Desordre!

[liszmaninopin]

I've spent time today learning the first pages of Ligeti's Desordre and Autumn and Warsaw.  Autumn wasn't that bad, but Desordre is very tough-it requires rather clever fingerings in those quick little runs, and one has to accent just the right notes.  Has anybody here ever brought Desordre up to performance level?  I'm thinking that I'll approach this piece by learning to play it smoothly at low speed first, then speed it up.

[liszmaninopin]

If anybody else here wants to play Ligeti, I have a bit of a suggestion.  So far, I've found it helpful to play his music hands separately a few times first.  The edition I have is very friendly to this, as it splits the hands up well.  Once you have the fingerings down, then combine them.  When I tried doing hands together first, it was more difficult.  Also, Ligeti put many performance notes in his scores, use them!  They can sometimes offer interesting insight into interpretation.

[liszmaninopin]

Today, I've been practicing them some more.  Autumn is coming nicely-I have 4 pages learned smoothly at slightly below tempo.  Desordre is still very tough.  All of a sudden, I realize that I really like all the Ligeti etudes.  Does anybody else find these works very fascinating?

btw, those versions of vertigre, la escalier and coloana for player piano are rather shocking-I would recommend them.

[faulty_damper]

I've never heard of Ligetti's works so I am going to ask a very general question:  what would you recomend I listen to?

I'll be in the music shop tommorow and would like some suggestions as to music scores to purchase.

[ahmedito]

The best version of the piano etude is the one with Aimard. When he played them here in Mexico, the composers literally threw the theater's door down to get in, because it was sold out. My favorite etude is number 15 White on White, followed by desrodre. You should do an analysis of desordre, its extremely complicated. It is based on a very wierd algorithm which determines the whole piece, but you have to be extremely good at calculus and all that kind of stuff to actually understand it. I did a paper on it for my analysis class some months ago.

[ahmedito]

Here is an explanation of the actual algorithm that controls desordre (this is taken from a doctorate thesis, I had to plow through this thing and it took me about a month before it stated to make sense) for the full thesis, google it:

Both foreground lines consist of cyclic repetitions of a constant step pattern. With each cycle, this pattern is transposed diatonically by a constant interval. The pattern for the upper part consists of 26 steps, 7 for each of the A phrases and 12 for phrase B. The pattern for the lower part has 33 steps, again 7 for each of the A phrases but this time 19 in the extended phrase B.


The contours of both patterns are highly similar, and especially the upper part, which could have easily been generated by a context-sensitive grammar, exhibits strong motivic features. In contrast to the lower part's pattern, whose B phrase extends by 2 bars beyond the expected 8 bars and ends in a whole note, however, the upper part's B phrase falls short by 2 bars and loops instantly back to its beginning.

There are overall 14 cycles in the upper part, each of which is transposed diatonically one step upwards and, due to its greater length, only 11 cycles in the lower part. The smaller number of cycles—which translates into fewer transpositions—is overcompensated for by a two-step diatonic transposition downwards and the fact that the lower part's pentatonic mode has fewer steps per octave than the heptatonic mode in the upper part. The cycles align with the score as follows:

Cycles:
 Lower Part:                        Upper Part:
  #  Transp. Start                   #  Transp. Start
 ===================                   ===================
 ---------------------- Section I: -----------------------
  1: ds3     2:1.0                    1: b4      2:1.0
                              2: c5      2:2.7
  2: as2     2:3.5
                              3: d5      2:4.7
  3: fs2     3:2.2
                              4: e5      3:2.6
 --------------------- Section II: -----------------------
  4: cs2     3:4.4                    5: f5      3:4.4
                              6: g5      3:4.11
  5: gs1     4:1.3
                              7: a5      4:1.7
  6: ds1     4:2.3
                              8: b5      4:2.5
  7: as0     4:3.2
                              9: c6      4:3.3
                             10: d6      4:3.10
  8: fs0     4:4.1 (1)
 --------------------- Section III: -----------------------
             4:4.7                    11: e6      4:4.7
  9: cs5     5:1.2
                             12: f6      5:2.4
 10: gs4     5:3.7
                             13: g6      5:4.4
                             14: a6      6:2.4 (2)
 11: ds4     6:2.4 (3)


