Scene 1
Scene 2
Scene 3
Scene 4

Michael Leibundgut as "Lucifer"
 in the 2013 Munich Production
(LUCIFER's Dream, or Piano Piece 13)
for Bass vocalist and piano
1981 [36']

No. 51 1/2 (ie - 51.2): KLAVIERSTÜCK XIII (Piano Piece 13), for solo piano, 1981 [36']
No. 51 2/3 (ie - 51.3): TRAUM-FORMEL (DREAM-FORMULA) for solo basset-horn, 1981 [9']

          LUZIFERs TRAUM (LUCIFER'S DREAM) is the 1st Scene of Stockhausen's dramatic music work SAMSTAG AUS LICHT (SATURDAY from LIGHT), which was the second-composed entry of his 7-part, 29-hour opera cycle LICHT (Light).  LICHT is a work for acoustic and electronic operatic forces, divided into the 7 days of the week (one opera for each day).  This opera cycle revolves around 3 archetype characters, MICHAEL, EVE and LUCIFER, and over the 29 hours each of these characters are introduced, come into conflict, face temptation and finally come into union.  The music is almost entirely based on a "super-formula", which is a 3-layered melodic-thematic representation of the 3 characters.  These formula-themes are together and separately threaded throughout the opera's vocal and instrumental fabric.  Story-wise, actors and narrative can (and often do) change from scene to scene, and the libretto text is sometimes made up of non-traditional grammar (or even purely phonetic sounds).

     SAMSTAG is LUCIFER's day, which is the Day of Death (and Resurrection), as well as the Night of the transition to the LIGHT.  In LUZIFERs TRAUM, the character LUCIFER, played by a bass vocalist, has a dream which is interpreted as a piano solo.  At the end of the scene, LUCIFER is entranced by a "simple melody" and apparently "dies".

     Lucifer (a bass vocalist) leans on a cloud (or sits in a chair) and looks into the distance. He plays a few chords on his piano. "Majella" (apparently his personal pianist/companion) enters and takes over the piano, allowing Lucifer to fall into a trance (his eyes remain open). Majella essentially provides the musical contours of his dream-reverie, which consists primarily of elaborated forms of the Eve and Lucifer formulas (a scrolling, 5-layer "light show" is projected which is designed to symbolize the musical melodies being played).

     During this dream/trance, Lucifer sometimes mumbles in his sleep (numbers, musical terms, etc.). Majella also contributes spoken numbers, whispers, whistling and plays the inside strings of the piano (sometimes with a "bone-headed mallet"). After one of Lucifer's half-conscious rants, Majella launches (small) rockets up into the sky towards a projection of the Earth (signifying Lucifer's distaste for the Earth and war against Michael). Shortly thereafter, Majella plays a "simple melody", based on a simplified form of Eve's formula. Lucifer jerks awake, enchanted. However, soon Lucifer begins "dying" from this entrancing melody. Majella begins playing the piano keys with her arms, legs and buttocks. After Lucifer has apparently expired (ironically, Lucifer's own companion has "killed" him!), she walks around the piano making magical gestures and then finally departs. However, Lucifer secretly sneaks a wink at the audience at the end, signifying that he will be back.

          Also known as KLAVIERSTÜCK XIII (Piano Piece 13), this piece was apparently originally designed as a work for solo piano and then 4 bass vocal solos were added to it to create its dramatic arc of being LUCIFER's dream.  The melodic formulas of MICHAEL, EVE and LUCIFER and their derivations from the full LICHT super-formula are interwoven throughout LUZIFERs TRAUM both as actual melodic material and as transposition pitches for several repetitions of the EVE and LUCIFER formulas.  However, despite the construction as 5 temporal layers, the whole work really does feel like a "dream", with lots of melodic ruminations.

