No. 73: TRUMPETENT for 4 trumpeters (1995) [approx. 16 min.]
No. 73 1/2 (ie 73.2): MITTWOCH-FORMEL (Wednesday Formula) for 3 percussionists (metal, wood and skin) (2004) [23'35"]
No. 73 2/3 (ie 73.3): KLAVIERSTÜCK XVIII (Piano Piece 18) for electronic keyboard (synthesizer) (2004) [12'12"]

     These 3 works are chamber arrangements of melodic themes from Stockhausen's opera MITTWOCH AUS LICHT (Wednesday from LIGHT), but the works are not actually found in the opera itself as arranged here.  However, it could be said that these 3 works are drawn from the melodic structure of the climactic vocal sextet "MENCHEN, HÖRT" ("MANKIND, HEAR"), the last sub-scene of MICHAELION, the last Scene of MITTWOCH AUS LICHT.  "MENCHEN, HÖRT" is based on 4 traversals of the LICHT super-formula (a 3 staff, 19-measure melody-theme), starting from simplified "nuclear" fragments, and progressing to the complete super-formula in the 4th cycle.  Each cycle is separated by held fermatas.  TRUMPETENT also completes the LICHT super-formula at its climax, preceded by 3 cycles mostly characterized by drones and tremolos, and is performed by 4 roaming trumpeters.  MITTWOCH-FORMEL (Wednesday Formula) is a version of 3 super-formula cycles adapted for 3 percussionists assigned either wood, metal or skin-based percussion, performed at 3 different tempos.  KLAVIERSTÜCK XVIII (Piano Piece 18) is an adaptation of MITTWOCH-FORMEL for synthesizer, and uses electronic means to characterize each of the 3 formula layers.

     The common theme of this group of chamber works is perhaps "rotation": rotation in space, rotation of timbres, rotation of melodic material, etc...  This idea is also expressed in the CAROUSEL section of MICHAELION, the 4th Scene of MITTWOCH AUS LICHT.

Formula Layers
     The music of the LICHT opera cycle is almost entirely based on a "super-formula", which is a 3-layered melodic-thematic representation of the 3 characters MICHAEL, EVE and LUCIFER.  These formula-themes are together and separately threaded throughout the opera's vocal and instrumental fabric. 

The form structure for the first 3 Scenes of MITTWOCH AUS LICHT.  The bottom 3 staffs are the LICHT super-formula with the "rotations" of the layers indicated (M/E/L).  Above the 3 super-formula staffs are the stretched out Wednesday measures.
The form structure (continued) showing the 4th Scene of MITTWOCH AUS LICHT, MICHAELION.  Unlike the previous 3 Scenes, this Scene has a layer rotation in the middle (at subscene OPERATOR).

     When Stockhausen mapped out the 7 operas of LICHT, he divided the 19-measure LICHT super-formula into 7 "day sections", starting from Monday.  Wednesday is the 3rd day of the week, so it is mapped to measures 6 and 7 (the somewhat middle measures).  In the version of the LICHT superformula above, the bottom 3 staff lines are the full LICHT super-formula, with the major difference being that the 3 staff layers are "rotated" into different orders a few times (with the timing matching the Scene changes mostly).  The staff lines above the bottom 3 lines are a "stretched" version of the 2 Wednesday measures over the full 19 measures of the LICHT superformula below them.  This layering of an extremely slowed-down fragment over the full super-formula is a technique Stockhausen uses in all 7 of the LICHT operas, and notes and durations of the stretched-out fragment are sometimes used to determine pitch transpositions, scene durations, background drone textures, etc...
     Note: The first staff system (above left) only has 4 lines since that part of the Wednesday measure has silent rests for the MICHAEL and LUCIFER layers (only the EVE staff is shown).  Also, the first 2 notes heard are from the ending of the Tuesday segment of the EVE formula.

