Theme and variation in music: Boléro, Maurice Ravel
Before you read this reflection, listen to Boléro, a musical piece written in 1928 by Maurice Ravel. If you don’t have it in your music collection, watch this interesting performance, or this one. For the purists among you, here is a full-length performance.
If you are already familiar with this music, listen to it afresh.
If this kind of music, or music in general, is really a foreign language to you, simply listen to the piece, and try to notice its main melody or theme, its main rhythms, and how both are modified as they are repeated.
Boléro is an example of a musical form loosely called theme and variation. Well-known examples of this form through the centuries include Canon in D, by Johann Pachelbel (composed around 1694), Variations on a Theme by Haydn, by Johannes Brahms (1873), and Enigma Variations, by Edward Elgar (1898-99). Most jazz is also theme and variation, with variations either planned or improvised. Any of these works would do just as well for this Reflection, but the melody of Boléro’s theme is familiar to many, short and hummable, and easy to hear in its many variations all the way through the work.
Most theme-and-variation pieces begin with a simple statement of a musical theme, followed by repeats in which the theme is modified in a variety of ways. Means of variation are endless, but include changes in tempo (musical pace), key (which is often the home or ending pitch of a tune), harmony (notes played against the melody), ornamentation (figures played around the melody), and instruments playing during each repeat. In short, all musical elements can be included in the tools for building variations. In most examples, the underlying theme is never far below the surface, and often comes back in fuller and more complex apparitions, sometimes rising to a climactic finish. In jazz, the variations can wander quite far from the theme, but if you are determined, you can still sing the theme through verse after verse of the variations.
The tools of variation in Boléro are actually very limited compared to many works of this type. The orchestration is the primary, and in the minds of some, including Ravel, the only variable:
It constitutes an experiment in a very special and limited direction, and should not be suspected of aiming at achieving anything different from, or anything more than, it actually does achieve. Before its first performance, I issued a warning to the effect that what I had written was a piece lasting seventeen minutes and consisting wholly of "orchestral tissue without music" — of one very long, gradual crescendo. There are no contrasts, and practically no invention except the plan and the manner of execution.
Ravel’s Boléro begins with a solo snare drum playing a repeated pattern of rhythm that will carry on throughout the piece as an accompaniment to the melody (dum, da-da-da-dum, da-da-da-dum, da-da-da-da-da-da-da-da-da-[dum ... as before]). A small group of violas and cellos immediately enter with a repeating plucked four-note phrase. This combined pattern is called an ostinato, a term suggestive of its obstinate persistence. Over the ostinato comes a clarinet with the first statement of the melodic theme, twelve tuneful phrases (depending on how you count the pauses).
With each succeeding repeat of this theme, additional instruments join in on each of the three components: the percussion rhythm, the four-note phrase, and the melodic theme. The tempo gradually accelerates. The three components pass from one instrument or group to another, with larger and larger groups taking each part. Some groups bring harmony to the starting components. Changes of the home pitch (key) of the theme contribute to the feeling of growing excitement. At the end, every player has joined in, the volume has gone from barely audible to thunderous, and the piece reaches a spectacular climax.
Theme and variation in proteins: a family of protein-cutting enzymes

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| Models of three protein-digesting enzymes. If you recently ate a meal, all of them are now at work in your small intestine. |
Maybe it’s just me and my fixation on biochemistry (probably is), but when I think about theme and variations, I think about proteins. Musical theme and variation is an apt metaphor for describing variations in protein structure that give rise to the spectacular diversity of protein families, and the fascinating variation within families.
Now, what exactly is a protein “family?” How do families differ from each other? How are family members related to one another? And what are the similarities to theme-and-variation in music?
A widely studied example of theme-and-variations in protein structure is the family of enzymes called serine proteases. Each of these enzymes is composed of about 250 building blocks (amino acids). Their folded structure is quite different from that of cytochrome b5 (See Biochemistry for Citizens, Unit 2b), but comparison of models of the various serine proteases certainly show the similarities you expect to see in any family portrait.
Serine proteases specialize in cutting the chains of other proteins, a widespread function in living organisms. Processes in which protein cutting plays a role include digestion of proteins, blood clotting, turning inactive forms of hormones into active ones, and many more.
An important branch of the serine protease family is involved in digesting proteins in your stomach and small intestine. To describe the variations on the serine protease theme, I need to give you a simple imaginary model of protein building blocks and chains. Imagine each building block as a short string with a hook on one end and an eye on the other, the kind of hook-and-eye that serves as discreet closures on vintage clothing.
From the middle of the string extends another short string, which biochemists call a side chain). All amino acids have the same hook and the same eye, but there are 20 or so different side chains, some big, some small, some with positive or negative electrical charge, some oil-like (called non-polar) that tend to hide from water and end up hidden inside a folded protein chain, and some water-like (polar), that have high affinity with water, and tend to end up on the surface of a folded protein. These side chains have a lot to say about how a protein spontaneously goes from being a long, disorganized chain to being a compactly folded molecular machine.
Translation of gene instructions into protein chains involves building a continuous chain by joining hooks to eyes, leaving side chains hanging off the main chain. As the building blocks are linked one by one, the protein folds up, driven by the tendency of oily side chains to hide in the middle, charged side chains to seek other chains of opposite charge, and water-like side chains to seek water at the surface.
