Drawing the Wrong Conclusions

The other day I read a technical article about music, a subject in which I have great interest, but less talent, except for appreciating it. According to the article in the May 2011 issue of Discover, a scientist investigating the structure of music used the technique of lossless compression [“which exploits repetition and redundancies in music to encode audio data in fewer bits without losing content”] to analyze the structure of musical compositions.  He discovered, amazingly, that pop music was far more complex than classical music.

Although no one has yet pointed it out, so far as I can tell, he was wrong.

His rationale was that when he used the lossless compression technique, popular compositions only shrank to sixty to seventy percent of their original volume, while compositions by Beethoven shrank to forty percent of their original volume.  From this, he deduced that, underneath the apparent complexity, classical music must be composed of simpler patterns,


All music is composed of, or built up from, simpler patterns, including pop music and rap.

What he apparently isn’t considering is that classical music pieces are far, far longer than pop pieces, and incorporate a complex structure that contains repetitions of motifs, restatement and re-orchestrations, etc., all of which can be encoded in such a way as to compress the music to a greater percentage than can be done with a simpler and shorter work of music.

By way of analogy, take the statement, “Mary had a little lamb.”  There’s no way to reduce that statement more without losing clarity or meaning.  You might be able to remove the “a,” and get a reduction to 94%.  Then take something like, “Sheep (Ovis aries) are quadrupedal, ruminant mammals typically kept as livestock. Like all ruminants, sheep are members of the order Artiodactyla, the even-toed ungulates. Although the name “sheep” applies to many species in the genus Ovis, in everyday usage it almost always refers to Ovis aries. Numbering a little over one billion, domestic sheep are also the most numerous species of sheep.”  The second passage can indeed be reduced in volume without losing meaning, possibly by twenty to thirty percent, but because it can be reduced in size more than the first statement does not mean it is simpler.

The scientist is question appears to be drawing the wrong conclusion from correct data, or using accurate but incomplete data.  This is, of course, an age-old human failing, which includes the Ptolemaic astronomers who created elaborate models of the solar system with the earth at the center.  When I was an economic market research analyst I saw this happen more than a few times, where senior executives would look at the data, which was as accurate as we could make it, and then draw unsupportable conclusions, like the senior executive who used reliability findings to support developing a technically superior compoment that no one would buy because the customers didn’t need a component that was reliable for 30 years when the product to which it was attached had a useful life of five years.

In the first case, that of the compression of music, long classical pieces can be compressed more than shorter popular pieces.  That’s a fact, but it’s not because the popular pieces are more unique, but because they’re shorter and simpler, another bit of data not considered by the scientist in question… and a reason why some scientists end up in trouble, because they don’t think beyond the scope of the problem they’ve addressed.

And… most likely, the fettered simplicity of pop music is exactly why it’s popular… because listeners don’t have to work out all the patterns.

11 thoughts on “Drawing the Wrong Conclusions”

  1. Richard Hamilton says:

    He’s drawing quite the right conclusion, but it may not relate to the human _perception_ of music (or at any rate to your interpretation of it). It relates strictly to the entropy of the bits of data in the file being losslessly compressed, which isn’t going to be obvious how it relates to what we hear and perceive.

    For example, a plain text file in ASCII is usually very compressible. There are 256 possible characters (or 128 with 1 bit wasted on each), but only 30 to 40 that get used much, and different letters are more frequent than others, etc. So one can get quite a lot of compression on that with a scheme that tries to eliminate the redundancy. Compare that to compressing a binary file like an executable, which uses more different combinations more uniformly – more random if you will – and doesn’t compress as well.

    If you wish, you can say pop is more random than classical. Certainly those who prefer classical would say that. 🙂 Pop tends to be more improvisational, sometimes less precise, frequently less predictable. The “variations on a theme” of classical music, although to the ear they sound complex, are actually quite redundant – you could take most of it away and still recognize the theme(s). Pop is often designed to challenge the listener by doing the unexpected or even jarring, while classical challenges by using simple and almost formal principles, meticulously built up, which do require more attention and engagement to appreciate.

    I suspect Bach would compress even better than Beethoven, perhaps better than anything else, since it’s been said that Bach compositions could just about be calculated. But I haven’t actually tried that experiment, and anyway, it would be tough to pick reasonably fair examples to compare (similar polyphony and length, say).