Three Incarnations of the Wednesday Formula
Trumpets.  Tent.
     TRUMPETENT (TROMPETENT) was a commission from Die Michaelstrompeter (The Michael-Trumpeters), a group of 4 trumpeters formed during the opera production of DIENSTAG AUS LICHT (Act 2's INVASION  uses a troupe of trumpeters).  The members of Die Michaelstrompeter include Markus Stockhausen, Marco Blaauw, Andreas Adam, and Achim Gorsch). One of their aims is to perform in unusual spatial surroundings, which TRUMPETENT certainly provides.  On the stage is a large white TENT with 4 "portholes".  During the first 3 sections (cycles of the LICHT super-formula) the trumpeters independently move both through the audience space along the lines of the compass (North, South, East, West) and also counter-clockwise along the walls.  In between each cycle are sustained harmony fermatas.  In the final section, they enter the tent on stage, and the Wednesday super-formula (the LICHT super-formula with an extra layer) is played as a 4-part invention for trumpets (with their trumpet bells sticking out of the tent portholes).  The stage movements and musical elements are further described below. 

Track Name Track
Start times Performer movements Musical texture
Space 1
(1st Cycle)
3:55 0:07 Players enter from the 4 compass points and approach the center of the audience space Independent, staggered held tones, sometimes with vibrato
2:41 Players reach the center, play a brief phrase, and then resume walking past each other going outside the hall Brief descending harmony phrase, then independent held tones return with lower notes
Space 2
(2nd Cycle) 
4:50 0:00 While outside, players begin a continuous trill and then return to the hall.  
Stationed at each of the 4 cardinal compass points along the wall, they begin to rotate counter-clockwise, changing the trill notes independently at each compass location
Trills and tremolo figures, changing dynamics and speed, position
3:38 After the 3rd rotation, the 4 trumpeters play a unison fanfare together Brief harmony phrase
3:49 Trumpet players play and walk out past the entrance foyer Independent legato bent notes and isolated accents
4:25 Players go outside while playing Ensemble chord with flutter-tongue
Space 3 
(3rd Cycle)
4:12 0:00 Players reenter the hall and go up the center aisle in pairs, pausing during the formula phrases and walking during the free sections.  They enter the tent. Long tones, varied bending ("wailing"),
from a distance getting closer
1:48 3 Nuclear formulas* (EVE, LUCIFER, MICHAEL, 20-24 secs each) separated by independent held trumpet fanfares (20-30 secs)
The section ends in a brief silent pause (fermata)
(4th Cycle) 
3:03 0:00 Players extend their trumpet bells through the tent "portholes" and play with trumpet bells sticking out The full MITTWOCH super-formula is played by the 4 trumpets in 4 layers
2:35 The trumpets retract, the players stick out their heads through the portholes to receive applause, then "evaporate" Final harmony fanfare
*Nuclear formulas are the formulas reduced to its pitch row with only duration and dynamics (ornamentation and articulation is left out)
     Trumpetent performed by Phillip Chase Hawkins, Jessica Waithe, Natalie Fuller, Aaron Hodgson at the 2013 Chosen Vale Center for Advanced Musical Studies International Trumpet Seminar in Enfield, NH:

Score cover featuring left to right: (Stuart Gerber) SKIN, (Oleg Dziewanaowski) WOOD, (Michael Pattmann) METAL
     MITTWOCH-FORMEL (Wednesday Formula) is the MITTWOCH super-formula (described in the above "Formula Layers" explanation) adapted for 3 percussionists playing instruments grouped as METAL, WOOD and SKIN.  Each percussion type (and player) is assigned a staff from the Wednesday super-formula (bottom 3 staff lines: METAL, WOOD, SKIN).  In essence, the 3 LICHT melodic formulas are played by the 3 percussionists, but at 4 points the continuation of the formulas are "handed over" (rotated) to a partner percussionist.  These 4 points are the divisions in the Wednesday Formula (above).

