Casual Fridays: What is complexity, and do we like it?

Musical complexity is bafflingly difficult to define. Is it just a lot of notes? Would a 100-note trill (the same two notes alternating over and over again) be more complex than 50 completely random notes? Most people would probably say "no." But what about the same trill versus just 3 random notes? Now maybe the trill gets the nod. A scale with a trill at the end is probably more complex than just the scale by itself. But what about "Mary Had a Little Lamb" with trills versus "Ode to Joy" without?

Researchers usually just take the easy way out and ask their listeners to rate each piece on a scale of complexity. Maybe complexity is like pornography: you can't define it, but you know it when you see it. For our Casual Friday study two weeks ago, we asked listeners to rate three songs for preference, but not complexity. Greta's research assistant had spent part of his summer listening to GarageBand loops, trying to find simple, average, and complex jazz piano songs. The complexity of the three clips we tested was based on his judgment. But maybe your judgment is different. Let's fix that.

Here are the three clips again, in no particular order. Your job is to rank them from simplest to most complex:

Clip 1:

Clip 2:

Clip 3:

Let's collect your responses in a poll:

Now, on to our results from our original study, conducted two weeks ago. I have analyzed them based on Greta's assistant's initial complexity ranking, which seemed right to me. But if the poll results tell a different story, then we'll discuss in the comments how that affects my analysis. There are lots of problems with our study's design, the most significant being the fact that we only rated three different clips. But we were hoping to overwhelm that problem with sheer numbers of participants. Did we succeed? I'll just give you the facts and let you decide.

In addition to rating how much they liked each musical clip on a scale of 1 to 10, respondents were asked to give their years of musical training, as well as their preferred musical style. I think if I was designing the study again, I'd have let people choose more than one style, because even with 250 responses to the survey, we didn't get enough answers within any given area of preference to get significant results.

We did, however, find *some* evidence of the inverted U preference map that Orr and Ohlsson found in their work. (If you don't have time to follow the links, here's a quick summary: People with little musical training tend to prefer moderately complex music to complex or simple music, which makes a graph shaped like an upside-down U. Experts don't appear to follow this pattern, and what pattern they do follow depends on the style of music they were trained in.)

Take a look at this graph of our results. Unfortunately, most of this is not statistically significant, but there are some interesting trends:


The only significant result is that when all responses were grouped together, the medium and most complex clips were preferred to the simplest clip. When we looked at the data for experts versus novices, without controlling for preferred musical style, there was no difference from this basic result. However, when we considered just those who prefer jazz music, an interesting trend occured. Novice jazz fans showed the inverted U pattern, preferring the moderately complex to the simplest and most complex music. More experienced jazz fans showed the same pattern as the overall group, except that they rated all three clips higher than the overall group. Again, these are just trends, but you could make the case that for our sample of experienced jazz fans, experts prefer more complex music compared to novices.

This is a different result from what Orr and Ohlsson found, but there were many differences between our study and theirs. Most importantly, they used many more musical clips: a total of 40 different jazz improvs, as well as 40 bluegrass improvs. They also used complete musical selections, while we used shorter excerpts from longer pieces. Finally, they had five different levels of complexity, while our study used just three. Even though there were only 22 expert musicians rating their clips, they found a significant result, while we did not with our group of 250 volunteers. If there's anything to be learned from comparing our study with Orr and Ohlsson's, it may be that experimental design is much more important than the number of people participating in a study. You might want to think about that the next time you see a USA Today poll asking 2,000 Americans about abortion, gun control, or who'll win the next election.

Oh, and what was our judgment on the relative complexity of the three clips? From simplest to most complex, 3-2-1.

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see, to me, they're all the same: straight jazz homophony (single melody line, chord-structure with figured bass accompanyment - yeah the chord system has differing rhythm from the melody, but very standard).

complexity to me implies multiple melodies (polyphony), excessive key changes, bitonality or atonality, and a variety of instruments or lines interacting WITH each other rather than one merely sitting on top of the other.

now if you had a jazz BAND playing, and you reach the point in the jam where two of the instruments (or more) are both going at it, THAT would be complex.

as the test of relative complexity to each other, I can see the 3-2-1 simplest to complex pattern, but just a solo jazz piano is to my ears extremely simple. doesn't mean its bad, of course, just not complex on the same scale as the genres i prefer.

By Joe Shelby (not verified) on 22 Sep 2006 #permalink

Now, look...I'm not a jazz lover, but I prefer the one behind door #3, regardless of complexity. My idea of complex is Charles Ives or Heinrich von Biber. Or anything by Mozart (the old saw---if you can predict the next measure, it's by Haydn).

I recommend 'Another Ground by Mr P.B.' on the disk 'Apollo's Banquet' for some music that makes me most proud to be human. Deceptively simple. The ode to joy goes without saying. 'Fraid you miss the point.

"Musical complexity is bafflingly difficult to define."

It is? I was going to go with a definition that says that the greater the amount of compression you can achieve on the sound file, the more complex it is.

(This relates to a definition of random data I once heard: random data doesn't get any smaller when you try and compress it.)

Sharon, I'm not sure I buy that. Some instruments have more variability in timbre than others, so by your definition the same song played on different instruments would probably be more "complex."

Not that I agree with Sharon, but there is something to the idea that variability in spectral density can be a factor in complexity. In fact, I listed timbre as a dimension of complexity in my post on the subject.

VJB: actually, I can predict Mozart quite easily for pieces I'd never heard before. And does the fact that its actually very easy or difficult to predict the "next note" really a sign of complexity (ala Beethoven, where what comes next seems to be the only note that could possibly come next - predictable at any given moment and yet full of polyphony and counterpoint throughout the works)?

i would doubt that.

By Joe Shelby (not verified) on 22 Sep 2006 #permalink

One problem with the test is that songs 1 and 2 are upbeat, while 3 is melancholic. I immediately passed on 3 because of this... entirely independent of complexity.

Also, I think one can rephrase the conclusion that trained ears like complex music. Rather, a trained ear is more likely to "understand" music and therefore perceive less complexity. For example, assume everyone likes X units of complexity in their music. Now, train half your group in musical theory. Once complex music starts to make "sense" to the trainees, it loses its percieved complexity. The inscrutable become obvious. Music which once provided X units of perceived complexity now provides X-1. To compensate, the trainees shift their listening habits to more complex music. An individual's desired perceived complexity wouldn't shift...but understanding and skill would shift what provided the desired perceived complexity.

By way of analogy...the Hard-of Hearing do not raise the volume because they like loud music; they raise the volume to achieve normalacy.

I am a classical pianist, with very little experience in jazz, and I felt #1 was the most complex because it had a denseness or thickness to it. I think I'm visualizing how the score would look on the page...

I think novices might be more inclined to equate faster tempos with complexity (or at least allow tempo to influence their complexity judgements more). That might help explain why the poll results aren't mirroring your predicted ratings.

Isn't a faster-tempoed song likely to have more total notes? That's related to complexity in my mind -- a simply-structured but long piece may have more total complexity than a sophisticated but short one.

By Caledonian (not verified) on 23 Sep 2006 #permalink

As a tangetial issue, it should be pointed out that in classical music there can be vast differences in the complexity of a single composition, depending on performance. The level of complexity is not just in the notes played. I'd say there are three areas where the level of complexity of musical experience in classical music would need to be considered if you really want to get at the issue: the composition itself, the performance of it, and the listener's reception of it. About the latter, many times listeners simply don't know there's something complex going on in the music and/or the performance, so saying they do or don't like complexity in a situation like that is basically worthless, because they don't know it's even there.

By unnamed source (not verified) on 30 Sep 2006 #permalink