KLAVIERSTÜCKE V - X

Nr. 4: KLAVIERSTÜCKE V–X
(PIANO PIECES 5-10)
Stockhausen at the Mozarteum in Salzburg, 1988.
www.karlheinzstockhausen.org)
1954, 1955 (IX & X rev.1961)
[total time for all 6: ~73']

Introduction
     This set of piano works, like the first  (KLAVIERSTÜCKE I-IV), organizes durations and pitches (rhythms and melodies) in a very different way than the piano pieces of Bartok and Debussy (not to mention Chopin and Schubert!).  Building on the chromatic, mathematically-ordered musical explorations of Schoenberg and Webern (as well as his own first set of KLAVIERSTÜCKE), Stockhausen uses serial distribution methods to create unpredictable and irregular rhythms and melodic shapes which have less to do with development of melodic themes and harmonic progressions, and more to do with the movements and patterns found in nature (stars, ocean waves, wind, volcanic eruptions, etc...).  The exploration of "point music" (isolated and scattered pitches in space) and "groups of points" continues from his first set of piano pieces, but added to these were new playing techniques, compositional pitch-grouping concepts and notational innovations.  As a group of piano pieces, all 6 of these works also use different compositional devices and playing techniques to summon a new spectrum of resonating colors out of the modern piano.  Click the below links to skip the introduction and jump to a specific KLAVIERSTÜCK:
Variable Form
     Though the completion of these 6 piano pieces span a time span of almost 7 years, they all use the "indeterminate" idea of allowing a performer's style and natural playing ability to define certain rhythmic shapes and speeds.  This was Stockhausen's first steps towards "aleatory" scoring, that is, writing with some musical elements "free" (rhythm and note sequence, usually).  Apparently, after having used a ruler to measure out exact (and obviously, determinate) time lengths on magnetic tape for STUDIE II, Stockhausen now took a different, contrasting path (this pattern of constantly switching approaches would continue for the rest of his life) and used the "human timing" of a performer's playing technique to measure out rhythmic durations. 

     Stockhausen dubbed this kind of performer-based composition as "variable form", and in KLAVIERSTÜCK V, the grace notes (actually strings of grace notes) were to be played "as fast as possible, but articulated clearly (slower in lower registers than in the upper) and not quasi-arpeggiated...."  Jonathan Harvey states (somewhat wryly, in "The Music of Stockhausen") that in KLAVIERSTÜCK V, "the grace notes, which exist independently of the tempo, have their own scale of speeds, depending on how awkward they are to play clearly."  These works are not quite "aleatory" however, since the durations are still based on the "fastest" speed a performer can play.  In later works (starting from 1959 in ZYKLUS), notes would be indicated and then a player could choose and place these notes in any order (and at any point) during a specified time span, making them truly free and aleatory. 
Clusters chords and Cluster glissandi in KLAVIERSTÜCK X (inverted colors)

New Piano Techniques
     Another new development in Stockhausen's piano vocabulary was the expansion of tone and chord colorations with various unconventional (or at least seldom-used) piano techniques:
  • A key is depressed silently, so that the undampened strings act as "resonator strings" when the next note or chord is struck.  This results in what is sometimes referred to as "halo notes" "While pressing down keys silently, higher notes can be struck so that the silently pressed keys' strings, which are longer, vibrate sympathetically and allow the struck notes to resound afterward, as resonance tones." - Stockhausen in 1992 (lecture)
  • A staccato attack is followed immediately by either silently re-depressing the key or depressing the damper pedal (the note continues softly in different colorations).
  • Gradually release a depressed key (the note becomes more and more soft and bright). 
  • Hand and forearm chord clusters and cluster glissandi (KLAVIERSTÜCK X)
  • Pedalling: Depress the right pedal partly down (half-pedal) to create a soft continuation of the initial attack.
     With combinations of these effects, Stockhausen could explore new vistas of piano timbre, enabling a kind of "bandwidth filtering" of the harmonic overtones of a sustained/arpeggiated chord.  Additionally, a chord's "spectral layers" could be organized, in that a chord's harmonic color could be built up through anticipatory grace notes (indeterminately-paced "satellite tones"), and then "taken apart" by the individual fade out of each note of a chord (and it's overtones).

     An interesting result here is that these playing techniques are indicated in the score, but the resulting coloration is very much dependent on the player's degree of touch and pedalling, as well as the piano and room itself (this is actually another layer of indeterminacy). This is true in classical piano style too, of course, but dramatically more so in these works.  These effects are admittedly subtle on first listen, but after repeated close listening (ideally live, or on good headphones) the colorations of each "group" become more and more apparent.

Overview
     There are 6 piano pieces in this set, and they each could be characterized (in as simple a manner as possible) this way:
  • KLAVIERSTÜCK V: Relatively short piece featuring central notes with surrounding grace note clusters ("satellite tones").
  • KLAVIERSTÜCK VI: Expanded exploration of satellite tones (as well as points and groups), in both mixed combinations and shorter, more focused sections. The relative tempo is notated with a sloping horizontal line.
  • KLAVIERSTÜCK VII: Exploration of resonating strings from silently-pressed notes (halo notes)
  • KLAVIERSTÜCK VIII: Polyphonic layers in dialogue with fast grace chords (satellite chords)
  • KLAVIERSTÜCK IX: Tremolo chords vs. scalar melodies, birthing a new irregular entity
  • KLAVIERSTÜCK X: Groups of chord and glissandi clusters, each followed by "echo groups"
     The sections below describe these KLAVIERSTÜCKE in more detail, sometimes using the CD timings from performances by Aloys Kontarsky and Ellen Corver (which were both recorded under the personal supervision of Karlheinz Stockhausen).  All of the score excerpts are copyright Universal Edition and www.karlheinzstockhausen.org.
Aloys Kontarsky
(actually from the cover of the MANTRA LP)

GGGGG
Ellen Corver's CD recording of KLAVIERSTÜCKE I - XIV
(Stockhausen Complete Edition CD 56)

KLAVIERSTÜCK V
     In this piece, melodies and chords are ornamented in different ways in order to provide a surrounding coloration.  The "normal" notes (scored with normal-sized note-heads) are referred to as "central tones", and the surrounding "satellite tones" (notated with small note-heads connected to a crossed tie-line) are placed before, after and surrounding the central tones.  These "solar systems" of harmony can be considered as individual groups.  With the use of pedalling, the harmonic coloration of a group can be manipulated further (beyond the note-based coloration of the grace note satellites).  This idea of central tones and satellite tones would, in the future, become very important as one of the "accessory effects" in formula-based compositions such as MANTRA and in the LICHT opera cycle.