     There are 3 iterations ("projections") of the Wednesday Formula, each one faster then the previous, and the assignment of the percussion timbres to the layers is different for each.  The "stretched" Wednesday formula segment is played on tubular bells for the 1st Projection, but in the 2nd and 3rd Projections the stretched Wednesday tones are incorporated into the melodic shapes of the other 3 layers (which is why, for example the opening EVE formula fragment in the 2nd and 3rd Projections have a more sudden leap from C to D than normal).  During the ending "counting" sections of the super-formula, the words "Wednesday from Light formula - skin, wood, metal percussion" are spoken in the first 2 Projections (in German and then in English).  One of the challenges of this work for the percussionists is the production of micro-tonal pitches through normally-pitched percussion instruments.  This work was premiered by Stuart Gerber (SKIN), Oleg Dziewanowski (METAL) and Michael Pattmann (WOOD) in 2005 during the Kürten Stockhausen Courses. 

     On the CD recording, the instrument groups are arranged low to high going from left to right - ie SKIN (left), WOOD (center), METAL (right).

Score cover with Antonio Pérez Abellán
     KLAVIERSTÜCK XVIII is an adaptation of the Wednesday Formula for multi-timbral synthesizer.  It is up to the synthesizer player to create the timbres to substitute for the 3 percussion groups.  The keyboardist, Antonio Pérez Abellán, assigned specific timbres to each of the MICHAEL, EVE, and LUCIFER formula elements themselves (as opposed to each staff).  What this does is to essentially highlight the rotations of the registers of the formula segments.  For example, LUCIFER is normally a low, bass clef melody.  In KLAVIERSTÜCK XVIII, the LUCIFER formula has this sequence of registers: high - low - middle - middle - low.  Each formula has its own sequence of 5 register rotations.  Since the layers are rotated for each of the 3 iterations, every section of each formula eventually gets to be played in all 3 registers.

     In the first iteration, the Wednesday "stretched" layer exists on a 4th staff ("bell-tones"), but in the 2nd and 3rd iterations the long Wednesday tones are incorporated into the other 3 layers (in the same manner, of course, as in the percussion trio version described previously).

     One unique aspect of the 3rd iteration of the Wednesday Formula is that Abellán gave each formula its own "organ mixture" - that is, the rotating MICHAEL, EVE and LUCIFER melodies each have a parallel harmony programmed into their timbre.  For example, the MICHAEL notes have a slightly softer harmony pitch 19 steps above it, EVE notes have a harmony 26 steps higher, and LUCIFER has a harmony 23 steps higher.  Abellán premiered this piece in 2005 during the Kürten Stockhausen Courses using a Kurzweil K 2600 X synth with volume pedals (due to the complexity of the dynamics, 2 layers were played "live", and the remaining layer(s) were pre-sequenced).  On the CD recording, the register layers are arranged low to high going from left to right.

"Comprehension of the formula construction is the rational aspect; 
being moved by the magic sound layers is the other, mysterious aspect... a performance with electronic piano, one cannot see how the sounds are produced.  
It is best to close the eyes and experience a HYPER SUPER FORMULA."
- Stockhausen, from the CD booklet (Stockhausen Edition CD 79)

Sound Impressions
     All three of these works examine the LICHT super-formula through a kind of Rubik's Cube lens.  The melodies and sound sequences are all recognizable, but the colors keep changing, or rather "something's different", but it's not always obvious right away what that difference is.  I think that might be what Stockhausen means by appreciating these works for their "mysterious aspect" as a "hyper super formula".  Even aside from the "familiar/unfamiliar" aspect of these pieces, these arrangements of the LICHT super-formula for trumpet quartet, percussion trio and synthesizer bring new light to the polyphonic fabric of the formulas.  The timbral choices for the percussion trio and the synth timbres are especially revealing.  Admittedly, some of the timbral details (such as the "mixtures" in KLAVIERSTÜCK XVIII) are a bit hard to discern on a CD recording, at least on my sound system.  The bottom line however, is that these are really rich and beautiful-sounding chamber works and show off the melodic aspects of the LICHT super-formula in a very concise and accessible way.

     From a theatrical standpoint, TRUMPETENT also has a mysteriously ritualistic atmosphere.  The blue symbol for MICHAEL (at top of page) indicates 4 horns pointing in the cardinal directions, which of course, is reflected in the movements of the 4 trumpet players.  Despite it's somber beginning, it ends on a fairly funny image.  Seeing the audience reactions in the video is amusing in itself!

Sound samples, tracks listings and CD ordering: