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Rhythm, Form, and Texture in “Fém” from György Ligeti’s Études pour piano, Book II

Stuart BeatchMUSIC 458 – February 25, 2014

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The three books of György Ligeti’s Études pour piano have quickly become standards of

piano literature since Ligeti began composition on them in 1985. Although the pianist and

scholar Maurice Hinson notes that these etudes “may be the most important piano etudes written

since Debussy’s,” he nevertheless adds that “very few pianists in the world could play these

etudes as indicated.”1 Not only do Ligeti’s works involve various exhaustive physical demands

for the performer, but he also combines them with true detail and musicality. In this paper, I will

discuss the theoretical aspects of rhythm, form, and texture as related to “Fém,” the eighth etude

from Book II, and in this process, reveal the complex compositional structures present in Ligeti’s

music.

The rhythmic structures present in this etude can be observed on many levels. At its most

microscopic, the etude is built out of series of eighth notes: groups of one, two, or three, each

separated by a rest. On a slightly larger scale, it can be observed that these groups occur in

cycles, each separated by two rests; however, the right hand and left hand perform opposing

cycles of differing lengths. The right hand performs 2-1-1-2-3-2 (with rests, 18 eighth notes in

length), while the left hand performs 3-1-1-3-2 (with rests, only 16 eighth notes in length). There

are two noticeable musical traits that arise from this procedure. First and foremost, any sense of

metre is destroyed since these opposing groupings of eighth notes create a complex interplay of

implied strong and weak beats. This is foreshadowed by the performance notes, where Ligeti

himself states that “there is no real metre here; the bar lines are only to help synchronisation.”2

Also, since the groupings are of varying lengths, there is also a great deal of complexity resulting

from the overlay of implied simple and compound metres at any one instant. Again, there is

evidence to be found in the score’s tempo indication, which is given in three versions: dotted

1 Maurice Hinson, Guide to the Pianist’s Repertoire, 3rd ed. (Bloomington: Indiana University Press, 2000), 481-82.2 György Ligeti, Études pour piano, deuxième livre (Mainz, Germany: Schott Musik, 1998), 12.

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whole note at 30, quarter note at 180, and dotted quarter note at 120.3 The greatest challenge in

this etude is in having enough control to realize these traits in an audible sense, since the etude

could just as easily sound like a study in syncopation.4

At a larger scale, these cycles of varying lengths between the two hands also create a type

of simplistic phasing, wherein the cycles realign every 144 beats (or 12 measures). Although the

pitch content does not remain constant, there is generally another musical facet which changes

every twelve measures at these moments of realignment, as if Ligeti is making the structure as

clear as possible to the listener. At measure 13, the dynamic changes to piano and the una corda

pedal is applied. Half-way through this cycle, the dynamic changes to fortissimo, but returns to

piano at measure 15. Another cycle is almost completed in the exact same way starting at

measure 25, but then Ligeti begins to interpolate additional eighth notes, which derails the

alignment. At this point in the piece, measure 34ff, there is a sense of rhythmic extension due to

the longer streams of eighth notes and the appearance of a departure from the original sequence

of notes and rests used in each hand. However, Ligeti keeps a compositional regularity: the left

hand’s cycle remains at 16 eighth notes in length, while the right hand’s cycle alternates between

17 and 18 eighth notes in length.5 Measures 40-41 act as an irregular moment in the piece: both

hands have several additional notes and rests interpolated into the series, which brings the hands

briefly into alignment in measures 42-43, then out of alignment by one eighth through measures

44-45. At measure 46ff, we have both hands utilizing the same rhythms as at the beginning, but

out of alignment by four eighths. Starting in measure 49, the surface-level rhythmic regularity

begins to deteriorate rapidly: the right hand plays the same rhythmic cycle as at the opening, and

3 Ibid.4 Ian Pace, “Maintaining Disorder: Some Technical and Aesthetic Issues Involved in the Performance of Ligeti’s ‘Études for Piano,’” Contemporary Music Review 31, nos. 2-3 (April-June 2012): 187.5 Barbara Podgurski, “Polymetric Layering and Tonal Language in the Piano Etudes of György Ligeti” (DMA diss., City University of New York, 2013), 35-36.

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gets through two repetitions, while the left hand plays a continuous stream of eighth notes. Upon

close examination, measure 52 appears to be the end of a repetition of the left hand cycle, and in

fact the stream of eighth notes can be abstractly identified as two further iterations, where the

rests have been entirely filled in with notes.6 Until the final coda section in measure 58, both

hands play irregular series of eighth notes and rests, reaching a rhythmic unison in measure 57.

