(with my color variation of a Lindsay Vickery slide)
Nr. 7: KLAVIERSTÜCK XI (Piano Piece 11)
(1956)  [approx. 14 min.]

     In the earlier analysis of Piano Pieces 5-10, I described the isolated phrases in those works as being in a way "snowflakes in a snowstorm".  In this 11th piano piece, that analogy becomes more appropriate than ever.  However, from a pianist's point of view, it may be more apt to use an "autumn leaves" analogy.  Here, 19 musical "leaves" are spread in front of the player.  He picks one up, "plays" it, returns it to the pile, and then picks up another to play (however, the way he plays this new leaf is affected by what he saw in the previous leaf).  Sometimes he will pick up one that he's chosen before, but he plays it anyway.  However, if he realizes that he's picked up the same leaf 3 times already, he stops, and the performance is over.  In Piano Piece 11, each leaf is a few measures of score, and at the end of each score fragment is the indication of how to approach the next chosen musical fragment (in the terms of tempo, dynamic, and articulation).  Instead of a "pile of leaves", all of these musical fragments are scattered over a huge sheet of paper, and the pianist chooses the phrases randomly.  He stops after he has hit the same fragment a 3rd time.

     (I should mention that Stockhausen has never called these 19 score fragments "leaves" (as far as I know), but I just find it handy to think of them that way.)

Polyvalent Form
     Because of the nature of this piece, there can be an almost unimaginable number of versions.  Each version could start from any one of the 19 "leaves", and end on any one of them.  This is an example of what is sometimes called "open-form" or "polyvalent form", since the composition itself has no set structural arc.  One idea that Stockhausen is exploring here is that each of these leaf fragments create their own "vibration" or color.  In the previous Piano Pieces, grace note "satellites" and "halo tones" were used to create a resonating color over a central note.   In this piece, each leaf (which also has its own internal central notes and satellites) could be considered a single central tone by itself, and the tempo/dynamic/articulation instructions at the end of each leaf are a kind of "resonant-coloration" which affects its surrounding "satellite" leaves. 

     Structurally, if one thinks of each one of these 19 leaves as a single note-entity (as just described), the chance sequencing of the leaves functions more or less the same way as putting these leaves into a serial sequence.  The basic purpose of serialism is to produce variety and unpredictability, and the method employed here can produce the same kind of unpredictability.  Naturally this "eye-contact serialism" is not going to be as "pure" as in a case where these leaves are put into a specific, non-repeating "leaf row", but since the previous piano pieces already covered serial organization on different time-scales, perhaps the idea of an open-form work which could produce a large variety of structural outcomes became much more important.  However, ironically, some pianists prefer to "pre-program" the sequence and play the same sequence of leaves from performance to performance (probably because it was simply too hard to do it the "honest way").

     Stockhausen points out that it doesn't really matter how these leaves are sequenced - in the end it's still a pile of leaves.  The work itself has its own unique "vibration".  "Piano Piece XI is nothing but a sound in which certain partials, components, are behaving statistically...  If I make a whole piece similar to the ways in which (a complex noise) is organized, then naturally the individual components of this piece could also be exchanged, permutated, without changing its basic quality."  (Conversations with the Composer, Jonatan Cott).

Rhythm and Pitch
6 of the 36 possible rhythm patterns from the "final matrix".
(from Truelove's "The Translation of Rhythm into Pitch in KLAVIERSTÜCK XI")
     The melodic material of each leaf was created through a fairly complex method of cross-breeding rhythm patterns (above), layer density and articulation tables (tremoli, trills, fermatas, satellite grace notes, halo tones, clusters, etc..).  The methodology is very structured and mathematical, yet there are many places where Stockhausen broke from the math for the sake of musicality ("composer intuition").  

     From a pitch-perspective, the notes were derived from proportionate durations contained in the melodic rhythms.  For example, if two notes had a proportionate duration ratio of 3:2 or 2:3, an interval of a 5th was called for (sometimes augmented or diminished).  A ratio of 2:1 would dictate an octave (sometimes flatted or sharped).  In Stephen Truelove's KLAVIERSTÜCK XI thesis (which was a major source of info for this particular section), he claims that these flat/sharp "alterations" were methods to make the work "atonal", but Stockhausen responded that these "off" notes are just approximations of harmonic relationships (I assume this is related to discrepancies between equal- temperament and just intonation).  In any case, the idea of translating rhythm into melody is a logical one because rhythm can be turned into pitch if played very fast.  In other words, if 2 different rhythms were looped at super-high speed, they would sound like 2 different noise drones, and if the rhythms were periodic, actual pitches could be heard.  If the ratio were 2:1, an octave interval would be produced (this idea is very important in the electronic work KONTAKTE).

     Additionally, after the melodic shapes were derived from rhythmic proportions, pitches could be freely shifted to higher or lower octaves, and in general, longer note values were given lower register pitches.  Satellite grace notes did not follow any duration-ratio rule (since they are to be played "as fast as possible", after all), so these pitches were chosen intuitively. 