Form Structure
This is the Saturday section from the LICHT super-formula.
The first 3 staves are the MICHAEL, EVE and LUCIFER formula layers.
The 4th staff is the complete LUCIFER Nuclear formula.
The scene structure of LUZIFER'S TRAUM is assigned the first measure.
There are 5 main temporal and cyclic layers derived from the LICHT formulas and formula fragments. 
  1. MICHAEL formula (one cycle/repetition)
  2. EVE formula (eight cycles, with transpositions based on the LUZIFER'S TRAUM segment of the EVE formula (8 descending notes, staff 2, m. 1 above))
  3. LUCIFER formula (one cycle)
  4. LUCIFER formula (five cycles, with transpositions based on the LUZIFER'S TRAUM segment of the LUCIFER formula (5 ascending notes, staff 3, m.1 above))
  5. LUZIFER'S TRAUM segment of the LUCIFER Nuclear formula (4 notes, 1 very long, then ascending to 3 short descending, staff 4, m. 1 above)
          The 2nd and 4th layer cycle transpositions are based on pitches from the 1st measures of the EVE and LUCIFER formulas from the LICHT super-formula's Saturday day-segment (the super-formula is divided into 7 segments, one for each day of the week).  The 5th layer is the first measure of the LUCIFER nuclear formula (simplified version of the formula).  There is also actually a 6th layer based on the LUCIFER's TRAUM measure of the LUCIFER formula (the 5 ascending notes in the 3rd staff).
The EVE Formula is traversed 8 times.
(click to enlarge)
The LUCIFER Formula is traversed 5 times.
(click to enlarge) 

          After a brief introduction consisting of 7 chords using the LUCIFER "signature" motif (major 7th) and a quotation of Layer 4 (5 ascending notes), the main "dream" begins.

          Layer 2 is the most obvious, and it is basically seven cycles (repetitions) of the complete EVE formula, each time starting on a different pitch, depending on the seven transpositions.  This is followed by an eighth cycle called "The Simple Melody", which is also based on the EVE formula.  These multiple statements of the EVE formula are put through a variety of elaborations and expansions, using all aspects of piano performance, including playing the inside piano strings (with fingers, nails or hammer), striking the piano frame, dense clusters, whistling, shaking Indian bells, vocalized counting and even small model rockets (site-permitting).  Melodic figures are also enhanced or simplified with additional harmonic and melodic elements.

          Simultaneously, Layer 4 is played, consisting of five cycles of the complete LUCIFER formula, each time starting on a different pitch, depending on their 5 transpositions.  These five LUCIFER statements are also elaborated on in the same way as Layer 2's EVE cycles.  Additionally, the melodic elements (called "human figures" by the bass vocalist) are temporally compressed and the percussive gestures (knocks, rests, whispers, etc...) are lengthened (see "Dissolution of the LUCIFER formula" down below).

          Layers 1 and 3 are each single iterations of the MICHAEL and LUCIFER formulas, but temporally stretched from the original formula length of 1 minute to about half an hour.  In other words these are slowed down to 1/30th of their original tempo.   Layer 5 is a single measure the length of a half note, stretched out to almost a half hour.  Actually, "temporally stretched" is probably not exactly a correct way to describe it, since notes do not sustain 30 times longer.  More accurately, the formula note "attack moments" are spread out over these long durations.  In other words, notes and sounds from the MICHAEL and LUCIFER formulas will just "drop in" on top of the more active cycle-based layers. 

          The final effect is a polyphonic work with a foreground layer based on the eight EVE cycles, a middle-ground layer based on the five LUCIFER cycles, and background (very background) layers created from the very slowly portioned out notes from single statements of the MICHAEL and LUCIFER formulas, and the basically too-sparse-to-be-heard 5th layer from the 1st measure of the LUCIFER nuclear formula.  The layers are graphically illustrated in the stage lighting form scheme (see Live Performance below). 

