The System of LICHT

Karlheinz Stockhausen’s opera cycle LICHT is many things and as a great work of art it is subject to multiple, if not endless, interpretations. These interpretations are multiple because the opera is made up of living symbols. As Carl Jung taught, it is possible to distinguish between a symbol and a sign. A symbol is the best possible expression for something that is unknown, whereas a sign is something specific, such as the insignia worn by a military officer showing his specific rank.

 For this work the specific and very rich symbolism of LICHT will be set aside to look at it from a structural and systems point of view. The way Stockhausen gave his work specific limitations shaped the work in unique ways. His adept and intuitive grasp of combinatorial procedures within the limits of the system gave him a wide ranging freedom to play with the materials he had chosen, shaping the raw ingredients into an astonishing and sensual feast of sound, color, and movement.
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Opening up the lid of the opera cycle it’s possible to see how its individual components create a musical engine whose individual circuits sync together in a series allowing for a dynamic flow of energies and psychoacoustic forces. Let’s look under the hood of LICHT to see how its various pieces fit together.

Conception of LICHT: Formula & Super Formula   

            Great ideas often come as revelatory seeds into the mind of those who are prepared. By the mid-seventies Stockhausen had been composing for a quarter of a century and he had already explored a vast territory of sound implementing new ideas for the arrangement of music in time and space. He had played with intuitive music, aleatory processes, and had mastered new electronic music techniques in the studios of WDR, just for starters. The soil of his mind and spirit were fertile, waiting for the next big idea to be planted.

Another tactic basically invented by Stockhausen was formula composition and it came out of his deep engagement with serialism. It involves the projection, expansion and ausmultiplikation of either a single melody-formula, or a two- or three-voice contrapuntal construction. In serial music the structuring features remain basically abstract but in formula composition properties such as duration, pitch, tempo, timbre, and dynamics are also specified from the formula. By using concise and specific tone succession based on the single melody formula both the macro structure and micro details of the composition can be derived.
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The roots of his method of formula composition can be traced back to his once withdrawn orchestral piece Formel where the first basic pattern of notes are gradually transformed over the course of the work. The central pitch is first broadened out before the notes are removed leaving only the low and high extremes. He continued to use serial operations on his next batch of works, Kreuzspiel and Punkte, and then introduced musical pointillism into the methods as explored in Kontrapunkte and Gruppen.

​Then for a time he moved on to other musical tactics and explorations but came back to the practice with ferocity in Mantra from 1970. Written for two ring modulated pianos, the pianists are also required to play a chromatic cymbals and a wood block. One of the players also has a short-wave radio tuned to a station sending morse code, or when CW isn’t readily available live on the air, a tape recording of morse code is played. It was the first composition that he wrote where he used the term formula, and was one of many watershed moments in his musical thinking. The formula involved the expansion and contraction of counterpointed melodies. 

His next piece to use formula composition was Inori from 1974. By this time Stockhausen had already been working extensively with writing music that incorporated elements of theater. Inori took it to another level and he had the insight that he could use the formula, not just for music, but as a way to compose gestures. This was another component that would become essential in LICHT.
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Inori is a long work with performances lasting around seventy minutes. The formula for the piece is made up of fifteen notes using 5, 3, 2, 1 and 4 pitches respectively. When the formula is used on the macros scale for the work these five phrases are split into five segments Stockhausen to create a narrative sequence. Robin Maconie says it “lead[s] from pure rhythm . . . via dynamics, melody, and harmony, to polyphony: —hence, a progression from the primitive origin of music to a condition of pure intellect. The entire work is a projection of this formula onto a duration of about 70 minutes”

In 1977 Stockhausen went back to Japan to work on a commission for the National Theater of Tokyo. The idea for intermodulation of music had come to him in his first Japanese commission with Telemusik and he had played his music alongside nineteen ensemble musicians in the special spherical chamber designed for him at the World Fair in Osaka in 1970 for about five and a half hours a day, 183 days in a row. Japan had been a good country for his musical expression. The piece he came to work on when LICHT was conceived was to being written for traditional Gagaku orchestra and Noh actors. The dramatic elements for the production however came to him in a dream, just one of many dreams that gave him direct inspiration for compositions. While composing what became Der Jahreslauf, (Course of the Years), he had a revelation about a way to represent different levels of time by different instrument groups: millenniums are depicted as three harmoniums, centuries by an anvil and three piccolos, decades by a bongo and three saxophones, and years by a bass drum, harpsichord and guitar. These instrument groups became representations of vast forces and scales of time.

            This idea of composing music around the theme of various increments of time stayed with the composer for the rest of his life. While working on this commission, another idea was also transmitted into his mind, the super-formula that became the basis for LICHT. In a flash a small seed became the basis for a work of cosmic proportions. Subsequently he used Der Jahreslauf as the first act of Dienstag aus LICHT (Tuesday from Light). 

            In LICHT he realized his formula technique could be considerably expanded. The entire cycle of seven operas is based on three counterpointed melody formulas. Each of these is associated with one of the three principal characters that make up the dramatic element of the production. (Stockhausen himself said the formulas are the characters.) The melodies then define the tonal center and durations of scenes, and zooming in, give detailed melodic phrasing to more refined elements. The three characters are Eve, Lucifer, and Michael, and they are each associated with a specific instrument, bassett horn, trombone, and trumpet in turn.
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This explains formula composition, but what about a super-formula? 

In 1977 Stockhausen had been composing for just over twenty-five years.  In the super-formula he synthesized nearly all of his musical ideas into a musical tool that would occupy him for the next twenty-seven years until 2003 when the last bars for Sonntag aus LICHT were drying on the staff paper.

He had the insight to take the three formulas he had come up with for Eve, Lucifer and Michael and layer them horizontally on top of each other to make the super-formula. Now they existed as one, each with their own layer, named after the character, or force, in question. The super-formula then gets subdivided again, vertically, into seven portions, of two to four measures each. These seven vertical rows form the days of the week.

Combined the horizontal and vertical rows make up the rich matrix out of which the overall structure of LICHT is built. To expand the formula in time, every quarter note of the super-formula is equal to 16 minutes of music. This is how the maestro -or magister- used it determine the durations of the opera cycles various acts and scenes.

Stockhausen also decided to create a kind of skeleton key, bare bones version of the super formula for each of the three characters. These he called “nuclear formulas” (kernformel) and consisted of just the pitches, duration and dynamics. Boiling the bones down even further provides the broth that the music is bathed in. When the nuclear formulas are reduced to just the notes what is left is essentially a serialist tone row. These are known as the kernels, central tones, or nuclear tones. Nuclear, because they form the very atoms of the music.

With all of this in place the fun has a chance to begin. The super-formula can now be used in all manner of ways. Sometimes Stockhausen employed it in an inverted or retrograde fashion (upside down or backwards). It is very often stretched out across the time frame of scenes and whole acts. Other times it is transposed vertically. Once the listener becomes familiar with each of the formulas for the characters or forces, it is possible to pick out those forces at work in the music even though the formula is not really used as a recurring theme in the typical sense of classical music. Rather, as Ed Chang said, “In LICHT, the MICHAEL, EVE and LUCIFER formulas are used more as structural forces whose tonal characteristics exert a kind of planetary gravity over the surrounding musical ether.”

            LICHT is a complete system. The superformula, nuclear kernels, and nuclear tones form the mathematical and musical parts of the systems ecology. The content of the opera, its symbolism based around the days, and the spiritual realities of Eve, Michael, and Lucifer are another aspect of the system. All of this gave Stockhausen the raw material out of which to craft his magnum opus. The music and symbolism mix together and all are now subject to a remarkable game of combination and recombination. The system of LICHT forms the matrix of possibilities, and displayed within that matrix are an extraordinary blending and synthesis of constituent forms.

The idea of ausmultiplikation, which can be translated as "multiplying-out" bears further looking at in terms of how formula composition creates musical forms mirrored on the macro and micro scales. Stockhausen described the technique as when a long note is replaced by shorter "melodic configurations, internally animated around central tones". This bears a strong resemblance to the Renaissance musical technique of diminution or coloration, where long notes are divided into a series of shorter, frequently melodic, values. But Stockhausen also used the term to refer to when he substituted a complete or partial formula for a single long tone, often as background layer projections of the formula. Formula composition and its various components like ausmuliplikation can be seen as  Stockhausen’s way of creating a way to practice the Glass Bead Game in music.
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Robin Hartwell had the insight that when this is done at more than one level results resemble those of a fractal. If the formula compositions are fractal like, and he also used the idea of spirals throughout his work, one way of looking at LICHT is as a composed fractal music. Zooming in and out, the same structure is played in both minutely on the microscopic level, and at large on the macroscopic across the range of an entire work. Having boiled down of the musical components to microscopic levels, and having diluted them out to the macro, was one way Stockhausen prevented signal loss and maximized the transmission of his musical information. The super-formula is present and exists on every level and in every moment of LICHT.

