In this scene (from "Musical Forming", 1972), Stockhausen describes how
each one of the 12 starting pitches starts at an extremely high or low point
(in this case high), oscillates up and down (moving towards the middle
register and then back outwards), and finally ends up in the
opposite register (in this case low).
     In this post I cover two of Stockhausen's earliest works, both of which have a strong percussion element to them:

for oboe, bass clarinet, piano (with woodblock), 3 percussionists (tumbas, tom toms, cymbals)
(1951) [11'29"]

     The general form of KREUZSPIEL was composed in the late summer of 1951.  On the way to visit his soon-to-be wife, Doris Andreae, the full shape came to him while sitting on a rock during a rest stop (described in Michael Kurtz' Stockhausen biography).  This work was partly influenced by Olivier Messiaen’s "Mode de valeurs et d’intensités" (from "Quatre études de rythme"), but adds some significant transformational processes to the serial (and "point") operations in that piece.  The basic idea in KREUZSPIEL is that members of a set of 6 high notes and members of a set of 6 low notes cross back and forth (up and down) over a 6 octave range.  The sets gradually meet in the middle register and then move back outwards, with the original pair of 6 note sets ending up in opposite registers (see moving red dot in the picture above).   The structure of this idea came to Stockhausen almost spontaneously and completely formed in its shape, but without the details worked out (sort of like visualizing a mountain landscape but without drawing in each of the trees and rocks).  This work, which he considered his first "real" composition, also marked his first steps into "point" music, that is, manipulating notes to follow patterns based more on astronomical or biological processes, rather than forming thematic melodic motifs.  The work was eventually premiered at the Darmstadt Vacation Summer Courses the next year (alongside works by Pierre Boulez, Luigi Nono and others), but the performance was disrupted by a rowdy audience and "ended in a scandal".

     The "cross play" idea itself as stated above may make this work seem very simple in conception, but it's important to note that up until this time most composers were still using 12-tone rows to essentially create music which sounded like late-era Romantic music, but with liberated harmony .  The concept of treating notes as "points" subject to natural forces (directional processes) was largely unheard of (in fact, KREUZSPIEL's pair of 6-note rows begin shattering almost immediately, since they increasingly invade each others' pitch registers).  After the premiere, KREUZSPIEL was basically shelved, but then revised 7 years later after Boulez began developing similar ideas (Robin Maconie, The Works of Karlheinz Stockhausen, 1st ed.).  It was eventually recorded in 1973 by the London Sinfonietta during a period in the 1970s where Stockhausen was reviving many of his early works for re-release.

     One of the most interesting aspects of this first work is that its compositional development follows a working style which would be employed even up to HIMMELS-TÜR (2005), written just 2 years before his death:
  • First, a basically fully-formed aural "vision" of a work, then...
  • Working out the mathematical proportions of the individual elements
  • Writing out a fully-notated score, and at the same time...
  • Changing abstract elements as they occur to make them more "musical" (ie - changing registers, shifting rhythmic values of notes to create chords, etc...), sometimes adding "inserts" (improvisations breaking from the original structure)...
  • And finally, revising the score during rehearsals or after initial performances.
This quote from Mya Tannenbaum's book "Conversations with Stockhausen" seems appropriate:
     The checking and the chiseling, once things are done, concern details, while the plan of an entire work is there in front of me right from the very beginning of every large-scale work - a plan, which, above all, fixes for me all the proportions, the duration, the dynamics, the sound quality, the ranges, the harmonies…(etc..).  From the time of KREUZSPIEL onwards, I’ve planned the structure of all my works, from the number of movements to the evolution of single parameters to the analysis of the particles of sound or groups of sound to be used.
     Of course, it's doubtlessly true than many composers have a similar work procedure, but in Stockhausen's case these steps are extremely well-documented in interviews, sketches, performances and newly-revised editions of his works, and this thread is present for his entire career.