     The player starts by choosing one of 6 tempi and playing the first randomly-selected leaf.  At the end of that leaf is the tempo, dynamic and articulation for the next randomly-chosen leaf.  After a pause, or during a sustained chord, the next leaf is chosen and then played with the indicated markings.  If a previously-played leaf is chosen a second time, the leaf is to be played in a slight variation, such as in a new octave (like looking at the backside of a leaf?).  Not every leaf needs to be played in a performance.  If the same leaf is chosen a third time, the pianist ends the performance (without playing the thrice-chosen leaf).

     One of the interesting things to consider is that each of these 19 leaves can be played in 19 different variations (depending on the tempo, dynamic and articulation instructions from the previously-played leaf).  Out of these 361 leaves, theoretically anywhere from 2 to 39 could end up being played for a given performance. The number of possible performance sequences is....well, very big.

     Below are 5 of the 19 leaves (melodic fragments).  Ellen Corver recorded 2 versions of KLAVIERSTÜCK XI on Stockhausen Edition CD 56.  The first version (Disc 2, Track 2) starts with the 3rd and 4th score examples below. The second version on Track 3 begins with the 5th example.  All of the score excerpts below are copyright Universal Edition and www.karlheinzstockhausen.org.
This leaf descends into a long trill.
T1 indicates that next leaf should be played at the lowest speed, the indication "N" means "neutral" articulation.  The "(8....)" at top means that the 2nd time this leaf is played, it should be an octave higher.

This leaf has large interval leaps.
T6 means that the next leaf is to be played at the highest speed.  The "(8....)" at bottom means that the 2nd time this leaf is played, it should be an octave lower.
(with wide and narrow tremoli; the articulation for the next chosen leaf must use staccato attacks with silent redepressions)
(with pedaling and halo chords)
(dense syncopation with intermittent pauses, halo chords, etc...)

Live Performance
Prodromos Symeonidis, February 2006

Sound Impressions
     The general textural language of this piece fits very well as somewhere in between KLAVIERSTÜCK VI and X (naturally).  Because of the pauses and fermatas between (and inside) the fragments, there is a natural tension and release in the flow, and plenty of time to absorb the silences.  Because of the open nature of a performance, each can be something of a new experience.  However, unlike a "set" work where repeated exposure can help the listener become familiar with larger dramatic arcs, this one could be different every time (and of course, there is no "normal" score to follow visually).

     Stockhausen considers the whole work to be an atomized timbre, stretched out over several minutes, and I suppose one could listen to it like that, but perhaps there are a few other ways to follow this work.  One possibility is to try to get a feeling for each of the leaf fragments as they occur, and then re-appreciate them when they repeat (in a new tempo/dynamic, etc...).  Another idea is to compare the juxtapositions of the leaves.  Since the leaves are chosen at random, some transitions would naturally work better than others.  Repeated listenings of different versions of KLAVIERSTÜCK XI would eventually make the leaves familiar, and these ideas of comparing returning leaves and leaf sequences would probably be easier.  Even if only a few leaves become familiar, their appearance could bring out these aspects to the listener.  In a live performance, it's easy to know the transitions between leaves since the pianist will look up at the score to choose the next fragment (hopefully).

     The use of random eye-contact does bring a few questions to mind, though.  As just mentioned, Stockhausen conceives of this piece as a single, vibrating molecule made up of aleatory sub-particles (randomly-chosen and articulated), but I think a performer would naturally have certain "non-random tendencies" after he/she has become familiar with all of the leaves.  Is it possible for a pianist to be truly random after becoming intimately familiar with the piece?  Or perhaps, Stockhausen expects sub-conscious factors and familiarity to affect the choices of leaves...  Interestingly, Lindsay Vickery has proposed (or maybe completed, at this writing) a software score display program (Decibel ScorePlayer) which I gather will do all of the choosing for you, getting rid of the eye-contact element and just randomly choosing the next leaf.  I assume the performer would have to be very familiar with the work to pull this off effectively.

     Personally, I would have preferred that Stockhausen had published a "Cologne Version" sequence, just to have a "director's cut" version of this piece.  MIKROPHONIE I and MOMENTE have such published realizations, and something like that here would have been interesting.  I suppose that since the Aloys Kontarsky and Ellen Corver versions were recorded under Stockhausen's supervision, these would be the closest to something like that.

KLAVIERSTÜCK XVI (w. Sound Scene 12)

KLAVIERSTÜCKE I-XIV (Ellen Corver) Sound samples, tracks listings and CD ordering 
Buy the Scores 
Stockhausen on the KLAVIERSTÜCKE (1955,1957)
"Clavier Music 1992", Stockhausen on Piano Music (1992)
"The Translation of Rhythm into Pitch in Stockhausen's Klavierstück XI" (Stephen Truelove, Persp.of New Music Vol. 36.1)
"Mobile Scores and Click-tracks: teaching old dogs" (2010) Lindsay Vickery
KLAVIERSTÜCKE I-XI by Aloys Kontarsky (flac)