FORMEL Score Cover
(showing the first 4 formula segments marked out
on the first score page)
SPIEL Score Cover
(showing the duration scale and the rising migration of the pitch row for the 2nd layer of the 2nd movement)

Nr. 1/8 SONATINE (SONATINA) for violin and piano, 1951 [10'32"]
Nr. 1/6 FORMEL (FORMULA) for orchestra including piano, vibraphone and harp, 1951 [12'57"]
Nr. 1/4 SPIEL (PLAY) for orchestra, 1952 [16'01"]

     These 3 works are all "student works", though Stockhausen did perform SONATINE live on the radio, and the other works were intended for submission to publishers or music festivals.  The orchestral work FORMEL was written right after KREUZSPIEL was completed (in the free hours Stockhausen had when not playing piano accompaniment on tours with the magician Adriano (Adrion)).  SPIEL's two movements were originally the second and third parts of FORMEL (originally titled, "Studie für Orchester"), but since their style was much closer to "point music" than the first movement's theme-based "formula" style, Stockhausen split it off into a separate work.  SPIEL was premiered (with Stockhausen on the piano part) in a slightly edited form at the 1952 Donaueschinger Musiktage festival, along with works by Paul Hindemith, Bernd Alois Zimmerman, Igor Stravinsky and others.
From DG LP back

SONATINE (SONATINA) for violin and piano 
1951 [10'32"]
     This work was one of Stockhausen's last student "assignment" works, and was premiered in 1951 on Cologne Radio (with Stockhausen playing the piano part).  The 3 layers (violin, left and right piano hands) of all 3 movements are all based on one 12-note pitch sequence (row) in which none of the 12 notes repeat.  This sequence can be used in backwards (retrograde) order or upside-down (inversion) form (these are, of course, examples of Arnold Schönberg's serial "12-tone technique").

     As seen in the sketch above of the beginning of SONATINE, the middle staff (piano right hand) has the 12 note "basic" row labeled from 1 to 12.  In the top staff (violin) the 12 note row is inverted (labelled with upside-down numbers).  The 3rd staff (left hand piano) has the 12 note in retrograde (backwards) order.  Stockhausen mentions that the durations and dynamics of the notes are also organized from a single row, but this is not really apparent in the example above (in KREUZSPIEL this aspect would become much easier to detect).  Here, the durations can be heard more as rhythmic motifs.  In "The Works of Karlheinz Stockhausen", Robin Maconie also characterizes these 3 movements as 3 contrasting Bartokian/Hindemith-like studies of "couple relationship" (male and female).  The timings below are from the recording on Stockhausen Edition CD 1 (featuring Saschko Gawriloff and Aloys Kontarsky on violin and piano respectively).
  1. Lento expressivo: Basically polyphonic (as seen in the sketch above).  It has a few tempo changes, but is generally lyrical/rhapsodic.  The 3 forms of the 12-note pitch row bounce around the 3 voices (sometimes with "echoes" and "pre-echoes", as seen above in the 1st staff's 3rd measure and 2nd staff 's 4th measure), and since the melody is expressed in different rhythms, the layers quickly go out of sync.  This sometimes results in a canon-like effect.
    • 0:05: Piano trill begins the 3 layers (as seen in sketch above)
    • 0:32: Tempo becomes more lively
    • 0:39: Bass line surfaces, texture becomes a long piano trill
    • 0:57: Rhapsodic violin over agitated piano, gradually meeting in texture 
    • 1:28: Violin starts basic row again
  2. Molto moderato: Homophonic with the violin floating above and away from a "slow boogie woogie" bass pattern in the left hand piano part.  Often times the violin and the piano right hand layers alternate single melodic lines with chordal harmony lines.  Maconie notes that the movement ends by layering the violin's 6-beats/bar on top of the piano's 4 beats/bar. 
    • 0:00: Boogie-woogie piano bass line begins
    • 0:10: Violin enters
    • 0:18: Piano melody enters
    • 0:53: Piano melody becomes chordal
    • 1:53: Violin becomes chordal, piano melody thins again
    • 2:26: Violin returns to single notes after a brief soloistic figure, piano becomes chordal again, etc...
  3. Allegro scherzando: This movement is probably the most humorous and "dance-like", and has a strong feeling of characters in dialogue (Maconie notes that it consists mainly of stacked (poly)chords, ending in the movement's basic 3-note triad motif).
    • 0:00: Sharp piano motifs separated by sustained violin lines
    • 0:33: Dance-like violin over march piano
    • 1:18: High, closely-voiced (dissonant) piano chords with rhapsodic violin on top
    • 2:01: A somewhat "wry" piano solo, leading into a dialogue with the violin
    • 2:44: March-dance duet returns
    • 3:09: Tentative dialogue with previous motifs, some boogie-woogie piano returns
    • 3:33: Build-up to final march-dance coda
A performance by Jörg und Heinz Lengersdorf:
FORMEL (FORMULA) for orchestra including piano, vibraphone and harp
1951 [12'57"]
      FORMEL (premiered belatedly in 1971) was written after KREUZSPIEL, but unlike the "point music" aspect of that work, FORMEL employs a process of growth and transformation on an initial "12-segment" melodic formula (or an "initial gestalt").

