A question to the musicology-experts: When I try to read a LICHT-score I always look to the 3 formulas: which is working here right now. And to discern this I look for the pitches. Is this an appropriate impression that in this method of composing it is a return of pitch-predominance - something that falls back from the original impulse in serialism that all parameters are of equal importance, a step back to Schönberg?

Thomas, this is a very good question. I would begin by countering it with another: Was equality of parameters ever the case? From studying the scores of the early 1950s, I would have to say that pitch and duration almost always take priority over timbre and dynamics, for example, even in those works where the composer does his best to offer "equal rights" (Gleichberechtigung, which I think was the German term preferred at the time to Gleichgewichts , Gleichwertigkeit, or Gleichheit—"equality"). In this respect, I am agreeing with Leonard B. Meyer (Music, the Arts, and Ideas, second edition, 1994), who maintains that these two "parameters" alone are what so-called total serialism was really concerned with. In the English-language literature, the sense of Gleichwertigkeit is usually assumed, and while this has led to some interesting discussions (for example, Charles Ames, "Statistics and Compositional Balance", Perspectives of New Music 28, no. 1:80–111), it tends to miss the point somewhat where European serialism is concerned.

To the issue of Schoenberg: It seems clear to me that formula composition is still as much concerned with a "serial" deployment of durations as it is with pitches, and that was never Schoenberg's way. He retained an almost completely traditional approach to his rhythms and pitch contours, which were chosen freely following inherited pattens of construction. This was what put him squarely in Boulez's gunsights (in the notorious essay "Schoenberg est mort"), and also led Stockhausen to dismiss him in somewhat less strident terms.

I also should not leave the impression that there are "four parameters" of pitch, duration, dynamics, and timbre, as the textbooks are in the habit of saying. Not only are there other dimensions of music generally, such as register, spatial location, vertical and horizontal densities, bandwidths, and so on, but these parameters also may be dealt with on several different scales simultaneously (for example, durations of whole operas, durations of the component scenes, durations of sections, etc., down to durations of individual notes). Not only that, but even on single scale levels, multiple sets are often compounded to form, for example, groupings of varying sizes. All of these things are technical details, however, that result in an overall mode of thinking that is called "serial." This "serial thinking" is surprisingly difficult to explain plainly, perhaps because it is compounded of so many disparate elements. One goal of early serialism (I should clarify that I am speaking of the period from about 1950 to 1955, so a very short time) of course was to reduce all of the so-called parameters to a single logical framework. Stockhausen himself claimed not to have found a way of doing this until KONTAKTE, in 1958–60, and so well after the period of intensive concern with this Gleichberechtigung. By this time also the "number of parameters" had vastly increased, in part through the evolution of formal concepts such as groups composition, statistical composition, mulitlayered textures, and so on (and of course I am not thinking only of Stockhausen's music here).

We know that following the world-wide unrest in 1968, many composers reacted by rethinking the complexity of their techniques and aesthetics. Particularly well-known examples include John Cage, György Ligeti, Luciano Berio, Luigi Nono, and, yes, Stockhausen. Boulez is an outstanding exception to this trend, although until 1973 he was in a period of compositional withdrawal. From today's perspective, it is amusing to see this radical simplification taking place in so many composers of the generation born between 1912 and 1932, only to be followed (about five years too late) by the "rebellion" against them by the Neue Einfachheit composers, amongst others. Of course by this time Stockhausen had long since begun composing with "formulas," which can plausibly be seen either as a method to rein in the excesses of serial complexity, or as a return to a more traditional manner of melodically oriented composing.

Does this mean an abandonment of the principles of "total serialism"? Perhaps. On the other hand, it is well to remember what Stockhausen said in "… wie die Zeit vergeht …", not about theoretical ideals but about compositional practicalities:

Zitat

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A … fundamental contradiction is found between material and method, which means, ultimately, between instrumental music and serial music. … The question remains as to how the composer of serial instrumental music will react …: whether he will compose "tonally" again; whether he will accept the contradiction and compose directly out of this dialectical relationship, since it often seems more fruitful to proceed from a contradiction than from the definition 2 times 2 is 4; whether he will scrap instrumental music altogether and compose only electronic music; or whether he will give some thought to how a completely different path may be taken in the case of composition for instruments—through an entirely new conception of musical time, in fact. The last seems to be the most plausible for general development.

