Imagine that you are standing at a craps table in a casino. You don’t know the rules, and are trying to learn the game through observation alone. You would notice certain consistencies: One player at a time throws two die, which must always fall on the craps table. Certain actions provoke certain reactions: If the shooter throws a two, the “house” always calls out “Snake eyes” and the shooter is replaced. Through careful observation, you could rapidly apprehend the rules. Not only that, you would soon become caught up in the game. You would never know what would happen next: Every roll would be unexpected; bets would be waged in surprising, shifting patterns. Yet everything that did happen would fall within comprehensible parameters.

Similarly, a music listener relies on consistency to understand what is happening. Many times, we do not consciously recognize these consistencies. A key part of appreciating music is to learn to become conscious of and articulate the most essential consistencies of a musical work.

What were to happen if the consistencies were suddenly broken? Suppose you are standing at the craps table, elbow to elbow with the other gamblers, calmly stacking your chips. A shooter steps forward and throws only one die, then two, then three. When he throws twelve die, everyone at the table throws their die all at the same time. You would pull your chips off the table: Its consistencies broken, the game would have become incomprehensible.

Similarly, if you were to change the basic premises of a piece of music in the middle, how would the listener be able to make sense of what happened? In craps, you would withdraw your bets; in music, you might withdraw your attention.

Consistency does not imply predictability or monotony. In any game, the consistencies must be flexible enough to allow for an endless variety of play. Consider the following example from baseball. Perhaps the strangest no-hitter of all time occurred in the 1920’s: The opposing pitcher, the worst hitter on the team, hit a line drive to the gap and legged out a double. But, in rounding first base, he missed the bag and was called out on an appeal play; that erased his hit, turning it into an out. He and his teammates never mustered another hit. This no-hitter was so rare, it has only happened once in the history of baseball. Yet no rules were broken: Instead, the consistencies of baseball were stretched to allow something exceptional.

Similarly, the consistencies in a piece of music still leave plenty of room for the unexpected and the unusual. Composers often strive to see how far they can stretch their consistencies without breaking them. As an illustration, consider a classical theme and variations. The composer begins by presenting a theme. He or she then repeats the theme over and over, preserving certain aspects of the theme while varying others. Although each variation is unique, they share an underlying identity. In general, the variations tend to get farther and farther removed from the original. The later variations may be so disguised that the connection to the original is barely recognizable. Yet, like the rare no-hitter, no “rules” are broken: The marvel of these late variations is that the composer has managed to stretch the consistencies so far without actually violating them.

For instance, listen to the first half of the theme from Beethoven's Piano Sonata in c-minor, Opus 111.

Repetition and pattern recognition underlies how we understand almost everything that happens to us. Physics might be described as an effort to discover the repetition and consistencies that underlie the universe. One of the powerful modern theories proposes that the basic element of the universe is a “string." The vibrations of these infinitessimally small strings produces all the known particles and forces. To string theory, the universe is a composition on an enormous scale, performed by strings. Continuity and coherence are created through the repetition of basic laws. Miraculously, out of a few fundamental elements and laws, enormous complexity, constant variety and an unpredictable future are created.

We ourselves are pieces of music, our personal identities created through an intricate maze of repetition. Every time we eat and breathe, new molecules are absorbed by our bodies, replenishing our cells and changing our molecular structure. Yet, though countless millions of molecules are changing inside us every minute, we feel the continuity of our existence. This sense of self that we all feel so tangibly is really a dazzling performance: The new molecules maintain our identity by constantly repeating our basic structures.

Thus, repetition lies at the heart of how we understand music, ourselves and our world. We have a great faith in the richness and significance of repetition. In listening to music, we rely on repetition as the bearer of meaning.

Repetitions come in different sizes, from small gestures to entire sections.

The repeating element may be as brief as a single sound. For instance, Arnold Schoenberg's Piano Piece, opus 19, no. 2, opens with an "atomic" sound that repeats over and over.

More commonly, the repeating element is a short figure, often called a motive.

But repetition of longer units can occur. A phrase is a complete musical thought; it is often compared to a sentence. The opening phrase of Mozart's Symphony in g-minor has a lot of internal repetition. But it also creates a longer musical statement that is repeated, sinking slightly in pitch the second time.

