Yes, that's what I'm doing here every day, but I'm not on a mission to educate.

Well, Ex-kyoooooooze me!! I was asleep! It's night time here.

Anyway, here is an abstract structure from the sketches of Klavierstueck X

7 1 3 2 5 6 4

It governs everything in the piece, but the numbers mean nothering until they are assigned to sonic events, time values, dynamics, formal units, etc. -- nevertheless, he looks at this 7-value row and constructs "versions" of the row not through retrograde or inversion but as follows

7132564713256471325647132564713256471325647132564
7132564
 1 2 6 7 3 5 4
  3  6  1  5  7  2  4
    2    7    5    1    6    3    4
     5     3     7     6     2     1    4
      6      5      2      3      1      7      4

That's a facsimile right out of Henck. The process of taking each 2nd, then each 3rd, then each 4th number, etc is by my definition an abstract one, but it leaves that last value (#4) at the end each time (a by-product of the number being prime: try doing this with 8 numbers, for example), which has concrete musical implications. Remember that Character IV represents the midpoint between extremes.

What can "abstract structure" mean but an array of numbers? And what is the above scheme but an array of numbers? I have a hard time believing that he constructed this scheme with specific sounds in mind, but looked for an appopriate musical way to express the process that so appealed to him here (all things collapse toward the middle.) I imagine him fumbling faffing around (as I do) with numbers idly while waiting for trains or for his coffee to percolate, or for his next message from the duMont Verlag, and then discovering something that might be musically useful. 'Tworks both ways, believe I. Yet those matters that have no concrete musical value get discarded, or at least filed away to be gazed upon another day, when one is in a more charitable mood.

Absolutely in agreement with that - it's probably not possible to give an account of anything musical without some recourse to metaphor (competing discourses on music usually simply advocate one form of metaphorical engagement over another). But the point is that we are still there referring to something made manifest in sound, rather than simply at the means viewed in isolation. I'm not for a moment denying the importance of looking at serial techniques, say, if we are trying to see how Stockhausen or others achieve their results; however, I'm not convinced an awful lot of writing on serial music really does that or even seems particularly concerned about it. You can read a lot about manipulation of series, but little about what effect this might have upon what one hears.

Let me try to clarify what I mean on this matter, as I think it becomes the sticking point. Appealing to 'the sounds themselves' is not intended to imply they have no wider meaning, by any means - far from it (if they didn't, at least in the sense of producing some sort of meaningful response in the listener, I doubt anyone at all would find reason to listen to the music) - but attempting to make a distinction simply between that which relates to perception and that which might only ever be meaningful to the composer or those who study the sketches and techniques. There are compositional techniques which it could be argued have no audible bearing upon the result (in the sense that the sonic results are not meaningfully different from what might be produced by other techniques, perhaps arbitrary or random ones); fine, composers can write however they want, but it's at the least questionable whether these things can be considered of such primary importance in terms of the work that is produced. If the means are very intricate, but the result sounds relatively undifferentiated or undistinct, then the central importance of the means is questionable. I don't believe this is the case in Stockhausen, on the whole (nor in Boulez, Ferneyhough, or numerous others), and think it's surely quite fundamental to appreciating the music to grapple with why certain means produce more distinctive sonic results than others.

No, they are an "abstract structure". What have I been saying?

Well, I was using this to demonstrate a structure that came before a sonic imagination. It's "just numbers" -- and it takes a considerable capacity for "abstract thinking" to read through Henck's treatise and realize that this stuff has any musical value.

It is curious how the number seven keeps recurring in musical discussions. Here we have it in jolly old Stockhausen, it comes up too in our own system of convenient ratings, and it was of course particularly important for Scryabine.

The latter first became acquainted with theosophy in Paris in 1906, when a friend told him that his vision of Mysterium, of the union of humanity with divinity and the return of the world to oneness, had much in common with theosophy. Scryabine used theosophical terms quite loosely. He adapted them to his own ideas, aspirations, and yearnings and employed theosophical postulates as formulae to describe his own experiences. He said to his brother-in-law, "You may not accept the doctrine of Seven Planes as the ultimate truth, but to me it serves as a convenient framework for classifying natural phenomena and for creating order out of the chaos of factual data." And the doctrine of Seven Races attracted Scryabine with its psychological ramifications, even when he no longer tried to interpret it in a literal sense. Each race, according to this interpretation, reflects a certain phase in the evolution of man's spiritual life, so that the history of the races becomes a history of the human psyche, which acquires senses and desires vested in the flesh and then gradually denudes itself, abandoning its belongings and returning to the simplicity of the primordial oneness. Having accepted this postulate, Scryabine reorganized in his own terms the entire history of humanity, of which the cycle of his own psychic life was a particular case. This gave him a key to the understanding of world history. In the winter of 1907-1908, he formalized the content and the subject of his Mysterium, which he understood as a history of the races of man and of individual consciousness or, more accurately, as an evolutionary psychology of the human races. This phase of Scryabine's spiritual development owed most to theosophy, which supplied him with the necessary formulae and schemes, particularly in the notion of Seven Races, which incarnated in space and time the gradual descent of the psyche into matter. Even when he began to retreat from theosophy he still felt greatly beholden to Mme. Blavatsky's Secret Doctrine in his own development; indeed, he felt tremendous admiration for Mme. Blavatsky to the end of his life. He was particularly fascinated by her courage in essaying a grandiose synthesis and by the breadth and depth of her concepts, which he likened to the grandeur of Wagner's music dramas. As time went on, Scriabin's spiritual life acquired a new depth and gradually assumed a religious character as a result of the growing awareness of his mission--a conviction that he was predestined to perform a certain appointed task entrusted to him from a source independent of his own volition.

It may indeed have been we who first introduced this concept of the spiritual into the discussion group; in the Shostacowitch thread, in relation to that composer's three wives, when we said that he was evidently not a spiritual man. But yesterday of course we made the meaning perfectly plain: the spiritual composer is he whose life and labour are guided by a worthwhile noble or elevated aim.