When you eat proteins, protein-digesting enzymes like serine proteases dismantle them, mostly in your small intestine, by releasing hooks from eyes. But they don’t do it randomly. Although all of the serine proteases are identical in the “active site” area that undoes the hook and eye (the main theme in serine protease music), and although all of them undo the connection in the same manner, they vary in the sites they choose to unhook. One serine protease, called trypsin, unhooks only if a large, positively charged side chain is next to the connection. Another, chymotrypsin, unhooks adjacent to large, non-polar side chains. A third, elastase, unhooks next-door to very small side chains. Together, they chop dietary proteins into relatively short chains.
At the same time, the dietary proteins and their fragments are being acted on by structurally unrelated intestinal proteases (called peptidases), which specialize in unhooking residues at the ends of just the kinds of short, partially digested chains that the serine proteases produce. So the whole digestive strategy is divide-and-conquer. The serine proteases cut large proteins into manageable pieces, and the peptidases cut the pieces up into individual building blocks. This speeds up protein digestion immensely compared to having only peptidases working at the ends of very long protein chains.
You might be puzzled now, like the child first seeing the string figure called cat’s cradle (See the cat? See the cradle?) Where is the theme? Where is the variation? In the serine protease family, the main theme is the active site that unhooks protein building blocks from each other, freeing eyes from hooks. Relatively subtle variations in a region near the active site give each serine protease an affinity for different types of side chains, and allow the protease to hold tightest to those side chains, insuring that the active site cuts next door. Wider variations occur at other sites in the sequences, at residues not involved in function, but that stabilize the overall structure or interact with water to keep the enzymes from sticking to each other. In these sites, any of several different types of building blocks will do the job, so many mutations at these sites are not harmful, and accumulate at random. The result is that family members have gradually come to differ at sites remote from the active site. (These differences have helped to reveal details of the family relationships.)
Serine proteases are not just protein digesters. They are found almost everywhere that protein cutting occurs. One group of family members are involved in blood clotting. Clots are made mostly of proteins, and they begin to form when certain proteins aggregate with each other. These proteins are initially made in a non-aggregating form, with sections of chain that hide the sticky parts. In response to tissue damage, such as a wound, serine proteases go into action to chop off the aggregation-preventing sections of clot proteins, initiating clot formation. So the wider variations take protein cutting into realms far removed from digestion.
There are many other variations on the basic serine protease theme. The active site is one solution that evolution has found for the general problem of cutting proteins. The variations result in many specialist cutters that can turn processes like blood clotting on and off without wreaking havoc with many other proteins that are present in the bloodstream.
You might be wondering how cells can produce a whole set of variant proteins from a single progenitor.This means producing a set of similar genes from a single gene. A key step in the production of protein families is a common type of error in DNA replication (you will learn later that such errors are the raw material of evolution).
The process of DNA copying that produces eggs and sperm from their precursor cells is followed by a step in which the two newly completed sets of DNA align with each other and randomly swap identical regions of DNA. This results in greater mixing of parental DNAs than would otherwise be the case. During this stage, called crossing over, there are sometimes misalignments that result in unequal exchange. A misalignment in the area of serine protease genes might, for example, result in one of the two daughter cells getting two copies of a gene, while the other gets none. The unlucky cell might not survive, while the lucky one carries a backup copy.
In some cases, the gene in the normal position is still put to use, while the extra copy just goes along for the ride. If this happens, subsequent mutations in the extra copy are of little consequence, because the cell and its offspring are no longer relying on that gene. Many such extra genes eventually become completely nonfunctional (called pseudogenes), because mutations accumulate, but have no effect on cell survival. Our DNA is riddled with pseudogenes, one of numerous types of DNA that are sometimes referred to as “junk”. But calling any DNA ‘junk’ can be misleading or just plain wrong, because we know only a small amount about what much of our DNA does. Today’s junk is tomorrow’s exciting discovery of new functions in DNA.
Such extra copies of genes are thought to be among the raw materials from which family variations arise. They give evolution some elbow room to tinker with a gene by mutation, while the other copy keeps the normal function intact. It is as if a few members of the orchestra slip off stage with their instruments and try out some other variations, just to hear how they sound.
Most random changes in genes degrade the product, but in rare, important instances, random tinkering results in an altered or new, and advantageous, function for the lucky cell. Scientists believe that the many serine proteases all descended from an early general-purpose protein cutter, whose genes have propagated by gene duplication to produce a broad array of specialists.
Theme and variation is very common in protein structure and function. Scientists have found hundreds of families of proteins whose structures illuminate their common origin, and whose sequence differences allow family relations to be tracked back in detail. The emergence, in protein evolution, of new themes and their subsequent elaborations leaves an interpretable record in building-block sequences, which can be compared, in order to ferret out the details of evolutionary relationships.
By contrast, most musicians do not present their compositions to us in hopes that we will take them apart and figure out how they were conceived and constructed (although other musicians might love doing so). Instead, the composer, like any artist, arranges an experience for us, one that can be appreciated by those who know many, few, or none of the technical details of conception, construction, or performance. While theme and variation occurs naturally under evolution’s tinkering style, the artist has intentions; nature has none. While happy accidents undoubtedly have a hand in many human creations (ever taken a picture that came out much better than what you saw in the viewfinder?), we tend to prize art that gives evidence of intended effect, and skill in producing that effect. This tendency probably makes it very hard for some people to imagine that life, which superficially looks intended and skillfully produced, just happened.