The rhythmic picture is less clear due to rasterization effects in the acceleration and deceleration of the patterns. The sequence of rhythms in the upper and lower parts read as follows:

Rhythms Upper Part:
; ------------------------------; Sect. I Little Disorder            
 3 5 3 5 5 3 7                  ; cycle 1
 3 5 3 5 5 3 7
 3 5 3 5 5 3 3 4 5 3 3 5
 3 5 3 4 5 3 8                  ; cycle 2
 3 5 3 4 5 3 8
 3 5 3 4 5 3 3 5 5 3 3 4
 3 5 3 5 5 3 7                  ; cycle 3
 3 5 3 5 5 3 7
 3 5 3 5 5 3 3 4 5 3 3 5
 3 5 3 4 5 2 7                  ; cycle 4 -- Speed-Up
 2 4 2 4 4 2 5
 2 3 2 3 3 1 1 3 3 1 1 3
; ------------------------------; Sect. II Rapid Accelerando            [231 e]
 1 2 1 2 2 1 3                  ; cycle 5 -- start is in sync with cycle 4l
 1 2 1 2 2 1 3
 1 2 1 2 2 1 1 2 2 1 1 2
 1 2 1 2 2 1 3                  ; cycle 6
 1 2 1 2 2 1 3
 1 2 1 2 2 1 1 2 2 1 1 2
 1 2 1 2 2 1 3                  ; cycle 7
 1 2 1 2 2 1 2
 1 2 1 2 2 1 1 2 2 1 1 2
 1 2 1 2 2 1 2                  ; cycle 8
 1 2 1 2 2 1 2
 1 2 1 2 2 1 1 2 2 1 1 2
 1 2 1 2 2 1 2                  ; cycle 9
 1 2 1 2 1 1 2
 1 2 1 2 2 1 1 1 2 1 1 1
 1 2 1 1 1 1 2                  ; cycle 10
 1 1 1 1 1 1 2
 1 1 1 1 1 1 1 1 1 1 1 1
; ------------------------------; Sect. III Static                  [429 e]
 3 5 3 5 5 3 8                  ; cycle 11
 3 5 3 5 5 3 8
 3 5 3 5 5 3 3 5 5 3 3 5
 3 5 3 5 5 3 8                  ; cycle 12 (same)
 3 5 3 5 5 3 8
 3 5 3 5 5 3 3 5 5 3 3 5
 3 5 3 5 5 3 8                  ; cycle 13 (same)
 3 5 3 5 5 3 8
 3 5 3 5 5 3 3 5 5 3 3 5
 3 5 3 5 5 3 8                  ; cycle 14
 3 5 3 5 5 3 8                  ;
 3 5 3 5 5 8                  ;   cuts off here


