they get, the harder it is to be objective. Sure, you may be able to tell that there is a stylistical change in Beethoven's works that make one part more similar to the composers of the 18th century and another part more similar to 19th century composers. That's interesting. But by applying the terms "classical" and "romantic" you're already using musical knowledge, even cultural knowledge in general, since those terms aren't just musical ones. Just saying "well, from this piece on the music written in Europe sounded different" isn't enough to make me want to read an analysis. Why exactly from this piece on? What in particular changed and why? Why did certain other things not change? Could there be historical/cultural/biographical reasons for this change? This is what I call interpretation. Some of these you might even be able to approach with further statistical research, but many questions will remain speculative. But that doesn't mean you should just ignore them, in my opinion.

The same applies to the other example: Sure, you may be able to tell that one note in a piece falls outside every pattern and "doesn't fit". But that doesn't tell you anything about musical quality. A note that doesn't follow the structure of the other notes isn't necessarily wrong, maybe it's exactly what makes the piece "spicy". You're still stuck with subjective interpretation.

Also, one should not disregard another extremely important aspect of musical analysis: Asking interesting questions in the first place. Even if you have the best methods of getting answers, the results probably won't be interesting unless the questions were interesting in the first place. And this is exactly where musical knowledge and creativity come in. (E.g. if you ask questions like "What is the most common note in this piece?" or "Should Boulez be considered a Minimalist composer?" I'd seriously doubt you'd get an interesting analysis.)

Again, I'm NOT saying it's not a useful approach. I'm sure it can give you lots of interesting results. I just don't think it's sufficient all on its own.

And yes, an "analysis" that only consists of "it's in my opinion that" without anything supporting it isn't particularly useful, I never said one should do that.

Again, I'm NOT saying it's not a useful approach. I'm sure it can give you lots of interesting results. I just don't think it's sufficient all on its own.

You didn't. It was mostly in response to "What if I told you that someone with no music theory knowledge at all successfully did an analysis of a couple of Mozart's Sonatas?" - which I somewhat doubt. (But it depends on how you define music theory of course. If you just mean analysis methods such as functional harmony, traditional form analysis etc. you're of course right.)

I may have been stating the obvious, but at least we found out that way what we agree on, which was unclear to me. Sorry, if that was annoying.

You didn't. It was mostly in response to "What if I told you that someone with no music theory knowledge at all successfully did an analysis of a couple of Mozart's Sonatas?" - which I somewhat doubt. (But it depends on how you define music theory of course. If you just mean analysis methods such as functional harmony, traditional form analysis etc. you're of course right.)

I may have been stating the obvious, but at least we found out that way what we agree on, which was unclear to me. Sorry, if that was annoying.

Point being is that it can do the functionality of analysis and allow the human to do more in depth research. It can be programmed to find most, if not all, of traits you want to find in mere minutes and thusly giving you a road map, but you (the human) must decide to do with the information. It's the same concept used in science, let the math do the grunt work, and from there I'll do the hard stuff.

Point being is that it can do the functionality of analysis and allow the human to do more in depth research. It can be programmed to find most, if not all, of traits you want to find in mere minutes and thusly giving you a road map, but you (the human) must decide to do with the information. It's the same concept used in science, let the math do the grunt work, and from there I'll do the hard stuff.

If this can be done well, it'd be a super time saver~

But honestly, part of the fun is looking up the stuff yourself rather than letting the machine pick out the patterns and statistic information. Though, I guess if you're in a hurry...

I don't know, if you want to do it for fun, no one is stopping you from doing it, right? But if you are researching something else and your focus is on x, I think you'll find it hard to justify spending your time on y. BUT!!!!! Every little muffin has its own flavor.

Well it'd be a great tool to have regardless.

Point being is that it can do the functionality of analysis and allow the human to do more in depth research. It can be programmed to find most, if not all, of traits you want to find in mere minutes and thusly giving you a road map, but you (the human) must decide to do with the information. It's the same concept used in science, let the math do the grunt work, and from there I'll do the hard stuff.

I completely disagree. Where are these algorithms that can do this? It's one thing to say it can do this and another thing to have these algorithms.

How bout you write an algorithm that looks for subjects in a fugue. A simple task right? The brain does it instantly. In fact it shouldn't be too hard to do using brute force? What about when the subject is slightly altered? What about when it has a false entrance? tonal imitation verses real?

Hell, how bout you right an algorithm that determines the harmony of a midi file. Surely not too difficult(actually I've been meaning to write such a thing)?

The issue is that there are so many factors involved all resulting in what musicologists call "context". This is what is hard about the algorithms. It is on the same level as trying to create algorithms for androids/robots for human interaction. The complexity for a very good algorithm is almost impossible. (mainly because of the binary nature of computers but maybe some of the newer "fuzzy logic" algorithms will work better)

It's one thing to claim that algorithms could be created and something entirely different to come up with them.

Of course it also depends on the complexity that you want from the algorithm. It's very simple to take a midi file and find the exact occurrences of some motive. You can even extend this to transpositions, retrogrades, and inversions. But as the score becomes larger it takes longer and longer. To do it for inexact comparisons becomes extremely difficult(time complexity) if using brute force.

