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Jean Barraqué - "séries proliférantes"


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here  a function... to barraqué's techniques

 


(defun serie-proliferantes (row)
  (let* ((ri_row (pitch-invert (gen-retrograde row)))
         (row (loop for z in (loop for x in (pitch-to-midi ri_row)
                          collect (or (position x (pitch-to-midi row))
                                      (position (- x 12)
                                                (pitch-to-midi row)) 
                                      (position (+ x 12) 
                                                (pitch-to-midi row))))
           
                collect (nth z ri_row))))

    row))


(serie-proliferantes '(c5 ab4 g4 db5 e4 d4 bb4 eb4 b4  f4 fs4 a4))
=> (fs4 a4 g4 cs5 d5 c5 eb5 gs4 b4 f4 e5 bb4)

 

 

seen here:

https://www.amazon.de/Jean-Barraqué-Musik-Konzepte-Heinz-Klaus-Metzger/dp/3883774499

 

page 19-20

 

 

IMG_9474.jpeg

 

IMG_9475.jpeg

 

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Thank you for this function / script regarding "les séries proliférantes". By carrying out a research on the book "Jean Barraqué, Ecrits" and published by the "publications of the Sorbonne" I discovered this site around Jean Barraqué and in particular examples of the scores and the booklets of "Séquence (1950-55) , "Le temps restitué (1959)", "... au delà du hasard (1959)", "Chant après chant (1966)" and "Concerto (1968)". I tell myself that under the documentation that might be of interest to members :

 

WWW.BAERENREITER.COM

Concerning "Ecrits Jean Barraqué, réunis, présentées et annotées par Laurent Feneyrou", for those who read French, I found a communication and an article published on the site "Entretemps". The communication to "Samedi d'Entretemps of October 26, 2002," Jean Barraqué: de l'écrit, le devenir" by Franck C. Yeznikan, evokes in particular the analyzes published in the book on Beethoven, Debussy, Webern, Messiaen:

 

 

"Le Souci du Développement chez Barraqué" by François Nicolas, published in Entretemps n ° 5 in 1987, evokes the two main references of Barraqué according to the author, "Beethoven and Debussy ", his admiration of Webern and Schubert. Without forgetting the interest and taste of Barraqué concerning musical analysis.


And to stay on topic on "les séries proliférantes", a theoretical explanation on this technique developed by Barraqué to escape the immutable intervallic structures of series 

 

 

JeanBarraque.jpg

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i tried to program it briefly for several generations, but I didn't quite get it - something i do not understand.... 

so i got wrong outputs after 3 generations...  maybe OPMO would like to CODE this? 🙂

 

this is my new version... but when i have i look to the barraqué-examples (order  0 - x)... there  is a different output after 3 gens... 

 

Ordre 0: C Ab G Db E D Bb Eb B F Gb A      (c5 ab4 g4 db5 e4 d4 bb4 eb4 b4 f4 fs4 a4)

Ordre 1: A C Db G Eb Ab E D F B Bb Gb    (a4 c5 cs5 g4 eb5 gs4 e5 d5 f4 b4 bb4 fs4)

Ordre 2: Gb A G Db D C Eb Ab B F E Bb    (fs4 a4 g4 cs5 d5 c5 eb5 gs4 b4 f4 e5 bb4)

Ordre 3: Bb Gb Db G Ab A D C F B Eb E    (bb4 e4 eb5 a4 c5 f4 gs4 fs4 g4 cs5 b4 d5) ????  wrong...

Ordre 4: E Bb G Db C Gb Ab A B F D Eb

Ordre 5: Eb E Db G A Bb C Gb F B Ab D

Ordre 6: D Eb G Db Gb E A Bb B F C Ab

Ordre 7: Ab D Db G Bb Eb Gb E F B A C

 

efun serie-proliferantes* (basicrow &key (gen 10)(ordre nil))
  (let* ((row basicrow)
         (ri_row (pitch-invert (gen-retrograde basicrow)))
         (serie (cons basicrow
                      (loop repeat gen
                        append (list ri_row 
                               (setf row (loop for z in (loop for x in (pitch-to-midi ri_row)
                                                          collect (or (position x (pitch-to-midi row))
                                                                      (position (- x 12)
                                                                                (pitch-to-midi row)) 
                                                                      (position (+ x 12) 
                                                                                (pitch-to-midi row))))
                                           
                                           collect (nth z ri_row))))
                        do (setf ri_row (pitch-invert (gen-retrograde row)))))))


    (if (not (null ordre))
      (position-filter ordre serie)
      serie)))

