Florida State University Libraries

Electronic Theses, Treatises and Dissertations The Graduate School

2017 Learning and Understanding the Piano Etudes of Chopin and Ligeti Nolan Miller

Follow this and additional works at the DigiNole: FSU's Digital Repository. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY

COLLEGE OF MUSIC

LEARNING AND UNDERSTANDING THE PIANO ETUDES

OF CHOPIN AND LIGETI

By

NOLAN MILLER

A Treatise submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Music

2017 Nolan Miller defended this treatise on April 3, 2017. The members of the supervisory committee were:

Read Gainsford Professor Directing Treatise

Michael Buchler University Representative

David Kalhous Committee Member

Deborah Bish Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the treatise has been approved in accordance with university requirements.

ii TABLE OF CONTENTS

LIST OF MUSICAL EXAMPLES...... iv

ABSTRACT...... vi

INTRODUCTION...... 1

PART 1: LEARNING THE CHOPIN ETUDES OP. 10...... 2

PART 2: INFLUENCES AND INVENTIVENESS IN LIGETI'S ETUDES, DEUXIÈME LIVRE...... 15

CONCLUSION...... 30

REFERENCES...... 31

BIOGRAPHICAL SKETCH...... 33

iii LIST OF MUSICAL EXAMPLES

Example 1.1: Etude Op. 10 No. 1, mm. 1-2...... 4

Example 1.2: Etude Op. 10 No. 8, mm. 74-82...... 7

Example 1.3: Etude Op. 10 No. 2, mm. 1-4...... 8

Example 1.4: Etude Op. 10 No. 5, mm. 79-80...... 9

Example 1.5: Etude Op. 10 No. 3, mm. 1-4...... 10

Example 1.6: Etude Op. 10 No. 7, mm. 1-2...... 11

Example 1.7: Etude Op. 10 No. 10, mm. 1-2...... 12

Example 1.8: Etude Op. 10 No. 9, mm. 1-3...... 13

Example 1.9: Etude Op. 10 No. 11, mm. 1-3...... 14

Example 1.10: Etude Op. 10 No. 4, mm. 27-28...... 14

Example 2.1: L'escalier du diable, m. 31...... 16

Example 2.2: Vertige, mm. 1-6...... 17

Example 2.3: Columna infinit!, mm. 1-3...... 18

Example 2.4: Coloana f!r! sfâr"it, mm. 1-3...... 19

Example 2.5: Entrelacs, mm. 1-6...... 20

Example 2.6: Asymmetrical groupings in Entrelacs, mm. 70-75...... 21

Example 2.7: 4:3 ratio in Entrelacs, mm. 58-59...... 22

Example 2.8: Rhythmic ostinati in Fém, mm. 1-4...... 23

Example 2.9: Deviations from rhythmic ostinati in Fém, mm. 33-36...... 23

Example 2.10: Der Zauberlehrling, mm. 67-69...... 24

iv Example 2.11: Rhythmic ostinati in En Suspens, mm. 1-8...... 25

Example 2.12: En Suspens, mm. 32-35...... 26

Example 2.13: Galamb Borong, m. 1...... 27

Example 2.14: Entrelacs, m. 22...... 29

v ABSTRACT

This treatise is in two distinct sections. The first part uses the Etudes Op. 10 by Frédéric Chopin as a vehicle through which to examine aspects of the learning process. Topics discussed include mindset, the role automatic behaviors play in learning music, and characteristics of deliberate practice. The paper proposes practice techniques for specific passages in the etudes based on the principles of these psychological theories, and discusses approaches to avoid. The second part deals with compositional elements found in the Études pour piano, deuxième livre by György Ligeti. Several influences on Ligeti's style are examined, including artwork, mathematics, and non-Western music. The paper discusses Ligeti's use of asymmetrical rhythms and rhythmic ostinati, his treatment of multiple simultaneous pitch collections, and other features unique to specific etudes. In both sections of the paper, the primary focus is on practical and technical concerns for performers of these pieces, rather than on subjective aspects of musical interpretation.

vi INTRODUCTION

This treatise is based on content from two separate lecture recitals, originally delivered on April 25, 2015, and November 19, 2016. The first lecture was given alongside a performance of Ligeti's Etudes, deuxième livre, and the second, with Chopin's Etudes Op. 10; in this paper, the order of the two sections is reversed, as the discussion of learning psychology found in the first part is also relevant to the second part. The focus of the first part of the paper is primarily on the learning process itself. Due to their high level of difficulty, the Chopin Etudes serve as an ideal vehicle through which to examine methods and strategies for learning and performing music. Most of the etudes are constructed of one or two types of basic figuration that are repeated throughout the entire work; thus, the same muscle groups are being taxed from the beginning through the end of each piece, and the performer must be careful to avoid movements that result in an excessive buildup of fatigue. This requires a high degree of self-awareness regarding matters of technique, and necessitates a thoughtful approach to learning the etudes. While the Ligeti Etudes are also very technically demanding, perhaps their greatest difficulty lies in the realm of organization. In many of the etudes, the rhythmic structure is far more complex than any found in the works of earlier etude composers, such as Chopin, Liszt, or Rachmaninoff. The texture is frequently constructed of several different layers, each of which acts independently of the others. Although there are traditional bar lines in the score for each etude, this is more for visual clarity than to indicate metrical divisions. Frequently, the two hands will be out of sync for extended periods of time, and there is rarely any sense of a traditional beat structure with downbeats and weak beats. Although the psychology involved in the learning process is discussed in much greater depth in the first part than in the second, the research presented on this topic bears equal relevance to both sets of etudes. The amount of information present in the Ligeti Etudes often makes it very difficult to pay full attention to all of the details in a performance; thus, a basic understanding of the methods the brain has for storing information is indispensable when learning these pieces.