     Structurally, Piano Piece 5 is in 6 sections, each with its own basic tempo but with many ritards and accelerandos (the initial section starts at tempo 80, moves up to 113 in the middle, most active section, and then drops down to 63.5 as the piece fades out, with a few coda-like groups).  The grace notes themselves start out as mostly loud in the first tempo section, then soft in the second tempo, and then a mixture from then on (but organized in different ways).  There are also 2 places where a sequence of chords and notes are played with a constantly changing dynamic - kind of like a "loudness row" (I like to think of these as Stockhausen "inserts" - a frequent technique of his, where he breaks from the "main idea" and goes on a "diversion" of sorts, to concentrate on an interesting secondary sound or idea).  Various chord groups (and sustained points) are spread throughout, and a "fully notated" note cloud (ie - not grace notes, but very fast) occurs in the middle section as well.
A single G# (in red) is trailed by 5 satellite tones.
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A single C# (in red) is surrounded by 4 satellite tones.  This is followed by Insert 1: a sequence of different intensity attacks ("loudness row").

     One approach to listening to this work is to mentally separate the grace notes from the central notes to hear the layers of coloration.  The central melody created from the central tones  is relatively slow and simple (and often sustained with pedal), and could almost be played with one hand, while the clouds of grace notes are scattered before, after and around the central notes.  In other words, the piece can be considered as 2 layers - the mostly-slow, rhythmically-irregular layer of central tones, and spurts of fast, evenly-played grace notes clinging to the central tones (the slow layer follows the scored  tempos, but the grace notes are always "as fast as possible", which results in fast, even rhythms).

     One could also consider these groups as "exploded chords".  Since there is lots of sustained pedalling, complex vertical harmony is additively-created by melodically adding one note at a time.  On the other end of the central note attacks (explosions), different kinds of timbres can be heard as the individual notes of a sustained harmony each fade out (low notes on a piano ring longer than high notes in a held chord, but Stockhausen also uses keying and pedaling to create other kinds of "fade outs").  As with the first set of Piano Pieces (1-4), the rests and silences in between the notes are just as important as the sounding notes.

     In the table below, the timings are from the Aloys Kontarsky performance.  The 6 sections are not really "audible", since the rhythms are irregular and the tempos fluctuate within each section, but they are a good way to "symbolically" divide the work at least.
Section Initial
Tempo (♪)
Nr. of
Groups
CD
Time
Structure
(per Jonathan Harvey's analysis)
Features
1 80 7 0:00 "Exposition" Loud grace note satellites tones, sustained melodies, a soft held chord, a rest, ending with scaled dynamics in a middle/low register chord sequence (Insert 1, 0:26)
2 90 14 0:50 "Development" 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
3 71 4 2:07 "Climax 1" (most varied character group types linked by common pitches, climax of repetition of pitches) Scaled dynamics in bass chord sequence (Insert 2, 2:18), followed by a fully-notated cloud of tones (47 non-grace notes)
4 113 3 2:37 "Climax 2" (fastest, densest, shortest section) held chord, rest, fast high points (pedal sustain, not grace notes)
5 101 14 2:55 "Climax 3" (least repeated chromatic notes - "climax of pitch information") chords w single grace notes (similar to the inserts), becoming sparser, lower
6 63.5 14 4:00 "Coda" grace note clouds, becoming sparser, and softer


KLAVIERSTÜCK VI
     One of the longest of the six pieces (the other being Piano Piece 10), its premiere (as an early 1955 version of this piece) was rudely interrupted and eventually derailed by a loud cricket and a rowdy audience, despite Pierre Boulez and Luigi Nono's attempts to rectify the situation.  It was finally performed without interruption by David Tudor in 1959 at the same venue (Darmstadt Summer Vacation Courses Concerts).  Revised up until 1961, this piece has the notational novelty of using a sloping horizontal line on a 13-line graph staff to indicate relative tempo (high is fast, low is slow, no line is pause).  If the top tempo (fastest possible speed for a performer's ability) is 180, then the graph indicates 12 successively slower tempos down to 45.  The tempo is further limited (beyond a player's dexterity) by the ability of the notes to be clearly articulated (I have to note that this unconventional tempo notation makes it quite a challenge to follow with the score!).

     In a letter to David Tudor, Stockhausen points out that the tempo indicated by the graphic line is often "disturbed" 5 to 6 times by super-imposed accelerandi and ritardandi in the music notation (see Stockhausen's example below). 

As the "principle tempo" speeds up (M.60 to 110), 6 instances of "relative tempo curves" occur, which add or subtract from the rising principle tempo.
www.karlheinzstockhausen.org)
This passage from the score is a fairly good example of the phenomenon Stockhausen describes in the letter to Tudor.
The tempo gradually rises, but is disturbed by small "kinks" of increasing/decreasing tempi figures.
Oftentimes these brief accelerandi/ritardandi follow a scalar melodic figure.
     Additionally, the use of held notes whose decay (or resonant echo) is manipulated by various pedaling techniques is explored.  The note(s) are sometimes allowed to ring out into space until they fade away, allowing the "inner life" of these sounds to be highlighted.  Stockhausen calls these moments "time fields".

