Music 680, Fall 2005: Special Topics in Music Theory - Algorithmic Composition
Lecture 2: September 19, 2005 - Serialism I: Stockhausen

Stockhausen, Darmstadt, and Kreuzspiel
	"the shock of the encounter with Messaien and Goeyvaerts is all there in the leap from the from the
		Sonatina for violin and piano, completed soon before, to Kreuzspiel... written in the immediate
		aftermath. One might even speak of a conversion, specially when what exhilarated both 
		Stockhausen and Goeyvaerts was the spiritual dimension of their work: the possibility of
		liberating, more than creating, sound structures which would have nothing human in their
		composition, which would be images of divine unity. Since at this point Stockhausen was a
		devout Catholic, the form and title of his first piece after the Darmstadt experience cannot have
		been accidental, through the 'crossplay' is also a direct extension from Goeyvaerts' method...."
	"...this is, already, a characteristic Stockhausen piece, not only in its perfect digestion of its models
		but also in its intriguing introduction of discrepancies, its delighted newness, and its brio.
		...The discrepancies include disturbances to the pitch pattern when a pitched attack coincides
		with one in the percussion: Stockhausen may have been concerned to make some connection
		between the two streams...."
	"It cannot be contemplated that the crossplays described are to be followed by the listener: their
		effect, rather, is of a ruthlessly channelled disorder, of unseen hands moving notes according to
		unknown rules, as if one were observing a complex game with no prior knowledge of its
		etiquette. Where order is glimpsed - for instance in repetitions of intervallic motif - it will likely
		be adventitious. Kreuzspiel flies free from the thematic-harmonic continuity that Schoenberg had
		wanted to preserve, and does so not by punishing that continuity, as Boulez had done, but by
		ignoring it."
			-- register as a crucial counter-example here? Morgan's "concern for large-scale processes"
	"(...His [Stockhausen's] strategy was to draw up a scheme, follow it through, and then look at the
		results. Such an approach to composition would justify the use of such terms - much vaunted at
		the time - as 'experiment' and 'research', and would partly explain the pattern of Stockhausen's
		output, which to some extent has continued: a pattern of one-offs)."
	
cultural contexts for serialism
	the Schoenberg - Webern - Messaien lineage; Cage as the algorithmic and parameterizing outsider
	postwar reconstruction and the Stunde Null
	the CIA, Darmstadt, and artistic abstraction as a form of defense against communism

Zeitmasze and constrained mobility
	taking deliberate advantage of the temporal variabilities of performance
	frequent use of "as fast as possible" or "as slowly as possible in one breath"
		while using several such layers simultaneously

Gruppen and the logarithmic scale of 12 tempi which can be "transposed" by altering the unit pulse
	"a rise of a perfect twelfth would have its analogue in a change of tempo in the ratio of 3:2
		(the frequency ration of a perfect fifth, if one discounts the samll discrepancies of temperament)
		coupled with a halving of the rhythmic unit. So any pitch line could be turned into a duration-
		tempo succession, a melody of rhythm, and one could also change the timbre of the rhythm, as
		it were, by adding 'partials' in the form of other duration-tempo successions going on at the
		same time, their number limited only by the practicalities of performance....  As Jonathan
		Harvey has shown, the whole rhythmic structure is the vast amplification of a serial melodic
		thread.
	"Having derived the need for orchestral antiphony [three ensembles and three conductors] from 
		his structural scheme, Stockhausen was characteristically drawn to take advantage of the
		opportunities for spectacle, notably in the sonorous climax where a brass chord is hurled from
		one orchestra to another...."

[all these quotations are from Paul Griffiths Modern Music and After]

more Scheme programming
	(let) and local variables
				
the Common Music algorithmic composition environment (atop Scheme)
	(cd "Documents/teaching/680-fall-2005") ; directory change for saving MIDI files

	(define (series values start-time)
 		 (if (null values) nil
      		(let* ((current-value (car values))
            		 (current-rhythm (float (* 1/12 (+ current-value 1)))))
        			(cons (new midi 
                			:time start-time
                			:keynum (+ 60 current-value)
                			:amplitude current-rhythm
                			:duration current-rhythm)
          		    		(series (cdr values) (+ start-time current-rhythm))))))
		 ; need to handle transposition!
 
    	(events (series (list 0 1 2 3 4 5 6 7 8 9 10 11)) "test.mid") ; monophonic line
	(events (list (series (list 0 1 2 3 4 5)) (series (list 6 7 8 9 10 11))) "test.mid") ; two-voice polyphony

(define (rotate-left values)
  (attach (car values) (cdr values)))

(define (attach element values)
  (if (null values) (list element)
      (cons (car values) (attach element (cdr values)))))

(define (rotate-right values)
  (cons (last-element values) (all-but-last values)))

(define (last-element values)
  (if (= (length values) 1) 
    (car values)
    (last-element (cdr values))))

(define (all-but-last values)
  (if (= (length values) 1)
    nil
    (cons (car values) (all-but-last (cdr values)))))