In the coda section, the rhythmic unit has been tripled to the dotted quarter. As well, the usage of

original rhythmic series from each hand is maintained, but additional notes and rests are freely

interpolated and substituted as to render it nearly unrecognizable.7

To analyse the form of this work, I chose to observe both the moments when the cycles

fall into alignment, as well as the treatment of the rhythmic material within. For comparison, I

also provide an alternative analysis obtained from one of my sources. The form is as follows:

My Analysis Sara Bakker’s Analysis8

mm. 1 – 12

A

Cycle 1; loud and similar register throughout Establishment

mm. 13 – 24Cycle 2; begins soft and in a low

register, becomes loud and moves higher Continuation I

(mm. 13 – 33)

mm. 25 – 36

A’

Cycle 3; begins soft and low, becomes loud and moves higher; additional notes are interpolated and the length of the RH pattern

alternates

Development I(mm. 34 – 45)mm. 37 – 42

Cycle 4; soft and low, then loud and high; further notes are

interpolated

mm. 42 – 48 A’’

Continuation of Cycle 4; hands begin in rhythmic unison, then move out of sync; the original

rhythmic patterns are only audible at rare moments

Continuation II(mm. 46 – 51)

6 Sara Bakker, “Playing With Patterns: Isorhythmic Strategies in György Ligeti’s Late Piano Works” (PhD diss., Indiana University, 2013), 69. Bakker provides a graph which clearly outlines where Ligeti has “substituted” the rests for additional pitches.7 Ibid, 78.8 Ibid, 66.

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mm. 49 – 57 A’’(cont.)

Cycle 5; fragmented; the RH begins with the original rhythmic material, but both hands become increasingly frantic at the climax

Continuation II (cont.)

Development II(mm. 52 – 57)

mm. 58 – 78Coda[A’’’]

Cycle 6; coda section, soft and distant; rhythmic values are

tripled, with many additional notes and rests interpolated to

mask the original rhythmic series

Conclusion(mm. 58 – 76)

Stop(mm. 77 – 78)

I consider the rhythmic cycles to be the most basic and important form determinant in

this etude, and I base my analysis on the macrostructure of where rhythmic cycles begin and end.

Initially, each large section contains two cycles; however, the exceptions are A’’, where the

material clearly separates from the beginning of the cycle and morphs quite radically, and the

coda, where the longer rhythmic values only allow one full cycle before the piece ends. I offer

the alternative designation of A’’’ for the final section, as the rhythmic structure still remains

from the opening material, though clearly altered. However, since nearly every other audible

parameter has been altered as well at this point, and the piece is obviously at a denouement, I still

prefer to consider it as ending material.

Bakker’s analysis offers another approach to the piece. Instead of observing the location

of isorhythmic cycles, she based her analysis on her own theoretical framework for analysing

isorhythmic pieces. She considers every work to begin with an “Establishment,” and end with a

“Stop.” Before the stop, there may be a “Conclusion,” and in the body of the work, there may be

one or more instances of “Continuation” and “Development.” In many ways, it is almost akin to

an altered sonata form, but one with a great deal more freedom in repeating or omitting sections.

In the context of this piece, Bakker considers the first cycle as the establishment, and bases the

division of the rest of the material before the coda on whether the right hand material is

presented properly, or is altered in some way. Since this disregards the rhythmic structure

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between the two hands, and also does not consider other musical parameters such as pitch and

dynamics, I find this to be a less satisfying analysis.

Another formal characteristic of Ligeti’s music is his use of the Golden Section. One way

of analysing if this is present in “Fém” is by calculating the occurrence of the golden mean over

the duration of the etude. As noted at the end of the score, this should be 3’05”, or 185 seconds.

Multiplied by the Golden Mean (0.618), the Golden Section should occur around 114 seconds in.

At the initial tempo of 30 measures per minute, or one measure every two seconds, this means

exactly 57 measures will pass, with the Golden Section beginning at measure 58: precisely at the

coda. By reviewing several recordings, such as those made by Pierre-Laurent Aimard and Simon

Smith, and calculating the Golden Section based on the length of each individual performance,

most pianists still keep the Golden Section within a few measures. This is due to the various

tempi used, especially at the coda, and is made more inaccurate by the apparent predilection of

most pianists to ignore the final two measures of rest at the end of the etude.