     KLAVIERSTÜCK VI's first, long section continues the previous Piano Piece's exploration of serially organized points, groups, grace note/chord satellites, sequences of dynamic values, and pedaling techniques. This is followed (from around page 25, 12:58 in the Kontarsky recording) by sections of more concentrated "character pieces" separated by the "time fields".  Jonathan Harvey identifies these character identities as:
  • chords
  • fixed pitch pedals
  • silences, single notes and certain intervals
  • a single pedal (middle D#)
  • chromatic grace notes up or down
  • tempo expressed by wavy line becomes more purposeful (oscillating)
  • etc...
     From a tempo standpoint, the work is organized as 8 cycles.  In each cycle there are 6 sub-sections, each with 1 of 6 "central tempi" (each of the 8 cycles have a different permutation of tempo sub-sections).  Within each tempo sub-section, the central tempo is either maintained, gradually increased or gradually reduced, and these tempo movements are additionally "disturbed" (as described above in the letter to Tudor) in various different ways.  However, it's probably quite difficult for any but the most technically-minded to detect these tempo groups.  It may be more enjoyable to simply appreciate KLAVIERSTÜCK VI as a "fantasia-like" approach to exploring all of the previous ideas highlighted and developed in the previous KLAVIERSTÜCKE.  Since the flow could be characterized as "bursts of groups" separated by "time field" rests or held tones, it may be appropriate to appreciate each cluster of activity as a unique, many-faceted snowflake in a (lengthy) snowstorm.  Nonetheless, below is a rough table of some of the more easily-heard cadences (timings from the Aloys Kontarsky recording):
CD
Time
Some Highlights? Score
Page
0:00 Opening overture with groups of pitch systems.  
(At 4:14, a loud, low E (with delayed pedal) sustains to its final "time field" decay, colored by preceding satellite tones, and with traffic noise bleeding in, pg. 9)
1
6:25  Dense satellite cloud followed by "time field" fermata (waiting for high A decay end) 12
7:22 Continuation after long "time field" rest 14
8:16 Polyphonic 16
8:47 Isolated short groups, becoming continuous but with changing dynamic envelope 17
11:28 Continuation after "time field" rest, slightly more restricted dynamics 22
12:36 Quieter, some pedal-like pitch centers 24
12:58 Quiet, dense 25.2
13:49  Slow, resonant 26
14:50 Legato groups 27
15:08 Scalar satellite shapes, rolled chords 27.2
17:47 Continuation after long "time field" rest, then another rest 33.2
18:01 Brief pedal tone figure, then mixture using wide pitch registers 34
19:16 Scalar satellite shapes, disintegrating into groups (score excerpt below) 36.2
20:52 Isolated chords 39
22:37 Arpeggiated satellite tones and isolated points 40.2
23:34 Low chords figure, then "oscillating/jagged" tempo 42.2
24:14 Slow points, stable tempo 44

The central tones (in green) are connected by rising and falling satellite tones.
Because each satellite scale figure is played in a crescendo, it sounds like grace notes "ramping up" to the central tones.
The graph at top is the relative tempo (which, in this exceptional case, also relates to the satellite tones as they accelerate/decelerate with the rising/falling scales).
(Thanks to Benjamin Kobler for some insights into the tempo structure of this piece).

KLAVIERSTÜCK VII
     The most important idea behind Piano Piece 7 is the use of sympathetically-resonating piano strings left "open" by silently depressing keys (notated with diamond note-heads) and then playing loud attacks on other keys.  This technique (sometimes referred to as "halo notes") is built in to the sound of an Indian sitar, which has 12 (fixed) sympathetically-vibrating strings, each tuned differently.  This piece looks at sympathetic piano vibrations created from silently depressing halo notes in front of both clouds of staccato accents as well as held accent notes.  KLAVIERSTÜCK VII also continues the use of grace note satellite tones around a central tone in a few places as previously explored in KLAVIERSTÜCK VI (that work actually had one brief halo chord as well). 

     "You will hear at the beginning a C#. It comes back several times. This C# is coloured each time with a different resonance...You will hear in KLAVIERSTÜCK VII not only the first C# with various tone colours, but in the course of time a series of pitches. Each pitch is composed more or less frequently with quite unpredictable durations and intervals of entry, each time with a different colouring. You will notice this at once with the second or third attack of such a note: the point is the coloration. " 
 - Stockhausen in 1992 (lecture)

     Jonathan Harvey describes the work as being in 5 sections, each with a C# central tone but in different registers, and sometimes joined by a 2nd note (actually the C# pedal is only really prominent in the 1st section as far as I can tell).  Each section approaches the idea of exciting un-hammered strings differently.  Some sections are separated by long tones or rests, but all are generally interspersed with chord clusters among the central-tone "resonance fields".  The timings below are from the Aloys Kontarsky recording.
Section 1 0:00

(♪=40)
Central tone = Middle C#
Section 2 1:45

(♪=63.5) 
(C# omitted)
Section 3 1:57

(♪=57) 
C# placed in 4 registers
Section 4 2:07

(♪=71)
A# 3 octaves lower (from 2:23),
then A with satellites (3:18)
Section 5 4:06

(♪=50.5)
Low A#, high C, middle B, low Bb, C#/D# high, etc...  ending in a slow, wide oscillating exchange and a final satellite group.

     In a way, one could think of this piece as a meditation on several 1-note themes, with each strike of the central "pedal note" having an effect like a rock being dropped into a pond.  The resonating halo notes and satellite tones are somewhat like ripples on the surface.
A repeated C# (in red) is treated to different resonating effects from satellite tones and
silently-depressed halo notes (small diamond-shaped noteheads).
Yellow diamonds are C# halo notes, orange diamonds are other halo notes  (colors are added by me).



KLAVIERSTÜCK VIII
     This piece, the shortest of the set, has 2 main ideas which engage in a kind of dialogue (but is otherwise organized serially).  The first idea is polyphony, in which short melodic groups overlap.  These contrapuntal groups are separated ("punctuated") by the second idea: short chord fragments played as rapid satellite tone attacks.  Since these chord flurries are always to be played as fast as possible, it creates a marked tempo contrast with the polyphonic statements (which are somewhat more leisurely).  This is a short, concise, beautiful gem of a piece.
Grace chord flurries (satellite chords, circled in yellow) punctuate contrapuntal segments.