Modular Music

Another way Licht can be seen as a musical system is by how it is structured in component modules. First of all, it should be considered that each of the operas is a work capable of being appreciated and understood unto itself, without having to hear or see the other sections. While listening to the whole cycle certainly enhances the experience of individual parts, those individual parts can also be enjoyed one at a time in and of themselves. Each opera, act, scene is self-sufficient. Even some parts of scenes can be extracted as solitary works. Certain other extra-curricular or auxiliary works have also been extrapolated out of the formulas of LICHT and its modular structure. All of these contain the essence of LICHT and give the listener one of many ways of enjoying the various elements of the cycle.  
           
This was all made possible due to the practical aspects of Stockhausen’s life as a composer. After he began LICHT, when he received a commission for a new work from this or that person or cultural institution, prescribed for this or that choir group, string quartet, or other group of instrumentation, he would incorporate the work on that commission into LICHT. It was an elegant solution that allowed him to finish the massive project.
           
​Some of the examples of modular works that can be extracted from LICHT include Klavierstucke XII and Michael’s Reise from Donnerstag; Weltraum is an assemblage of the electronic greetings and farewells of Freitag; Kathinka’s Chant for flute and electronics is an extract from Samstag; Angel Procession’s for choir comes from Sonntag; Ypssilon for flute and Xi for basset horn from Montag; the electronic layer from the second act of Dienstag becomes the piece Oktophonie; and the infamous Helicopter String Quartet is a section from Mittwoch. These are just a few of the pieces he was able to write in a modular fashion to fulfill a commission and thus complete a section of LICHT. Alternately he was able to adapt an already written section of LICHT as a module to fulfill a commission and thereby create a smaller chamber type work. 

Ars Combinatoria
            These smaller modules, extracts and auxiliary works from LICHT represent another fractal like aspect of the cycle as a system. They are separate and yet also a part of the system. The formula and super-formula interact with themselves, alongside the set symbolism of the days of the week, to produce an array of combinations perceived and permutated through Stockhausen’s intuitive imagination. Through this thoroughly disciplined act of creation and applied artistry Stockhausen has shown himself to be a “Magister Ludi” or master of the Glass Bead Game.

            He has fused mathematics and music together and along these strands and placed connecting beads from the various religious and mystical traditions of the world. He used traditional correspondences, such as in Samstag for instance, associated with Saturday, and the planet Saturn, and it’s symbolism of contraction, limitation, and death. In Samstag he wrote the section Kathinka’s Gesang as Lucifer’s Requiem. Thus the mysteries of death become a main feature of this section of the work. In this piece the flautist performs a ritual with six percussionists. The ritual consists of twenty-four exercises based on Stockhausen’s study of the Tibetan Book of the Dead. It was written as a chant protecting the soul of the recently departed (in this case Lucifer) by means of musical exercises regularly performed for 49 days after the death of the body, and lead the recently deceased into to the light of clear consciousness. For these exercises he permutated the Lucifer formula into a showstopper of extended flute techniques of deft virtuosity.
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            And the piece may really be used by the living, and played for 49 days after the departure of a loved one to help assist them in their afterlife transition. 

The entire cycle is filled with this plentitude of subtle correspondences between music, science and various world cultures. These become the raw data for his applied musical calculus that is dancing in an elaborate play upon all these correspondences, inside a defined system, to express in multiplexed forms, that which is universal. 
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            After finishing the 29 hours of Licht, a feat some of his critics never expected him to complete, Stockhausen begin writing a series of chamber pieces called Klang, with the intent of writing one for each of the twenty-four hours of the day. Having conceived the musical forces of the days of the week, he was zooming in again to explore the musical forces behind each hour of the day. Formula composition gave him the tool he needed to explore these hours. Having written 21 of the pieces the cycle was unfinished at the time of the composer’s unexpected death in 2007 when he voyaged forth into the greater harmonies of cosmic space and time.

Read the rest of the Radiophonic Laboratory series.

References:
Other Planets: The Complete Works of Karlheinz Stockhausen 1950–2007, by Robin Maconie,Rowman & Littlefield Publishers, Maryland, 2016. 

Ed Chang's website in general has been super helpful in understanding the super-formula. It is a great journey through the Space of Stockhausen. 
http://stockhausenspace.blogspot.com/2014/08/a-brief-guide-to-licht-pt-1-drama-and.html
http://stockhausenspace.blogspot.com/2014/09/a-brief-guide-to-licht-pt-2-super.html

Threats and Promises: Lucifer, Hell, and Stockhausen's Sunday from Light" by Robin Hartwell in Perspectives of New Music 50, nos. 1 & 2 (Winter–Summer): 393–424.

Into the Middleground: Formula Syntax in Stockhausen's Licht" by Jerome Kohl in Perspectives of New Music 28, no. 2 (Summer): 262–91.