The textural component of this etude is one that deserves some close scrutiny as well. In

general, the piece clearly revolves around the interval of the fifth, with the constant perfect fifths

in each hand imitating “the non-harmonic overtones of the double bell in Central and West

African instrumental ensembles.”9 This cross-cultural appropriation is no different than the

influence Javanese gamelan music has had on composers like Claude Debussy, Colin McPhee,

and Claude Vivier, and African influences such as this appear in several of Ligeti’s etudes under

structural, textural, and timbral guises.10 The open fifths give the etude a clear texture in the

opening, one which is both brittle and bright due to the high register. In measure 13, there is a

9 Amy Marie Bauer, Ligeti’s Laments: Nostalgia, Exoticism and the Absolute (Burlington, VT: Ashgate, 2011), 153.10 Martin Scherzinger, “György Ligeti and the Aka Pygmies Project,” Contemporary Music Review 25, no. 3 (June 2006): 239-256. This article also touches heavily on the ethical issues of cultural appropriation, and addresses the manner in which Ligeti incorporates these sources into his music. While important to consider, I do not find it necessary for my analysis.

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shift in register and dynamic, with the basic rhythmic and pitch material remaining the same; this

has the result of indirectly thickening the texture and giving it a fuller sound. At measure 19,

there is a shift back to the original register, but now with a louder dynamic, and introducing more

complex intervals, changing the timbre and resonance quite drastically. Here, Ligeti begins

incorporating stacked fifths in the arrangement of a second and a fourth. These added

dissonances have the effect of changing the character of the piece, making the music somewhat

frantic and giving it more of a crystalline sound. Ligeti continues to alter the register and

dynamic between these two “registrations” until the next change at measure 34: the eighth-note

groupings become extended into longer streams, and the register is stretched upwards even

further. In measure 49, the change is made in the opposite direction, so that the register is

extended in both hands to the low extreme, and the longest stream of steady eighth notes occurs

here over a course of three measures. From there until measure 57, both hands build up to a

climax in both dynamics and register.

Throughout these sections of the piece, therefore, we can make several generalizations.

First, dynamics are generally associated with register – with the loudest dynamic markings

reserved for the highest part of the keyboard – and the music shifts back and forth between these

registral areas. Second, there is a gradual acceleration throughout with regards to how often the

music shifts register and dynamic. Third, there is a general thickening of texture throughout with

the addition of more complex intervals and the interpolation of additional notes creating longer

eighth-note streams. All of these first three sections can then be considered as one macro-gesture,

where the music begins somewhat one-dimensional, which builds through several musical

parameters to the climax.

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At the coda, there is much less to talk about with regards to texture. The dynamic is

pianissimo with a decrescendo at the end, and it is a calm, distant section where each hand

simply wanders through various dyads and trichords. The only thing of interest texturally is the

rhythmic alternation between the two hands, sometimes appearing to be in sync and other times

very distant from each other, which is clearly a remnant of the rhythmic patterns from earlier in

the etude. Further, the very colourful and complex trichords Ligeti utilizes in the coda is perhaps

a continuation of the earlier section; despite the fact that the rhythmic pulse, dynamic,

articulation, and character have all changed drastically, he kept the complexity of harmony that

had been built up over the etude as the one parameter that would remain. Indeed, it also seems

that in the final measures, one can also observe a breakdown of this complexity: measures 74-76

return to utilizing nothing but perfect fifths and quintal chords.

In “Fém,” Ligeti has written an etude with a multiplicity of theoretical possibilities and

avenues of analysis. Although the topics mentioned here – rhythm, form, and texture – could all

be discussed in much further detail, it is my hope that this essay has offered a brief, yet

satisfying, insight into the depth and complexity present in this etude.

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Bibliography

Bakker, Sara. “Playing With Patterns: Isorhythmic Strategies in György Ligeti’s Late Piano

Works.” PhD diss., Indiana University, 2013.

Bauer, Amy Marie. Ligeti’s Laments: Nostalgia, Exoticism and the Absolute. Burlington, VT:

Ashgate, 2011.

Hinson, Maurice. Guide to the Pianist’s Repertoire. 3rd ed. Bloomington: Indiana University

Press, 2000.

Ligeti, György. Études pour piano, deuxième livre. Mainz, Germany: Schott Musik, 1998.

Pace, Ian. “Maintaining Disorder: Some Technical and Aesthetic Issues Involved in the

Performance of Ligeti’s ‘Études for Piano.’” Contemporary Music Review 31, nos. 2-3

(April-June 2012): 177-201.

Podgurski, Barbara. “Polymetric Layering and Tonal Language in the Piano Etudes of György

Ligeti.” DMA diss., City University of New York, 2013.

Scherzinger, Martin. “György Ligeti and the Aka Pygmies Project.” Contemporary Music

Review 25, no. 3 (June 2006): 227-262.