KLAVIERSTÜCK IX
      The next two piano pieces were completed several years after the first four, and though they have much in common with the first few, they also more directly point towards the future in some ways, particularly in their use of more "free" or "irrational" elements in their performance.  Like Piano Piece 8, Piano Piece 9 focuses on two main ideas (each with their own tempo) and creates an alternating dialogue between them.  However in this case, the dialogue becomes a fusion, and the piece ends up "birthing" an entirely new texture.

     The first idea is a 4-note chord in an even rhythm, somewhat like a slow tremolo.  In the first section, the chord is played 139 times in a gradual (but rhythmically even) decrescendo, and then immediately 87 more times with the same dynamic decrescendo (both the right and left pedals are used to control resonant sustain).  Theoretically, this reduction in the number of attacks (but not dynamic range) forces the performer to make the dynamic "steps" of the decrescendo slightly larger (from 1/139 of the dynamic range to 1/87, which is about 38% larger if my math is correct).  The fascinating thing about this idea is that the "imperfections" of performing a repeated chord in this impossible way are drawn out.  In other words, each attack is inherently slightly different (due to the decrescendos) and this results in various harmonics and overtones being accented depending on individual finger pressure (however, the story goes that Stockhausen had to direct Aloys Kontarsky to play "less perfectly" in order to get the variety of harmonics he wanted).  When this tremolo chord texture is revisited throughout the piece, the even rhythm becomes layered and syncopated, and scale degrees of dynamics are used to create more resonating colorations (also with usage of pedal of course).  Additionally, the durations and pauses are partly derived from the Fibonacci series, which is a departure from the serial organization of the previous works.

     The second texture (beginning from 1:42 in Ellen Corver's recording) mostly consists of slow, irregular, transparent chords (expressed in the beginning as a slow, ascending, halting single-voice melodic line).  Jonathan Harvey further subdivides this "irregular" texture into 6 types:
  1. an ascending scale melody
  2. polyphony
  3. staccato chords with partial pedaling
  4. soft chords and isolated points
  5. high ornamental note groups
  6. bass note central tones
     The work proceeds to alternate between (and eventually blend) the evenly-struck 4-note chords and the rhythmically irregular point-like chordal figures, and after several sections of contrast and variation (notably with trills, etc...), a final section is reached (at 8:30 in the Corver recording, 7:46 in the video below), in which a high, fast crystalline texture made from grace note satellites is featured.

     I suppose in popular music terms one could call this piece the classical piano equivalent of thrash metal meeting slow jazz and giving way to bebop.  Below is a video created by Nick Redfern which displays the score as the music plays.



KLAVIERSTÜCK X
     The final piece of this set is known for its exploration of cluster chords and cluster glissandi.  After an overture-like explosion of sound figures, the piece proceeds to lay out isolated groups of eruptions and after-tremors exploring individual elements from the opening overture.  It has several fascinating aspects, described below in no particular order.

Proportionate Notation:
     Firstly (and most visually obvious from the score), the rhythmic notation has a new kind of indeterminate notation.  No tempo is indicated, in fact the performer plays the whole work "as fast as possible", but with the proportionate duration values in the notation.  Above the staff, note duration values are given for a melodic group, and the performer proportionately "fits in" the notes to that duration to the best of his/her ability.  Also, tempo changes are indicated by whether the thick horizontal tie-lines go up or down (basically a variation of the graph-line tempo notation used in Piano Piece VI).
Mauricio Pollini performing KLAVIERSTÜCK X, wearing fingerless gloves and about to land an arm cluster.
Clusters:
     The main textural elements featured here are cluster chords and cluster glissandi (for which fingerless wool gloves are recommended).  After an initial explosion of activity, the piece begins dissecting these clusters and glissandi in a "development" section characterized by shorter sections ("Echoes") separated by long pauses (during which the pianist remains completely still).  As the piece progresses, the clusters have a tendency to expand in pitch range and increase in dynamics (as per Henck, see below).
Forearm cluster chords (circled in brown) lead to hand cluster glissandi (circled in red).
The large duration values above the staffs indicate how much time is allowed to fit in all of the notes below (before the next duration mark).
The thick, jagged sloping lines below the first staff indicate the relative tempo (accel/ritard/stable/rest).

Contrast between Order and Disorder:
     After the initial explosion (5 and a half pages worth of "disorder"), concentrated and isolated figures ("order") become more frequent.  In isolated "Echoes", repetition of character elements create a sense of order by making these elements "familiar".  The chords begin as dense clusters, but gradually progress towards more transparent triadic chords (with a brief reprise of dense clusters at the end).  The idea of order vs disorder is also expressed in the level of difficulty in playing the densely cob-webbed passages within the short time durations (though Piano Piece VI actually looks harder to play to me).  This aspect of performer limitation would be much later explored by the so-called New Complexity composers (Brian Ferneyhough, etc...).

Form Structure:
     This work is (probably) more highly structured than the previous works, both on a large and small scale.  On the smaller perspective, there are at least thirteen separate dimensions organized into 7-degree scales (as per Herbert Henck's "Karlheinz Stockhausen's Klavierstück X: A Contribution toward Understanding Serial Technique: History, Theory, Analysis, Practice, Documentation", 1980):
  1. density of chords (1–7 notes)
  2. density of clusters (3, 6, 10, 15, 21, 28, or 36 notes per cluster)
  3. basic subdivisions of duration (1, 2, 4, 8, 16, 32, 64 units)
  4. proportions between actions and rests
  5. note values dividing the action durations (1 to 7 divisions)
  6. attack densities (a two-dimensional scale, or 7 × 7 matrix)
  7. degrees of order/disorder
  8. dynamics (ppp, pp, p, mf, f, ff, fff)
  9. pitch range (band-width)
  10. forms of motion
  11. sound-characteristic (chained clusters, repetitions, arpeggio, etc.)
  12. rests
  13. pedalling
     ("Pitches are the only thing not organized in sevens. Rather, they are in sixes, built from transposed permutations of the chromatic hexachord" - Henck).