KREUZSPIEL's stage arrangement.  Since the piano keyboard faces the audience,
it is easier to see the pianist's fingers playing the low and high alternating notes.
      This section describes KREUZSPIEL's compositional strategies in slightly more detail, but for most people (including myself), some of it is not very easily heard. In his 1972 British Lecture "Musical Forming", Stockhausen charts his development from "points" to "groups" to "statistical" and aleatory forms, but points out that this was not a planned evolution, that this conceptual arc is only apparent in retrospect.  For this reason, I think Stockhausen in later years didn't dwell too much on the permutational strategies used here, and the simple imagery of points meeting and then parting will be enough for most people.  However, it's interesting to more closely examine this starting point of Stockhausen's compositional journey from "point music". 

    "Cross-play" is simply described by Stockhausen as 2 sets of different notes which start high and low (on piano), eventually meeting in the middle (on oboe and bass clarinet) and then crossing over to the opposite side from their starting register.  Composer Jonathan Harvey describes this crossing concept in more detail in his book "The Music of Stockhausen".  Just on the pitches alone, there are several kinds of "crossings" going on over 12 permutations of the original 12 note (2 x 6) pitch row sequence.
  1. 1 to 6 high notes are traded (cross over) back and forth with 6 low notes, and at the end of 12 permutations, the 6 high notes have traded places with the 6 low notes
  2. In each of the 2 6-note sets, the "untraded" notes are rotated in sequence (from permutation to permutation) 
  3. The number of traded notes in each permutation first increases, and then decreases
  4. The notes are at first played only on the high and low registers of the piano, but they soon gravitate towards the middle registers, at which point the oboe and bass clarinet begin taking over the notes.  Eventually 4 of the "voices" have an equal number of notes (3), and after that the oboe and bass clarinet "own" most of the notes.  The process then reverses, leaving high and low piano alone at the end..
     Numbers 1 and 4 from above are described pretty well by Thomas Johnson ("Kreuzspiel, Louange à l’Éternité de Jésus, and Mashups"): "Pitch classes that start in the seventh octave of the piano in the right hand move eventually to the second octave in the piano left hand, then to the fifth octave in the oboe, etc. If a note starts in the left hand, it proceeds through this rotation in reverse." This process is also shown in the picture at top of the page ("animated" notes are my own elaboration) from Stockhausen's British Lecture. 

     Each pitch also has an assigned duration and dynamic value (an idea used in Messiaen's piece), in other words, each note here is considered a "point", with its own independent characteristics.  However, Stockhausen often "massages" some of their personalized traits to make their interactions more musical (in this way, he fought against the dryness of purely mathematical composition).

A pair of Tumba drums
     Percussion-wise, there are 4 drums used in the 1st stage, made up of tumbas (or congas) and tom-toms.  The tumbas (high, thin bongos) play a continuous "pitter-patter" in the 1st stage, but have intermittent accents at points according to a "duration" sequence which is also permutated (in fact, the percussion sequences coincide with the pitch sequences (about 6 1/2 measures each)).  A woodblock accelerando marks the point where the percussion duration series has become completely "backwards", after which it begins a process of reversing back to its original duration sequence (a ritardando).  The woodblock crescendo also marks the point where all of the pitches are spread equally over the 4 voices.

     In the 2nd stage, ringing cymbals replace the rhythmic drums.  Pitch-wise, the oboe and bass clarinet own all of the pitches at the start, after which the notes spread out to the high and low piano registers and then return (a reversal of the 1st stage's procedure).  The piano here (as revised in 1959) also plays additional soft chords in between the single note points, and in general the "cross play" is not as methodical as in the 1st stage.  In fact, it's actually more intuitive and almost foreshadows "statistical" methods to come, as observed by Jerome Kohl in "Serial and Non-serial Techniques in the Music of Karlheinz Stockhausen from 1962-1968".  Additionally. Johnson's above-mentioned thesis points out that the permutations reorganize the pitch series in adjacent "groups" of notes, which foreshadows ideas soon to be explored in KONTRAPUNKTE.

     In the 3rd stage, the 1st and 2nd stage processes and percussion instruments are combined (super-imposed) and played backwards (except for the tumbas from the 1st stage). The oboe and bass clarinet basically just play material from the 1st stage.  The percussion parts (drums versus cymbals) have exchanged rhythmic meters (16th-notes vs. 16th note triplets), which is another expression of "crossplay" (Johnson again).  There is no rhythmic tremolo pattern from the 1st stage, but instead the tom-toms dominate with rolled attacks.

