Fragment I-IV was composed between 1959 and 1961. I premiered the piece myself on February 12, 1962 at a concert where Fragment V for violin and piano and Fragment VI for six orchestra groups were also performed.
The four piano pieces contain the first audible results of my preoccupation with the fractal “infinity series”, discovered in 1959. “Fractal” designates the property of, for example, visual form patterns that appear in a process of infinite “microscoping”, where the figures reappear for the spectator in constantly enlarged segments of the original fractal form. In much the same way the score-reader as well as the listener can follow how, in for example Fragment III, the six notes of the first measure reappear in a much slower figure an octave lower in the left hand (that only manages to get through these six notes in the course of the entire movement) analogous to the zooming-in on a visual fractal form. Each Fragment has its own defining appearance:
Fragment I consists of two staccato melodies (with built-in rests) that are tied to a distinct third melody.
Fragment II stammers and stutters its way through various shorter note values that are almost identical to boot (for instance they include isolated triplet notes that come immediately before or after notes of another equally short duration). Great demands are thus made on the pianist’s scrupulous attention to the details of this fine-grained universe of rhythms!
Of the four pieces, Fragment III offers the most directly accessible demonstration of this composition technique – as mentioned above, its opening measure fractally projects itself six times as slowly, and an octave lower, in the left hand through the rest of the movement.
Fragment IV is a kind of shadow that reproduces – in a vague, “dreaming” manner – all the melodic notes from Fragment III, but now even as “vertical” impressions (chords).
Fragment III and Fragment IV (1961) are thus the first pieces based on the so-called
infinity series, but personally I perceive Fragment I (1959) and Fragment II (1960) as the most forward-pointing of the set, with their transparent “unison polyphony” and ambiguous rhythms.
The only audible connection between the four fragment movements is probably that they all represent a whole new approach to my mode of composing in comparison with my works from before 1959.”
Per Nørgård 2009