     Jonathan Harvey on the other hand, contributes a list of 19 character types which I'll here group into 9 broader categories (though the clusters and glissandi are really the main thing):
  1. fast chromatic ornamentation
  2. 2-7 note chords of varying intensity, but generally louder with greater numbers of notes
  3. cluster chords and cluster glissandi played with fingers, hands, forearms
  4. rising/falling arpeggios
  5. tremolo notes/clusters
  6. 1 trill
  7. half pedal to create soft reverberation
  8. silent depression of a low forearm cluster (resonance)
  9. silent depression of keys immediately after an attack to create soft reverberation
     On a higher structural level, the piece could be considered to be organized into 4 sections ("sonata form").  The "exposition" opens with a relatively soft prelude, followed by a Cluster Group overture (or "main theme") which is almost a combined layering of the rest of the piece (almost like MANTRA's final "fast revue", but here at the beginning, instead of the end).  This is followed by "Echoes" of the main theme, and ending on a 7-note chord "cadence".  The "development" follows, and consists of several cycles of Preludes, Cluster Groups and Echo Groups.  A "recapitulation" is eventually entered with a tremolo "insert", and the work ends with a "coda" which slowly expands vertically (in pitch range).  Now, having described the "classical form" of the piece, in reality the concept of this work as being in sonata form is a bit crude in some ways (but used by Jonathan Harvey in his analysis), and most likely Stockhausen didn't write it to follow an "epic form" arc (come to think of it, Beethoven never actually wrote specifically with such a form in mind either, since sonata form is primarily a musicologist's tool, and not a compositional one).  Perhaps another way to look at Piano Piece 10 is to think of it as having a big initial explosion of clusters and glissandi, followed by a series of smaller explosions, each with their own substructure. 

     The table below (with timings based on the Ellen Corver recording) points out the general structure (divided into Preludes, Cluster Groups and single chord Echoes, and using some of the sonata structure idea).  This could be used as a listening guide, but after the first "exposition", it's probably not necessary, since the rhythm of the structure itself becomes fairly easy to feel.

Section CD
Time
Main Musical Gesture
Exposition 0:09 Glissandi Prelude
0:41 Cluster Overture
3:51 6 soft Glissandi Echoes
5:29 6 hard Cluster/Glissandi Echoes
8:36 End cluster chord
Development 9:08 Glissandi Prelude
9:56 2 Cluster Groups
10:54 3 Chord Echoes
12:07 Glissandi Prelude
12:29 3 Cluster Groups
13:05 1 Echo chord
13:23 2 Cluster Groups
14:30 2 Chord Echoes
15:11 Glissandi Prelude
15:23 2 Cluster Groups
16:29 Glissandi Prelude
16:45 3 Cluster Groups
17:48 6 Chord Echoes
Recapitulation 19:06 Cluster Group
19:28 Tremolo figures blend in (can be thought of as clusters "lying on their side")
20:41 Glissandi Prelude
20:59 6 Chord Echoes (using both clusters and glissando preface material)
22:24 2 Cluster Groups
23:00 5 Chord Echoes
23:32 Cluster Group with tremolo element
24:18 Glissandi Prelude with quintuple-chord end figure
25:11 1 Echo chord
25:23 Final Cluster Group
Coda  25:43 Descending bass and ascending high melodic figures

Below is a video created by Nick Redfern which displays the score for the first half of KLAVIERSTÜCK X as the music plays.

Sound Impressions
     Each of the descriptions of the individual pieces contain some "impressions" I have of them, but one thing which links all of them is the sense that these are all constructed with a highly refined sense of both the large and small scale of things.  The larger structural balance is partly reached by the use of serial techniques (as well as Stockhausen's own intuitive sense of balance) to organize the various focal elements of each piece.  On the smallest scale, each group, cluster or rhythmic gesture is crafted so that each one could be taken out of context and appreciated as a micro-world in itself.  I think it's pretty useful to know the general shape of the landscape as described in the above narratives, but at the same time it's quite a rich experience to digest some of these large dishes one bite at a time (sorry for the mixed metaphor :) ).

     A couple brief notes about the two recordings of the KLAVIERSTÜCKE by Aloys Kontarsky and Ellen Corver:  The Kontarsky CD (on SONY Classical) has a very entertaining booklet in which Stockhausen describes Kontarsky's cuisinary preparations for the recording date.  The recording has a darker sound, with very percussive low register "bombs" (very "macho", so to speak).  The stereo field is distributed so that the listener is facing the pianist (low notes to the right, high notes to the left).  I personally prefer listening to piano music from the player's point of view, so I switch the channels when listening to this recording.  Ellen Corver's recording uses some new recording techniques developed by Stockhausen to better capture the resonances of the piano strings.  The higher register overtones ring out much more clearly here than in the Kontarsky recording.  The booklet also includes a few pages written by Corver describing her experiences with these pieces.  This CD set also includes KLAVIERSTÜCKE XI to XIV.

Links, Sources, Videos
KLAVIERSTÜCKE I-XIV (Ellen Corver) Sound samples, tracks listings and CD ordering 
Buy the Scores 
KLAVIERSTÜCKE Wiki 
Stockhausen on the KLAVIERSTÜCKE (1955,1957)
"Clavier Music 1992", Stockhausen on Piano Music (1992)
KLAVIERSTÜCKE I-XI by Aloys Kontarsky (flac)
Compositional techniques in the music of Stockhausen (1951-1970) (Kelsall, 1975)
The Music of Stockhausen (Jonathan Harvey) Amazon link
The Works of Karlheinz Stockhausen (Maconie 1976/1990) Amazon
"Overview of Pitch and Time Organization in Stockhausen's. Klavierstück IX (Ending section)"(Mehmet Okonsar, 2010, PDF)
Flash Animation Analysis of KLAVIERSTÜCK X (Florent Boffard)
YouTube Videos:

POLE, EXPO

The Process Plan Works (aka - the "plus-minus pieces")
PROZESSION KURZWELLEN SPIRAL POLE EXPO

The German pavilion at the Osaka 1970 world's fair where Stockhausen performed 183 shows in a row.
Nr. 30 POLE (Poles) for 2 players/singers with 2 shortwave radio receivers
(Feb 1970) [variable length 22-65 minutes]

