Where does the title of this work from 1986 come from? Stockhausen himself refers to the greek letter and writes, that the meaning of this letter is "unbekannte Grösse" - could we translate it as "unknown being"? But where does this meaning of the greek letter come from? One could think of mathematical equations, where the "x" is the unknown that is asked for - or the "X" in Kant's critique of metaphysics, the unknown in the known - but all that is not related to the greek letter. Has anybody an idea?
Dear Ulrich: I think the official translation is "unknown quantity" though, as you say, this is not a mathematical usage exclusive to this Greek letter. Doesn't Stockhausen give the same definition for Ypsilon? In both cases, the exact values of pitches is variable, depending to some extent on the microtonal capabilities of the instrument being used. Perhaps Stockhausen preferred not to use the common mathematical default of X, in order not to make an apparent connection to the idea of a "crossing", as in KREUZSPIEL.
There are several specific usages of the letter. The capital Xi is used in particle physics to represent "cascade particles", or "Xi baryons". This might have some relationship to Stockhausen's interest in subatomic particles (such as the muons found in the text of ATMEN GIBT DAS LEBEN). The lowercase Xi has an entire constellation of uses in mathematics, generally related to randomized functions (i.e., "unknown quantities"): aleatory (or stochastic) variables in probability theory, spatial frequency, as a coordinate in fluid dynamics, the remainder term in Taylor's Theorem. Particularly interesting is the Killing vector in general relativity (named, I hasten to add, for Wilhelm Killing): <http://en.wikipedia.org/wiki/Killing_vector_field>.
On the other hand, perhaps there is a sly joke here, and "unbekannte Grösse" is meant to be read as "unknown greatness". Stockhausen is known to have had a disdain for the works of a certain 20th-century composer whose name begins with the letter Ξ. (Perhaps this is stretching probability too far.)
This is all speculation, of course. I know of no evidence beyond Stockhausen's programme note.
Obviously there is a lot of possibilities you could refer to; and that is not the case just in this questions, but over and over again. I especially think on LICHT. Only take the names of the days: the stars, the Gods connected to them - always a whole universe of traditions with partly very different meanings. A lot of phantasy is activated when you try to interpret and for me that is part of the joy and the fascination Stockhausen has to offer to everybody who comes to his world. And I wonder if that is not connected with the basic motive of serial thinking, this alchemistic touch of his spiritual world, where everything is connected and can be transformed just to the opposite - because everything stems from the same source.
Yes, it is clear that the "alchemistic touch"—this ambiguity or, as Stockhausen called it, Vieldeutigkeit, or "polyvalence"—is exactly the central fact of serial thinking, and I like very much your thought that the cause is that "everything stems from the same source." Thank you for that characterization.
It's cool that the costume actually represents the title of the piece:
I actually didn't catch that until a little bit later.
Xi uses a microtonal scale of up to 7 micro-divisions in between 2 "normal notes" (semitones). Interestingly, after a recent visit to Turkey I learned that Turkish modes (makams) use a 9-division microtonal scale (but in between a whole tone, so Stockhausen still "wins"). However Xi of course sounds completely different from Turkish music, at least in my opinion. I wonder if Stockhausen studied Arabic/Turkish melodic scales. Does anyone know?
- Ed Chang - Stockhausen - Sounds in Space: Analysis, explanation and personal impressions of the works of the avant-garde composer Karlheinz Stockhausen. - http://stockhausenspace.blogspot.com/
I feel that it could be useful to have a discussion-forum on the music of Stockhausen. There are so many people from all over the world, young and old, learned and eager to get into contact with this musical world: musicologists, composers, musicians, music lovers; people who plan concerts - who write books or have to give lectures and so on. So there should be much stuff, many ideas that we can share. And when we have open questions, there may be people who studied just that and could give a hint or a stimulus.
A problem might be the English language, but i feel that is the only possibility that many people who are interested can participate. And we can exercise tolerance to mistakes!