!1 PART 1

LEARNING THE CHOPIN ETUDES OP. 10

The 27 Etudes of Frédéric Chopin were written between 1829 and 1839 and published in three sets: twelve in Op. 10, twelve in Op. 25, and the final three without opus number. The first set, which will be the focus of this paper, represents a rare example of exceptionally mature writing from such a young composer. The pieces are technically innovative, musically satisfying, and pedagogically effective; qualities which have earned them a lasting place in the standard repertoire. As the music itself is familiar to musicians and non-musicians alike, this paper will examine the process of learning the etudes. A point of some contention among pianists is whether or not natural advantages, such as large hands or exceptional finger independence, are necessary to be able to play the etudes. On the one hand, it must be acknowledged that the etudes are difficult pieces, requiring a high playing level as a prerequisite. It is also true that the variety of technical challenges found in them may mean that some pianists are better suited to certain etudes than to others. Playing the most difficult passages in the etudes requires a keen understanding of technique, but in very few cases are pianists truly prevented from playing the etudes due to physical limitations. One factor that contributes to whether a pianist is successful in learning the etudes is the mindset with which the task is approached. The concept of mindset is very broad, and has been the subject of much research by developmental psychologists. The Implicit Theories model, originally proposed by Carol Dweck and E. S. Elliott in 1983, places individuals on a spectrum between "incremental theorists," or those with a "growth mindset;" and "entity theorists," who hold a "fixed mindset." The former believe that intelligence is malleable and can be developed, while the latter tend to attribute abilities primarily to innate characteristics. Studies have shown that having a growth mindset can be linked to greater potential for academic, professional, and social success, and researchers have also demonstrated that it is possible for entity theorists to be taught to adopt growth mindsets (Blackwell, Trzesniewski, and Dweck, 2007).

!2 On a general level, a fixed mindset might manifest in the form of an individual believing that he or she is not athletic, but is good at math; or that he or she has no talent for music, but is gifted at visual arts. But even within a specific domain, such as playing the piano, fixed mindsets can hold a person back. For example, pianists who believe that they can't play the etudes because of natural limitations are exhibiting traits of a fixed mindset. Learning to play the etudes requires an investment of hard work; even with a growth mindset, the process can be daunting, and a fixed mindset only increases the chances of failure. When undertaking a project like learning the etudes, it can be helpful to understand a few things about how the brain processes information. Research has shown that humans store information by grouping together simple bits of data into larger groups, or "chunks" (Miller 1956). This process, referred to as "chunking" or "recoding," has important implications for both short- and long-term memory. Miller's article suggests that the brain can only store approximately five to nine distinct pieces of information in immediate memory, depending on the type of information, and more recent estimates have put the number as low as three to five (Cowan 2010). Most people can commit approximately seven digits to short-term memory on a single hearing, but it's rare for anyone to be able to remember much more than that. However, it has been demonstrated that with training, this apparent limit can be surpassed many times over. Chase and Ericsson (1982) describe how a distance runner they had been testing was able to recall as many as 82 digits after hearing them only once. The runner had spent 20 months developing a system in which he grouped together three or four digits and associated them with a race time or an important date in history. As he listened to a string of digits, he translated them into this system. After hearing the entire number, he could then reverse the process to reproduce the individual digits. By expanding this system to include "super-groups," or groups of groups, he eventually learned to interpret far more than seven digits as a single piece of information. However, as this system was specific to decimal digits, even after the training, his memory capacity for other types of information remained unchanged. As tedious as it may seem to develop this type of system, similar examples are actually common in many areas, such as language. Few people are capable of memorizing more than six or seven random letters of the alphabet on one hearing, but most fluent English speakers could

!3 easily recall the sentence: "The big black dog runs in the park," which contains 27 letters. They would surely be thinking of the sentence as eight words, not 27 letters, but if they knew how to spell all of the words, producing the letters themselves would not be difficult. Furthermore, remembering eight words after a single hearing is only possible because of the fact that they make sense in English syntax. By comparison, lists of random words are much more difficult to memorize. Similar phenomena exist in music. An experienced musician learns to recognize common patterns such as scales, arpeggios, and chords, and treat them as single units. Even the movements used to play passages can be treated as chunks; by working out the choreography of a gesture containing dozens of individual notes, the expert musician can treat this whole passage as a single piece of information, thereby greatly simplifying the process of recalling the piece from memory. Etude No. 1 represents a clear demonstration of how the principle of chunking can be applied to music (see Example 1.1). Adherence to Chopin's metronome marking of 176 requires the pianist's right hand to play between 11 and 12 notes per second. Consciously recalling and executing each note would demand superhuman concentration and speed, but the structure of the etude allows it to be partitioned easily into chunks. The first four notes in the right hand, C G C E, are immediately repeated an octave higher, and almost the entire etude is constructed by adapting the figuration and contour of the first two bars to each successive harmony. This makes memorizing the etude relatively simple.

