“As Maurits Escher sought the illusion of a non-existing per- spective, so I seek the illusion of unplayed rhythmic struc- tures.”182
Ligeti commanded a profound knowledge of the tonal and technical peculiari- ties of individual instruments. All of his instrumental works are suitable to the instruments used in both conception and execution, and that goes for the keyboard works as well as for the chamber music, and of course for all the
concertos. About his Continuum, composed in January of 1968, he wrote to his friend Ove Nordwall in February that “technically” it was “invented entirely from the possibilities of the harpsichord” and was to be played on two manu- als in the same position183.
In a listener coming from traditional music and hearing the piece for the first time, Continuum might create the impression of a perpetuum mobile. In any event, it represents the type of “mechanical” music. The sketches indeed in- clude the note “like a precision mechanism”, and Ligeti in fact initially thought of entitling the piece “Mechanismus” but then called it Continuum. A continuum in mathematics is a continuous geometric construct created by the connection of numerous points, such as a line or a circle. It is very likely that in settling on the definitive title Ligeti had this mathematical concept in mind: in the quoted letter to Nordwall he compares the plucking of the strings to “points” that fuse into lines.
In the printed edition, Ligeti writes about the piece:
Prestissimo = extremely fast so that the individual notes are hardly perceptible any longer but fuse into a continuum. To be played very evenly without any articulation. The correct tempo will have been at- tained if the piece (without the final pause) takes less than four minutes. The vertical dotted lines are not bar lines (there is no beat or meter) but only serve for orientation.
The remark not only is important for the recital but also provides insight into the conception and character of the piece. The sketch also has the note: “The legato comes about in that the keys remain depressed during the next notes and [are] let up only when necessary for the new [?] stroke.” This direction was suppressed in the edition, but Ligeti wrote to Nordwall: “The sounding together of the strings (direction: key to be left depressed until the same fin- ger is needed again) creates the impression of continuity.”184
Ligeti’s calculations as to the length of play in the sketches are instructive. Both there and in the printed edition the orienting “bars” comprise 16 notes (strokes) each. The piece was initially conceived with four seconds for 48 = 3 x 16 strokes (thus 12 strokes per second) in mind. Accordingly the duration of the piece was to be 4’32”. The definitive direction prescribes an even shorter recital length: “less than four minutes.” To attain that, the pianist must manage to play 14 strokes per second.
Continuum has no rests or breaks. Nevertheless, latent caesuras enable one to
first part mm. 1-56 second part mm. 57-91 third part mm. 92-152 fourth part mm. 153-204
While the first two parts make a rather static impression in spite of the unin- terrupted figuration, the third part is dynamically agitated: the two hands begin in the middle position and move quasi chromatically in opposite direc- tions. The last part stays in the highest register and ends abruptly.
Beginning with Continuum, Ligeti distanced himself from his micropolyphony and its highly complex rhythmic structures and gives artistic expression to a different idea: that of a simple and uniform rhythm. The principle according to which the piece is constructed is that of an ostinato repetition and gradual transformation of figures comprising from two to eight notes, which are played on both manuals. There are passages where both hands concurrently play figures of two, three, four, five, six or eight notes, and others where fig- ures of different length are counterpointed. For example, in mm. 13/14, the right hand plays a three-note, the left a two-note figure. In mm. 15/16, three- note figures appear in both voices, but in a characteristically off-set manner. In m. 17, a three-note figure (right) is combined with a four-note one (left), and in mm. 218-20, a four- with a five-note one (Ex. 14). As one can see, the notation is grid-like, and in fact Ligeti called the technique of the simultane- ous combination of differently structured figures “Gitterüberlagerung” or “grid superimposition.”
Ex. 14 Continuum: Grid superimposition
For a different example, in a number of places, the same figure is played by both hands but in quasi canonic displacement (Ex. 15).
Ex. 15 Continuum: Grid superimposition
Ligeti professed an aesthetic of the illusionary: he had a soft spot for deceptions, both in visual art and in music. He prized the prints of Maurits Cornelis Escher above all on account of their optical deceptions. He once observed about this artist:
Aesthetically, I do not even regard him as so great an artist, but in terms of his ideas and their executions he is akin to me. My way of working with constructions that yet are not mathematics, with geo- metric and arithmetic divisions, nets, grids – they resemble his way of working. As he sought the illusion of non-existing perspectives, so I seek the illusion of not-played rhythmic structures. But I found pat- terns of rhythmic illusion long before I ever knew Escher – already in
my piece for a hundred metronomes or in Continuum (1968).186
M. C. Escher, “Upstairs and downstairs”, detail: (re Ligeti’s aesthetics of the illusionary)
Continuum indeed yields impressive examples of acoustic deceptions. One illusion-
ary effect is the manner in which motion, despite the extreme speed, seems to pass over into stasis: in several places one seems to hear slowly changing, densely struc- tured clusters. No less remarkable is the fact that, along with the real motion, the impression of an “ideal” motion often makes itself felt, which, in Ligeti’s words, “results from the tonal superposition, like two billowing motions that are alternate-
ly coincident with and displaced against each other.”187 Thus the motion in mm.
125-149 lets the “ideal melody”, formed of the high crest notes g2 – g#2 – a2 – a#2 –
b2 – c#3 flash up, while the corresponding counter-motion in the bass suggests a
melody formed of the low keel notes f – e – eb – d – c#. Ligeti may have been quite
surprised when he read Gerhard Kubik’s account of inherent tonal sequences and
melodies in Central-Africa music,188 since numerous such patterns are concealed in
his own harpsichord piece.
Like Lux aeterna, Continuum is a key work for Ligeti’s compositional development. The direction he entered upon with this piece he continued to pursue in subse- quent compositions for the piano, for example in the second of the Three Pieces for
Two Pianos of 1976. Even the tricky polyrhythmics and polymetrics of the Piano Etudes, it would be no exaggeration to say, are rudimentarily preformed already in
the Continuum.