    In the context of mathematical descriptions of lossless compression versus randomness, “simpler” doesn’t necessarily mean what one intuitively might think it does. And all other things being equal, something longer might be more compressible than something very short, but past a certain point, even that probably isn’t a major factor.

    Where I’m really going with this is that probably the original article, and apparently your response to it, are trying to relate an aesthetic interpretation to a mathematical phenomenon, and that’s just not likely to be accurate or objective. The math lives in its own world. It’s real, and defines ours, but analogies to explain it are easy to get wrong, or at least don’t always mean the same thing to different people. Articles like the one described are very easy to get wrong, very hard to write in such a way as not to be misleading. Putting math and science into accessible but still meaningful non-mathematical language is much more difficult than many that attempt it realize.

    So even if I agree (and I mostly do) with your (partially subjective) comparison of the nature of pop vs classic, I can’t agree that either that or the original article usefully make the comparison between that distinction and the behavior of lossless compression; however it seems to me as if the original author probably knew what he meant, but didn’t do a good job of conveying it. A more widely recognizable analogy might describe pop not so much as more complex, but rather as less _predictable_ in the sense of being able to anticipate the next note even before repetitions. “predictable” might perhaps be more consistently perceived than “complex”, or maybe it actually is a better conceptual fit to “compressible”.

    There’s a _perceived_ (not necessarily real) paradox with compression anyway: that which seems very information-dense is actually quite compressible, but pure noise (which seems to convey no information) is pretty much not compressible. The resolution to that may be subjective – that we’re so biased toward pattern recognition that noise – which may also be thought of as what would result if you mixed billions (really an infinity, I suppose) of individual sounds all together – seems simpler to us than highly ordered information.

    One would have to speak very precisely indeed (mathematically) to meaningfully relate complexity and information content. (Unfortunately, I’m mostly self-taught on these matters, and weak on the theory, so I’ve done about the best I can trying to describe this. But in terms of producing a description that can be related to without theory, maybe that’s not such a drawback after all.)

    (The following is not particularly pertinent, but is added to keep anyone from drawing the wrong conclusions. Ignore it if not interested.)

    Information theory (as I understand it, which is not formally), says that no lossless compression scheme, nor any combination of lossless compression schemes, will be able to shrink all possible inputs. Some will always be too random to have any recognizable redundancy to remove (although that would usually be something that expressed as sound would just be noise). This makes sense if you imagine that the a bit stream is redundant as an expression of non-random sequences of that length, but is the shortest possible expression of _all possible_ sequences of that length.

    All of the above only applies to lossless compression; lossy compression, usually only for sound, images, or video, by contrast also throws away some redundancy that depending on the quality setting, may not be much noticed by limited human ears and eyes. So on applicable data, lossy compression can usually achieve much higher compression ratios, but cannot exactly reconstruct the original input – which is why it’s not used for something like text or executables, where exactly recovering the original input is essential.

  2. Richard Hamilton says:

    Oops, I got something wrong in that last paragraph. Lossy compression is probably throwing away mostly _non_redundant information whose absence ideally wouldn’t be noticed, since that stands in the way of achieving better compression. One sort of notices that on very low quality compression of a photograph.

  3. Richard Hamilton says:

    One thing that astounds me is that the original author either didn’t bother to do any background research, or else drew precisely the wrong conclusion from it as to how to describe what he saw.

    Just for curiosity, I tried a fairly obvious google query:
    “music theory” “information theory”

    which gives as its first hit

    which does rather well demonstrating how predictability is the better analogy to compressibility, rather than conventional perceptions of complexity. The example texts do quite a bit to make the point, I think.

    The text of James Joyce’s books might by that standard be less compressible than say Charles Dickens’. But they’re sufficiently different that other sorts of comparisons might not do either justice.

  4. Bob Howard says:

    The larger issue is the inability of most Americans to understand very basic concepts in science, either through ignorance or willful disregard. A case in point is global climate change. How often do you see news reporters or the chattering class make a point about how a cold winter (or even one big snowstorm) clearly destroys the theory of global warming?…partly this is just the typical lay person’s lack of understanding of the difference between “climate” and “weather,” but partly this is also a willful disregard of the science underlying the theory (and of course the difficulty most scientists have in explaining complex processes with non-technical simplifications). Same with evolution and other “controversial” theories…too many people use ideological, emotional or philosophical filters when interpreting scientific information.