Rhythms Lower Part:
; ------------------------------; Sect. I Static                  [404 e]
 3 5 3 5 5 3 8                  ; cycle 1
 3 5 3 5 5 3 8
 3 5 3 5 5 3 3 5  5 3 3 5 3 5 3 5 5 3 8
 3 5 3 5 5 3 8                  ; cycle 2
 3 5 3 5 5 3 8
 3 5 3 5 5 3 3 5  5 3 3 5 3 5 3 5 5 3 8
 3 5 3 5 5 3 8                  ; cycle 3
 3 5 3 5 5 2 7                  ;         -- Speed-Up
 3 4 3 4 4 2 2 4  4 2 2 3 2 3 1 3 3 1 4
; ------------------------------; Sect. II Rapid Accelerando            
 1 3 1 2 2 1 3                  ; cycle 4 -- start is in sync with cycle 5u
 1 2 1 2 2 1 3
 1 2 1 2 2 1 1 2  2 1 1 2 1 2 1 2 2 1 3
 1 3 1 2 2 1 3                  ; cycle 5
 1 2 1 2 2 1 3
 1 2 1 2 2 1 1 2  2 1 1 2 1 2 1 2 2 1 2
 1 2 1 2 2 1 2                  ; cycle 6
 1 2 1 2 2 1 2
 1 2 1 2 2 1 1 2  2 1 1 2 1 2 1 2 2 1 2
 1 2 1 2 2 1 2                  ; cycle 7
 1 2 1 2 2 1 2
 1 2 1 2 2 1 1 2  1 1 1 2 1 1 1 1 1 1 2
 1 1 1 1 1 1 2                  ; cycle 8
 1 1 1 1 1 1 2
 1 1 1 1 1 1 1 1  
; ------------------------------; Sect. III Allargando            
              5 3 3 5 3 5 3 5 5 3 8
 3 5 3 5 5 3 8                  ; cycle 9
 3 5 3 5 5 3 8
 3 5 3 5 5 3 3 5  6 3 3 5 3 5 3 6 5 3 8
 3 6 3 5 5 3 9                  ; cycle 10
 3 5 3 5 6 3 8
 3 5 3 6 5 3 3 5  6 3 3 5 3 5 3 6 5 3 9
 3 7 3 8 9 3 13            ; cycle 11
 3 11 3 21
   
The Model
This analysis translates fairly straightforward into a model of the combined foreground structure. First, the tempo is set according to the specification in the score:

;;;
;;; Tempo
;;;
;;; Set as ration in order to work around floating point rounding problems
;;; in cm timing.

(defparameter *eigth-note-pulse* (rationalize (rhythm 'e (tempo 76 w))))
   
This cosmetic hack allows calls to make-item-stream to be embedded in item stream constructor macros.

;;;
;;; Allow the use of make-item-stream in constructor macros

(defprop make-item-stream :item-expand t)
   
Then an algorithm is defined for the upper foreground. As suggested by the anaylsis above, the algorithm is driven by four sets of data: the part's mode, its step pattern, its transposition pattern, and its rhythmic pattern.

;;;
;;; Upper Foreground

(defparameter *upper-mode* (transpose (mode white 2 2 1 2 2 2 1) 'c4))

(defparameter *upper-fg-steps*
 '( 0  0  1  0  2  1 -1                  ; Phrase a
   -1 -1  2  1  3  2 -2                  ; Phrase a'
    2  2  4  3  5  4 -1  0  3  2  6  5))      ; Phrase b

(defun make-upper-fg-notes (start-note)
 (intervals (make-item-stream 'items 'cycle *upper-fg-steps*)
          from (steps 1 initially-from (modeify (degree start-note)
                                      *upper-mode*))))

(defun make-upper-fg-rhythms ()
 (items 3 5 3 5 5 3 7                  ; cycle 1
      3 5 3 5 5 3 7
      3 5 3 5 5 3 3 4 5 3 3 5
      3 5 3 4 5 3 8                  ; cycle 2
      3 5 3 4 5 3 8
      3 5 3 4 5 3 3 5 5 3 3 4
      3 5 3 5 5 3 7                  ; cycle 3
      3 5 3 5 5 3 7
      3 5 3 5 5 3 3 4 5 3 3 5
      3 5 3 4 5 2 7                  ; cycle 4
      2 4 2 4 4 2 5
      2 3 2 3 3 1 1 3 3 1 1 3
      1 2 1 2 2 1 3                  ; cycle 5
      1 2 1 2 2 1 3
      1 2 1 2 2 1 1 2 2 1 1 2
      1 2 1 2 2 1 3                  ; cycle 6
      1 2 1 2 2 1 3
      1 2 1 2 2 1 1 2 2 1 1 2
      1 2 1 2 2 1 3                  ; cycle 7
      1 2 1 2 2 1 2
      1 2 1 2 2 1 1 2 2 1 1 2
      1 2 1 2 2 1 2                  ; cycle 8
      1 2 1 2 2 1 2
      1 2 1 2 2 1 1 2 2 1 1 2
      1 2 1 2 2 1 2                  ; cycle 9
      1 2 1 2 1 1 2
      1 2 1 2 2 1 1 1 2 1 1 1
      1 2 1 1 1 1 2                  ; cycle 10
      1 1 1 1 1 1 2
      1 1 1 1 1 1 1 1 1 1 1 1
      (items (items 3 5 3 5 5 3 8      ; cycle 11-14
                  3 5 3 5 5 3 8
                  3 5 3 5 5 3 3 5 5 3 3 5)
           for 3)
      3 5 3 5 5 3 8                  ; cycle 14
      3 5 3 5 5 3 8
      3 5 3 5 5 3                  ;   cuts off here
      ))