Nr. 31 EXPO for 3 players/singers with 3 shortwave radio receivers
(Dec 1969 - Jan 1970) [variable length 25-35 minutes]

Development
     Despite the numbering, EXPO was composed first (in Kürten, Germany between December 1969 and January 1970) and POLE was written second (in Bali, February 1970).  These 2 works were then almost immediately premiered during Stockhausen's 1970 stay in Japan, where he oversaw performances of his works at the world's fair in Osaka ("EXPO '70").  In a large spherical auditorium (designed by Stockhausen and developed by Fritz Bornemann), the audience was literally surrounded on all sides (including the floor and ceiling) by 50 loudspeakers.  Against the wall at one end, Stockhausen controlled the vertical and horizontal positioning and movement of the sound mix, sometimes creating rising and falling circular motions (spirals) using a "rotation mill".  The performers (including Stockhausen Group musicians Peter Eötvös, Harald Bojé and Michael Vetter) played from various balcony stages or on an opposite-side podium.  Works were performed daily from 3:30 to 9pm for 183 days (20 musicians participated - see SPIRAL) and this German pavilion became one of the main attractions at Expo '70 (some of the other interesting exhibits included moon rocks, the first IMAX film, LAN technology and the first mobile phone).

     Compositionally, at this point Stockhausen had in the previous year completed and premiered KURZWELLEN (Short-Waves) and SPIRAL.  These works basically have the performer(s) draw thematic material from shortwave radio stations, after which they then perform progressively mutated reflections of these chosen shortwave sounds by expanding/compressing the radio material dynamically, registrally, duration-wise and/or through rhythmic subdivision).  The score uses so-called "plus-minus" notation (for reasons which will be very obvious) to organize these transformations into short sections ("Events"), connected by quiet transitions. 

     EXPO for trio and POLE for duo are both very similar to SPIRAL (for soloist), but obviously differing in the number of players.  They also have several new instructions mostly designed to shape and direct the exchange (imitation) of musical material between the 2 or 3 players.  More significantly I think, POLE includes a spatial movement score, which is scored in 2 additional staffs below the players' parts.  The spatial notation is designed to indicate movement in a sphere (such as laid out in 4 stacked circular layers, with controls for circular placement and height).  If a spherical auditorium is somehow unavailable ( :) ), the piece can be performed using an 8-channel speaker arrangement set up in 2 sets of 4 rows each.
Sideview cutaway of Stockhausen's Osaka spherical concert hall.  The loudspeakers were arranged in 7 circular layers (A - G).
Stockhausen mixed from the left (above the entrance stairs), and the players were situated on the right ("Orchester")
or on the balconies (Solisten Podium"). 
www.karlheinzstockhausen.org)
Shortwave Radio
     The shortwave radio is obviously not as common a household object as it was in the 1960's (Stockhausen:"Doesn't almost everyone own a short-wave receiver?").  When radio was first invented, it must have been a little spooky.  In fact, Stockhausen's own mother wondered why the voices didn't talk back to her.  The other fascinating thing about shortwave is that due to its habit of "bouncing" across the atmosphere, it's possible to receive signals from stations on the other side of the world.  For more on shortwave radio, see the page on SPIRAL.

SPIRAL
     The scores for EXPO and POLE use the same plus-minus notation and basic instructions as SPIRAL, so instead of repeating a bunch of text I ask the reader to refer to that page first.  The first "new rule" from SPIRAL is that an Event can be also be realized by a radio alone (previously an Event was radio + soloist, or soloist alone).  Below, I include the additional aspects unique to EXPO and POLE.

EXPO for 3
     EXPO is arranged in 3 "staffs" and grouped into 15 sections.  The Events are loosely coordinated amongst the 3 players through the use of "signal" sounds (in Michael Vetter's vocal versions, he uses harmonica, cowbell and megaphone, whereas in the Eötvös/Bojé versions (for electrochord and electronium) I suspect the crotales and woodblock sounds are the signals).  EXPO's additional notations (in addition to SPIRAL's, that is) include 3 kinds of instructions to direct one's own playing, and 7 to direct how one relates to another person:
  • hold sound
  • hold duration
  • add segments freely for the duration of the marking
  • intermittently imitate another person ("insert some of what is heard...into one's own event")
  • intermittently interrupt another person ("insert single segments into the other players' events")
  • play (an unlimited number of) echoes of another person
  • imitate a part of another's event ("play 1 of any other person's segments")
  • begin synchronously with another, also begin and continue to play synchronously ("all segments")
  • "relate" to another's event (typically a dialogue-like "hand-off" kind of thing)
  • play a Signal to coordinate amongst the players a transition from one section to the next (typically followed by a "relating" Event)
     Solid vertical divider lines indicate scored shortwave events.  These "forced" shortwave events help maintain coordination amongst the players, along with the pre-determined signal sounds.  One special event, a kind of "rhythmic refrain insert", occurs twice (once near the end of Section 2 and once at the end of Section 10, both times with radio):
[ ] : "Add 1 SLOW insert and 1 FAST insert, each one lasting up to 2.5 minutes; taking a synchronized beat, all players repeat 1 segment of the previous event PERIODICALLY, varying it slightly (syncopations etc...).  Make general pauses."

Complete EXPO score in 3 connected staffs.  Each staff has 3 layers, one for each player.
(graphic from Jerome Kohl's "Composing Processes: SPIRAL, POLE, EXPO", with a few additional colorations)
 (© www.karlheinzstockhausen.org)
     The structure of EXPO has been described by Jerome Kohl (at least, in an intermediary analysis breakdown) as being in 7 sections (of which I added a couple minor observations as well):
  1. 1st beginning (preparation for Insert 1), Player II leads
  2. Duo between II and III
  3. Dialogue (alternation) between II and III
  4. Trio in canon-form (III/II/I), staggered "SPIRAL" events, after which the sounds are all exchanged (as "echoes")
  5. 2nd beginning (preparation for Insert 2), Player III leads, also just before this is a 2nd canon-form (III/I/II)
  6. Rotation of events (passed around and transformed)
  7. Synchronous events (unison), ending in a kind of "7 chorus refrain" and Player II coda
(In his lecture notes, "Composing Processes: SPIRAL, POLE, EXPO", Kohl continues to break down EXPO into further subdivisions in order to derive a possible underlying serial structure, but for the purposes of this page, I'll leave it at the initial 7 sections.)