  5. j says:

    I haven’t read the article you’re discussing but I think there may be a few misconceptions here. I have done graduate study in musicology, composition, and audio engineering.

    Compression of a musical sound file does not work the same way as the compression of a written text, unless, perhaps, you’re talking about a written score. In this case I am assuming that the article is about compression of a sound file, because to compare two compressed scores, it would be necessary to transcribe into written notes the examples from popular music. The scientist has given no indication that he has done this, nor is it likely that he could.

    Now, here is the interesting part: if you were to transcribe a pop song as performed by a full band into score and compare it to an orchestrated song-score like a Mahler lied, you would be likely to find that the classical score was more complex and more resistant to compression, because there is less repetition. If you were to compare the written score of a popular song for voice and guitar or voice and piano alone, you would probably find a similar level of complexity to a Schubert song from, for example, Winterreise.

    However! If you compare two musical _sound_ files for their ‘compressibility,’ the pop song will likely be harder to compress, as indicated in the article you discuss. The reason for this is nothing like what you, or at least the scientist, proposes. Audio compression cannot recognize musical notes such as you would find in a score, and compress on the basis of repeated note patterns. What it does recognize is variations in wave frequency, whose complexity is primarily timbral. In other words, the suggestion of the article is in effect that popular music has more detailed and more complex timbres and covers a broader range of frequencies.

    There are several reasons why this is the case. In the first place, a recording of a ride cymbal from a few feet away has an enormous amount of high frequency information in it that is difficult to compress. The same sound heard from a greater distance loses much of this information. A tone from a clarinet or oboe or similar instrument has comparatively much less complex timbral content, even though, in terms of the ‘notes’ as they appear on paper, its part may be a great deal more ‘complex,’ e.g. contrapuntally.

    To come to the point, a simple drum set playing a repetitive part, recorded with a sensitive microphone from medium or close distance is probably going to be harder to compress than an entire orchestra recorded, as is common, from a relatively far distance. As far as the musical complexity goes, this calculation of compressible ‘complexity’ means absolutely nothing, as I’m sure you can see: a toddler drumming away nonsensically would be harder to compress than a great pianist recorded from 10 feet away in a great hall.

    However, as a general rule popular music tends to be more focused on timbre, and classical music more on pure note structures–an important observation in itself. Timbrally oriented compositions are less obviously complex than the vast contrapuntal edifices of classical music, but, in my view, they may be just as complex, only in a less obvious way that is hard to transcribe intelligibly. A pop group may write a simple song, and then spend a month trying to perfect the timbres of the recording (choice of individual instruments, microphone placement, reverb and other treatment, etc.), while a classical composer may spend a month writing the notes of a piece, and worry no more about timbres than assigning them to the stock instruments of the orchestra (already a difficult task in itself, admittedly).

  6. I appreciate all the explanations and clarifications, and it appears to me that all of you made the point better than I could have. In short, the “lossless compression test” indicates pure random noise is the most complex, followed by loud percussive popular music, with complex Bach compositions coming out as the least complex. All of which shows why scientists need to be extremely careful in their public presentations.

  7. Joe says:

    @lemodesittjr : Yes. Lossless compression works by finding the key structure within a data stream and summarizing the stream in terms of that structure. Sounds are converted into the frequency domain where there is more obvious structure. Noise is random, which means even in the frequency domain it has no structure, so the compressor can’t summarize it. On the other hand classical instruments have very clearly defined structure in the frequency domain and are easy to compress.

  8. hob says:

    The more interesting thing here is that the article prompted such a response. Mr Modesitt, if the public felt that “Pop Music” was more complex than Classical music, do you feel that classical music would lose its fans?

    Which brings us to an even more important question–do people listen to Classical music because it sounds nice or the romanticist/marketing around classical music? Because it is clear you feel even Educated people can be easily confused about the value of classical music in comparison to pop music.

    Since the intent of the article is to show how people who are not well versed in interpreting Data respond to such interpretation, what does that say about high culture and all the arts associated with such?

    Is music complexity “better” or the extended implication of working with complexity better? And in our economic models, who would benefit from such encouragement?