Majella Stockhausen from score cover

Second column is CD track numbers for Stockhausen Complete Edition CD 33 featuring Majella Stockhausen.
Bar CD 33
Layer 4
Layer 2
EVE Cycles
Layer 1

Layer 3

Layer 5
LUCIFER Nuclear Formula
1 38
LUCIFER as a bass vocalist leans on a cloud (or chair) and looks into the distance.
MAJELLA (the pianist) plays 7 major 7th LUCIFER chords in G
(some stacked with BbM7th intervals and a high F, probably from the L's TRAUM LUCIFER and LUCIFER Nuclear formula segments)  
as LUCIFER the bass vocalist intones 5 ascending notes 

Cycle 1

Cycle 1

LUCIFER sits down and falls into a dream, interpreted by MAJELLA.

LUCIFER Cycle 1 (Layer 4) begins with Ab pedal rhythm
EVE Cycle 1 (Layer 2) also begins in right hand
1st note
1st note

Nuclear formula
1st note

16 40 high cluster glissandi etc...
high tremolos (Bb/Db and Bb/C) w slow ascending bass
21 41 1st knocking phrase
2nd knocking phrase
EVE Thursday gesture: 8 colored glissandi
30 42 LUCIFER's 7 numbers (whispered), 
fingernail string gliss, plucks
whistle descending/ascending
back and forth fingernail "scrubbing" on strings
35 43 end fingernails
38 44 dense LUCIFER (Layer 3) tremolo on C begins etc...
whistle descending/ascending
LUCIFER Friday gesture: 
3 voiceless calls ("piu")
47 45 Layer 3 C tremolo continues
(MICHAEL formula silent pause)

LUCIFER's 5 numbers (whispered)
w finger gliss on strings
52 46 E2 EVE Cycle 2 begins
"Pa!", handslaps
57 47 EVE "shhh" descending gliss
59 48 tremolo on A and F#
accel. knocks
thumps under the keyboard

66 49 LUCIFER's 12 numbers (whispered),
cluster gliss.

EVE Thursday gesture: 
several colored glissandi
MICHAEL cluster briefly interrupts EVE's glissandi
LUCIFER bass vocal solo: "13…1, Majella..." 
(LUCIFER Nuclear formula retrograde melody, hence the backwards numbers)
(EVE yodels?)
descending whistle gliss 
77 50 L2 LUCIFER Cycle 2 begins


MICHAEL cluster briefly interrupts chord rhythm


86 51 high clusters
90 52

98 53 E3 EVE Cycle 3 begins (from part of m.97)
101 54 ascending scale
LUCIFER's 8 numbers (1...7, 1)
106 55 end count



112, 113
(MICHAEL & LUCIFER Layer 3 formulas silent pause)

knocks w tongue clicks
117 56 after clicks
122 57 LUCIFER Friday gesture: 
3 voiceless calls ("piu"), string pizz.
fingernails on strings
128 58 LUCIFER's 8 numbers (mysteriously),
Indian bells

LUCIFER's 5 numbers
140 59 bass pedal notes
(momentary "full voice" counting from LUCIFER slow formula)
147 60 E4 EVE Cycle 4 begins (end of 146), 
LUCIFER's 13 numbers

counting becomes witch-like
LUCIFER bass vocal: "13…5, Majella - crescendo decrescendo, colored silence, noises...shades, colors of nothing" 
(retrograde LUCIFER & EVE formulas)
nail glissandi on strings


159 61 L3 LUCIFER Cycle 3 begins

hand slaps
165 62 EVE Thursday gesture: 
several colored glissandi w clusters and hissing
descending whistle  
nail glissandi on strings

177 63 nail glissandi on strings again

185 64 LUCIFER's 8 numbers, 


192 65 end counting
(LUCIFER slow formula silent pause)
197 66 even 8th note figurell
204 67 E5 EVE Cycle 5 begins (actually 202)
209 68 EVE "Wind", 
inhale, exhale breathing
212 69 LUCIFER Friday gesture: 
3 voiceless calls ("piu") gliss, bells
216 70 high register large interval tremolos
Count 1-5-1-5, knocks
225 71 count ends
EVE Thursday gesture: 
several colored glissandi
234 72 bells, LUCIFER Friday gesture: 3 voiceless calls ("piu"), very slow
use mallet to strike and rub low strings
242 73 Big scale run before count
LUCIFER's 13 numbers, very slow
250 74 LUCIFER bass vocal: "Compression of figures, of humans' music, expansions and pauses for annulment of time." 
(retrograded forms of LUCIFER & MICHAEL formulas)
Also whistling/counting