(serie-proliferantes* '(c5 ab4 g4 db5 e4 d4 bb4 eb4 b4 f4 fs4 a4))
=> ((c5 ab4 g4 db5 e4 d4 bb4 eb4 b4 f4 fs4 a4) (a4 c5 cs5 g4 eb5 gs4 e5 d5 f4 b4 bb4 fs4)
    (fs4 a4 g4 cs5 d5 c5 eb5 gs4 b4 f4 e5 bb4) (bb4 e4 eb5 a4 c5 f4 gs4 fs4 g4 cs5 b4 d5)
    (d5 b4 gs4 e4 f4 cs5 fs4 bb4 eb5 a4 g4 c5) (c5 f5 eb5 a4 d5 fs5 b4 g5 gs5 e5 cs5 bb4)
    (bb4 d5 gs5 e5 c5 b4 f5 cs5 eb5 a4 fs5 g5) (g5 gs5 f6 b5 cs6 a5 eb6 d6 bb5 fs5 c6 e6)
    (e6 f6 eb6 a5 d6 fs5 bb5 gs5 g5 c6 cs6 b5) (b5 a5 bb5 eb6 d6 c6 e6 gs5 cs6 g5 f5 fs5)
    (fs5 eb6 e6 bb5 d6 g5 b5 gs5 f5 cs6 a5 c6) (c6 eb6 b5 g6 e6 cs6 f6 bb5 d6 gs5 a5 fs6)
    (fs6 eb6 f6 cs6 b5 gs5 d6 g6 e6 bb5 a5 c6) (c6 eb6 d6 gs5 f5 bb5 e6 cs6 b5 g5 a5 fs5)
    (fs5 eb6 e6 bb5 d6 g5 b5 gs5 f5 cs6 a5 c6) (c6 eb6 b5 g6 e6 cs6 f6 bb5 d6 gs5 a5 fs6)
    (fs6 eb6 f6 cs6 b5 gs5 d6 g6 e6 bb5 a5 c6) (c6 eb6 d6 gs5 f5 bb5 e6 cs6 b5 g5 a5 fs5)
    (fs5 eb6 e6 bb5 d6 g5 b5 gs5 f5 cs6 a5 c6) (c6 eb6 b5 g6 e6 cs6 f6 bb5 d6 gs5 a5 fs6)
    (fs6 eb6 f6 cs6 b5 gs5 d6 g6 e6 bb5 a5 c6))

 

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Thank you, for the information !!

André, could you do a brief explanation of the function, please ?

I´m interested in ways of construction 12 tone sequences, aka rows...

Unfortunately, I can´t read german despite my german surname...

All the best !!

 

Here is some recent review articles about AIR series, by Marco Nardelli

 

https://www.researchgate.net/publication/342093979_The_Hitchhiker's_Guide_to_the_All-Interval_12-Tone_Rows

 

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thanks, julio...!!!

 

 

if i got it right, it works like this: 

 

1. take a basic row 

2. the r-i of the basic row

3. read the positions of all pitches of the r-i within the basic row 

4. apply this positionlist to r-i 

 

=> outout is :

ordre 0 => basic row

ordre 1 => r-i

ordre 2 => proliferante 1

= more or less ONE GEN of production

...

 

so the question could be: is ordre 1 the new basic row, or proliferante 1 ... to produce the next GEN?

 

 

 

here is some code to check it... i have no idea at the moment... 😕

 

 

;;; ONE GEN

(defun serie-proliferantes (row)
  (let* ((basic_row row)
         (ri_row (pitch-invert (gen-retrograde row)))
         
         (row (loop for z in (loop for x in (pitch-to-midi ri_row)
                               collect (or (position x (pitch-to-midi row))
                                           (position (- x 12)
                                                     (pitch-to-midi row)) 
                                           (position (+ x 12) 
                                                     (pitch-to-midi row))))
           
                collect (nth z ri_row))))

    (list basic_row ri_row row)))

;;;; X GENS

(defun serie-proliferantes** (n row)
  (loop repeat n
    collect (setf x (serie-proliferantes row))
    do (setf row (third x)))) ;; when you write here second/third x => then it would be ordre 1
                              ; ;or prolifer 1 as new starting point

(serie-proliferantes** 3 '(c5 ab4 g4 db5 e4 d4 bb4 eb4 b4 f4 fs4 a4))

 

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Thanks, André !

 

It´s interesting to note that it relates to the idea of what is considered among the forms of the any 12 tone row.

The question is if the proliferant series resultant are some kind of transposition, inversion, rotation, retrogradation or multiplication of the original tone row.

 

In the studies about the enumeration of tone rows this is a decisive point. What is considered to be related or derived of a first tone row ?

I´m not absolutely sure about it, but I´m using this as a reflection...

So, maybe we can consider the following as byproducts of a given 12 tone aggregate, in original (O) form:

 

1) There wil be 12 transpositions of  (O)

2) the Inverted Form ( I ) and 12 transpositions of it;

3) the Retrograde Form ( R ) and 12 transpositions of it;

4) the Retrograde Inversion Form ( RI ) and 12 transpositions of it;

 

This (O, R, RI and I) sums 48 derived rows of one 12-tone aggregate and this is the basic matrix.

 

This is the trivial 12-tone theory, but beyond that, what can we consider as being derived from the same ordered set ?

It´s not difficult to accept that all rotations of a 12-tone ordered set are derived from it. Take for example this Opus 25 tone row from "Arnie":

 

E–F–G–D–G–E–A–D–B–C–A–B♭  (O, rot 0)

    F–G–D–G–E–A–D–B–C–A–B♭-E (O, rot 1)

        G–D–G–E–A–D–B–C–A–B♭-E-F (O, Rot 2)

            D–G–E–A–D–B–C–A–B♭-E-F-G  (etc)

                  G–E–A–D–B–C–A–B♭-E-F-G-Db

                        E–A–D–B–C–A–B♭-E-F-G-Db-Gb

                             A–D–B–C–A–B♭-E-F-G-Db-Gb-Eb

                                   D–B–C–A–B♭-E-F-G-Db-Gb-Eb-Ab

                                       B–C–A–B♭-E-F-G-Db-Gb-Eb-Ab-D

                                           C–A–B♭-E-F-G-Db-Gb-Eb-Ab-D-B

                                               A–B♭-E-F-G-Db-Gb-Eb-Ab-D-B-C

                                                   B♭-E-F-G-Db-Gb-Eb-Ab-D-B-C-A

                                                        E-F-G-Db-Gb-Eb-Ab-D-B-C-Bb

 

1) The 12 rotations of ( O ) and all this transpositions (144)

1) The 12 rotations of ( I ) and all this transpositions (144)

1) The 12 rotations of ( R ) and all this transpositions (144)

1) The 12 rotations of ( RI ) and all this transpositions (144)

 

So, thinking this way, there are actually 576 derived forms of one each 12-tone row.

In some special cases, the ( I ) can be the same of some retrograde or transposing form, in the case of invariance. 

The same goes for some types of hexachordal combinatoriality. 

 

And there are the multiplication series...

 

Just some food for thoughts

 

All the best !

 

Julio

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thanks, julio...

 

could you have a quick look to the function? and to the article from didier.... perhaps you see my mistake (or the mistake in the article) subito 🙂 ?

barraqué described the mechanism and it seems easy to code it. but where is the mistake with more  then 3 gens? 

 

perhaps didier has an idea?

 

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violà... now it works fine 🙂  - OPMO could integrate it....  

 

it's easier than i thought: a single index-series is read from the r-i and only this one is used! similar to LACHEMANN, only he determines this index-series himself (for that i coded this simple row-permutation-function)...

 

greetings

a.

 

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;; SUB
(defun row-permutation (n row rules  &key (one-based nil))
  (let* ((rules (if (equal one-based t)
                 (mapcar '1- rules)
                 rules)))
  (loop repeat n
    collect (setf row (position-filter rules row)))))

;;; MAIN
(defun serie-proliferantes (n row)
  (let ((index-no (loop for x in (pitch-to-midi (pitch-invert (gen-retrograde row)))
                    collect (or (position x (pitch-to-midi row))
                                (position (- x 12)
                                          (pitch-to-midi row)) 
                                (position (+ x 12) 
                                          (pitch-to-midi row))))))
    (list row
          (pitch-invert (gen-retrograde row))
          
    (row-permutation n  (pitch-invert (gen-retrograde row)) index-no))))
                  
(serie-proliferantes 6 '(c5 ab4 g4 db5 e4 d4 bb4 eb4 b4 f4 fs4 a4))

=> ((c5 ab4 g4 db5 e4 d4 bb4 eb4 b4 f4 fs4 a4) (a4 c5 cs5 g4 eb5 gs4 e5 d5 f4 b4 bb4 fs4)
   ((fs4 a4 g4 cs5 d5 c5 eb5 gs4 b4 f4 e5 bb4) (bb4 fs4 cs5 g4 gs4 a4 d5 c5 f4 b4 eb5 e5)
    (e5 bb4 g4 cs5 c5 fs4 gs4 a4 b4 f4 d5 eb5) (eb5 e5 cs5 g4 a4 bb4 c5 fs4 f4 b4 gs4 d5)
    (d5 eb5 g4 cs5 fs4 e5 a4 bb4 b4 f4 c5 gs4) (gs4 d5 cs5 g4 bb4 eb5 fs4 e5 f4 b4 a4 c5)))

 

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Thanks Julio. I made other graphs, Pitchs and intervals series with in particular the results of René. I'll post them tomorrow.

 

Bravo René.  It's excellent. I have some questions about your script for you. Greetings. Didier

 
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