     All of this pitch and rhythm "set juggling" is frankly not as easily heard as Stockhausen's more simplified explanation, but they are interesting in that this kind of meticulous construction produces a subconscious effect of cross-transformation, and also creates a feeling of continuous unpredictability - but with an underlying direction of change.

     Besides the 3 stages, the work has a 13-measure introduction which is based on the first 3 permutations of the 12-note series, but expressed as soft chords.  The stages have brief transition phases between each other which are usually percussion-based.  The below "form table" is based on the recording of KREUZSPIEL found on the Stockhausen Complete Edition CD 1.  The first 6 tracks feature other early works, so here the first part is numbered track 7.

Trk Dur Time Bar Section
7 3:09 0:00
(silent pause)
0:05 1-13 Introduction A constant tumba tremolo pattern provides a background "groove", but uses accents to express 2 sets of 12 duration values.  The second set (starting with 1st tom roll) is simply 1, 2, 3, 4, etc...(accent ritardando).
Isolated high and low piano notes bracket soft middle register chords (built from the pitch series).  A tom-tom crescendo leads to the 1st stage.
0:42 14-90 Stage 1 The tumba tremolo groove continues but with increased tom-tom accents.  The high and low notes gradually spread from the piano parts to the bass clarinet and oboe (the bass clarinet enters at bar 28, oboe at bar 32).  At 1:46 (bar 46), an accelerating woodblock crescendo (the retrograde of the 2nd tumba series (12, 11, 10, etc...)) signals the moment of even distribution in all registers and voices.  The process then reverses (winds retreat).
8 3:35 0:00 91-98 Transition Low tumbas play a rhythm with cymbal accents.
0:27 99-141 Stage 2 In this slower, somewhat lyrical section, the rhythmic drums are replaced by ringing metal percussion.  Notes spread from the wind instruments' registers out to the piano's high and low registers, and then starting from 2:02 (bar 120) reverse direction.  The piano also plays soft middle register chords throughout. 
9 4:47 0:00 141-145 Transition A tumba rhythm with accents is played against a held piano and bass clarinet chord from the previous section.
0:19 146-202 Stage 3 The percussion is more syncopated and dominated by rolled tom-tom attacks, and the tempo is faster again (same as Stage 1).  The 1st and 2nd stage pitch material for the piano are combined (played at the same time), but in reverse.  The winds play material from Stage 1 in reverse.  The 2nd stage middle register piano material (w cymbals) enters at 0:45 (bars 153-190).  In general this stage is the most dynamic, and ends after a brief percussion climax on a fading tom-tom note.

     Despite all of the serial and statistical inventions of KREUZSPIEL, a "musical" element of KREUZSPIEL is highlighted in this interesting quote found in Mya Tannenbaum's 1988 interview with Stockhasuen (also pointed out in Johnson's thesis):
     …I’d like to make it clear that no one up to today has ever recognized that in the middle of the first movement (and at the beginning and the end of the second, and in the middle of the third), there’s a very singable episode contained within the interval of an octave (these are the places where the 2 rows completely converge). People tend not to take note of the process of coming towards (of preparation for) melody.  The musical texture goes on, in fact, without any deviations until it arrives just one time at the moment of song…  And here, in fact, there’s a brief interlude for woodblock, just to point up the shapely appearance of the melody - an easy, singable melody…  To look for singability in the entire course of a composition is absurd.  The moment reserved for song must always be very mysterious…  In this sense, there is in every one of my compositions the moment in which I sing my song, too…  All the rest is just preparation for that moment.
The 1st page of KREUZSPIEL.