Example 1.1: Etude Op. 10 No. 1, mm. 1-2

!4 However, just recognizing that the etude is organized this way is not enough to make a performance successful if it is not reflected in the technique being used. Beginning pianists often learn music by reading and playing one note at a time, a habit that American pedagogue Abby Whiteside refers to as a "note-wise procedure" (2003). According to Whiteside, whose writings frequently discuss the etudes, this approach does not work when playing these pieces. At a slow tempo, it is possible to play all of the notes of the first etude this way, but this sort of technique eventually reaches its limit as the tempo is increased. At a faster speed, even if the pianist does manage to play all of the the right notes, the hand will feel tight and quickly become fatigued. This approach has the further downside of making it difficult to avoid overemphasizing every note, which can make the piece sound stiff. Because of the wide intervals in the first etude, it is often misclassified as an exercise in playing with the hand stretched. The basic unit in the first bar covers an interval of a tenth. Most pianists can reach somewhere between an octave and a tenth, but for many, even a ninth is an uncomfortable stretch. And even for pianists with an especially wide span, keeping the hand stretched like this is exhausting. At a slow tempo, it is possible to play the etude this way, but once again, this method can only be taken so far. A more successful approach is to keep the hand as closed as possible, and to group notes together into gestures. As the hand moves across the piano, the fingers are drawn toward each other at every opportunity, allowing the pianist's hand to maintain a position closer to its natural resting state. This means that even pianists with smaller hands can play this etude, as the hand is rarely required to stretch beyond an octave at any given time. In addition to preventing fatigue, closing the hand also prepares the thumb to play the first note in the next group; thus, once a gesture has been worked out for the first four notes of each measure, it is relatively simple to replicate the same choreography in each successive octave. Researchers in the area of expert skill acquisition emphasize the importance of motivation, design, feedback, and repetition in practice activities, referring to methods that conform to these criteria as "deliberate practice" (Ericsson, Krampe, and Tesch-Römer, 1993, 367). They draw attention to the fact that deliberate practice activities require effort and are not inherently enjoyable, and that individuals who engage in practice of this sort are motivated

!5 because they recognize that it leads to improvement (368). They argue that the potential to achieve expert performance is not dictated by innate traits, but rather depends on the quantity and especially the quality of time spent acquiring necessary skills (365). Other researchers agree that deliberate practice is important, although there is some disagreement on whether it is the sole determiner of success. Campitelli and Gobet (2011) acknowledge the necessity of deliberate practice, but claim that many other factors are equally important. Practice activities used by musicians often satisfy some, but not all, of the criteria for deliberate practice. Most musicians practice in a way that involves a certain degree of repetition, and feedback is available both in the form of how it sounds and feels to play a passage, and in the response given by audiences, colleagues, teachers, and friends. Although a thorough discussion of motivation is outside the scope of this paper, it is related to the topic of mindset discussed above. However, many common practice methods fall short of true deliberate practice due to their lack of clear purpose and design. To address this, a helpful question can be, "What's currently standing between where this piece is and where it needs to be?" Ericsson, Krampe, and Tesch-Römer (367) assert that an active search for new practice methods can often be linked to clear improvements. One example of this would be searching for the reason that a certain passage is not working, or identifying the primary challenge associated with that passage, and then experimenting with new ways to address the specific issue that is preventing the successful execution of the passage. If the problem is that the technique being used does not match the demands of the passage, repeating it over and over the same way will not fix it. At times, this may mean that an entire change in approach is necessary. In the first etude, an example of deliberate practice would be to start by exploring different ways to play the basic figuration, adjusting the movement until it feels easier and sounds better, and then solidifying this movement through repetition and applying it to the rest of the piece. In some of the etudes, the figuration is less straightforward than in the first one. Example 1.2 shows an excerpt from the end of Etude No. 8, in which the texture is both more complex and more varied than in No. 1. The left hand part contains moving lines in several voices, exhibits both dotted and straight rhythms, and makes use of accents on weak beats. Meanwhile, the right hand outlines the harmony of each measure, but is heavily decorated with non-chord tones, and

!6 the figuration changes frequently. Due to the complexity of the passage, it is difficult for the performer to pay attention to everything that is happening when the piece is played at full tempo. However, due to the phenomenon of automaticity, it is not actually necessary for the pianist to attend to all of the details during a performance. Automaticity of behaviors is not fully understood by psychologists, but there has been increasing support in the last three decades for the idea that automaticity is a function of memory, and is therefore governed by the same laws as other aspects of memory (Logan 1992, 321). This means that automatic behaviors can also be organized into chunks, allowing simple movements to combine into efficient and sophisticated gestures.

Example 1.2: Etude Op. 10 No. 8, mm. 74-82

!7 Despite the necessary role of automatic behaviors in playing the piano, not all such movements are helpful. A well-choreographed gesture involves a large number of different joints and muscles working together, providing ample opportunities for bad habits to develop. The differences between successful patterns of movement and unsuccessful ones are often extremely subtle, but in the most difficult etudes, these differences can be very important. This is especially true of Etude No. 2. In this piece, shown in Example 1.3, the pianist plays rapid chromatic scales in the right hand with fingers 3, 4, and 5. Usually, playing chromatic scales would also involve the stronger fingers, 1 and 2, but in this etude, those fingers are needed to play the chords that fall on each beat. This etude is unique among Chopin's pieces in that he includes fingerings for almost every note, confirming that he did intend for the pianist

Example 1.3: Etude Op. 10 No. 2, mm. 1-4 to use the weak fingers in playing these scales. Because the right hand plays mostly chromatic scales, the hand has to adjust to the different heights of the black and white keys. This can be accomplished in several different ways. One is to reach with the fingers, lifting them higher for

!8 the black keys and dropping them for the white. But if the bulk of the work is being done with the fingers, they can quickly become exhausted, making it difficult to play through the entire etude. Another option is to lift the wrist slightly for the black keys and then drop it again for the white keys, allowing the hand and arm to help move the fingers into position for each note. This results in more total movement than a purely finger-based approach, but it spreads the workload more evenly by bringing larger muscles into play and requiring less exertion from the fingers. A third option is to rotate the entire forearm, causing some fingers to be lifted higher than others as the hand turns. In movements involving the wrist and forearm, too much motion can become inefficient and slow the pianist down, but as long as these movements are small and well timed, an approach based on a combination of these three types of movement can greatly reduce the demands placed on the fingers. In addition to reducing fatigue, subtle differences in approach can also have a sizable impact on note accuracy. This is especially true of Etude No. 5, popularly known as the "Black- Key Etude" because the right hand plays almost exclusively black keys. Since the black keys are much shorter and narrower than the white keys, precision is especially important in this etude, as adjustments of only a few millimeters can cause the pianist to miss notes. For most of the piece,