(algorithm upper-fg-mono midi-note ()
 (vars (ntes (make-upper-fg-notes 'b4))
     (rhys (make-upper-fg-rhythms)))
 (setf note (unmodeify (item ntes) *upper-mode*)
     rhythm (* *eigth-note-pulse*
             (item rhys :kill t))))
   
The algorithm for the lower part foreground is driven by the same types of data. However, since it is eventually pitch-warped into the treble clef after it hit the bottom of the keyboard (4:4.7), its transposition pattern adds a warp function that shifts notes 5 octaves (i.e. 20 mode steps) up after 7 cycles, two 7-note phrases (A and A') and 4 measures of the B phrase (8 notes).

(defparameter *lower-mode* (transpose (mode black 2 3 2 2 3) 'cs4))

(defparameter *lower-fg-steps*
 '(0  0  1  0  2  2  0                        ; Phrase a
   1  1  2  1 -2 -2 -1                        ; Phrase a'
                                   ; Phrase b
   1  1  2  2  0 -1 -4 -3  0 -1  3  2  1 -1  0 -3 -2 -3 -5))


(defun make-lower-fg-notes (start-note)
 (let* ((cycle-length (length *lower-fg-steps*))
      (warp-point (+ (* cycle-length 7) 7 7 ))
   (intervals (intervals (make-item-stream 'items 'cycle *lower-fg-steps*
                                 :for 1)
                   on (items (items 0 for warp-point)
                           (items 20
                                in sequence
                                for most-positive-fixnum))
                   for cycle-length)
            from (steps -2
                    initially-from (modeify (degree start-note)
                                      *lower-mode*)))))

(defun make-lower-fg-rhythms ()
 (items 3 5 3 5 5 3 8                  ; cycle 1
      3 5 3 5 5 3 8
      3 5 3 5 5 3 3 5  5 3 3 5 3 5 3 5 5 3 8
      3 5 3 5 5 3 8                  ; cycle 2 (same)
      3 5 3 5 5 3 8
      3 5 3 5 5 3 3 5  5 3 3 5 3 5 3 5 5 3 8
      3 5 3 5 5 3 8                  ; cycle 3
      3 5 3 5 5 2 7
      3 4 3 4 4 2 2 4  4 2 2 3 2 3 1 3 3 1 4
      1 3 1 2 2 1 3                  ; cycle 4 starts in synch w/ cycle 5u
      1 2 1 2 2 1 3
      1 2 1 2 2 1 1 2  2 1 1 2 1 2 1 2 2 1 3
      1 3 1 2 2 1 3                  ; cycle 5
      1 2 1 2 2 1 3
      1 2 1 2 2 1 1 2  2 1 1 2 1 2 1 2 2 1 2
      1 2 1 2 2 1 2                  ; cycle 6
      1 2 1 2 2 1 2
      1 2 1 2 2 1 1 2  2 1 1 2 1 2 1 2 2 1 2
      1 2 1 2 2 1 2                  ; cycle 7
      1 2 1 2 2 1 2
      1 2 1 2 2 1 1 2  1 1 1 2 1 1 1 1 1 1 2
      1 1 1 1 1 1 2                  ; cycle 8
      1 1 1 1 1 1 2
      1 1 1 1 1 1 1 1  5 3 3 5 3 5 3 5 5 3 8
      3 5 3 5 5 3 8                  ; cycle 9
      3 5 3 5 5 3 8
      3 5 3 5 5 3 3 5  6 3 3 5 3 5 3 6 5 3 8
      3 6 3 5 5 3 9                  ; cycle 10
      3 5 3 5 6 3 8
      3 5 3 6 5 3 3 5  6 3 3 5 3 5 3 6 5 3 9
      3 7 3 8 9 3 13                  ; cycle 11
      3 11 3 21                  ;   cuts off here
      ))

