Klavierstücke (Stockhausen)
[14] The notation Stockhausen used for Klavierstück I attracted much criticism when the piece first appeared, notably from Boulez,[15] and prompted several suggestions for how the player might deal with the complex, nested irrational rhythms.
[16][17] Leonard Stein's suggestion that the outermost layer of proportion numbers could be replaced by changing metronome values, calculated from the fastest speed possible for the smallest note-values, was later incorporated into the published score as a footnote, but has been dismissed by one writer as "superfluous" and "a mistake", holding that "the piece is playable in its own terms" by any pianist who can play Chopin, Liszt, or Beethoven.
[21] These groups are further organized using a set of characteristic shapes or "sound forms",[22] also called "modes",[23][24] which Stockhausen acknowledged to have come from Messiaen's concept of "neumes".
[26] Klavierstück III, the smallest of the cycle and the shortest of all Stockhausen's compositions,[27] has been compared by Rudolph Stephan to a German lied: the (unspecified) tone-row is used in such a way that some notes appear only twice, others three times, four, etc.
[28] Other writers have held that such appeals to traditional formal procedures are inappropriate,[29] and find Stephan's analysis "helpless in the face of the true significance of the work".
[18] This same set, treated as unordered, has been taken as a starting point for a lengthy analysis by David Lewin,[36] while Christoph von Blumröder has published one nearly as long favouring Maconie's view.
[44] One writer believes the pitch structure is built from the opening trichord of the piece, D♭, C, F.[45] Two others on the contrary describe it as a succession of chromatic aggregates, organized primarily by registral position.
Stockhausen drastically revised and expanded this early version, bringing the grace-note groups into less extreme registers, then using the result as a background for an entirely new set of superimposed figurations based on series quite unrelated to the original material.
[69] The process of composition already had entailed a number of revisions, and Stockhausen finally abandoned this version, evidently in part because of the drastic reduction in rhythmic subtlety, but also because of persistent difficulties in avoiding strong tonal implications caused by the chosen serial conception of the pitch structure.
The resulting Webern-cum-Messiaen harmony possesses a hothouse beauty recalling the heady, decadent world of Wagner's Tristan and Duparc's L'extase, but was stylistically so out of place with the other Klavierstücke that it is easy to understand why Stockhausen abandoned it.
The most striking feature of Klavierstück VII is the establishment of resonances by silently depressed keys, which are then set into vibration by accented single notes.
[75][10] Klavierstück IX presents two strongly contrasted ideas, an incessantly repeated four-note chord at a moderately fast speed in periodic rhythms, and a slowly rising chromatic scale with each note of a different duration.
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.
The mobile structure and graphic layout of the piece resembles that of Morton Feldman's Intermission 6 for 1 or 2 pianos of 1953, in which 15 fragments are distributed on a single page of music with the instruction: "Composition begins with any sound and proceeds to any other".
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.
Since Boehmer's labels have been used by a number of later writers,[104][105][106] 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[107] Klavierstück XI is dedicated to David Tudor, who gave the world premiere of Klavierstück XI on 22 April 1957 in New York, in two very different versions.
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".
Klavierstück XIII (1981) was originally composed as a piano piece and, with the addition of a bass singer, became scene 1 ("Luzifers Traum") of Samstag aus Licht.
[122][123] 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.
[124] 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.
[129]Just twenty bars long and lasting only about 6 minutes in performance, Klavierstück XIV is a much shorter piece than its two immediate predecessors, consisting essentially of a single, simple statement of the Licht superformula.
[114][131]) Second, while the Michael formula is essentially unaltered, both the Eve and Lucifer layers are made to seem to be inverted, by a process that Stockhausen called Schein-Spiegelung, or "apparent inversion".
In this piano piece that first, many-times repeated note becomes the F♯, which is followed by a downward leap with a crescendo to the low G, An adaptation of the scale-like figure then fills in the descending seventh.
According to the preface to the score, the composer's offer to rehearse individually with the pianists was rejected, so he did not hear the result but was told afterward that "they were completely lost and could not imagine how the piece should be played".
An early sketch shows the idea of forming this Klavierstück out of Mittwoch's second scene, Orchester-Finalisten, but the composer ultimately changed his mind and instead returned to the music of Freitag aus Licht for his material.
The comet is a traditional sign of impending disaster which, combined with the tolling bells of doom and recollection of the opera's scene of a terrible battle of children, express a pessimistic view of the world.
The score is dedicated to Antonio Pérez Abellán, who gave the world premiere on 31 July 2000 in a concert during the Stockhausen Courses at the Sülztalhalle in Kürten, Germany.
Klavierstück XVIII, subtitled "Mittwoch-Formel" (2004) is, like the preceding piece, for "electronic piano" (in this case specifically defined as "synthesizer"), but has no tape part.
[141] Similar to Klavierstück XIV, this is a simple presentation of the formula, though in this case the four-layered version Stockhausen developed for the composition of Mittwoch aus Licht, consisting of the complete superformula superimposed on a statement of just the Wednesday segment (which, as it happens, only has notes in the Eve layer).
[142] Like the preceding and following pieces, Klavierstück XVIII also exists in a version for percussion—in this case, a percussion trio titled Mittwoch Formel für drei Schlagzeuger.