Example 1.4: Etude Op. 10 No. 5, mm. 79-80

!9 the right hand plays only one note at a time, but in the passage shown in Example 1.4, each triplet begins with a harmonic third. The first two, B-flat to D-flat and E-flat to G-flat, are minor thirds, but the next one, G-flat to B-flat, is a major third. This means that the hand must open almost imperceptibly wider to play this interval compared with the other two. The difference is small enough that it is possible to play the passage without attending to this change in hand position, but neglecting this detail can lead to sloppy renditions. However, over time, deliberate practice can make even very small adjustments like this happen automatically. Up to this point, all of the etudes examined have been in a fast tempo, but the same concepts are just as important in the slow ones. Etude No. 3, shown in Example 1.5, represents one of only two slow pieces in the set. Although it does not have as much virtuosic passagework as most of the others, the texture is thicker, with each hand responsible for controlling several different lines simultaneously. To clarify the texture, the melody and bass line are usually played louder than the other parts, which requires significant coordination and control. Once again, deliberate practice methods can be used to make this control become automatic. One way to practice voicing the chords is to select each sound individually, by rolling the chords slowly from bottom to top, listening carefully to each note before moving on to the next. Once the desired sound is obtained, the pianist can play all of the notes of the chord together, maintaining the

Example 1.5: Etude Op. 10 No. 3, mm. 1-4

!10 same hand and finger positions. In a texture as thick as the opening of this etude, the middle voices may need to be played almost as quietly as the instrument will allow to avoid overpowering the outer voices while remaining within the piano dynamic marking. Greater control of voicing can also be achieved by pointing the fingers that should play loudest slightly more than the others, or flattening the fingers that should sound quietest. Attention to small details of this sort can make a big difference in how successfully the etudes are played. On the other hand, not everything can be solved through this kind of detailed work, and some of the etudes can be approached in several different ways. In Etude No. 7 (see Example 1.6) the pianist alternates between small and large intervals, usually thirds and sixths. The smaller intervals are played by the longer fingers, 2, 3, and 4, while the shorter fingers, 1 and 5, take the larger intervals. This means that the hand has to adjust to accommodate the different lengths of the fingers, which can be done in several different ways. One option is to use the wrist to move up and down, dropping the wrist on the small interval and lifting it on the large interval. Another is to do the opposite, lifting the wrist for the small interval, and dropping it for the large one. A third option is to move the arm in and out, rather than up and down, allowing both the short and long fingers to play near the ends of the keys. All three approaches share one common advantage: in each case, the arm takes care of most of the movement, meaning that the etude

Example 1.6: Etude Op. 10 No. 7, mm. 1-2

!11 actually relies much less on finger independence when played this way. The etude can be played with any of these three approaches, but certain pianists may gravitate more toward one in particular, or may even use a different approach from one passage to the next. Practicing all three different ways provides more choices in performance, which can help to reduce fatigue. Whether a pianist chooses one of these three approaches or not, having a general strategy of this sort for each etude can provide a framework on which to hang the more detailed practice. Texturally, one of the most unusual etudes is No. 10, pictured in Example 1.7. Like many of the others, this etude is written in perpetual motion. The time signature is 12/8, indicating a compound quadruple meter, but the right hand pattern repeats every two notes instead of every three, and is grouped in a variety of ways. Initially, the notes played by the little finger are accented, but in other passages, the thumb gets the accents, or the accent is passed between the top and bottom notes. Meanwhile, the left hand consistently follows the notated meter. This can create an organizational difficulty when the two parts are put together, as the hands seem sometimes to be in sync with each other, and at other times not. As with the other etudes, identifying the exact cause of the difficulty is the first step to devising practice methods to address it. For this etude, one option is to practice the hands separately until the proper groupings begin to become automatic. Then, the hands can be put together beginning with small

Example 1.7: Etude Op. 10 No. 10, mm. 1-2

!12 chunks, such as half of a bar. By focusing on such a small passage, the pianist can pay attention to whether or not the hands are following the correct groupings, and adjust as needed. Once the control is developed to play a short passage with the hands together, the size of the chunks can be increased until it becomes possible to play the entire piece at once. Deliberate practice requires intense focus and determination, but it pays off in more ways than one. One benefit to studying the Chopin etudes is that the challenges in these works can be found in many other pieces as well. Choreographies and principles that work in the etudes can be transferred into music by other composers, as well as to the other pieces within the set. One example of this can be found by comparing the first, ninth, and eleventh etudes, shown in Examples 1.1, 1.8, and 1.9. Despite the differences in the figuration of each etude, the unifying factor is that each requires the pianist to navigate wide stretches, meaning that the hands will quickly become stiff if tension is not released at every opportunity. Due to the similarity of principles behind these three etudes, a discovery in one can often lead to similar breakthroughs in the others as well. Etude No. 11 contains chords spanning intervals as wide as a 13th, which is beyond the span of virtually all pianists. Once a choreography has been found that allows these chords to be executed rapidly, accurately, and without excessive strain, the same movement can easily be adapted to a variety of smaller chords and other passages with similar demands.

Example 1.8: Etude Op. 10 No. 9, mm. 1-3

!13 Example 1.9: Etude Op. 10 No. 11, mm. 1-3

The second and fourth etudes represent another pair of related studies. Like the second, the fourth contains rapid scalar passagework, including some chromatic runs. Example 1.10 represents one passage from No. 4 that is very similar in figuration to No. 2. Like the second etude, this piece requires the pianist to find coordinated patterns of movement that utilize the entire arm, as the hand may lock up if the fingers are overloaded. Practicing one of these etudes can provide new insights into how similar patterns can be played in the other etude.