SCHLAGTRIO score cover
for piano and 2 x 3 timpani
(1952) [15'15"]

     SCHLAGTRIO was another work which was revived, from "the desk", as they say.  Originally scored for 4 performers (as SCHLAGQUARTETT), it also uses a similar concept of "attraction" in that a high register 12-note pitch row and a low register 12-note row move towards each other.  When they finally meet, a 3rd "entity" is created from this union.  The 2 "parent" melodies disappear and this "child" melody expands to fill the pitch space (this biological analogy is mine, but Stockhausen's terminology implies something of the sort).  The premiere in 1952 was so unsatisfactory that Stockhausen withdrew the work, thinking that the rhythmic attack types in the score were too demanding to be played effectively.  In 1974 it was revised and simplified for readability and altered so that 3 percussionists could play it.  The premier for this version was performed by Les Percussions de Strasbourg in 1975, and then recorded by Aloys Kontarsky (piano), Jean Batigne, and Georges von Gucht (timpani) in 1976.  Texturally, this work sounds very much like a natural progression from the 3rd stage of KREUZSPIEL, but with pitched percussion and without the wind instruments.

     An important difference from KREUZSPIEL is that here the percussion is used as a 6-note counterpoint to the piano (but with similar, analogous attack types), whereas in the earlier work it was used more texturally (with its own independent permutation scheme).  Additionally there is no "passing of notes" to middle range instruments such as an oboe or bass clarinet. The 2 opposing rows from the low and high ends of the piano are however somewhat similarly permutated so that they move towards the middle range and meet in the same register.

     Stockhausen's descriptions seem to imply that the 2 "parent" voices alternate between two kinds of actions:
  • chromatic permutations moving from one of the piano's extreme registers (high/low) towards the middle register
  • intermittent setcions where the piano is joined/replaced by timpani drums, tuned a quarter tone off ("temporarily obscured by a passing phase of change"), but which can be "located" in relation to the chromatic notes
     Stockhausen writes: "Both voices set off (from) the two extreme octaves and move alternately from the chromatic realm to the deviant pitch-spaces". Since the timpani is tuned to a 6-note whole tone scale, a quarter step lower than the piano (a "deviant" pitch space), each note is "relatable" (somewhat close) to adjacent pairs of semitones from the chromatic scale.  Each of the 6 timpani notes is also linked to 1 of the 6 octaves of the piano part.

     After several cycles of permutations, a 3rd voice is created at the convergence of the 2 melodies, using parts from each.  This new melody remains while the parent melodies withdraw to their original opposite extremes and disappear.  This process of 2 parent melodies meeting and sparking off a 3rd melody is frankly a bit confusing to me, but the broad textural form of the work is fairly easy to follow, which is described in the table below (based on the recording of SCHLAGTRIO found on the Stockhausen Complete Edition CD 2). In notes to MIXTUR, Stockhausen mentions that this work also features a "retrograde" (reverse) structure, which probably begins after the timpani solo section.

Bar Time Perc. Signal Process
1 0:05
opening chord, piano/timpani duo begins, piano voices start at extreme registers and begin slowly expanding towards the middle register
29 2:24 crotale 1st convergence of piano voices completed
31 2:35 crotale 1st divergence of piano voices begins (moving apart), more vertical alignment (chords)
59 4:54 triangle alternation/imitation between piano and timpani voices begins
78 6:25
timpani players alone
101 8:20
alternation/imitation between piano and timpani voices slowly returns
120 9:55 crotale piano/timpani duo again
148 12:15 triangle 2nd piano convergence
150 12:25 triangle 2nd piano divergence
178 15:15 triangle end chord
(crotales are also called antique cymbals)

     Other factors (besides the pitches) are also permutated.  12 different rhythmic values, 8 dynamic levels from ppp to ffff, and 8 modes of attack (mallet articulation, etc) also have a hybridization scheme similar to the one used for the pitches.

