In addition to a basic melody the "nuclear" version of the formula , each line is also interrupted at intervals by inserted ornamental figurations, including soft noises called "coloured silences".
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These strands are superimposed to form a contrapuntal web which Stockhausen calls the " superformula " Kohl , — The superformula is used at all levels of the composition, from the background structure of the entire cycle down to the details of individual scenes Kohl , The first three of these pieces are drawn from scenes in which the piano is dominant in the opera Frisius This scene is formed according to the second note of Michael's "Thursday" segment of the Licht superformula, an E divided into three parts: The three superimposed polyphonic melodies "formulas" of the superformula are registrally rotated in these three statements, so that the Eve formula is highest for the first section, the Lucifer formula is highest for the second, and the Michael formula is uppermost for the third.
This corresponds to the dramaturgy, as Michael recounts to the examining Jury his life on earth from the successive points of view of his mother, representing Eve, his father, representing Lucifer, and himself Kohl , The upper line in each case is also the most richly ornamented of the three. Each melody begins with a different characteristic interval followed by a semitone in the opposite direction, and this three-note figure continues to predominate in each section: In the opera, Michael is portrayed in the first examination by the tenor singer, in the second by the trumpet with additional accompaniment of basset-horn , and in the third by a dancer.
He is accompanied throughout the scene by a pianist.
The surface is created primarily from the "ornaments" and "improvisations" of the superformula Kohl , In the version for piano solo, the tenor, trumpet, and basset-horn material is either incorporated into the piano texture, or is hummed, whistled, or spoken by the pianist, adding to the polyphonic layers played on the keyboard. The vocal noises, as well as sweeping glissandi and individual plucked notes made directly on the piano strings, come directly from the superformula and constitute what Stockhausen calls "coloured silences"—that is, rests that are "enlivened" by brief accented notes or gliding noises.
Because of the proportioning series of the three sections, the middle one is the shortest and most animated, while the last is the slowest and longest of the three Frisius The work was written for the composer's daughter Majella, and the solo piano version was premiered by her on 10 June in the Teatro Regio in Turin Stockhausen a , The key components of this piece are sounded at the very start: These five contrapuntal layers are developed from the three-layer Licht superformula in three steps.
First, the three layers of the sixth, "Saturday" segment bars 14—16 are extracted for the background structure of the opera Samstag aus Licht. Second, a fourth layer, consisting of complete statement of the "nuclear" form of the Lucifer formula—the eleven pitches of the Lucifer formula, with the basic durations but without rhythmic subdivisions or the seven Akzidenzen inserted between the main segments "scale", "improvisation", "echo", "coloured silences", etc.
Third, for the opening portion, corresponding to just the first scene of the opera, a fifth layer is added.
The rhythms of the five layers divide the total duration of the piece The density of rhythmic activity in these formulas is progressively increased by dividing the notes in each of the five sections by the first five members of the Fibonacci series: Finally, a process of "extreme compressions which begin to destroy the form to the point of its no longer being perceptible so as to bring about silence and motionless sound" is imposed over the course of the work. This is accomplished through a serial permutation scheme of compressions Stauchungen , stretchings Dehnungen , and rests, designed to achieve maximal dispersion of the erosions so as to avoid progressive modification of the same elements each time around Kohl , —17; Rigoni , 56— This gradual process, supported by the steady rise in pitch from one section to the next of the Lucifer formula, is paralleled by the descent from the upper register of the Eve formula, characterised by intervals of thirds.
A third melody the Michael formula remains in the highest register throughout, and is exempted from the distorting process. Shortly before the end of the piece, the Lucifer and Eve formulas converge.
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At this point, the Eve melody asserts itself and, the formal process now completed, the music fades away and the piano lid is lowered Frisius ; Kohl , The piece is dedicated to her, on the occasion of her twentieth birthday. With the addition in of a part for girls' choir, it became act 2, scene 2 of Montag aus Licht Stockhausen a , , Two months before composing this first component part of Montag aus Licht , Stockhausen said:.
I have had the feeling for some time that Monday will be very different—very new for me too, because I have the feeling Monday is the reverse, because it's the birth. So it's the reverse of everything that I have done up to now. Most probably all the formulas will be upside-down, will be mirrored: I think all the structural material all of a sudden is going to change drastically in the detail.
Stockhausen and Kohl , Stockhausen made two major changes to the superformula when adapting it for the piano here. First, the Eve formula the middle line of the original superformula is transposed into the upper register, exchanging with the Michael formula which is lowered to the middle, while the Lucifer formula remains in its original position in the bass.
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