The Formula
     Each of the formula's 12 segments has 1 to 12 unique pitches (see below), and the higher the number of pitches, the smaller the subdivisions given to each note (from 12 16th notes down to 1).  Melodically, the composition is based on a 12-note row, but the row is basically transformed as groups of motifs, rather than on a note level (such as in KREUZSPIEL and the first version of PUNKTE).
The 12 Formula segments (from Bennett Lin's "Serialism in Stockhausen's FORMEL").
The orchestration of the first 4 segments can be seen on the score cover shown at top of this page.
The full score wrap-around cover and CD booklet show the orchestration for all 12 segments.
      Robin Maconie describes FORMEL's harmonic aspect as being based on 12 segments which (in its "initial gestalt") progress from having 12 single 16th notes to 11 dyads (with the length of 2 16th notes), to 10 triads (of 3 16th notes length), etc...ending with 1 12-note chord of 12 16th notes' length (the number of notes in each chord type is matched to the number of notes in the melodic fragment of each segment).

     The vibraphone plays the melody of the 12 formula segments in the beginning.  Afterwards the melody is passed around (see "Form Structure" below).  Some of the other identifying timbral features for the 12 segments in this first section are noted below, but again, these are different each time the segment reappears during the remainder of the piece.  The timings below are from the recording on Stockhausen Edition CD 2 (featuring the SWR Radio Orchestra conducted by Stockhausen).
  1. 0:05 (harp, cello)
  2. 0:08 (oboe, celesta, piano)
  3. 0:12 (pizz strings enter)
  4. 0:18 (violin solo)
  5. 0:24 (melodic trill figure)
  6. 0:30 (vibr, cel., piano)
  7. 0:37 (pizz strings return)
  8. 0:47 (vln & vibr. duo)
  9. 0:55 (low pizz accents in rhythm)
  10. 1:01 (clarinets)
  11. 1:06 (bassoon)
  12. 1:10 (vibraphone scale, basically a 12-tone chord)
    Form Structure (Formula Transformation)
    The sequence and instrumentation of each occurrence of a formula segment
    (image from Bennett Lin's "Serialism in Stockhausen's FORMEL".  Click to enlarge.)
         The 12 melodic fragments occur in different permutations for the remainder of the piece (ie - the formula segments continue after the first 12 with 1, 2, 1, 3, 1, 4, 3, 2, 1, 5, etc...).  This can be seen in Bennett Lin's excellent chart above (the black squares show which instruments are playing the main formula melody as well).  Also, after the initial sequence, each basic fragment appears once as a solo in the 4th octave, and is afterwards transposed for each re-occurrence, always moving to the outer extremes.  In other words, the pitch range spreads out from the middle and migrates out to the upper and lower registers (leaving the middle register empty).  Some of the formula segments sound a little bit alike, since a few basic motivic figures (such as the up-down-up-down shape) appear more than once.  This helps make the piece a little bit "mantra-like", perhaps.  In any case, see Lin's thesis (link at bottom) for more information.

    SPIEL (PLAY) for orchestra
    1952 [16'01"]
    (Evergreen Game, a famous chess match from 1852)
          SPIEL was Stockhausen's very first commission (for the Donaueschinger Musiktage Festival), based on interest generated by KREUZSPIEL. As mentioned previously, it was originally the back half of FORMEL, but since it's "point music" texture was so different from that work, it was separated out. One of its original percussion instruments is a drinking glass, which promptly shattered on its final downbeat at Donaueschinger (Stockhausen: "provoking one of those legendary scandals which my early compositions usually evoked.").   The performance was still a success, however, in that it won Stockhausen the attention of the music publisher Universal Edition, which soon started publishing his scores. The reason behind the title "Play" (or "Game") may be because of the almost "turn-based" entries of the notes of the orchestra groups, as if they were playing a game of chess between them. 

