A parallel idea is found in the tale of Nimrodel, who sang by the waterfall that ever after bore her name. It was said that the echo of her song could still be heard in the music of the waterfall in the time of Frodo's adventure.

According to "The Silmarillion" the first thing that the Elves saw when they awoke in Cuivienen was starlight, and that thus they love starlight and revere Varda, Queen of Heaven, above all the other Valar. It is also said that the first sound that they heard was that of water falling over stone. It might be inferred, then, that they also have a primevally deep love for the sound of water, and that it must be seminal to their musical inspiration. This idea could be corroborated by the close relationship between the Elves and Ulmo, Vala of the Waters.

What could Tolkien have meant by music being "filled with the sound of waves upon the shore"? How could the sound of a waterfall contain audible remnants of a song? It seems unlikely to the point of the preposterous to think that the music literally sounded like waves, brooks, or waterfalls, especially in light of the fact that Elf music was primarily solo voice (What, were they gurgling, then?), and when accompanied, almost always by harp. It must be that the music was on some subtle level reminiscent of flowing water, that it had analogous characteristics. What, then would those characteristics be, and how would one go about incorporating them into a Gothic-style composition?

First, we must answer this: what essentially comprises the sound of flowing water? This question, surprisingly, could not have been satisfactorilly answered at the time that JRRT wrote these stories. It is a fine example of his astonishing level of ontological insight and foresight that he recognized the principle of it in some abstract way. In any event, the sounds of water trickling over stone, roaring in waves against the shore of the sea, and rushing headlong over a falls are all examples of what physicists have come to refer to as chaos. In this sense it means not disorder but rather a disguised order consisting of layers of recurrsive patterns called fractals.

Consider a visual example of fractals, the leaves of an maple tree. Looking at the tree from a distance, it appears to be a broad, symmetrical shape with jagged edges, and a stem (trunk). On closer inspection, individual leaves can be seen, each of which looks more or less like a tree: a broad, symmetrical shape with a stem. Looking more closely at the leaves, we see that they look very similar to each other, so similar that it is easy to distinguish any maple leaf from the leaf of any other tree. However, the leaves are not identical: like snowflakes and fingerprints, no two maple leaves are exactly alike. Examining a single leaf more closely yet, we find sets of points that are similar to, yet slightly different from, each other. Looking closely at one of those points, we see even smaller points, and etc. Visit Julien C. Sprott's Fractal Gallery to see more examples of fractal patterns that arise from the equations of chaos.

The sounds of water in motion cover a broad frequency range. They seem to adhere to no particular pattern. But consider the case of tree leaves: if they were entirely dissimilar, how would you be able to instantly recognize an oak leaf from a maple? Similarly, if there were really no pattern at all to the sounds of flowing water, why would they be so distinctive? Anyone who has ever visited a beach instantly recognizes a recording of the sound of waves against a shore. Anyone who has been near a waterfall can recognize a recording of one. Obviously, there is pattern recognition going on here.

What are these patterns like? They are described mathematically by the equations of chaos theory. Many such equations have been discovered. Some pertain to flowing water and some do not.

How does one apply these equations to the composition of music? That's a question I don't yet know how to answer completely. I think it's safe to say that the Elves would not have consciously used equations to formulate compositions. Rather, they would likely have translated their love of the sounds of water into their music in subliminal ways. But I cannot rely on my own instincts to do this, since I am a real human, not a mythical Elf of Middle-earth. It might be worth exploring ways to subtly incorporate fractal patterns into compositions.

Another (but related) approach is to use musical patterns of a cyclic nature that repeat at the same intervals observed in ocean wave behavior. Happily, the timings of these are known. According to Ray Tomes, who has spent years collecting and analyzing data on the seemingly related waves in all the physical cosmos,

It's also worth noting that chaos theory and fractal patterns pervade all of nature, not only sounds of flowing water. The Elves loved trees and forests, stars, animals, had extraordinary control over fire, and could blend into almost any natural environment and travel without being seen or heard. All of these suggest a more intimate connection with and understanding of much of the natural world than other races had. That makes a potential chaos connection to Elf music all the more compelling and interesting.

While it may not be appropriate to use chaos theory directly to generate compositions that are supposed to be by Middle-earth Elves, I think that it's beneficial to understand the basics of chaos theory before diving deeply into the composition of music that purports to be Elvish. One way to get a feel for it is to play with programs that use fractals to generate images or MIDI data. To go even deeper, generate raw data using many different chaotic algorithms, covert the results to MIDI, and listen. You may be surprised to hear things that clearly remind you of water running, trees swaying in the wind, snowflakes falling, and other natural phenomena. Say, with a little help from a computer maybe you could be like a descendant of Fingolfin afterall! :-)

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