Please note that you must have the most recent copy of Macromedia's Flash plugin installed to play the musical examples. In order to more fully appreciate music—any music, familiar or unfamiliar--let us begin by considering music from the “ground up,” free from the constraints of a particular era or style. What is music and how does it make sense to us? Music is a time-art: It needs time to unfold. Whereas it is possible to have an instantaneous view of a painting, it is not possible to have an instantaneous hearing of a piece of music. We can all remember those electrifying moments when we round a museum corner and, suddenly, a favorite Rembrandt or Picasso bursts into view: We can take in the entire canvas in a single glance. Music does not offer such short cuts: There is no way to hear a favorite musical work other than to listen all the way through. Music is ephemeral. A painting or sculpture exists in concrete physical form. When the lights are turned off in the museum, the painting is still there. But music is a performance art: Each moment is temporary, washed away by the next. A sound exists in its precise “now,” and then vanishes. Once the performance is over, the music is gone. Music is unstoppable in time. Like music, fiction is a time-art. But the reader is in control of the pacing: He or she may read the book in a single sitting or over the span of several months. In contrast, a musical performance is not meant to be interrupted; the pacing is out of the listener’s control. Furthermore, the pages of a novel are all accessible at any time: The reader may review passages at will—meditating on the meaning of an ambiguous paragraph or looking back to confirm an important clue. The reader may even give into the temptation to skip ahead to the ending. No such luxury exists at a concert. You can’t raise your hand and say, ”Forgive me, Maestro, I didn’t understand that last passage” and have the maestro reply,” Yes, you in the tenth row, no problem, I’ll take it over again from measure nineteen!” Music rushes by, unimpeded by the listener’s questions, distractions or desire to linger. Finally, music is abstract and non-verbal. The meaning of a word may be colored by context; but there is has an enduring, stable meaning, which any of us can look up in the dictionary. If I use the word “egg” as a metaphor for birth or renewal, the metaphor only succeeds because you and I share a common definition. On the other hand, musical sounds do not have literal or fixed meanings. Musical sounds may evoke moods or images, may suggest yearnings, loss, or surprise: But these interpretations are far more subjective and open-ended. You can never say “Please get me a soda from the 7-11” in abstract musical sound. Music is not designed to be that literal. Although music is often referred to as a “language,” its sounds are never anchored to any specific meaning. Thus, music is abstract and non-verbal art-form, unstoppable in time. Under those conditions, how is it possible for music to be intelligible? When you think about it, it's quite a challenge! Music places tremendous pressure on the listener: It asks him or her to follow an argument that is racing by, made up of impermanent sounds with no fixed meaning. The answer to this question is extraordinarily important, because it transcends all questions of era or style. We believe with all of our hearts that music speaks to us. But how? It is invisible and insubstantial; it is not referring to anything "real." Theater and ballet are also time-arts: But theater uses words and ballet has the human body as a frame of reference. What does music have to direct our attention and guide us through its narrative? The answer is that repetition is the key to musical intelligibility. Repetition creates the enduring presence at the heart of a work's fleet, impermanent existence.

The Power Of Consistency 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. From this austere first statement, listen to how far Beethoven stretches his theme in this variation. Though the theme is still recognizable, its consistencies have been stretched: It is in a higher register. The texture is more complex, with a very rapid accompaniment. The melody is more flowing, with new material filling in the theme's original resting points. While staying true to the theme's identity, this variation pulls the theme unexpectedly far from its original starkness. Baseball manager Bill Veeck once said: "I try not to break the rules, but merely to test their elasticity." The same may be said of music's greatest composers. Each listener's reaction to the Beethoven variation will be personal, the words and metaphors to describe it subjective. But, as subjective as these emotional responses may be, it is the stretching of the material that has called them forth. The transformations are readily accessible to the ear and can be objectively described: The variation is not lower than the theme, it is higher; it is not more restful, it is more active and continuous. Appreciating music begins with recognizing how much we are already hearing, and learning the ability to make conscious and articulate what we already perceive. 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.

Repetition of Different Sizes 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. Listen to the entire one-minute work. You will notice that, as everything changes around it, this repeating sound remains like a "beacon" of stability. More commonly, the repeating element is a short figure, often called a motive. Here is the famous motive of Beethoven's Symphony No. 5. In the opening phrase, this short figure is repeated eleven times, with greater and greater intensity: In the "Anvil Chorus" of Wagner's Das Rheingold, the short figure is a rhythmic pattern. In this brief excerpt, the rhythmic motive is repeated six times as the orchestra builds in intensity on top of it. 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. Here is the phrase by itself: Here is the phrase with its repetition: Notice that, in the approximately the same amount of time that Beethoven is able to repeat his motive eleven times and Wagner six, Mozart is only able to repeat his longer phrase twice. Here is a similar example from Igor Stravinsky's ballet Pétrouchka. Similar to the Mozart, notice that the phrase is repeated in a slightly new form. Even longer units of repetition can occur. A group of phrases can be joined together to create a theme; this might be compared to a paragraph. In the following example from Beethoven's Piano Sonata, Opus 53, "Waldstein," the theme again contains a lot of internal repetition. But the theme itself is repeated in its entirety, with a more animated accompaniment. In this excerpt from Bela Bartok's Concerto for Orchestra, the theme is repeated with a more elaborate instrumental accompaniment. Finally, even a complete section of music can be repeated--a scale that might be likened to a chapter. This is what happens in Luciano Berio's brief folk song, Ballo. Thus, repetition can occur in a variety of sizes, from "atomic" elements to longer time-spans.