When you start taking into account harmony, melody, and rhythm then it becomes virtually impossible. We still can't, AFAIK, have a decent algorithm to determine meter.

Of course one has to start somewhere... The real issue is that music is ambiguous so rule based algorithms are going to have a hard time. You can add to the algorithms by increasing the rule count but eventually it will get out of control.

Another example to show the complexity is to try and write an algorithm that can compose different types of music. It's easy to write something simple but to write something good has yet to be done. A fugue or canon is a simple thing, right? You start with a subject and write counterpoint(which is heavily rule based, at least on the surface). But it's not so simple as that ;/ I guess here it is because there is probably no way to encode aesthetics into the algorithm because we ourselves do not understand it(if we did, or someone did, then they could most likely compose very good music). Probably only the great composers actually had some intellectual clue about aesthetics and I suppose if you wanted to write such an algorithm it would be best if you were a great composer too.

Don't get me wrong though... I look forward to the day when such algorithms exist(or maybe not because then chances are everyone can be a great composer). I do think that one can probably write a decent enough algorithm to be useful though.

I suggest you first try to write one that analyzes harmony properly(not just label chords by guessing at the chord tones). In this case one has to take into account a bit of context which might be enough for the majority of cases.

Where are these algorithms that can do this?

The simple FACT of the matter is that there exist a segmentation process that will find harmony, that will determine meter, that will determine a subject in a fugue, that will determine basically any fundamental trait in music.

Of course context matters, thus Simon's model which implicitly states that despite lipf's ratios, the order of organization of music is the key determine factor of music. What information theory allows you to do is take the fundamentals that you would've had to find manually, find them automatically while at the same time highlighting common occurrences that you may not have found yourself.

I think most of your text stems from ignorance, but I don't blame you for that ignorance, I haven't provide much information. I'm looking for English sources that are not bogged down in set theory, but so far to no avail. =/ I'll keep trying.

It's up to you to demonstrate the algorithm. Your claims are all fantasy until you actually can come up with something.

Your so called algorithms are for general processes that have no clue about music and asthetics. You can beta prune, classify, parametrize, markovianate all day long but it doesn't do a damn bit of good unless the results are meaningful.

Just because "algorithms" exist does not mean they provide useful results on arbitrary inputs.

Since your such an algorimator use one of your algorithms to actually do something useful with music such as analyzing a fugue's harmony!

But I atlas you seem to have a deficiency in seeing what is practical and what is fantasy. You wouldn't happen to be a liberal would ya?

In any case I do not think you have enough music theory knowledge to make such algorithms. Finding common occurrences? What do you plan on having your algorithm do, look for most used scale degree in a piece by composer x?

There's much more to music theory than some simple analysis that you seem to believe. May I ask what kind of music background do you have? I have a degree in pure mathematics and have been studying music theory for the past 10 years. I have written several pieces and play the piano and guitar. What about you?

Well, I have a PhD in Applied Mathematics and Theoretical Physics from Princeton University and I have been performing music since I was four and actively studying music since I was 10 and went on to college as a math physics music major. Just in case, my undergraduate was at the University of Texas, with extended Research at Fermilab and REU at Harvard.

As for pieces I have written, I also have written "several pieces" and I also play the piano and the guitar. How neat. But nevertheless your statement is still pointless, but let's not make this into a pissing contest. I'll win, the large dick thing gives me certain advantages ;).

The beauty of segmentation is that it needs new musical theory knowledge. It identifies what a person with music theory would identify with music theory but it doesn't call it anything besides section A section B, etc etc etc.

Of course there needs to be someone to interpret the information that is provide, but that's true for really any field. The point is that information, like just linear algebra, is a tool that can be used to provide more insight into a composer's creative process. You can choose to reject using the tool, but I don't see a reasonable reason to do so.

what it will say of free improvisation and noise music?

I'll win, the large dick thing gives me certain advantages ;).

but. come to think about, it's really big - imagine, when it is very advanced, it starts to reconize that all patterns, in all music have some crazy similarity between them, something that will resemble a body, of a woman, and even in women's compositions! and, some day, there'll come some neo-freudo-lacanians and declare that actually it's not woman, but a dick, many of them composing the woman (on a higher level view) - it's all about dick. bach fugue would seem many small dicks sequencing each other, but on a better look - presumably some neo-chomskian - it would revel a huge dick under all those small ones - general bass! when analysing drone music, at first it wouldn't be clear what the heck is this - sure it cannot be the pattern of just one number! but, there would come some neo-post-enstein and declare that if we take a look at some more compositions of the same kind we would find that there evolves pattern, and yes you guessed right, a dick again, disseminated dick, like a intracultural huge pennis! it will all go very smooth until there'll come time for analysing some strange size - presumably - dick as well - one that is 4,33: that'll be the fuss! some would declare that it's not a thing at all, nothing to interprete about it, some will say that you have to see how contours of it sort of let all the unmeasured dicks to be seen. of course, the neo-anarchist will declare that, quote: ''it's not a dick, people, it's a cat! the essence of all dick! you saw dicks, where it was all pussies!''...

the common people will still see women, scientists would see numbers or dicks, regarding their stance on matters of properties, and the lone anarchists will listen to the pussies melancholically reminding the dicks to mind the gap.