Example 1.10: Etude Op. 10 No. 4, mm. 27-28

!14 PART 2

INFLUENCES AND INVENTIVENESS IN LIGETI'S ETUDES, DEUXIÈME LIVRE

The 18 Piano Etudes of György Ligeti, written between the years 1985 and 2001, represent the works of a brilliant and original composer at the height of his creative abilities. They are divided into three books, bearing the French designations premier livre, deuxième livre, and troisième livre. Containing eight of the etudes, and two separate versions of one of them, the deuxième livre is the most extensive, and will be the focus of this paper. It is reasonable to expect that these works will retain a lasting place in the standard piano repertoire. Prominent pianists including Jeremy Denk and Pierre-Laurent Aimard have already championed the works, the former drawing favorable comparisons between the etudes and the final piano sonata of Beethoven, which he paired together on the CD "Ligeti/Beethoven." Denk describes the etudes as instant classics, a sentiment which seems to be shared by critics, reviewers, and other music lovers. Nevertheless, the extraordinary difficulty of learning and performing these pieces may deter some pianists from fully exploring them. This paper will endeavor to make the etudes more accessible to listeners and performers alike by examining some of the compositional techniques involved, as well as the role played by outside influences, both musical and non-musical, in shaping the construction of the pieces. A fitting word to describe the etudes might be "extreme." Several of them use every single key on the piano, and the dynamic range goes from pppppppp to ffffffff. Denk describes these unusual dynamics rather humorously in the blog post "Ligeti's Infinities," dated September 22, 2010, where he writes, "How to interpret eight fortes? I think maybe I should hurl my whole body at the piano as violently as possible and hope for the best. They would find my bloody corpse weeks later amid the moldy coffee cups, odiferous testament to my devotion to the composer's intent. How would 8 be different from 7? Both must be so searingly loud as to be painful, a distinction between degrees of agony: if 7 fortes is like being disemboweled by a wolf, then 8 is like being disemboweled by a bear."

!15 The imagery suggested by this quote may seem appropriate when one looks at the scores themselves. Example 2.1 shows an excerpt from Etude No. 13, L'escalier du diable. This passage is densely packed with information: the music is written on four staves, with detailed damper and sostenuto pedal markings, abundant accidentals, a variety of articulation marks, and numerous rhythmic values and tied notes. But despite the apparent complexity of the music, there are several patterns that can be observed. The top staff oscillates between two chords, lasting a quarter note and a dotted quarter respectively. The lone chord in the second staff is a carryover from the previous line of music, sustained by the sostenuto pedal. Like the top staff, the third staff contains two alternating chords, lasting a dotted quarter and a half note each. On the bottom line, chords built primarily on open fifths ascend chromatically.

Example 2.1: L'escalier du diable, m. 31

The construction of this passage is typical of many of the etudes; frequently, several relatively simple patterns are layered on top of each other, producing a variety of unique interactions due to the mismatched lengths of these figurations. Steinitz (1996a) has discussed Ligeti's fascination with math, and in particular with chaos theory; of the etudes Vertige, L'escalier du diable, and Columna infinit!, Steinitz writes, "All three are initially deterministic

!16 systems containing hidden variables, in which the amplification of error leads to more-or-less dramatic developments. Like many of the studies, therefore, they encompass mathematical as well as musical issues; although, as Ligeti's remarks . . . suggest, that kinship may be more intuitive than calculated" (17). In most of the etudes, a few basic rules loosely govern the way an entire composition plays out, and tiny deviations from these rules--such as adding or leaving out a single note in a recurring pattern--can have lasting effects on the structure of the piece. The opening of Etude No. 9, Vertige (see Example 2.2), consists of 16-note chromatic scales overlapping with each other at varying time intervals. Although slurs are dispensed with after four bars for the sake of visual clarity, the pattern begun in these four bars continues. The first 16 entrances in this etude consist of the exact same notes: a chromatic descent from B down to the A-flat a ninth below. Many of these scales are spaced five or seven eighth note pulses apart, although time intervals of two, three, four, and eight pulses are also used. Here and elsewhere in the etudes, Ligeti demonstrates a preference for groupings based on prime numbers

Example 2.2: Vertige, mm. 1-6 and powers of two. With the 17th entrance, the range is expanded: this time, the chromatic scale terminates on a G, rather than an A-flat, bringing the total number of notes in this scale up to 17.

!17 The 22nd entrance is the first to begin on a different note, starting from C instead of B. After this, the changes become more frequent, with the scales progressively beginning higher and terminating lower. By gradually expanding the range in both directions, Ligeti creates the sense that the music is both ascending and descending simultaneously. Steinitz (1996b, 13) compares the earlier etude Automne à Varsovie from the premier livre to the 1960 lithograph Ascending and Descending by M. C. Escher, whose artwork Ligeti admired. A similar comparison could certainly be made here as well. The illusion of endlessly climbing is also present in Etudes No. 13 and 14, L'escalier du diable and Columna infinit!. Each etude is constructed of material that slowly moves up the

Example 2.3: Columna infinit!, mm. 1-3

keyboard, with each hand breaking off its pattern from time to time to begin again in a lower register. In Columna infinit!, shown in Example 2.3, Ligeti employs a dynamic range of fff to

!18 ffffffff, and the rapid progression of thick chords generates such a dense mass of sound that it is not always obvious when one of the parts has dropped out. Columna infinit! is the revised version of what was originally to be the fourteenth etude. The original version is titled Coloana f!r! sfâr"it, and bears the performance indication, "for player piano (ad lib. live pianist)". After completing the etude, Ligeti deemed it too difficult to play, and wrote the simpler version that is usually done instead. As can be seen by comparing Example 2.4 with Example 2.3, the construction of Coloana f!r! sfâr"it resembles that of