258 75 L4 LUCIFER Cycle 4 begins

265 76 tremolo before EVE Cycle 6
E6 EVE Cycle 6 begins F#

269 77 staccato scale run
EVE big descending gliss
278 78 end gliss
knock on piano edges
284 79 hammer against metal bell stand, whistling, string scraping begins

LUCIFER's 8 numbers, vary fast
knocks F

EVE Thursday gesture: several colored glissandi w nails on strings
293 80 whistle
whistle ends, 
nail and string brushing, pizz.

310 81 LUCIFER Friday gesture: 
3 voiceless calls ("piu")

314 82 Low tremolo accel.
319 83 LUCIFER's 5 numbers, 
fast and repeating
322 84 chordal

EVE Cycle 7 foreshadow
332 85 E7 EVE Cycle 7 begins
338 86 EVE big descending "shhh" gliss, bells
LUCIFER's 5 numbers, 
increasing to 13, witchlike
343 87 LUCIFER's numbers repeating with different speeds ("7" loudly during LUCIFER's solo)
LUCIFER bass vocal (stares at the ceiling, raises hands, uses "finger language"): "Elements five thirteen - Air, Rhythm, Water, Melody, Earth, Harmony, Fire, Dynamic Light colors, Colors, Timbre - Saturday of Light!" (sits back down into dream)
(retrograde forms of all the previously sung LICHT formulas)

Rockets are fired at a projection of the Earth (unheard).
The rockets signify LUCIFER's distaste for the Earth and war against MICHAEL.
EVE Thursday gesture: 8 colored glissandi
357 88 L5 LUCIFER Cycle 5 begins

Clap, open arms in a large arch above head
361 89 whistle end, cluster chords
369 90 restless scalar runs


389 91 end scalar runs
LUCIFER's 7 numbers fast, backwards
396 92 The


Simple Melody Cycle begins, emphasizing the EVE Nuclear formula

EVE Cycle 8 - 
LUCIFER suddenly jerks to attention
cluster gliss
knocks w tongue clicks
cluster gliss
(end of very slow Layer 5 -  LUCIFER's TRAUM LUCIFER nuclear formula segment)
404 93 whistle, nail and string scrubbing
413 94 (Enchanted, LUCIFER listens to the simple melody)
before cluster gliss
421 95 LUCIFER bass vocal solo: "Eins….." ("1…")
EVE Sub-cycle
forearm clusters
431 96 "zwei…", knocks
EVE Thursday gesture: several colored glissandi
LUCIFER: "drei…..", knocks
438, 441
right thigh/buttock chord cluster gliss, nail string gliss, pizz
448 97 left buttock chord cluster with LUCIFER's 13 numbers, witch-like

LUCIFER: continued (8, etc...)

453 98 full leg chord cluster, buttock sliding clusters
ascending vocal gliss, double-handed chord cluster
456 99 LUCIFER closes his eyes and slumps
big descending cluster gliss with thigh clusters

MAJELLA walks around piano making magical gestures.  After pizz. note, slap strings gently. 
LUCIFER winks at audience.
MAJELLA catches him and he pretends to sleep again.
MAJELLA inspects his cheek with a finger, shouts "piu!".