I see I'm not the only one who's slightly drunk. :happy:

what it will say of free improvisation and noise music?

well, I have a PhD in Applied Mathematics and Theoretical Physics from Princeton University and I have been performing music since I was four and actively studying music since I was 10 and went on to college as a math physics music major. Just in case, my undergraduate was at the University of Texas, with extended Research at Fermilab and REU at Harvard.

Sounds to me then you shouldn't even be posting such questions anywhere. With that kinda resume you shouldn't have any problem using your "pre-existing" algorithms to solve not only all analysis problems of music but of humanity.

Why didn't you mention your Phd in biology, scientology and pottery making? Didn't you get those from Harvard?

So start analyzing!! Use your super duper martingale learning algorithm to figure out all the complex relationships that exist in one of Bach's preludes! I don't care for a tabulation of all the times he resolves his 7th down by half step immediately verses half step above. Doesn't do any good.

If you really had the experience and knowledge you claim you would see that music is a very complex art form where things are recursively dependent, somewhat fractal in nature, and highly irregular.

Do you know what a context free grammar is? Well music isn't context free. It's "grammar" is highly contextual and any true analysis will need to try and understand it. For example, To determine structural tones you first have to determine the harmonic outline. To do this you need to know what NHT's are... but to determine NHT's you need to know the harmonic outline. In many cases rhythmic accent is the key in clearing up harmonic ambiguity but not always.

But this is just basic analysis. What about motivic fragmentation? Form analysis? (telling the difference between 2 and 3 part might be easy but determining if that bar in the middle of the phrase is an extension or integral is entirely different) Style? Is that piece romantic or classical? What is romantic? Is it just a an expanded use of harmony?

In any case, if you really had a Phd in mathematics then you would know something about "ill-definedness" and with your musical experience you would know that music is ill-defined... or at the very least, extremely vaguely defined. At least if your more interested then just tabulating simple statistical properties of pieces. This won't be much help in determing who the composer by any significant margin and it won't help someone understand a piece. Not saying it's not somewhat useful but not so much by itself.

Here's some simple tasks you can do with your uber brain. Write a harmonic analysis tool that analyzes music properly(i.e., take into account function. I'll even only allow it to work only on tonal pieces). I guess something that even just gets 50% of the chords will be ok.

So stop collecting phd's and get on with writing the algorithms!

Wow, your above post is probably one of the most worthless thing I have read all day and I had to read my wife's essays from high school.

1-I have a PhD from a famous university, so what? Stop holding it against me and stop attempting to mock me about it. I'm not holding it over anyones head, so I'm not really sure what your problem is.

2-You seem to misunderstand what segmentation is and what information theory is.

a-so I find it hard to see why you are being so aggressive with your limited knowledge.

b-You also seem to misunderstand the algorithm.

a1- The algorithm doesn't find exact things like chords, harmony ect, it finds patterns and forms a complete image and shows how the images interconnect. Sure YOU the HUMAN have to see that the relationship shown in the imagine is such and such, but the point is that it shows the relationships and it might be able to show you something you overlooked.

a2- With that said, why do you have a problem with this tool? Does it threaten you for some reason?

b1- You seem to think that this tool is impossible, despite the fact that it has already been made, and have been used in many different fields, ranging from cancer research to genome project, to yes even music.

As for your little spew about music being ill-defined, how does that stop someone from making a mathematical model of a physical reality? Certain parts of music are considered well-defined, like chords, note, etc, while others like meaning, purpose, emotion, etc are ill-defined aspects.

The application of the theory is any more difficult than proving Every tournament (V,A) has a Hamiltonian path.

edit: upon rereading your post, it's readily apparent you didn't bother to read much of this thread.

You asked, "can it tell the difference between styles?"

The answer is obviously yes, based on a previous answer I gave to SSC.

JonSlaughter: I understand your scepticism towards a "magic pill" that comes without a detailed description. But does "proof" really matter so much that we have to turn this into a flame war? We can still just discuss the theoretical idea outlined by DOFTS and it's possible merits and drawbacks as well as we can with the given information, without getting all upset.

No analysis ever explains every single aspect of a piece from every possible perspective. That's not the point of it. The point is asking a question and getting an answer that tells you something about a piece. Does it really matter whether that happens by writing down harmonic functions, motives, formal structures etc., or whether it means finding general patterns by a mathematical method? In both cases, the final result depends on how clever you work with these tools and in both cases it will only be a limited description of the piece. Thinking you can sufficiently understand any piece by writing down chords, rhythms and motives is simplifying music at least as much as an algorithmic process like this.

Not even to mention that there are many kinds of music where using analytical methods rooted in a certain "musical grammar" is absolutely useless. (I'd guess the approach mentioned by DOFTS would be a lot more suitable for analysing a late Var

I think Jon is just angry because he didn't come up with the idea first. :/