Music and Roller Coasters

I’d originally posted these notes to a private online forum back in 2002. This is their first walk out in public. What I say about music pertains to the other temporal arts: literature, film, theatre, and dance.

One thing you frequently find when reading about music, especially musicological material about Western art music in the so-called classical tradition, are discussions of large-scale structure. Some of these are relatively informal, but others may be quite detailed and rigorous, even formal (in a logical or mathematical sense). In any case, these discussions purport to be about something that really exists in the music.

This brings up a problem (which has been discussed at least since the late 19th century, see Jerrold Levinson, Music in the Moment, Cornell UP, 1997): we don’t seem hear or experience music that way. It’s easy enough to take in a whole painting, for example, in a single glance. But we never take in music that way. Music arrives note by note. We can anticipate some ways into the future, we can recall what we heard, and we have the sense that we’ve heard something like this before, but we never grasp it all at once. Various psychological experiments indicate that the present extends about 3 or 4 seconds; that is to say, our conscious awareness covers that much time, but no more.

Given that, what are we to make of the large-scale structures revealed by analysts and often consciously constructed by composers? Ultimately I think the issue can only be resolved by understanding how the brain works, but short of that, I propose an analogy: the roller coaster.

Roller Coasters and Music

Even as we’re approaching the amusement park we can see the roller coaster snaking around high in the air. We can take it all in at a single glance and we can focus our attention its various parts. But no matter how much we visually inspect the form, how much we think about it, that’s not going to give us the sensations we get from riding the roller coaster.

Things begin to change once we’re strapped in and it starts moving. We can no longer see the whole structure, but only what’s in front and to the side (though, with some effort, we can turn our heads so that we’re looking directly behind us). Some part of the roller coaster is very very close while other parts are more distant.

But that’s secondary to the vigorous vestibular, haptic, and kinesthetic sensations we experience while riding. We may also be anticipating what’s about to happen – especially during the long and relatively slow ride up the first “rise.” These sensations are what the ride is about; these sensations are, in the physical nature of things, closely linked to the over all form we observed from a distance, but they do not in any way depend on our knowledge of that form. If, when we first approached the amusement park, we had been blindfolded so that we never saw the roller coaster, and thus had no knowledge of its form, we would still get the vestibular, haptic, and kinesthetic sensations that are the object of the ride.

And this, in some sense, is how music works. It is a device for producing sensations. Those sensations are a function of the device’s form, but we don’t need to know that form in order to experience the sensations.

Complications

Of course, this analogy, like all analogies, has its limits. Musical form, when it’s well constructed, often has a sense of finality, of closure, at the end. Something has somehow been resolved. Roller coaster rides aren’t like that. They simply come to an end as the cars slow down and then stop. The exciting sensations cease and we’re certainly in a different state from what we were in before the ride (probably breathing faster, and a faster heartbeat), but nothing has been resolved or completed. Music thus seems to have a cumulative effect that roller coasters do not have. Our awareness may be confined to a 3-second window, but something is going on behind the scenes, and that too is as aspect of form.

If we push things to an extreme, however, we can find a hint of this in the roller coaster analogy. There are (I read in Sports Illustrated some time ago) people who like to get on roller coasters and stay on ride after ride after ride, for a period of hours, even days. If someone does this long enough their nervous system reorganizes so that, when they finally get off and return to moving around on the still ground, they are now disoriented and feel as though the ground were heaving beneath them. This lasts for a while (hours, days? I forget) and they return to normal as the nervous system once again adapts.

Considering what we now know about neural plasticity this is not terribly surprising. And we may even get such effects from sustained musicking – such as would happen during a multi-day ritual with music and dance going on for hours upon hours each day and through the night – but I think it reasonable to look to more modest effects for most music. The nervous system consists of millions of circuits of varying lengths and connectivity (including connectivity to various systems regulating bodily activity). While some inputs vanish rather quickly, others set up reverberations that linger for seconds and tens of seconds and minutes, etc. We can further imagine that, as a performance continues, more and more circuits are recruited to service that performance (whether it is one you are making or only listening to), thus increasing its “penetration” into the nervous system.