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Jerry, may I ask a complementary question. All depends on the way „serialism“ is defined. You already wrote that it is very difficult to explain. I heard Boulez say (answering a sly question by Hartmut Lück about the reality of a »serial century«) that „serialism“ was a „tunnel of two years“ (H.-K. Jungheinrich [ed.] Das Gedächtnis der Struktur. Der Komponist Pierre Boulez. Mainz 2010, p. 119). This answer was triumphally repeated all over the book, the German conservative musicologists were extremely pleased. However, it was clear from the context that Boulez thought of the so-called „total serialism“.
On the other hand, I read with benefit the book of Arnold Whittall on „Serialism“ (Cambridge 2008) who stated that the 20th Century may be called rightly a serial one. I understood that he thought a bit like Stockhausen who spoke less of serialism than of serial thinking which was much more widely spread according to Whittall as is generally known. On pp.213ff., the reader meets a certain Jerome Kohl who is cited concerning Stockhausen's „Serialism in excelsis“.
What do you think? Is it possible that in 100 years music lovers will listen to the music of the 20th Century and feel that it was not quite so differentiated as the contemporaries believed? That it had much more in common?

Jerry's answer hits the major points. The only thing I would add is that the influence of the super formula's pitches varies from scene to scene. They almost always are a major organizing concept in a piece, but in certain scenes the more predominant parameter lies elsewhere. For example, the significance of Helikopter's pitches are made obvious by the reduction that Stockhausen provides in the upper staff, but would anyone listening to the scene say that these pitches are its defining feature? They provide a map for Stockhausen to get from the beginning to the end of the work, but what the work is most concerned with is the "local dialect" of the super formula's glissandi.

In some scenes, the pitches of the tripartite formula are the most fundamental aspects of the music. In others, they are simply the background to other concerns.

In response to Adorján's question: "Serialism" is one of those words which, like "tonality," and "taste," often means whatever the speaker wants it to mean. Most Americans (and perhaps also the British) identify it so strongly with Schoenberg's twelve-tone technique that as soon as you tell them a work is a "serial composition," they start looking for twelve-tone rows. If pitches are completely or mostly absent (as with ZYKLUS or Pousseur's SCAMBI), then they want to know where the twelve-element rhythms are, because they just cannot get pitches out of their heads.

Then we get into "post-serialism," which some writers use to decribe the music of composers like Boulez, who are seen as the successors to the era of Schoenberg. So we have got some writers who describe, for example, Book 1 of STRUCTURES for two pianos as "serial", while others try to distinguish between this and what Schoenberg did by using the expressions "total" or "integral serial", and still others who call this "post-serial." Next, we have the critics who find something changed in certain composers' works in the middle 1950s. Here I can cite a specific case: the American composer and critic (who worked mainly in Europe) Everett Helm, who hard Stockhausen's ZEITMASZE for the first time at the ISCM in Strasbourg in 1959, found there was a huge difference from what he had heard of Stockhausen's earlier music (which he had been told was "serial"), and loudly proclaimed that Stockhausen had "abandoned serialism." This brings us to the absurdity that, in one of the first compositions after his student works in which Stockhausen uses a twelve-tone row, he is supposedly abandoning serialism. (Perhaps there is a cause-and-effect relationship here?) Thank goodness it didn't occur to Helm to invent "post-serialism" all over again, which only happens about 1960 (with repsect to Ligeti, amongst other); and then again in the later 1960s, and again in the 1970s, and so on. Meanwhile, Stockhausen is busy explaining that everything he has been doing all along has been "serial."

So, by the 1970s, this has become a completely useless terminological mess, because on the one hand, different people are using the same word to describe quite different things, and on the other, the same things are being described by different terms, some of which proclaim their relative position by using the prefix "post." This is why, when I wrote my dissertation back in 1981, I offered the conspiracy theory that these terms actually were created by advertising executives working for American breakfast-food manufacturers: Total Cereal was a well-known product manufactured starting in 1961 by the Minneapolis firm of General Mills, and one of General Mills's leading competitors was Post Cereal, of St Louis, Missouri. The latter was founded in 1895, which settles once and for all the question of whether the "post-serial" comes before or after the "total serial."