(algorithm lower-fg-mono midi-note ()
 (vars (ntes (make-lower-fg-notes 'ds4))
     (rhys (make-lower-fg-rhythms)))
 (setf note (unmodeify (item ntes) *lower-mode*)
     rhythm (* *eigth-note-pulse*
             (item rhys :kill t))))
   
At this stage, both foreground processes are implemented and may be listened to by issuing a

Stella [Top-Level]: mix upper-fg-mono,lower-fg-mono 0
Enhancements
A further improvement adds octaves and simulate the background layer:

;;;
;;; Add Octaves and a fake background.
;;;
;;; Background notes are "muted" when the foreground is active.  To
;;; accomplish this, the names of the background containers must follow the
;;; foreground container names alphabetically.  Local variables are set up
;;; to communicate information between containers.

[ahmedito]

(defparameter *foreground-amplitude* .55)
(defparameter *background-amplitude* .4)

(merge desordre-v1.0 ()
 (let ((upper-fg-time 0) (upper-fg-note 0) (upper-fg-eighths 0)
     (lower-fg-time 0) (lower-fg-note 0) (lower-fg-eighths 0))

   (algorithm 1a_upper-fg_v1 midi-note (amplitude *foreground-amplitude*
                              channel 0)
     (vars (ntes (make-upper-fg-notes 'b3))
         (rhys (make-upper-fg-rhythms)))
     (if (evenp count)
       (setf upper-fg-time time
           upper-fg-eighths (item rhys :kill t)
           upper-fg-note (item ntes)
           note (unmodeify upper-fg-note *upper-mode*)
           duration (* *eigth-note-pulse* upper-fg-eighths)
           rhythm 0)
     (setf note (+ note 12)
           rhythm duration)))

   (algorithm 1b_upper-bg_v1 midi-note (length 1064 rhythm *eigth-note-pulse*
                              channel 1)
     (setf note (unmodeify
             (item (steps 1 (2 weight .33) (3 weight .15) (4 weight .05)
                        in random
                        for (expr upper-fg-eighths)
                        from (expr upper-fg-note)))
             *upper-mode*)
         amplitude (if (= time upper-fg-time) 0 *background-amplitude*)))

   (algorithm 2a_lower-fg_v1 midi-note (amplitude *foreground-amplitude*
                              channel 2)
     (vars (ntes (make-lower-fg-notes 'ds3))
         (rhys (make-lower-fg-rhythms)))
     (if (evenp count)
       (setf lower-fg-time time
           lower-fg-eighths (item rhys :kill t)
           lower-fg-note (item ntes)
           note (unmodeify lower-fg-note *lower-mode*)
           duration (* *eigth-note-pulse* lower-fg-eighths)
           rhythm 0)
     (setf note (+ note 12)
           rhythm duration)))

   (algorithm 2b_lower-bg_v1 midi-note (length 1064 rhythm *eigth-note-pulse*
                              channel 3)
     (setf note (unmodeify
             (item (steps 1 (2 weight .2) (3 weight .05)
                        in random
                        for (expr lower-fg-eighths)
                        from (expr lower-fg-note)))
             *lower-mode*)
         amplitude (if (= time lower-fg-time) 0 *background-amplitude*)))))
   
Finally, this code adds realism by simulating the chords that occur in both foregrounds in section three:

;;;
;;; Finally, add more realistic foreground voicings.