And that is what musical form is about, accumulating the more or less temporal effects of musical sensations. To understand how musical form works we’re going to have to understand the temporal properties of the nervous system. I do believe, however, that such understanding can move in both directions, from the nervous system to music, but also from music to the nervous system. As far as I know, none of the various systems we’ve got for characterizing musical form are based on neurodynamics (certainly not Schenker, or Lehrdahl/Jackendoff) and that gives them, for me at least, a somewhat provisional quality. They seem mostly descriptive and not explanatory. Explanatory value must come from neurodynamics.

But surely our cumulative knowledge of musical forms can give us clues about neurodynamics. That fact that this or that musical performance is satisfying means that the nervous system must be able to construct it. If we already understand the neurodynamics of components of some form perhaps the form itself will give us clues about new neurodynamic capabilities.

Symbolic Rules vs. Analogue dynamics

When music analysts describe musical form they think of their description as being a description of a complex musical object, which is as “substantial” an object as a roller coaster ride. It is something existing “out there” in the world. To some extent this illusion is fostered by the existence of scores, which really are objects, “out there” in the world. The musical score is treated, in effect, as though it were analogous to the design drawings for a roller coaster ride. The analyst studies the drawings, discovers their “hidden structure” and attributes that structure of the music as it is performed-and-heard.

Then you have the Lerdahl/Jackendoff theory (A Generative Theory of Tonal Music), which is modeled on Chomsky’s approach to the grammar of natural language. On this model music is treated as though it were a formal system in which “valid” musical lines are derived from a limited set of premises using a limited set of procedures. These are all assumed to be part of the mental machinery people use to listen to, perform, and compose music.

Among the many rules in their system are rules for grouping notes into phrases, and smaller phrases into larger phrases. And this allows us to contemplate a comparison made by Eric Clarke in an article on “Rhythm and Timing in Music.” He points out that N. P. M. Todd has developed a radically different approach to a similar problem. He’s interested in rhythm and meter in both language (including poetry) and music. And he’s worked out his ideas in an analogue and non-symbolic account of speech and music perception. His model was inspired by David Marr’s approach to edge-detection in visual processing, which is based on low-pass filters operating at several different filters. In the visual case the filtering is done in space while in the auditory it is done in time. It is possible to produce a visual representation of the output of such an auditory filter bank. This representation is called a “rhythmogram.”

The interesting thing about these rhythmograms is that they exhibit tree-like structures analogous to Lerdahl/Jackendoff time-span grouping structures. Thus when a computer simulation of the model was presented with a performance of a brief Chopin Prelude (Op, 28, No. 7, 16 bars long) it produced a rhythmogram having the same structure as you would get by applying the appropriate Lerdahl/Jackendoff rules. And yet, as Clarke points out, Todd’s model doesn’t contain any such rules at all. The model does analogue processing of real physical signals. The fact that the operation of this analogue model exhibits the structure specified by symbolic rules suggests that the human mind isn’t employing such a rule set at all. Why does it suggest this? Because one can imagine – in a general way – how neural circuitry could do the analogue processing required by Todd’s model, but it is much more difficult to imagine any direct scheme by which neural circuits could implement a complex set of symbolic rules. I thus suggest that such rule-based systems for musical analysis are simply analytic fictions, and that they do not correspondent to any real mechanism by which people perform and interpret music.

[We know, in fact, that the nervous system does somehow implement at least one complex symbol system, natural language. But we don’t know how it does so. We have no a priori reason to believe that purely instrumental music requires any kind of symbol processing.]

Clarke, E. F. (1999). Rhythm and Timing in Music. The Psychology of Music. D. Deutsch. San Diego, Academic Press: 473-500.

Todd, N. P. M. and G. J. Brown (1996). "Visualization of Rhythm, Time and Metre." Artificial Intelligence Review 10: 253-273.