Soft grace note satellites, low and high sustained pitches, ending w grace notes, flurried chord groups w wide intervals, long rest followed by brief points. Scaled dynamics in bass chord sequence Insert 2, 2: As the "principle tempo" speeds up M. This passage from the score is a fairly good example of the phenomenon Stockhausen describes in the letter to Tudor. Opening overture with groups of pitch systems. Dense satellite cloud followed by "time field" fermata waiting for high A decay end. Continuation after long "time field" rest. Isolated short groups, becoming continuous but with changing dynamic envelope.
Continuation after "time field" rest, slightly more restricted dynamics. Continuation after long "time field" rest, then another rest. Brief pedal tone figure, then mixture using wide pitch registers. Scalar satellite shapes, disintegrating into groups score excerpt below.
C placed in 4 registers.
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Join Our Free Trial Now! Although note is counterbalanced by a group of grace notes preceding its next entry, and by other tones, the opening few bars "tend to group around this unassailable centre" Grant , This is achieved by silently depressed keys and by use of the middle pedal, in order to release the dampers so that certain notes may be set into sympathetic vibration by striking other notes.
Klavierstück IX, for piano
In this way many different timbres can be created for the same pitch. The repetitions of these central notes makes them particularly obvious Stockhausen , It consists of two tempo groups tempo no. These ideas are alternated and juxtaposed, and finally resolved in the appearance of a new texture of irregularly spaced fast periodic groups in the upper register Smalley , 31— Stockhausen deliberately exploits the impossibility of playing all four tones of the repeated chords at exactly the same time and intensity another example of "variable form" , so that the tones constantly and involuntarily shift in prominence.
The idea of this repeated-chord variability was inspired by an improvisation Mary Bauermeister made on the piano in Doris's and Karlheinz's apartment in Cologne-Braunsfeld when, probably with non-European music in mind, she repeated a single chord on the piano, varying finger-pressure slightly on the individual chord tones from one repetition to the next to produce a kind of micro-melody Bauermeister , The rhythmic proportions throughout this piece are governed by the Fibonacci series Kramer , —25 , used both directly 1, 2, 3, 5, 8, 13, 21, etc.
Frisius , The performance of them requires the performer to wear gloves with the fingers cut away Godwin , Over the course of the piece, there is a process of mediation between disorder and order. From a uniform initial state of great disorder, there emerges an increasing number of ever more concentrated figures. By the end, the figures become unified into a higher supraordinate Gestalt Stockhausen , Stockhausen abandoned the original plan for this piece, which prescribed three large sections, and replaced it with a new plan based on scales of seven elements.
A basic series beginning with the strongest contrasts and progressing toward the central value was chosen: The overall form is produced from this series in a complex way, resulting in a seven-phase form, to which Stockhausen added an eighth, preliminary section which compresses the seven main phases into a single one Henck b , There are at least thirteen separate dimensions organised into seven-degree scales Henck b , 17— Pitches are the only thing not organised in sevens.
However, the score was not finished in time for Tudor to learn it, and subsequently his international touring did not leave him in a position to do so. Consequently, the piece was finally premiered by Frederic Rzewski on 10 October , during the third Settimano Internazionale Nuova Musica in Palermo.
On 22 December Rzewski made the first recording for commercial release, in the Ariola sound studios in Berlin Henck b , 5—6. The mobile structure and graphic layout of the piece resembles that of Morton Feldman 's Intermission 6 for 1 or 2 pianos of , in which 15 fragments are distributed on a single page of music with the instruction: In the same year, Earle Brown had composed Twenty-five Pages for 1—25 pianists, in which the pages are to be arranged in a sequence chosen by the performer s , and each page may be performed either side up and events within each two-line system may be read as either treble or bass clef Anon.
When David Tudor, who at the time was preparing a version of Feldman's piece, was in Cologne in , Stockhausen asked him,. Tudor and Schonfield , Apart from the layout on the page, Feldman's piece has nothing in common with Stockhausen's composition. Rather than rhythmic cells, its components are single tones and chords, with no rhythmic or dynamic indications Frisius , The performer may begin with any fragment, and continue to any other, proceeding through the labyrinth until a fragment has been reached for the third time, when the performance ends.
Markings for tempo, dynamics, etc. Though composed with a complex serial plan, the pitches have nothing to do with twelve-tone technique but instead are derived from the proportions of the previously composed rhythms Truelove , —25; Truelove , The durations are founded on a set of matrices all of which have six rows, but with numbers of columns varying from two to seven. These matrices "amount to sets of two-dimensional 'scales'" Truelove , The first row of each of these rhythm matrices consists of a sequence of simple arithmetic duration values: These "two-dimensional scales" are then permuted systematically Truelove , , — , and the six resulting, increasingly larger matrices were combined together to form the columns of a new, complex Final Rhythm Matrix of six columns and six rows Truelove , , — Stockhausen's design appears to have been to select an equal number of fragments from each row degree of complexity of subdivision and each column overall duration of the fragment , except for the first column shortest duration and last row most complex subdivision.
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This is suggested by the fact that he originally selected column 6, row 3 for the last fragment marked with an x in the illustration , then changed his mind in favor of the lower-right cell Truelove , When writing out the fragments, Stockhausen doubled the note values from the ones in the matrix Truelove , , so that, in the score, fragments 1—4, 5—7, 8—10, 11—13, 14—16, and 17—19 have overall durations of 3, 6, 10, 15, 21, and 28 quarter notes, respectively.
Within each of these groups there is a "main text" of melody or chords. Interspersed into these are groups of grace-note chords and clusters, as well as tremolos, trills, and harmonics, and these two levels are constructed independently Toop , One of the earliest analysts of this piece, Konrad Boehmer , 71—84 , observed the distinct sets of group durations but, apparently not having seen the sketches, established a different taxonomy and made a mistake counting the duration of one group. Since Boehmer's labels have been used by a number of later writers Hellfer ; Rigoni ; Trajano , the correspondence with the numeration from the sketches may be useful:.
The nineteen fragments are then distributed over the single, large page of the score in such a way as to minimize any possible influence on spontaneity of choice and promote statistical equality Boehmer , Tudor wrote to apologise, and Steinecke accepted that he would have to settle for the European premiere, but then Tudor planned to play the piece in Paris two weeks before Darmstadt.
Stockhausen: Sounds in Space: KLAVIERSTÜCK XI
However, Tudor fell seriously ill early in July and had to cancel his European tour, and so the European premiere took place on 28 July , the last day of the courses, in the Orangerie at Darmstadt, in two different versions played by the pianist Paul Jacobs and billed in the programme book as the world premiere Misch and Bandur , , , — However, this set never got beyond the planning stages Toop , The pieces from XII to XIX are all associated with the opera cycle Licht — , and appear not to continue the original organizational plan.
All of the material of the Licht cycle is made from three melodic strands, each called a " formula " by Stockhausen, and each identified with one of the three archetypal protagonists of Licht: Michael, Eve, and Lucifer.
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". 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.
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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 ,