Thus, repetition can occur in a variety of sizes, from "atomic" elements to longer time-spans.

Repetition is often local and immediate. But repetition, especially of larger units, can occur after intervening music has taken place.

When a repetition occurs after intervening music, we will call it a recurrence. The module "Time's Effect on the Material" is devoted to the study of recurrence.

Thus far, we have seen that musical repetition can occur in different sizes and over different time-spans, from local to large-scale. We have also seen that smaller repetitions can be "nested" inside of larger ones: Notice, for instance, how the section from Beethoven's Bagatelle has internal repetition of short patterns and longer phrases, and also eventually recurs in its entirety.

In popular music--as well as children's songs--repetition is often literal and direct. This makes the music more readily accessible and immediately intelligible.

What distinguishes classical music from most pop music is that, in classical music, the repetition is more frequently varied and transformed. This makes the repetition flexible, capable of assuming of many forms and moods. When Elizabeth Barrett Browning writes "How do I love thee--let me count the ways/I love thee to the depth and breadth and height my soul can reach...I love thee to the level of every day's most quiet need....I love thee freely, I love thee purely," she is using varied repetition to make her point. Similarly, one of the guiding principles of art-music is repetition without redundancy. The music will repeat its main ideas, but constantly in new ways.

In the popular "South Beach Diet," dieters are at a first restricted to a very limited regimen of foods: no bread, fruit, alchohol or sugar. The challenge of the diet is to create a varied menu from such a circumscribed list of ingredients. Otherwise, the dieter will begin to stray. So, a lot of effort and inventiveness goes into designing recipes that makes the daily staples lively and tasty.

In classical music, the goal is similarly to maximize the minimum. That is, the goal is to take a limited number of ingredients and create the greatest possible variety. A composer such as Beethoven or Bartok can take just a few basic elements and create the musical equivalent of a complete meal of soup, main course, salad and dessert--all with distinctive flavors, so that you sometimes can't even recognize the presence of the same ingredients in every recipe.

Let us study the concept of varied repetition in several works.

Composers are often divided up by era and style: Bach, Chopin, Stravinsky and Reich would rarely be grouped together. However, beneath their unique personalities and styles, these composers are all striving to create musical intelligibility through varied repetition. In the examples above, each has found a different way to achieve this underlying goal.

Varied repetition is not only a guiding principle in Western art-music. In a jazz work, a pattern such as the famous "twelve-bar blues," will provide an underlying consistency on top of which the band will create ever-changing, spontaneous improvisations. In an Indian raga, an underlying rhythmic pattern, called a tala, creates the framework for elaborate improvisations. Music sustains itself, evolves and spans the globe because of the richness of possibilities created by varied repetition.

Listening to explicit, literal repetition is like eating a simple carbohydrate: It is easily digested and quickly absorbed. That is why popular music has so much literal repetition: Its success depends on making an immediate impact. On the other hand, listening to transformed repetition is like eating a complex carbohydrate: It takes longer to digest. More of our attention is engaged: What changed? By how much? How fast did it happen? How long will it persist in the new form? Observations lead to interpretation: Why did it change? What are the consequences of what happened?

More and more, nutritionists are emphasizing that complex carbohydrates are healthier for our bodies. Similarly, transformed repetition may be healthier for our musical minds: It demands greater concentration, more astute observations and more careful reasoning--in short, more active listening. Learning to recognize and evaluate transformed repetition is a crucial aspect of music appreciation.

Because music is an abstract, non-verbal time-art, repetition lies at the heart of how music makes sense. In pop music, the repetition tends to be more literal, while in classical music, it is often varied and transformed. As much as composers are often searching for new sounds and instrumental combinations, they are also inventing new means of building repetition.

Musical repetition offers powerful and suggestive models for how we understand the world and ourselves. The composer Mario Davidovsky, one of America's great living composers, has said that he listens to music not with knowledge but rather for knowledge, for guidance in understanding and grappling with life. Through its imaginative and ever-changing use of repetition, music constantly presents us with new ways to recognize the unities and consistencies underlying our experience.