      Jerome Kohl has written several articles (links at bottom) which delve into some of the more subtle aspects of LUCIFER's TRAUM:

      In his article "The Evolution of Macro- and Micro-Time Relations in Stockhausen's Recent Music" (Perspectives of New Music 22), Kohl describes the tempo/durational structure of LUZIFER's TRAUM as being in 5 cycles of 18 groups each. Each cycle (parallel with the 5-cycle Layer 4) has proportional tempo elements which relate to intervals in the LUCIFER formula.
      Kohl also mentions (in his article "Into the Middleground: Formula Syntax in Stockhausen's Licht", Perspectives of New Music 28.2) that the 4 bass vocal solos at the ends of the first 4 LUCIFER cycles is based on retrograded forms of the LICHT formulas. First the LUCIFER Nuclear formula is sung in retrograde (backwards), then LUCIFER (Nuclear) and EVE are combined and in retrograde, then LUCIFER and MICHAEL formula forms retrograded, and then finally all 3 previously sung formulas are sung in retrograde.
      The LUCIFER formula goes through 5 cycles, but in each iteration after the first, a process of progressive "dissolution" occurs. Stockhausen does this by increasingly compressing the melodic figures and expanding the pauses and "colored silences" (the bass vocal text in bar 250 actually states this outright). In "Time and LIGHT" (Contemporary Music Review 7, 1993), Kohl describes Stockhausen's initial sketches for LUCIFER's TRAUM and how he realizes these distortions in the final score. In sections 2 through 5, 20 "distortion events" (pauses or mostly un-pitched "noises" such as the knocking, etc...) are spread out and are increasingly lengthened with the use of the Fibonacci series and "magic square" matrices. These progressive expansions of "null time" are a bit hard to detect, but the counting bit obviously gets slower and slower.
      In addition to the 5 layers described above, there is also a 6th layer which is very subtle (maybe more so than Layers 1 and 3). This 6th layer, based on the LUCIFER's TRAUM measure of the LUCIFER formula expresses the 5 crossed ascending notes as what Jerome Kohl calls "halo chords" (also described in notes from his lecture, "Neotonality in SAMSTAG AUS LICHT"). These are chords which are pressed down silently with the middle piano pedal down. For large sections of the work, this pedal is held down so that when the rest of the notes in the piece play, the notes from the silent chords subtly vibrate as a background texture, and new notes which are part of these chords are emphasized. There are 18 of these held chords, but they are divided into 5 main tonalities, each matched with one of the 5 rising notes in the 6th layer. The 5 notes are labeled in the LUCIFER formula as "voiceless", so the usage of silent chord pedaling is very appropriate.
      See KLAVIERSTÜCKE V–X for more on halo tones...
The lowest staff is labeled Gesäß ("Buttocks").  "Stand up, lay entire left leg on the keyboard...slide buttock each time, suddenly head pulled back, chest forward..."  The last text is an instruction to use the hammer as a wedge to keep the right sustain pedal down so that the clusters continue to ring after the pianist has left the stage.

Live Performance
Above: stage form scheme showing either the melodic shapes of the layers or their transpositions:
Layer 1: MICHAEL formula (BLUE outline)
Layer 2: Eight EVE cycle transpositions (GREEN outline)
Layer 3: LUCIFER formula (BLACK outline)
Layer 4: Five LUCIFER cycle transpositions (RED outline)
Layer 5: LUCIFER Nuclear formula 1st measure (BROWN outline
          For a staged performance, the actual form structure of the 5 layers is visualized as 5 changing bands of light, moving from right to left.  The score has indications of when to change the projected light height so that the change of notes in the MICHAEL and LUCIFER formulas or the beginning of a new LUCIFER or EVE cycle are visible to the audience.  The shades of color in these bands of light indicate the dynamic intensity of the notes as well (the colors I used to highlight the formulas above are NOT the colors of the bands of light to be used in the stage production).

 Nino Jvania (Zhvania) performs the solo concert version of KLAVIERSTÜCK XIII.
New England Conservatory, Williams Hall, Boston, MA, USA, 05.15.10

          TRAUM-FORMEL, or "Dream-Formula", is very similar to LUZIFER's TRAUM in that it creates a polyphonic 6-layered web from the Saturday LICHT formulas.  It's a very virtuosic piece because Stockhausen places the layers in different registers in order to separate them, and so the bassett-horn has to constantly make large interval leaps.

