Stockhausen, Information Theory, Systems & Cycles

Stockhausen picked up his interest in information theory by way of Werner Meyer-Eppler during his time as a student at the Bonn. Meyer-Eppler himself was something of a scientific polymath, having studied mathematics, chemistry and physics at the University of Cologne in the late 1930s before going to the Bonn where he became a scientific assistant in the physics department, and then a lecturer in experimental physics. After WWII ended his attention turned with laser beam focus to the subject of phonetics and speech synthesis. In 1947 Paul Menzerath brought him into faculty of the Phonetic Institute of the University of Bonn. It was in this time period when Meyer-Eppler started publishing essays on the Voder, Vocoder, and Visible Speech Machine. One of his contributions to the field that is still in use today was his work on the development of the electrolarynx.

            Information theory made many contributions to many fields. Linguistics was one of those fields where it was influential in studying how frequently words were used, word length, and the speed words could be read. Shannon had tested the information theory principle of redundancy, or the amount of wasted space used to transmit a message, by having his wife predict the number of repeating letters in a random crime novel he pulled off his bookshelf. Sometimes redundant is better, when it comes to getting a message across. Redundancy is added while communicating over noisy channels as a method of error correction.

​            Shannon had the insight that this was a baked-in purpose behind the repetition of letters in Englsih. He had also showed that he could use stochastic processes to build something that resembled the English language from scratch.

Werner had been following these developments of information theory with special attention to their applications in linguistics and speech. Later in the 50’s Meyer-Eppler became concerned with how statistics and probability, core tools of information theory, might be applied to creating electronic music as explored in his book Statistic and Psychologic Problems of Sound. In this work Meyer-Eppler introduced the word “aleatoric” into the musical lexicon. According to his definition “a process is said to be aleatoric ... if its course is determined in general but depends on chance in detail”.

Aleatoric music is made when some element of the composition is left to chance or when a significant portion of how the composition is realized is left up to the performer or performers. Aleatoric composition has a precedent in the dice games of the 18th century. The word itself comes from the Latin alea, meaning dice.

There are many methods for applying aleatoric processes to music. One of the ways Stockhausen tackled it was by using a polyvalent structure, or writing a piece that was open to a number of different interpretations. Klavierstucke XI is an example of such a piece that he wrote for piano.

The piece is made up of 19 fragments printed on a very large piece of paper. There is no turning of the sheet music. The pianist may start with any fragment they wish and from there continue on to any other fragment they wish to play. It is polyvalent because each performance could begin and end in new places. There is no set musical narrative; it is more like reading a choose-your-own adventure, or wondering through a maze, or labyrinth which the pianist enters, circumnavigates, and then returns. Each time the pianist may enter the labyrinth from a new entrance and likewise, reemerge in a different place.

The pianist shares responsibility with the composer for the eventual shape of any given performances. The possible permutations are vast, yet even in different interpretations it may be heard as the same piece of music, its essential characteristics remaining the same no matter the order they are played.
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Commenting on the piece the composer said, "Piano Piece XI is nothing but a sound in which certain partials, components, are behaving statistically...  If I make a whole piece similar to the ways in which (a complex noise) is organized, then naturally the individual components of this piece could also be exchanged, permutated, without changing its basic quality."

Considered as a whole Piece XI will sound the same even though every time it is played it will sound different. It is a system unto itself, and as a system, even when the component parts are rearranged in the order they are played it is still the same system, and will still sound like itself. Listened to statistically the musical values remain the same.

Stockhausen would go on to use polyvalent form again and again. In his percussion piece Zyklus (Cycle) from 1959 the score is printed as a spiral and the performer may start anywhere within the spiral he or she chooses. Furthermore, they may play the piece from left to right or right to left. The piece is finished when the player reaches the original starting point. In the performance space the cycle is shown again visually with the percussion pieces laid out in a circle with the performer moving around them in the manner determined by a chosen starting point.
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Zyklus also shows the amazing diversity of possible interpretations demonstrated before in Piece XI. It is however the interpretation of the scored is a bit more closed. On one side of the score the music becomes increasingly aleatoric, giving more freedom to the player in how it is interpreted. On the other side of the spiral the composition is exactly fixed and predetermined. Played on way it moves from fixed to open, and in the other direction from open to closed. 

Stockhausen was obsessed with cycles. Specifically cycles of time. His mid-seventies composition Tierkreis (Zodiac) consisted of twelve melodies for each of the twelve zodiac signs. Originally written for custom made music boxes, Tierkreis can be played on any melody instrument and peformed in a number of different ways. For the purpose here a complete performance begins with the melody for the corresponding zodiac sign for the day when the performance is being held. For instance, if the performance was held on August 22 the performers would begin with the Leo melody and proceed through Virgo, Libra, and the rest until they return to the starting melody of Leo. Each melody is played at least three times and may be improvised upon. This gives considerable variation to individual performances. Further variations are specified by the composer.
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  In his chamber opera Sirius written a few years later the Tierkreis melodies are employed again in a section of the piece called The Wheel. Here the music may be heard in four different ways, depending on the season it is performed. If played in the Winter the section starts with the melody for Capricorn, if in the Spring with Aries, Summer starts with Cancer, and Autumn with Libra. 

In all of these cyclical works an echo of the tape loop may be heard. Stockhausen had worked with tape loops extensively in his piece Kontakte, using them to show relationships between pitch, timbre and the way musical events can be perceived in time and space through the process of slowing things up or down. I wonder, if besides the strong grounding Stockhausen had in religion, philosophy, and science if the eternal return and recurrence of the tape loop at all framed his cosmic conception of the vast cycles of time. 

The cycles continued in his magnum opus LICHT (Light): Die sieben Tage der Woche (The Seven Days of the Week). Written between 1977 and 2003 it is a cycle of seven operas, one for each of the seven days of the week. Stockhausen described the work as an “eternal spiral” considering there to be “neither end nor beginning to the week.” Clocking in at a total duration of 29 hours, deft intricacies exist within the piece on a micro and macro scale and many volumes have already been and will continue to be written about it. Within the broad palette afforded by an opera cycle longer than Wagner’s the Ring, Stockhausen was able to play the role of a Magister Ludi, or master of the Glass Bead Game. LICHT is a system, and within that system Stockhausen playfully and masterfully displayed with pyrotechnic virtuosity a comprehensive knowledge of combinatorial and permutative arts as applied to music.

These arts of combination were a central component of the Glass Bead Game as played in the novel.

To show how all of these interlocking parts fit together the basic structure of the opera must be examined. And to understand LICHT as a system a slight change of lanes onto the parallel track of Norbert Wiener and his theory of cybernetics is in order.

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. 

Klavierstucke XI essay by Ed Chang: 
http://stockhausenspace.blogspot.com/2015/06/klavierstuck-xi.html

The Glass Bead Game by Herman Hesse, translated by Clara and Richard Winston, Holt, Rinehart and Winston, 1990