POLE for 2
POLE score in 4 continued staffs.
The top 2 rows of each staff are transformation directions, the bottom 2 rows are for spatial movement.
(Cover of EMI Electrola LP)
Some of POLE's notations repeat EXPO's, some do not carry over (no rhythmic inserts), and 3 are new:
  • hold sound
  • hold duration
  • add segments freely for the duration of the marking
  • intermittently imitate another person ("insert some of what is heard...into one's own event")
  • intermittently interrupt another person ("insert single segments into the other players' events")
  • play (an unlimited number of) echoes of another person
  • imitate a part of another's event ("play 1 of any other person's segments")
  • begin synchronously with another, also begin and continue to play synchronously ("all segments")
  • "relate" to another's event (typically a dialogue-like "hand-off" kind of thing)
  • play a Signal to coordinate amongst the players a transition from one section to the next (typically followed by a "relating" Event)
  • play at the extreme range of 1 parameter (register/duration/dynamic/tempo)
  • "shadow" the other player
  • intermittently join another person and connect the segments ("legato")
     Unlike SPIRAL and EXPO, POLE has no "mandatory" shortwave radio Events, leaving these at the discretion of the performers.  The most apparent score difference is the bottom 2 "spatial motion" staff lines, which are graphically arranged in 8 degrees of vertical columns (or shapes), indicating which of the 8 speakers are "on" (2 sets of 4).  It is designed especially for the Expo '70 spherical auditorium, but on CD the different degrees are conveyed by reverb and stereo placement.  For example, on Stockhausen CD 103, Michael Vetter's male vocal goes (from 1 to 4) hard left/dry to hard right/heavy reverb.  Natascha Nikreprelevic's female vocal goes (also 1 to 4) hard right/dry to hard left/heavy reverb.  Some of the shapes can be described as follows:
  • extreme top/bottom/right/left
  • continuous transitions (spatial glissandi)
  • stepwise transitions (spacial scalar steps)
  • paired movements
  • shaded shapes indicating that all speakers are "on" in that range
  • intermittent spikes and improvisation sections
  • crossfades
  • etc...
Peter Eötvös playing the Electrochord, at Abbey Road. 
From the POLE/EXPO score cover. 
Photo Richard Bird.  
(Note the violin bow at far right.  A picture of the Electronium can be found on the PROZESSION page.)
Recordings
      On Stockhausen Complete Edition CD 15, POLE is performed by Peter Eötvös and Harald Bojé playing Electrochord (a contact-miked and processed bowed/plucked zither, with a synthesizer and sometimes a folk wind instrument) and Electronium (an accordion-based synthesizer with reverb control), respectively.  Both players also seem to have ring modulation and variable-speed tape loop (sampler-delay) effects at their disposal.  A few months later, another recording of POLE was made by this duo (and mixed by Alan Parsons!) and released on EMI Electrola records.
     Below, I have a kind of "listening narrative" to the 1st Eötvös/Bojé recording of POLE on CD 15.  Trying to match up the musical gestures to the plus-minus symbols can be very tricky business, especially without knowing the parameters chosen for each Event or the nature of the Signal sounds (or even which "sections" were played).  So I basically include here merely a chronology of the more broad sonic gestures.  I'm taking a guess that Eötvös' bell (crotale) and Bojé's woodblock are Signal sounds, which basically indicate a "now follow me" kind of message.  The "home" position of the electrochord is on the left, and the electronium is on the right.
  • 0:07: Shortwave: high and middle register tremolos (w slow middle register gliss) and low hum.  Both players follow, switching between the layers (Electrochord bowing, Electronium high melodic points)
  • 1:09: Shortwave tremolo descends in pitch
  • 1:54: Electronium solo
  • 2:15: Shortwave: lower register tremolo, Electrochord returns
  • 2:29: Electronium: accents w pluck sounds over tremolo
  • 2:40: Woodblock Signal begins (ends 3:04)
  • 3:13: Electronium: high pitch melody
  • 3:39: Electrochord: plucks in pitch-shifted melodic clusters, Electronium: adds high tone melodies
  • 4:43: Bell Signal over Electronium high held tones
  • 5:57: high tones solo/duet, with pulses (slowing) and then glissandi
  • 7:05: pulse ritard, middle register wide vibrato "saucer wobble"
  • 7:44: Shortwave search phase
  • 8:13: low register impact and echo, followed by noise accents
  • 8:41: Electronium low notes, then Electrochord vocal articulations
  • 9:46: low drones/humming
  • 10:21: Electrochord: isolated plucks
  • 11:41: Electrochord: low bowing
  • 12:17: Bell Signal, Electronium begins changing timbre/register
  • 14:18: Shortwave search phase, ending on rising/falling tremolo, then imitated
  • 15:47: Shortwave search phase, finding descending "club band" fragment, imitated by Electrochord
  • 17:13: Shortwave solo - talking (German).  Popping noises and a high tones gradually appear
  • 18:20: rhythmic accents (insert?), eventually slowing down
  • 20:30: high tones with Shortwave static
  • 21:22: Shortwave search phase, settling on uptempo orchestral fragment and announcer



(Nikreprelevic/Randomiz/Vetter)
     On Stockhausen Complete Edition CD 104: EXPO, F.X. Randomiz plays electronics for the top staff, Michael Vetter sings/plays the 2nd,, and Natascha Nikreprelevic sings the 3rd.  In the first version, the stereo spread (left to right) is Vetter/Randomiz/Nikreprelevic.  On the second version the spread is Nikreprelevic/Randomiz/Vetter, but they play the same staffs as before. The CD tracks correspond to the 15 sections of the score (circled numbers in the graphic above).
     On Stockhausen Complete Edition CD 103: POLE, Michael Vetter (starting from the left) sings the top staff, and Natascha Nikreprelevic (starting right) sings the 2nd staff.  The attributes which are expanded/contracted (duration/dynamic/etc...) as well as places where a shortwave event was used are here added as annotations to the full score printed in the CD booklet. The CD tracks are broken into 7 sections corresponding to the large sections in the score.
     These 2 CDs also have copious notes from the performers themselves, describing their approach to the works and their experiences exploring them.  Michael Vetter himself had performed plus-minus works at EXPO '70, and returned to them much later to record the first "complete" version of SPIRAL (CD 46) in 1995.  POLE and EXPO were recorded in 2012 and 2013, respectively.