Example 2.4: Coloana f!r! sfâr"it, mm. 1-3

Columna infinit!, but with thicker harmonies. Both etudes are inspired by and named after a statue by Constantin Brâncu"i, also titled Columna infinit!, located in Târga-Jiu, Oltenia, Romania. The tower is nearly 100 feet tall, and is made up of many similarly-shaped modules stacked on top of each other. The top portion is incomplete, an attribute that is reflected in the

19! music: in both versions of the etude, the figuration climbs to the top of the keyboard and ends abruptly, with the performance note: "stop suddenly as if broken off." Although traditional time signatures are used in the notation of each etude, these bar divisions are more frequently employed to organize the music visually on the page than to indicate the metrical structure. In most of the etudes, there is a continual pulsation of rapid notes in the background, above which one or several melodies move at varying rates. In Etude No. 12, Entrelacs, shown in Example 2.5, the right hand melody notes occur every 13 pulsations, with

Example 2.5: Entrelacs, mm. 1-6 the left hand playing a slightly slower melody every 17 pulses. As the piece progresses, additional melodic lines are layered on top of these two, each moving at a different speed. The piece builds to several rhythmic climaxes where as many as seven different melodies are sounding simultaneously, moving at rates of 3, 4, 5, 7, 11, 13, and 17 pulses. The complexity

!20 generated by having this many simultaneous melodies running at the same time creates localized rhythms that seem chaotic and random despite their high level of organization, especially given that most of the groupings used are prime numbers. At each climax, all of the melodies drop out except for the original two, which continue to sound every 13 and 17 pulses. Toward the end of the piece, the repeated rhythmic patterns are further split into asymmetrical subdivisions. Example 2.6 shows a passage from near the end of the etude, in which 16-pulse groups in the

Example 2.6: Asymmetrical groupings in Entrelacs, mm. 70-75 right hand are divided into a recurring pattern of 3+6+3+4, and 16-pulse groups in the left hand are divided into 3+4+9. An additional 16-pulse group runs in the left hand from the downbeat of measure 76 through the end of measure 83, but is not divided into subgroups. Rhythms based on multiplications of an atomic pulse rather than divisions of a constant meter can be found in

!21 earlier pieces by Ligeti as well, and owe something to the composer's interest in the music of Phillip Glass and Steve Reich, Balkan folk music, and sub-Saharan Africa (Taylor 2003, 87). A further level of rhythmic complexity in Entrelacs arises from the various ways in which the background pulsations interact with each other. Initially, both hands play a sort of notated trill, oscillating back and forth between two notes, but later in the piece more complex patterns are juxtaposed. Example 2.7 shows a passage where the ratio between the background pulsations is 4:3, but elsewhere in the piece ratios of 2:3 and 5:3 can also be found. Taylor (88) remarks that Ligeti had a fascination with 12-beat groups that can be divided into groups of either three or four; this may be part of the reason he chose to notate six of the eight etudes in the deuxième livre using 12-note bars.

Example 2.7: 4:3 ratio in Entrelacs, mm. 58-59

Etude No. 8, Fém, utilizes a ratio of 18:16 as one of the primary metrical structures of the piece (see Example 2.8). Throughout the etude, the right hand repeats an 18-beat rhythmic ostinato subdivided into 1-, 2-, and 3-note groups, while the left hand plays an ostinato that is 16 beats in duration. This slight mismatching of lengths causes the two patterns to get out of sync with one another, resulting in a variety of interactions between the two parts. The piece is notated in 12/8; in this meter, the two patterns return to their original alignment every 12 bars. Each realignment marks a structural division of the piece, and is marked by a change in

!22 Example 2.8: Rhythmic ostinati in Fém, mm. 1-4

Example 2.9: Deviations from rhythmic ostinati in Fém, mm. 33-36

!23 dynamics. For the first two sections, the rhythmic ostinato in each hand is exactly preserved, but at the end of the third section, in bar 35, slight deviations in the form of missing beats or filled-in rests begin to appear (see Example 2.9). The fifth section is truncated, lasting only 9 bars (49-57) instead of the expected 12, and the sixth and final section of the piece lasts 21 bars, featuring an artificial tempo change brought about by a shift from the eighth note to the dotted quarter as the basic pulse. A compositional technique found in several of the etudes is the use of different scales in each hand, which together form the complete chromatic pitch collection. This technique is used in Galamb Borong, Der Zauberlehrling, En Suspens, and Entrelacs. Example 2.10 shows an excerpt from Etude No. 10, Der Zauberlehrling, in which this technique is used. In this section, the right hand plays entirely white keys, while the left hand plays only black keys. This means that all 12 possible pitches are present, but the right hand material is drawn entirely from a diatonic pitch collection and the left hand is pentatonic. The aural effect of such passages is dependent on the spacing of the two hands: when the hands are close together or overlapping, it can be difficult to distinguish the two separate scales being used, but when the hands get farther apart, the individual characteristics of each scale are more easily perceived.

Example 2.10: Der Zauberlehrling, mm. 67-69

!24 In En Suspens and Entrelacs, Ligeti combines two diatonic pitch collections. In both pieces, one hand is notated in five flats while the other plays no sharps or flats. This allows for all 12 pitches to be used, while retaining a diatonic flavor within each part. At points of formal

Example 2.11: Rhythmic ostinati in En Suspens, mm. 1-8

division in each etude, the pitch collections switch hands, giving the impression of a modulation. Like Fém, En Suspens makes use of rhythmic ostinati in each hand. In the A section (bars 1-17), the right hand part, notated in 6/4, is constructed of 9-beat, 10-beat, and 5-beat phrases, subdivided into groups of 3+2+2+2, 3+3+2+2, and 3+2 (see Example 2.11). There is one beat of rest separating each appearance of this ostinato, bringing the total length of the pattern up to 25 beats, or four bars plus a beat. The left hand part is written in 12/8, featuring the dotted quarter as the basic pulse, and contains an ostinato exactly three bars in length. Thus, were it not for the extra beat of rest in the right hand ostinato, the A section would exhibit a macroscopic 4:3 ratio.

