# Ligeti's Piano Concerto: an analysis of the third movement (second part)



## aleazk (Sep 30, 2011)

(Desordre, continuation)

If you listen to the piece, note how the very bizarre rhythms that start at this point produce that kaleidoscopic ilusion in the polyphony Ligeti was talking about in his comments.

In terms of form, note how that shortening can be thought as a "perturbation". In chaos theory, small perturbations of a system can change drastically the output. Ligeti applies this idea, and he continues to make this kind of perturbations and so the rhythms become more fast and complex. Note how all this happens in the way Ligeti described in the second paragraph of the quote in the last blog entry.

In Automne à Varsovie we have another of Ligeti's obsessions: the lamento motif. The motif is composed of bits of a chromatic descending line. Ligeti sings it here 

In this étude, Ligeti uses the African technique to present the lamento motif at different and oddly contrasting speeds and in a kind of fugato way. Here's an extract from the score:









In that example, the two upper melodic lines are in a 4:5 cross rhythm relation (i.e., in the same amount of time in which the first voice plays four notes, of equal duration, of the motif, the second voice plays five). The basic pulse of the continuum is 1/16 (the 16th notes); in this way, the pulse of each note in the first voice is 5/16 and in the second 4/16.

Note how the situation here is quite different to Desordre, in which we had some kind of meter structure that was "shifted" between the two hands. And this is precisely where the power of the African technique resides: starting only with that basic continuum of fast pulses, you can build almost any rhythmic structure you want (from more traditional meter structures, to striking cross rhythms, etc.) and to apply all kinds of wild transformations to those structures you just built, thus creating very interesting rhythmic textures. Ligeti takes full advantage of this, he creates momentaneous meter structures for later destroying them, or cross rhythms that evolve to other types of cross rhythms. The possibilities are really incredibly diverse.

Going back to Automne a Varsovie, now these chromatic lines overlap with each other creating a dense and chromatic harmony.

The polyphony becomes denser and denser, some kind of conglomeration of the lamento motif. Again, we have the kaleidoscopic ilusion and the evolution order -> chaos in the form. The conglomeration of lines resembles the lines in Escher's drawings.

And now, finally, the third movement of the Piano Concerto.

(all of the following is taken from S.A.Taylor's dissertation on Ligeti's techniques, here; I strongly recommend it for anyone interested, a great reference)

The general form of the piece can be thought as a _rondo_, in which sections based on the lamento motif, and similar in character to Automne a Varsovie, alternate with "African" sections, based on African rhythms and sounds (i.e., not only the "abstract" techinque, but also explicit quotes of material present in African music; in Automne a Varsovie, the African influence is abstract, since it only can be traced to the rhythm technique used by Ligeti and not to the actual musical material).

We will follow Taylor's nomenclature. The sections and timings are (timings in relation to the video above):

-Introduction (0:00 - 0:13)

-Lamento 1 (0:13 - 1:18)

-African episode 1 (1:18 - 2:01)

-Lamento 2 (2:01 - 2:28)

-African episode 2 (2:28 - 3:13)

-Lamento 3 and then Coda (3:13 - 4:10, end of the movement)

(I will not enter in all the details, check the dissertation.)

The Introduction starts with a fast tremolo in the right hand. These are 16th notes and will comprise the basic and atomic pulse (1/16) of the continuum for this movement. After this, a slower tremolo starts in the left hand (the pulse of this tremolo is 3/16). This is similar to Ligeti's Continuum für Cembalo, a piece in which Ligeti started to apply these rhythm techniques for the first time. The flute picks this second tremolo.

The Lamento 1 starts then with a clear statement of the lamento motif in the piano, the pulse for each note of the melody is 7/16. In this section, the lamento motif will appear three times in the piano, each time faster and in a fugato way (at a moment, the pulses of the lines are 4/16 and 5/16). The orchestra part becomes more and more colorful with woodwind instruments that pick the motif or the tremolos. The continuum accompaniment in the piano also becomes more colorful since it unfolds in arpeggios and scales (often, whole tone scales, like in the étude Galamb borong; some of Messiaen's famous modes are also quoted!). The impression we get is captured by this sentence from the Ligeti quote _"is a kind of organic proliferation, as when lianas gradually grow over a primeval forest, in other words, a very complex polyphonic lianoid structure"_.

From a dense conglomeration of lines at the end of Lamento 1, the African episode 1 unfolds. The most notorious element of this section is the clear entrance of the rototoms (often replaced by bongos). The rototoms play a 4:3 cross rhythm ostinato:









This cross rhythm was already subtly present in the orchestra in the previous part (note the strings in pizzicato just moments before the entrance of the rototoms and the smooth timbral transition from this to the rototoms; this is typical of Ligeti). It's usually found in African music and the fact that it's played in a percussion instrument whose roots are African is what gives to this section its very characteristic African flavor.

At the same time, the horn and later the woodwinds play a new melody over the rototom ostinato. The meter of this melody is 11/8, which clash against the 12/8 ostinato of the rototoms, thus creating a polymeter in the polyphony of this section. Also, the melody is actually built in an additive manner:

(3 + 2 + 3 + 3)/8 = 11/8









These kind of additive rhythms are also present in Bartok, Ligeti's idol in his youth.

At the beginning, the piano keeps playing lines from the previous section, with pulses 5/16 vs 7/16.

Later, at 1:38, the piano picks the melody of this section in the right hand and harmonizes it with sharp and metallic fifths, producing a sound similar to the piano étude Fem ('metal' in hungarian). This is accompanied by the background continuum pulse on the left hand, which displays erratic rhythmic accentuations. The melody is doubled by brutal pizzicatos on the strings.

At 1:46, the hands reverse roles and the melody played by the left hand descends gradually to the lowest register of the piano, while the background continuum played by the right hand becomes more and more frenetic as it ascends in register.

Note that when the melody is picked by the piano at 1:38, the rototoms have smoothly changed from their 4:3 cross rhythm initial pattern to a more frenetic accompaniment to the piano. In fact, the rototoms are experiencing a metamorphosis that will take them from the 4:3 cross rhythm initial ostinato pattern to a (3 + 2 + 2 + 3 + 2)/16 = 6/8 additive pattern which can be heard at the final seconds of this section:









This metamorphosis is, of course, an explicit emulation of Escher's homonymous drawings. It's definitely one of the most striking details of this movement and a favorite of mine .


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