     From a letter Stockhausen wrote in 1952, he further describes his initial inspiration.  The 2 parent pitch rows each have 12 notes (one is a retrograde of the other, or backwards).  Over a sequence of 23 sections, the 2 parents overlap and then pass by each other.  The section in which both parents are "on top of each other" is section 12.  This is because 1 note (out of 12) is added in each section, and it's at the 12th section where the 12th and last note has finally appeared, and the pitch row has completely "unfolded".  Since the other parent has also been slowly adding a pitch at a time (from the retrograde row), both parents are fully unfolded and superimposed in the 12th section.  From the 13th section to the 23rd, the 2 parents begin eliminating notes from their rows, one at a time (first in, first out, essentially a mirror process of the first 12 sections).
(from SCHLAGTRIO score cover, ©Universal Editon,
     The above sketch is from the score cover and frankly, I don't know that much about it. However, I can make a few guesses.  One possibility is that the Roman numerals I and II refer to Parent 1 and Parent 2.  The "a" possibly means this is used for the 1st half of the 23 sections (1-12).  On the same page (not shown) are Ib and IIb, which may be for sections 13-23.  Another possibility is that "a" means "section a out of 23 sections, a through w", but I don't feel that.  In any case, each of the 2 parents have a 12-box table which contains the full "row" for their dynamic values and the note durations available (some are repeated, since there are only 8 unique dynamics, etc...).  The curving line shows the sequence in which the box values are used (ie - 1st top box, then 1st bottom box, then 2nd top, 2nd bottom, 3rd top, etc...).  The table for the Parent II has a curvy line going in the opposite direction.  The 12-element row is arranged in this way because the top row refers to piano octaves, and the bottom refers to timpani quarter tones - again, this is a guess, but it basically shows that Stockhausen was very methodical in his distribution of musical elements.  From a listening standpoint, it would be pretty difficult to hear these additive row operations, I think....

At bar 78, the 2 timpani players have a duet.
Sound Impressions
     Even though these works are basically part of the "avant-garde" classical movement of the post-war era (an era normally known for it's dry and impenetrable style), they are surprisingly accessible.  The percussion part for the 1st stage of KREUZSPIEL actually plays a continuous tremolo rhythm, which would never happen again in so continuous and obvious a manner in Stockhausen's percussion work.  The percussion parts of the 3rd section, as well as the dynamic timpani figures of SCHLAGTRIO, make these two pieces simply exciting to listen to.  Even without being aware of the "crossing" of pitch fields, the melodic elements of the pitched instruments interact with the percussive rolls and accents in a very organic, almost "jazzy" way.  It's fairly easy to appreciate the music just by listening to how the tom-toms and the piano parts set each other up.  Present also, of course, is the "song" Stockhausen mentions in several parts of KREUZSPIEL (where the points are at maximum convergence).

     SCHLAGTRIO presents the 6-note timpani melody as a kind of "shadow-mirror" to the 6 octave piano part.  On the first few listens the piano and fortissimo timpani accents dominate one's impressions, but on further listens the beauty of the timpani melody fragments become much more appreciable.  In the CD booklet, Stockhausen describes the concept of 2 "principles" coming together and creating a new, 3rd entity (after which they then "return to a situation which is beyond the physically representable").  However, I actually find listening to the "point" field and it's collective behavior against a canvas of "jagged" timpani dynamics to be more fun.

KREUZSPIEL Sound samples and CD ordering
Stockhausen Notes on KREUZSPIEL
DVD purchase of Rehearsal, intro & concert of KREUZSPIEL, 1992, Ensemble Modern, cond. by Stockhausen
    English translation of KREUZSPIEL concert talk (PDF)
Stockhausen British Lecture: Musical Forming - KREUZSPIEL (YouTube)
Kreuzspiel, Louange à l'Éternité de Jésus, and Mashups (Thomas Johnson thesis, PDF)
KREUZSPIEL rec. by Joey Ma, conducted by David Medine (Soundcloud audio)
KREUZSPIEL, conducted by Nacho de Paz, 2008, Madrid, YouTube

SCHLAGTRIO Sound samples and CD ordering 
SCHLAGTRIO, Stockhausen Courses, Simone Mancuso & Luca Congedo, timpani, Laura Alvarez, piano, YouTube
SCHLAGTRIO, Ludovico Ensemble, YouTube 
Stockhausen: Complete Early Percussion Works (DVD)

Purchase the Scores
The Music of Stockhausen (Jonathan Harvey)
Conversations with Stockhausen (Mya Tannenbaum, 1988)
Serial and Non-serial Techniques in the Music of Karlheinz Stockhausen from 1962-1968 (Jerome Kohl)
The Works of Karlheinz Stockhausen (Robin Maconie)