Sound Impressions
     At the core of these works is the idea of "fusing" with a shortwave radio event and then performing considered, disciplined explorations (solo, duo and trio variations) of these basically unpredictable sound events (unless one knows the local DJ and can make requests :) ).  It's possible that in POLE and EXPO that multiple layers ("trains") of radio themes could surface, but any parallel tracks usually end up joining due to the frequent instructions to "relate" to another person's layer.

     As I wrote in my SPIRAL impressions, I think the impact of these works has much to do with the players and their chosen instrument(s).  Stockhausen has arranged some of his other works for alternate instruments (IN FREUNDSCHAFT, TIERKREIS, etc...), and some others also have open-ended instrumentation (STOP, YLEM, SOLO, PLUS-MINUS), but I think none are as open-ended in content as these works, leaving the performers' instrumental timbre and playing style as defining characteristics for each interpretation (even the "intuitive music" works (AUS DEN SIEBEN TAGEN, FÜR KOMMENDE ZEITEN) have at their core the rhythmic concept of slow ensemble "vibrations").  The SPIRAL-POLE-EXPO trio of works seems more concerned with relative degrees and kinds of reflection between individual forces (including with oneself), rather than larger structural processes.  Processes do exist, but since the choice and degree of parameters are so open-ended, it's harder to sense these without having an annotated score at hand.  In fact, it's even expected that performers start from different assigned points in the score from performance to performance.  ZYKLUS and KLAVIERSTÜCK XI also have this kind of "polyvalent form", but those are quite thoroughly-notated for percussion and piano (respectively) and require the player to "finish" the piece in one performance.

     Probably more so than in any other Stockhausen work, the performers' individual instrumental style comes through as a primary focus when listening to these works, especially considering that there could be a relatively wide latitude to the interpretation of the score symbols.  In other words, it may be possible to consider the version of POLE by Eötvös and Bojé as "showcases" for their skills on electrochord and electronium, and the more recent versions led by Michael Vetter to be something like fast-paced Brecht-ian comic-operas, threaded through with absurdist sound poetry and ethnic folk stylizations.  Another version of POLE in 2010 featuring European free improvisors Frank Gratkowski (on saxophone) and Anton Lukoszevieze (cello) sounds very much like, well, European Free Improvisation (this performance probably shouldn't count though since - based on the pre-talk - it appears that the sound projectionist mistook the spatial score for a dynamics score...).

     Now, remarking on these performer-based factors is not meant to undercut Stockhausen's contribution, since the key idea of using a shortwave to germinate trains of development is unique, and the "velocity" (or perhaps "proportions of change") in these works is very Stockhausen-ian (and possibly even serially organized).  The notation symbols are also a novel way of forming clear dramatic arcs, but leaving room for many surprises at every performance.  POLE is also the only work of Stockhausen's which includes a "mix balance" score for live performance (other electronically-realized works of his have notated motions, but those are not really for a performer/sound mixer to interpret live).  But for most casual listeners, the appreciation of these works may in the end come down to how much the listener likes the natural improvisational style and instrumentation of the performers themselves.  Actually, come to think of it, one could say that these works are Stockhausen's gift to the creative improvising musician.

      Historically, these works were created at the end of the "intuitive music" era as performed by the longest-serving members of the Stockhausen Group.  It is reported that some of his intuitive music collaborators were feeling unhappy about the open nature of the "free" music they were playing and beginning to contest ownership of the composition rights.  On the other hand, Stockhausen has been described as being unhappy with the "dilettantish interpretations" he was getting from his players.  When a performer was in a physically or mentally distracted state (such as being sick or depressed), the music suffered as well.  This "fragility" of intuitive music would not be as present in fully-notated music.  MANTRA would soon come into being, and this work for 2 ring-modulated pianos is completely composed down to the last tenth of second (though in a sense it is "intuitively-composed" as the product of one person's intuitively-based musical deliberations at a much slower pace..).

     One final thought before leaving the "process plan" plus-minus-notated works behind...  Taken altogether, the plus-minus notation scheme could easily be applied to any fully-precomposed work, as a kind of analysis tool.  Since most Western music is based on transformation of thematic material, these symbols could be used as a useful annotation.  Perhaps an even more useful scenario in which to use these symbols would be in analyzing free-improvisation recordings.  Again, free improvisation is more or less based on imitation, contrast and transformation (not to mention "SPIRAL" events).  In fact, it would be interesting to use these symbols to compose many more structured "free" works besides the ones Stockhausen composed (though I'm not sure how the copyright would work!).

Links
Samples and CD ordering:
Buy the Score
POLE Wiki
EXPO Wiki
On Harald Bojé's Electronium 
On Peter Eotvos' Electrochord 
"The Ephemeral Architecture of Stockhausen's Pole für 2" (Michael Fowler) 
POLE (1st Recording with Electrochord & Electronium, YouTube clip) 
POLE (2nd Recording with Electrochord & Electronium, Abbey Road, YouTube clip)
POLE Live excerpt with Natascha Nikeprelevic, Michael Vetter
EXPO Live excerpt with Natascha Nikeprelevic, Michael Vetter, F.X.Randomiz 
EXPO Live rehearsal excerpt with Natascha Nikeprelevic, Michael Vetter, F.X.Randomiz 
F.X. Randomiz on EXPO (with sound samples)