!25 Ligeti's simultaneous use of 6/4 and 12/8 creates a constant cross rhythm throughout the piece. In bars 33 and 34, shown in Example 2.12, the basic pulse in the left hand is subdivided into groups of four, five, and six, resulting in additional cross rhythms. This etude is the only piece in the deuxième livre in which note values quicker than the basic pulse are used.

Example 2.12: En Suspens, mm. 32-35

In Etude No. 7, Galamb Borong, the right hand plays entirely notes of one whole tone scale while the left hand utilizes the opposite whole tone scale. As in Entrelacs and En Suspens, all 12 pitches are present, but there is overlapping pitch content. For ease of notation, Ligeti uses the unusual key signatures of E-flat and D-flat in the right hand, and B-flat, A-flat, and G-flat in the left, making accidentals unnecessary (see Example 2.13). However, accidentals do appear in bars 53-59, where the left hand plays the lowest A on the piano; although the scale suggests that

!26 this note ought to be an A-flat, the low register makes it difficult to discern the exact pitch. Similarly in bars 30-31, the highest C on the piano is used in place of what ought to be a D-flat, allowing Ligeti to expand the range of the piano artificially in both directions.

Example 2.13: Galamb Borong, m. 1

The rhythmic construction of Galamb Borong bears some resemblance to that of Entrelacs: in both etudes, sixteenth notes remain in the background throughout the piece, above which each hand plays one or more distinct melodic lines at various speeds. The words of the title are Hungarian, translating literally into English as "pigeon" and "melancholy;" however, Ligeti chose this title because the words sound Indonesian, and the music is partially inspired by Balinese gamelan music (Bauer 2008, 340-341). Bauer has provided a thorough analysis of Balinese influences in Galamb Borong. She notes the similarities between Ligeti's use of complementary whole tone scales and the paired tuning found in Balinese music, in which two instruments play scales with the same intervallic construction, but with one tuned slightly higher than the other. Virtuosity, extreme range and dynamics, and rapid mood changes are also important elements of Balinese gamelan, all of which are present in Galamb Borong. Despite the relatively brief performance time of the complete deuxième livre, around 22 minutes in total, the process of learning the etudes can take a considerable amount of time. One of the difficulties in learning these pieces is knowing where to begin in approaching each work. The amount of information present on each page of music necessitates an investment of time in

!27 order to make sense of the structure, and to identify the harmonic and rhythmic elements being used. Furthermore, the unusual key signatures in Galamb Borong and the simultaneous use of multiple time signatures and key signatures in several of the etudes require an adjustment in thinking for pianists unaccustomed to such devices. An additional challenge, both mental and coordinative, arises from the fact that often one hand will play accented notes while the other does not, with the accents passing between the hands in a rapid but irregular manner. Although the rules governing the rate at which melodic lines move are often consistent, as in Entrelacs, the resulting weave of accented tones is frequently so complex as to be virtually impossible to decipher in real time. One possible method that can be used to make sense of the most rhythmically complex sections of the etudes is to impose structure on the music artificially. Each of the etudes is notated in a traditional meter; although the bar lines are frequently unrelated to the actual meter, they provide a familiar way of dividing the music into smaller units. Many of the individual bars in the etudes contain a large amount of information, making it challenging fully to internalize even a single measure of any given etude at first, but by focusing on very small chunks at a time, even the most complex passages can be reinterpreted in simpler ways. Example 2.14 shows a measure from Entrelacs in which six different melodies are running simultaneously. In the right hand, half notes represent a melodic line that moves every 13 pulses, quarter notes correspond to a melody that moves every seven, and eighth notes represent a melody that moves every four. The left hand melodies move every 17, 11, and five notes. Ligeti indicates that the half note melodies, which move the most slowly, should be played the loudest, followed by the quarters, and then the eighths. Thus, the right hand has light accents on the first and fifth pulses, moderate accents on the fourth and eleventh, and a strong accent on the ninth. The left hand has light accents on the fifth and tenth, a moderate accent on the second, and a strong accent on the fourth. If keeping track of this many accents at once is too difficult, pianists learning Entrelacs may find it helpful to begin by practicing half of a measure or even a quarter of a measure at a time. In the performances notes for Galamb Borong, Ligeti recommends practicing the hands separately "more than is usual"; in all of the etudes, playing each hand separately before

!28 Example 2.14: Entrelacs, m. 22 combining the hands is one way of ensuring that the accent pattern is fully understood. A potential danger of practicing such short bursts is that the overall arc of the melodic lines can be lost, but practicing complete sections with the hands separately makes it easier to hear the longer lines. Regardless of whether the etudes are being played from memory or with the score, it is useful to have memorized them prior to performance. Because of the high degree of complexity found in the etudes, memorizing whole sections at a time may be difficult. However, adding a few notes at a time to a passage that is already memorized is more manageable. One method, which works well with these pieces, is to work backward from the end of a piece or section, adding a few notes at a time until the entire section is memorized. Even in performances where the score is being used, having developed the ability to play without the score can give the pianist a greater sense of freedom and security. One of the challenges in learning and performing these pieces is psychological. The music looks intimidating on the page, which can cause pianists to second-guess their ability to play it, resulting in unwanted tension and anxiety in performance. Despite the difficulty of the music, simple practice methods, such as playing through a section slowly, can still be useful. Once the challenges of working out the various rhythmic layers and putting the hands together have been overcome, slow practice can be especially helpful in solidifying entire sections and eliminating psychological barriers.