The MICHAEL Formula
The 6 layers of TRAUM-FORMEL are:
  1. The MICHAEL formula (at right)
  2. The LUCIFER formula (see earlier section)
  3. LUZIFER'S TRAUM segment of the MICHAEL formula (1 note)
  4. LUZIFER'S TRAUM segment of the EVE formula (7 notes)
  5. LUZIFER'S TRAUM segment of the LUCIFER formula (5 notes)
  6. LUZIFER'S TRAUM segment of the LUCIFER nuclear formula (5 notes)

           The main body is book-ended by an introduction (high expanding vibrato-trill, 57") and coda (ending with low vibrato tones with grace notes, 55").  The full cycle is completed twice (2'58"/2'52"), with 3 additional short "insert" sections.  The first insert is a slow, low 2-note figure (middle of the 1st cycle), the second is a long B note (between the 2 cycles), and the third is a tremolo on C# and a descending 2nd note, based on the LUZIFER'S TRAUM segment of the EVE formula (near end of the 2nd cycle).  Stockhausen also writes "If at all possible, DREAM FORMULA should be performed wearing a blue-black, green-black, glittering costume, nocturnal-erotic".  This description as well as some lighting cues come from a vision Stockhausen experienced.

Beginning of the main body.
The MICHAEL formula is traced in BLUE.
The LUCIFER formula is in RED.
The other layers' pitches are interspersed among these 2 main layers.
(score ©

Sound Impressions
     LUZIFER's TRAUM is has alot of meticulous structural elements, but its basic fabric is very "liquid".  Since the scene is that of a dream, the themes and gestures take on a quality of rumination - themes are savored before moving on to the next motif.  The EVE formula goes through 8 cycles, yet one never feels that one's been there before, due to the changing "tidal forces" of the other 4 layers.  However the EVE formula's Wednesday segment does surface many times as a welcome "anchoring" motif.  At times the work feels very jazzy and improvisatory.  Sometimes when the texture threatens to become too languid, a heavy tremolo or piano string scrape will suddenly break the spell.

     "Liquid", "tidal forces", "anchoring"... it seems that (for me at least), one form of imagery that comes to my mind when listening to LUZIFER's TRAUM is that of a dark and foggy ocean voyage, with the knocking, scraping and whistling of the pianist portraying the creaks of its hull as it bumps into the detritus of broken vessels floating on the waves.  Perhaps the story of Charon and the river Styx could be appropriate as well...  Come to think of it, a staged performance on nighttime cruise sounds like it would be a pretty interesting experience!  Finally, I find it interesting that EVE's "simple melody" lulls LUCIFER into a death-like sleep.  I never would have guessed that the formula for EVE (who represents "birth") could be "weaponized" this way :).  Then again LUCIFER is not really dead, as indicated by his wink at the end...

     TRAUM-FORMEL is one of Stockhausen's most impressive solo wind works and it's a great example where structural complexity is not sacrificed on the altar of virtuosity.  I think it might be interesting to hear arrangements of this piece for other instruments, such as has been done with IN FREUNDSCHAFT and AMOUR...

Sound samples, tracks listings and CD ordering:
The Evolution of Macro- and Micro-Time Relations in Stockhausen's Recent Music (Jerome Kohl)
Into the Middleground: Formula Syntax in Stockhausen's Licht (Jerome Kohl)
Time and Light (Jerome Kohl)
Stockhausen on Opera (Interview with Jerome Kohl)
Albrecht Moritz article on SAMSTAG AUS LICHT
KLAVIERSTÜCK XIII (Simon Smith, 2016, Youtube)
KLAVIERSTÜCK XIII (Apostolos Darlas, 2015, Youtube)
SAMSTAG AUS LICHT Staging 2013 (photos)
TRAUM-FORMEL Analysis (Vickery) (PDF)