Seriously, though, the textbook myth that "rigorous total serialism" make "the" four parameters of pitch, duration, dynamics, and timbre equivalent as well as independent, using parallel twelve-element scales in each one, is worse than an oversimplification. Accepting this definition puts us in the ludicrous position of having to admit there is not one single composition, either from the early 1950s or from any other point in history, that actually fits this definition. In this sense, Jungheinrich is wrong only to the extent that he has grossly exaggerated the size of his "tunnel" by multiplying its length by infinity, in order to obtain the finite number 2 years. This particular "total serialism" never existed at all.

In response to Joe, this thread was started with a question aimed primarily at the LICHT triple formula, so it is only right that you should direct your remarks to that particular object. However, Thomas also broadens the question to encompass formula composition more generally. So far as dynamics are concerned, the LICHT superformula does seem mainly to use them in their traditional role of supporting melodic lines structured primarily by pitch and duration. But INORI is also a formula composition, and here the parameter of dynamics is very much in the foreground, with a carefully devised scale of 60 degrees of dynamics (though the composer concedes that, functionally, it takes about five steps to make an audible difference). As to timbres, one of the notable features of LICHT is the elaborate use of trumpet (and trombone) mutes to create whole scales of vowel timbres. Other techniques are used along similar lines for the basset horn and other instruments, and of course one reason why the texts usually had to be written by the composer himself was that only he could shape the vowel colours appropriately to match his conception of the timbral composition. A magnificent example of this is found in the final scene of DONNERSTAG, where the trumpet mimics, echoes, anticipates, and counterpoints both the vowels and the consonants sung, spoken, and whispered by the tenor. Speaking of consonants, one aspect of timbre composition is the element of noise, which is also incorporated into the superformula at frequent intervals, and Joe has also pointed to the glissandos, which are in a sort of middle-ground between pitch and noise.

Gleichberechtigung does not imply a constant statistical equilibrium of all the parameters of a composition. This would result in dull uniformity—an overall medium-grey effect, with no contrasts, and no colour. What it does mean is that none of the parameters are reduced to being a mere shadow of some other one. Pitches can do certain things that timbres or dynamics cannot do but, conversely, timbres and dynamics have their own talents, and may be allowed to step to the front of the stage and take the lead when they can make a useful contribution. It is up to the imagination of the composer to devise situations in which these capabilities can profitably be displayed.

The example that immediately comes to mind where dynamics are of central significance in Licht is Welt-Parlament. Here, the color scale seems to be nothing more than window dressing, but it does highlight (like the crossing lines in Helikopter) the important function of dynamics in the piece.

Yes, Joe, I had forgotten about the dynamics in WELT-PARLAMENT. I would not be too quick to label the coloured markings of dynamics as "window-dressing," however. They are remarkably useful in following the dynamics while listening, and I imagine even more useful to the conductor and sound projectionist.

What I mean by window dressing is that they do not appear to have an indispensable influence on the piece. The color coding in Licht is so rigorous that when we see pp is blue and ff is red we must immediately think of Michael and Lucifer. But Eve's green is not in the middle. It sits next to Michael on the p side of the scale.

If one were to go through the piece using a color analysis based on the scheme of Licht thus far, it would do violence to the music (Believe me...I've tried!). I feel it has a clear dramatic meaning, and I discuss this in the Mittwoch chapter of my dissertation. But overall, I think the color matrix that Stockhausen created is, as you say, more helpful to the utilitarian purpose of the score. The dynamic lines are made clear for the reader, and that's no small part of the piece, of course.

If they were all deleted, would the meaning of the scene change? Or more to Thomas' question, are the dynamic markings in Welt-Parlament as formative as the glissandi in Helikopter? For Stockhausen, the dynamics are very important, but to the listener...? This is obviously an ongoing concern in Stockhausen's serialism. An internal concept that mattered greatly to him could often be indecipherable to the listener, even with his guidance.

Joe, has it not occurred to you that the colour-scale used for the dynamics in WELT-PARLAMENT is based on the usual colour spectrum, rather than on the colour symbolism found in the staging of LICHT?