!29 CONCLUSION

Each of these sets of etudes is extremely challenging. Both physically and mentally, they push the pianist to test the limits of what is possible. But with a positive mindset, determination to push through difficulties and succeed, willingness to keep taking one step at a time, and a creative approach to dealing with the inevitable challenges, almost any experienced pianist should be able to learn them. The task of learning these pieces can be daunting, but the principles of chunking can be used to break down the process into achievable goals. Studying either set of etudes provides ample opportunities for pianists to examine their approaches to learning music, and to receive new insights into the relative merits of various practice methods. The extreme difficulties contained in both sets necessitate the exploration and discovery of refined and efficient choreographies and practice techniques, and practicing the etudes has many benefits extending beyond the ability to play the specific pieces. The Chopin Etudes remain popular nearly 200 years after they were written. Although only time will tell whether Ligeti's etudes will remain in the standard repertoire, they share many positive traits with Chopin's: both composers' sets are challenging, original, and musically satisfying. Despite the incredible difficulty of the Ligeti Etudes, learning and listening to them is also very rewarding. The etudes challenge pianists to examine many aspects of technique, practice methodology, music-learning strategies, and performance issues. In exchange for these efforts, performers and audience members alike are rewarded with music that is humorous, intellectual, exciting, and beautiful. These etudes have already established themselves as some of the most important works for solo piano from the second half of the 20th century, and it is likely that they will continue to be studied and enjoyed for many years to come.

!30 REFERENCES

Bauer, Amy. 2008. "The Other of the Exotic: Balinese Music as Grammatical Paradigm in Ligeti's 'Galamb Borong'." Music Analysis 27 (2/3): 337-372. http://www.jstor.org/stable/40606821.

Blackwell, Lisa S., Kali H. Trzesniewski, and Carol Sorich Dweck. 2007. "Implicit Theories of Intelligence Predict Achievement across an Adolescent Transition: A Longitudinal Study and an Intervention." Child Development 78 (1): 246-263. http://www.jstor.org/stable/4139223.

Bouliane, Denys, and Anouk Lang. 2006. "Ligeti's Six "Etudes Pour Piano": The Fine Art of Composing Using Cultural Referents." Theory and Practice 31: 159-161, 163-207. http://www.jstor.org/stable/41054377.

Campitelli, Guillermo, and Fernand Gobet. 2011. "Deliberate Practice: Necessary But Not Sufficient." Current Directions in Psychological Science 20 (5): 280-285. http://www.jstor.org/stable/23045739

Clendinning, Jane Piper. 1993. "The Pattern-Meccanico Compositions of György Ligeti." Perspectives of New Music 31 (1): 192-234. http://www.jstor.org/stable/833050.

Colvin, Geoff, ed. 2010. Talent is Overrated: What Really Separates World-Class Performers from Everyone Else. New York: Portfolio.

Cowan, Nelson. 2010. "The Magical Mystery Four: How Is Working Memory Capacity Limited, and Why?" Current Directions in Psychological Science 19 (1): 51-57. http://www.jstor.org/stable/41038538

Drott, Eric. 2003. "The Role of Triadic Harmony in Ligeti's Recent Music." Music Analysis 22 (3): 283-314. http://www.jstor.org/stable/3700436

Dweck, Carol S., Chi-yue Chiu, and Ying-yi Hong. 1995. "Implicit Theories: Elaboration and Extension of the Model." Psychological Inquiry 6 (4): 322-333. http://www.jstor.org/stable/1448951.

Ericsson, K. Anders, and William G. Chase. 1982. "Exceptional Memory: Extraordinary feats of memory can be matched or surpassed by people with average memories that have been improved by training." American Scientist 70 (6): 607-615. http://www.jstor.org/stable/27851732.

!31 Ericsson, K. Anders, Ralf T. Krampe, and Clemens Tesch-Römer. 1993. "The Role of Deliberate Practice in the Acquisition of Expert Performance." Psychological Review 100 (3): 363-406. doi: 10.1037/0033-295X.100.3.363.

Logan, Gordon. 1988. "Toward an Instance Theory of Automatization." Psychological Review 95 (4): 492-527. doi: 10.1037/0033-295X.95.4.492.

———. 1992. "Attention and Preattention in Theories of Automaticity." The American Journal of Psychology 105 (2): 317-339. http://www.jstor.org/stable/1423031.

Miller, George A. 1956. "The Magical Number Seven, Plus or Minus Two: Some Limits on our Capacity for Processing Information." Psychological Review 63 (2): 81-97. doi: 10.1037/h0043158.

Searby, Mike. 1997. "Ligeti the Postmodernist?" Tempo New Series (199): 9-14. http://www.jstor.org/stable/945525.

Steinitz, Richard. 1996a. "Music, Maths & Chaos." The Musical Times 137 (1837): 14-20. doi: 10.2307/1003886.

———. 1996b. "The Dynamics of Disorder." The Musical Times 137 (1839): 7-14. doi: 10.2307/1003934

Svard, Lois. 2000. "Notes." Notes 56 (3): 800-804. http://www.jstor.org/stable/899705.

Taylor, Stephen Andrew. 2003. "Ligeti, Africa and Polyrhythm." The World of Music 45 (2): 83-94. http://www.jstor.org/stable/4170061.

Whiteside, Abby. 2003. Abby Whiteside on Piano Playing: Indispensables of Piano Playing - Mastering the Chopin Etudes and Other Essays. Portland: Amadeus Press.

!32 BIOGRAPHICAL SKETCH

Nolan Miller completed a Bachelor of Music in Piano Performance at Houghton College and a Master of Music in Piano Performance at Syracuse University before pursuing the degree of Doctor of Music in Piano Performance at Florida State University. He has been an active performer both as a solo and collaborative pianist, and has also performed with orchestras in both New York and Florida. In 2015 he was named the winner of the FSU Chapman/Neesen Competition for Graduate Pianists.

!33