(merge desordre-v2.0 ()
 (let ((upper-fg-time 0) (upper-fg-note 0) (upper-fg-eighths 0)
     (lower-fg-time 0) (lower-fg-note 0) (lower-fg-eighths 0))

   (algorithm 1_upper-fg_v2 midi-note (amplitude *foreground-amplitude*
                             channel 0)
     (vars (ntes (make-upper-fg-notes 'b3))
         (rhys (make-upper-fg-rhythms))
         voicing)
     (setf upper-fg-time time
         upper-fg-eighths (item rhys :kill t)
         rhythm (* *eigth-note-pulse* upper-fg-eighths)
         upper-fg-note (item ntes)
         note (unmodeify upper-fg-note *upper-mode*)
         )
     ;; add:         upper octave until  1 after  cycle 11 ...
     (if (< count 261)                  
       (sprout
        (object midi-note start time
              note (+ note 12) rhythm rhythm channel 0))
     ;; ... then add:  2 voices until  2 before cycle 12
     ;;                3 voices until 11 after  cycle 12
     ;;                4 voices thereafter
     (loop with nvoices = (if (< count 284) 1 (if (< count 297) 2 3))
           with voicing = (read-items (intervals 1 2 3 4 5 6
                                       in heap
                                       for (expr nvoices)
                                       from (expr upper-fg-note)))
           for degree in voicing
           do (sprout
             (object midi-note start time
                   note (unmodeify degree *upper-mode*)
                   rhythm rhythm channel 0)))))

   (algorithm 2_upper-bg_v2 midi-note (length 1064 rhythm *eigth-note-pulse*
                             channel 1)
     (setf note (unmodeify
             (item (steps 1 (2 weight .33) (3 weight .15) (4 weight .05)
                        in random
                        for (expr upper-fg-eighths)
                        from (expr upper-fg-note)))
             *upper-mode*)
         amplitude (if (= time upper-fg-time) 0 *background-amplitude*)))

   (algorithm 3_lower-fg_v2 midi-note (amplitude *foreground-amplitude*
                             channel 2)
     (vars (ntes (make-lower-fg-notes 'ds3))
         (rhys (make-lower-fg-rhythms))
         voicing)
     (setf lower-fg-time time
         lower-fg-eighths (item rhys :kill t)
         lower-fg-note (item ntes)
         note (unmodeify lower-fg-note *lower-mode*)
         rhythm (* *eigth-note-pulse* lower-fg-eighths))
     ;; add:         upper octave until 23 after  cycle  8 ...
     (if (< count 254)                  
       (sprout
        (object midi-note start time
              note (+ note 12) rhythm rhythm channel 2))
     ;; ... then add:  2 voices until 22 after cycle   9
     ;;                3 voices thereafter
     (loop with nvoices = (if (< count 286) 1 2)
           with voicing = (read-items (intervals 1 2 3 4
                                       in heap
                                       for (expr nvoices)
                                       from (expr lower-fg-note)))
           for degree in voicing
           do (sprout
             (object midi-note start time
                   note (unmodeify degree *lower-mode*)
                   rhythm rhythm channel 2)))))

   (algorithm 4_lower-bg_v2 midi-note (length 1064 rhythm *eigth-note-pulse*
                             channel 3)
     (setf note (unmodeify (item (steps 1 (2 weight .2) (3 weight .05)
                              in random
                              for (expr lower-fg-eighths)
                              from (expr lower-fg-note)))
                     *lower-mode*)
         amplitude (if (= time lower-fg-time) 0 *background-amplitude*)))))
   
The controls which this model offers over pitch structure and transposition factors are believed to be adequate to Ligeti's approach. The temporal processes, however, contain a fair amount of handcoding and are thus less easily transformed, although possibilities exist to replace them with more formal techniques.