          The 1st Movement begins with single note "points" being passed around among the various instrument groups, while the piano and celesta provide somewhat irregular but subtle background accents.  During this movement the points gradually expand into melodic fragments, and a percussion climax occurs in the middle.  The work PUNKTE would explore the "point" technique much further.  Wikipedia notes that the 1st movement is in 7 sections led by the vibraphone, but frankly it's a bit hard to hear this division (I think it may be tempo or dynamics-based?).  My timings below are from the recording on Stockhausen Edition CD 2 (featuring the SWR Radio Orchestra conducted by Stockhausen).
    • 0:05: Entrance swell and introduction
    • 0:14: Isolated single notes ("points") from various instruments
    • 0:40: 2-note fragments begin in low strings, and soon appear in other groups as well
    • 2:02: Climactic middle section featuring percussion begins
    • 2:20: After the percussion dies down, notes become longer (sustained) and more melodic "trains" appear
    Some of the more "exotic" percussion instruments in SPIEL: Indian bell, cinelli, Japanese woodblock, African pod rattle
    (from score ©www.karlheinzstockhausen.org.)
         In the slower 2nd Movement, the un-pitched percussion is a bit more present throughout.  The notes, durations and dynamics are still organized serially, but because of a 4-layered polyphony the notes do not appear so much as isolated colors (such as in the beginning of the 1st movement).  These polyphonic layers (each with its own "scale of durations") are each made of a pair of pitched and un-pitched instruments as listed below:
    1. Glockenspiel & Cinelli (small cymbals) (with bowed strings as a supporting color)
    2. Piano (left hand) & Drums (with electric organ and string accents as supporting colors) (sketch shown on score cover at top of this page)
    3. Piano (right hand) & Cymbals (with pizzicato strings as a supporting color)
    4. Vibraphone & Hi-Hat (with winds as a supporting color)
         Each layer gradually spreads out from its starting octave range (also seen on the score cover shown at the top of this page) . This movement originally had the notorious shattered goblet at bar 56, but which now uses a triangle/cymbal instead.  Shortly after this midpoint signal, the work proceeds in a reversal of the first part (from the 5:26 mark, in a palindromic mirror form).  Maconie describes this movement as a journey from amorphous resonances into distinct sustained pitches, and then a backwards return after the wine glass/triangle hit.
    Sound Impressions
          These works briefly trace Stockhausen's development from a student writing classroom exercises (thinking more about poetry than music, actually) to a soon-to-be-published mature composer receiving commissions for major music festivals.   Beyond their historical importance, they are all actually pretty enjoyable to hear! In fact, I think they come across as being fairly forward-thinking even in today's musical climate... 
         SONATINE has a very chromatic basic language, but it also has a clear dramatic form which keeps it interesting and easy to follow.  Interestingly, the idea of "echo" and "pre-echo" occurring here would reappear many times in the future, and is even one of the main "accessories" of the LICHT formulas.  FORMEL may be one of the most "hypnotic" of Stockhausen's serial works, in my opinion. The blending of "formula technique" with serial permutations makes it extremely accessible, and the melodic shapes of the formula are almost "singable". When Stockhausen composed MANTRA, he had actually forgotten about FORMEL, but, in fact, FORMEL has many elements which foreshadow the "formula technique" he would use for much of the latter part of his career.  SPIEL is probably most interesting to me as a possible "stand-in" for the "withdrawn" version of PUNKTE. PUNKTE was revised drastically in 1962, removing much of its actual "point" aspect, so SPIEL may be the closest thing to experiencing that unrecorded version.  Also, despite its serial nature, the formula used in SPIEL becomes much more obvious after a few listens.

          As a side note, it's somewhat ironic to me that, in the early works, the titles of some works sometimes seem to be better-suited to the work just previous.  For example "Points" describes SPIEL's note distribution somewhat, "Counter-Points" describes PUNKTE's eventual fate, and "Groups" describes KONTRA-PUNKTE's "point-clumping" in some ways... 

    SONATINE Sound samples and CD ordering
    SONATINE Wiki Entry
    FORMEL and SPIEL Sound samples and CD ordering
    FORMEL Wiki
    SPIEL Wiki
    Purchase the Scores
    Stockhausen Notes on SPIEL
    The Works of Karlheinz Stockhausen (Robin Maconie)
    "Serialism in Stockhausen's FORMEL", Bennett Lin, 2011 (PDF)
    Sonoloco Review