FIRE FRAGMENTER (FRAGMENT I-IV) (1959-61)

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For klaver.

Fire Fragmenter (I-IV) er del af en ”Fragment”-værkrække (Fragment I-VII, jf. nr. 70, 73, 74)

Tilegnet Margot Pinter.

Varighed: 5´

Værknummer: 67


VÆRKNOTE: FRAGMENT I-IV(1959-1961). For klaver.

De fire stykker rummer de første klanglige resultater af min fordybelse i den – i 1959 fundne – fraktale “uendelighedsrække” (fraktal angiver en egenskab ved fx visuelle mønstrede former, der kan optræde i en uendelig ´mikroskopering´, hvor figurer for tilskueren genkommer på stadig mere forstørrede udsnit af den oprindelige fraktale form). Således kan såvel nodelæser som tilhører i fx ”Fragment III” følge førstetaktens seks toner genkomme i meget langsommere skikkelse en oktav dybere i venstrehånden (der kun “når” at spille disse seks toner i løbet af hele satsen), analogt med fordybelsen i den omtalte visuelle fraktalform. Hvert Fragment har sin egen fremtrædelsesform: Fragment I består af to staccato-melodier (med indbyggede pauser), der forbindes til en helt tredje melodi. Fragment II hakker og stammer sig igennem (fire) forskellige, kortere tonevarigheder, der dog er næsten ens (og bl.a. omfatter enkeltstående triol-toner umiddelbart før eller efter toner af andre, ligeledes korte, varigheder). Store krav stilles herved til pianistens minutiøseopmærksomhed for denne fintkornede rytmeverdens detaljer!Af de fire stykker udviser Fragment III mest umiddelbart tilgængeligt kompositionsteknikken med den omtalte indledningstakt der fraktalt projicerer sig seks gange så langsomt, og oktaven dybere, i venstrehånden gennem resten af satsen. Fragment IV er en slags skygge, der reproducerer – om end vagt og “drømmende” – samtlige meloditonerne fra Fragment III, men nu også som “lodrette” aftryk (akkorder).Fragment III og Fragment IV (1961) er således de første stykker baseret på den såkaldte uendelighedsrække, men personligt opfatter jeg Fragment I (1959) og Fragment II (1960) som mest fremadpegende, i deres transparente “énstemmige polyfoni” og flertydige rytmik.Den eneste hørbare forbindelse mellem de fire fragment-satser er nok at de alle repræsenterer helt nye tilgange til min måde at komponere på sammenholdt med mine værker før 1959.””Fragment I-IV” uropførtes af mig på en koncert d.12. februar 1962, hvor også ”Fragment V” for violin og klaver (Mogens Brendstrup og Per Nørgård) og ”Fragment VI” for seks orkestergrupper (Århus Byorkester, dir. Per Dreier) opførtes.Per Nørgård (2009)

PROGRAMME NOTE: FRAGMENT I-IV for piano solo (1959-61)

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 like a fractal 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)