[ahmedito]

This actually shows that you can program the piece into a midi programer, since it structures so well to its series of algorithms... The final algorith, when fed into a midi sequencer, will play out Desordre out of the mathematical formula.



Ligeti is always a lot more complicated underneath the surface. What makes him such a great composer is the musical results he achieves from his thinking... when you listen to the piece, it has a musical idea and ellicits a psychological response. I cant say the same of Xenakis or Boulez.

[bernhard]

[thracozaag]

This actually shows that you can program the piece into a midi programer, since it structures so well to its series of algorithms... The final algorith, when fed into a midi sequencer, will play out Desordre out of the mathematical formula.



Ligeti is always a lot more complicated underneath the surface. What makes him such a great composer is the musical results he achieves from his thinking... when you listen to the piece, it has a musical idea and ellicits a psychological response. I cant say the same of Xenakis or Boulez.

 I agree completely.

koji (STSD)

[liszmaninopin]

thanks for all your imput!  I found the mathematical principles of Desordre rather fascinating.

[ahmedito]

The filosophical principle extreme order vs disorder is mindboggling, because the musical result is directly related to very tight mathematical principles. Its mathematical reasoned disorder so to speak.

[liszmaninopin]

to me, at first listening the etude "columna infinita" seemed the most disordered of all of them.  However, I've come to rather enjoy it now (although it looks very tough to play).  Are there any mathematical forumlas used in this etude that you know of?

[lingshu8]

Ligeti is probably best known in popular culture from the soundtrack to Stanley Kubrick's film "2001: A Space Odyssey."  Kubrick used several orchestral and choral pieces by Ligeti for the scenes with the black monolith.  Very atmospheric and otherworldly.

Matt

[Spatula]

I'm just so very lost and sad.

[super_ardua]

I would really like the try "Automne en Varsovie" (Autumn in Warsaw) one day).....how difficult is it?

[PasserBy]

[...snip...]
   
The controls which this model offers over pitch structure and transposition factors are believed to be adequate to Ligeti's approach. The temporal processes, however, contain a fair amount of handcoding and are thus less easily transformed, although possibilities exist to replace them with more formal techniques.

Dear Ahmedito,

It would have been appropriate to mention the source of your information.  The text and lisp code you have provided has been directly lifted off the Tobias Kunze paper which can be found here:

https://ccrma.stanford.edu/~tkunze/pbl/1999_desordre/ligeti.html

May I add, that this code was written in CommonMusic, a lisp-based programming language for algorithmic composition.  The code, as provided in Ahmedito's post, will not work in the current version of CM.  Working code is here:
https://pinhead.music.uiuc.edu/~hkt/nm/22/ligeti.html
but one has to buy the book to read all the explanations.

CommonMusic is an open source software available for free from commonmusic.sf.net and written by Heinrich Taube.

[liszmaninopin]

I've never heard of Ligetti's works so I am going to ask a very general question:  what would you recomend I listen to?

I'll be in the music shop tommorow and would like some suggestions as to music scores to purchase.

I would highly recommend the recording by Aimard on Sony that has both books of etudes as well as the Musica Ricercata.

https://www.amazon.com/exec/obidos/ASIN/B0000029P0/qid=1096850233/sr=2-1/ref=sr_2_1/103-8821744-6884641

These are absolutely superb performances of absolutely superb music.

I would really like the try "Automne en Varsovie" (Autumn in Warsaw) one day).....how difficult is it?

I've been practicing it lately-will be playing it for a competition in a while.  It's extremely difficult-I've played Scarbo, and Automne seems more difficult to me.  Some of the biggest technical challenges in it, IMO, are: extremely rapid repeated notes with the weaker fingers at very low volumes, generally very fine, fast fingerwork at low volumes, multiple voices at different tempos (all phrased properly), rapid chords, and chromatic scales.  On the bright side, it is fairly pianistic.