Local and Large-scale Repetition Repetition is often local and immediate. But repetition, especially of larger units, can occur after intervening music has taken place. For instance, in Beethoven's Bagatelle, Opus 126, no. 4, the following section occurs: After intervening music, the entire section is repeated exactly and in its entirety. The excerpt picks up at the transition to the return: 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.

Maximizing the Minimum 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. For instance, in this folk song sung by Pete Seeger, a short musical idea is repeated over and over exactly the same--sixteen times in a mere thirty seconds. On top of the quickly cycling music, Seeger presents a rapid fire list of animal names... 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. The basic pattern of Bach's C-Major Invention is the following: This basic pattern is repeated over and over again throughout the piece, but in constantly new forms. For instance, Bach plays the basic pattern in different registers: Bach begins the basic pattern on different pitches: Bach turns the pattern upside down: Bach fragments the theme, dwelling on different segments of it. In the next sample, he takes the first four notes and plays them at half-speed Here, he takes the last four notes, and extends them into an exciting rising figure He changes the groupings of the basic pattern, sometimes having several versions of the entire pattern in succession: Finally, he changes how the pattern is echoed between the hands. Sometimes, the left hand leads: Sometimes, the right hand leads. Notice, in this example, that Bach flips the basic pattern upside down and right side up in alternation. Now, please listen to the Bach: Invention in C-Major in its entirety. All of these flexible repetitions are beautifully coordinated, so that the piece creates a clear opening, middle, climax and ending. The fact that the basic pattern occurs in every measure creates consistency. The fact that it rarely occurs the same way twice contributes to the music's momentum and dynamism. The C-Major Invention is thus a case study in repetition without redundancy. In Frederic Chopin's Prelude in A-Major, the basic pattern is a rhythm: That rhythm occurs identically eight times. Here is the first time it is played. The stability of its rhythmic pattern gives the work consistency. At the same time, the music moves and progresses thanks to the variety of melody and harmony. Listen to how the pattern underlies the following examples: Now, listen to the Chopin Prelude in its entirety. Out of the eight times the rhythmic pattern is played, it only occurs the same way twice. As in the Bach, varied repetition helps to make the music both intelligible and dynamic. The following pattern accompanies the voice in Stravinsky's Akahito from his "Three Haiku Settings": In the Chopin, the rhythm was repeated exactly, but the pitches changed. In the Stravinsky, both the rhythm and the pitches are repeated: thirteen times in all in this short piece! So how is variety created? In this case, as the pattern is repeated over and over, an ever changing layer is superimposed upon it. It is as if the basic pattern is "bombarded" in different ways, disguising its reappearance. The first four times the pattern is played, it alone accompanies the voice. But the fifth time, the new layer is added: From then on, the added layer is constantly evolving. You will be able to recognize the presence of the underlying constant pattern, but its reappearance is camouflaged by the changing layer on top of it. Now, listen to Akahito in its entirety: In Bach and Chopin examples, the basic pattern is treated dynamically: Almost every reappearance is new in some way. In the Stravinsky example, the basic pattern itself is much more static. Yet the music never sounds the same because of the music superimposed on top of it is always changing. Thus, the goal of "repetition without redundancy" is accomplished in a new way. In his work Piano Phase, Steve Reich takes Stravinsky's procedure and goes one step further: Just like Stravinsky, he holds his basic pattern completely static. Just like Stravinsky, he superimposes an added layer: But, this time, the added layer is the basic pattern itself! The musical material of Steve Reich's Piano Phase for two pianos consists of the following pattern. In Piano Phase, the first player remains absolutely fixed, repeating the basic pattern over and over again. The second player plays exactly the same pattern, but gradually shifts its alignment so that it falls more and more out-of-phase with the first player. As the second player shifts alignment, new resultant patterns are created. As an analogy, imagine that you had two identical panels, each made of strips of colored glass. At first, you line up the panels perfectly and shine a light through them. The sequence of colors in the panels would be projected on the wall: Let us say it is blue, yellow, red, yellow, blue. Then, you keep one panel fixed and the slide the panel slightly over: In the new alignment, the red in the first panel is aligned with the blue of the second, the blue with the yellow, etc. When you shine a light through the panels, you get a new sequence of colors on the wall: purple, green, etc. Colors you've never seen before suddenly appear! As you can imagine, every time you shift one strip over, the resultant colors change. With startling efficiency, you can create constantly new patterns on the wall just by changing how the panels are aligned. Here is how the music sounds when the two pianos begin in alignment. A little while later, the second pianist shifts the basic pattern slightly out of alignment. Later still, the second pianist shifts the pattern further and further out of alignment. The farther out of alignment the two pianos get, the harder it is to recognize the underlying pattern. But ask yourself the following: Did the pianos change speed? Did the length of the pattern cycle change? Did the pianos play in a new register or at a different volume? When you think about it, you will be able to sense the steadfastness of the basic pattern. Here is one more example of the pianos out of alignment. Now, listen to this extended excerpt from Piano Phase. When you listen to the excerpt, you will notice that, when the second pianist shifts alignment, there is a brief "blurry" transition passage; then, the new alignment is established. The 3-minute excerpt will take you through the first three changes of alignment. Reich's method uses very minimal means to achieve the goal of varied repetition. He manages to create gradual variety without changing the register, loudness or density of the pattern. Furthermore, unlike the other examples, Reich is very patient in his presentation: He allows each stage of the process to persist, repeating over and over again, before shifting to the next. As a result, Reich's piece is more meditative and hypnotic than the other works; it has more in common with the stable repetition of pop music. However, Reich is still stretching his material by maximizing the miminum: Eventually, the work explores every possible superposition of the basic pattern with itself. 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.

Repetition and Recognition 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.

Conclusion 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.