  9. Good questions… but I doubt most people even care, although they should, because, from what I’ve seen and studied, the musical forms and structures of a culture reveal much of its future and fate, and it appears that, if you will, continued structured original creativity in music tends to suggest a strong society…

  10. Bob Howard says:

    I confess to a degree of elitism in regards to my own musical tastes in general, but also find compelling the argument that a diverse and creative musical scene does suggest a stronger, more vibrant society. At the same time, while I mostly loathe hip-hop and light pop, I also recognize that our culture is all the better for its amazing range of musical offerings and its seemingly endless font of creativity and innovation. Ignoring the more derivative and insipid aspects of so much of pop music, there is a strong and refreshing current of creativity across our musical spectrum–mark, as you say, of a vivid and energetic culture.

  11. Joshua Blonski says:

    Hob, speaking only from my own perspective and that of those I know who also enjoy both classical music and “pop” and rock and whatever other modern musical genres we listen to, we wouldn’t like classical music any less if it does turn out that pop is more complex.

    That being said (and to address the debate as a whole, and not just in response to Hob), I don’t believe the two are entirely comparable. Their goals are different. I’m going to ignore the use of “background music” for a moment while I explain what I mean.

    When I listen to classical music, I listen because it makes me focus. That focus puts me in tune or in touch with specific feelings, emotions, memories, and the like. It activates very specific areas in your brain -in conjunction- in order to perceive, decode, analyze, and ultimately understand the point of the piece. It does have redundancies, and in good classical music that is part of why it demands such attention. What minute changes happen in a repeated line are intensely important, no matter how small they are. This comes down to even decisive dynamic of a phrase, not just the notes played. Mischa Maisky, one of my favorite cellists, said he does not believe in repeated phrases in, for example, the Bach cello suites. That’s not to say he doesn’t play the repeats. It’s to say that he does not play them the same the second time around. Even changing a passage to a different string changes the color and the tone, despite the fact that the exact same notes are played, and that is a very subtle though very real difference in complexity.

    I’m not saying that pop music doesn’t also invoke feelings, emotions, memories, etc. I know it does. But it does in a different way. Usually it’s just in the lyrics. The words are understood in different areas of your brain though and then you attach an emotion to them, and THAT in turn activates your limbic system. It’s an overly simplified explanation, but classical music can more directly activate the limbic system in the brain. Rather than listening specifically because of what the music invokes in me, then, I listen to pop music simply because it is pleasing to hear. I sometimes just like hearing The Beatles or Alice in Chains or Depeche Mode. However, their music is mostly predictable as well, just in different ways. Most bands follow simple and static chord progressions, they stick in a single key per song, and they follow a format of how a song is supposed to flow. It’s no less predictable than classical music. There are some bands who produce music that are. Progressive bands like Pink Floyd were less predictable, but that’s what progressive rock strove for. Radiohead is less predictable, but that’s because they’re so “out there.” They’re sort of modern prog rock, if you will.

    The less predictable nature seems to me to come from the nature of the playing of the music itself. In classical music, we strive for near perfection and technical control. We strive to be as precise as we can. When I play my cello, my goal is to ring out each note exactly how I mean to, as clearly as I can, as perfectly as I can for a given passage. However, when I play my guitar, there is no way to predict the artifacts and other little sound quirks that come out of my wonderfully overdriven instrument. True overdrive (not electronic distortion) is somewhat unpredictable. Furthermore, I’m not aiming for the utmost precision when I play blues or whatever else. I’m aiming for simply jamming out a fun song. Maybe my hand accidentally strikes the strings harder today than yesterday, or in this particular repeat of the chorus than in the previous time. That’s okay. I don’t much care. And that lack of intense control creates a more unpredictable recorded sound. The little artifacts that come through in overdrive or in a phase effect or whatever else are not as mathematically precise. And that’s okay too. But it also creates a less predictable recorded sound. It adds in more noise, if you will.

    I will say this: when I want to sit down and write out a modern rock song, it’s a lot easier for me to do so. When I want to write a classical piece, it takes a lot more concentration and effort. Every single tiny note seems to matter more. Every dynamic change is intensely important. That could just be my take on it, and I could be in the minority, but another way to look at it also might add some weight. That is, how many people are out there writing modern rock and pop music? How many are writing classical? This could simply be a shift in our musical appreciations, but I’d argue that part of the reason why is because it is a harder task to write classical music. Similarly, how many people play guitar? Now how many play violin? Violin’s a hell of a lot harder to learn, and classical music is a hell of a lot harder to play well. Take from it what you will.

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