4 – Being Non-Linear

Open-form: the proto-minimalism of Janacek and Bartok :  collage structuring : example scores – collage-1 & 2: Dreaming Aloud for solo guitar – movement 1 : composing with modulated sine waves : graphical representations of collage structures : Live Coding.

One of the advantages of composing music within a CAC environment is that open-form and/or non-linear structuring of material is possible, indeed greatly simplified. Inspired and influenced by characteristics of their folk music, composers Leos Janacek and Bela Bartok pioneered the use of very short motifs of pitch and rhythm material as the building blocks for their often extended compositions. In the opening of the wind sextet Mladi by Janacek we hear a chain of micro melodies revolving between each other in different combinations.

Bartok’s Sonata for 2 pianos and percussion plays relentlessly and with extraordinary invention on a 4 and 6-note motifs. These pieces held a fascination for composers in the 60s and 70s and could be viewed now as a kind of proto-minimalism. Works such as Wildboy by Gordon Crosse and Ligeti’s Quartet No.1 (Métamorphoses nocturnes ) prefigure aspects of systems music and minimalism presenting a music of constant change of colour, direction and dynamic contrast without a relentless repetitive aspect.

4-1In composing situations where a collage-like approach is required, weaving together very short lengths of parametric material can be made through programming structures organised via symbolic ordering. Musicians are used to thinking of structural design with alphabetic symbols. Binary and ternary form uses A B A, A B C. Micro-structual forms as found in Janacek and later the minimalist Terry Riley work with many more symbolic elements (a to z even)  but in smaller metrical lengths, often only a few pitches within a single rhythmic expression. Think of Terry Riley’s In C, Mike Oldfield’s Tubular Bells, Rzweski’s Les Moutons de Panurge.  And in more recent music the intricate patterning found in the percussion music of Michael Van der Aa and Rolf Wallin.

Alongside such approaches to composing there is also potential of working in Open-Forms. This is where structural decisions about the placing and sequencing of sections are free. During the 60s and 70s open-form technique appeared variously in the work of Stockhausen, Boulez, Earle Brown and  consistently in the music of Henri Poussuer, notably his electronic work Scambi. However, Open-form has always been problematic in live performance  because of the difficulties surrounding the presentation and ordering of a physical score. Recently Open-Form has now entered the domain of musical and sonic installation in a powerful way and in graphic scores delivered by digital displays.

Although part of my own academic research has been involved with Active Notation, which makes Open-Form structuring possible in a live context with a small ensemble, it has proved a rich area to work with as part of the composition process, whether it be the ‘play’ of fragments within works for solo instruments (Array for solo violin, Dreaming Aloud and the movement Autumn from Sense of Place for solo guitar) or larger-scale ensemble works (with correspondingly larger sections of material) such as Self Portrait.

The premise of collage-structuring is very simple indeed. The little program illustrated below creates a collage of six phrases named a to g. The phrases are then structured here using a random generator to produce a collage of phrases controlled by the setting (or not) of the random seed.

(setf   a ‘(c4c2 fs4)
       b ‘(cs4cs2 g4)
       c ‘(c4 g4g3)
       d ‘(fs4 c5fs2)
       e ‘(fs5 cs5cs3)
       f ‘(g5 c5fs4)
       g ‘(g4c3 cs5))

(setf symbol-list
     (rnd-sample 24 ‘(a b c d e f g) :seed 2))
; => (e f g b e b e e b b b b g d b b c g c b f f b b)

(setf p-list
     (flatten (apply-eval symbol-list)));

; => (g4c2 cs5 fs4 c5fs2 fs4 c5fs2 c4c2 fs4 . . .

(setf phrases
 :length (span p-list ‘(e))
 :pitch p-list
 :velocity ‘(mf)

(def-score collage-1       
           (:key-signature atonal
           :time-signature (get-time-signature phrases)
           :tempo 80
           :layout (piano-grand-layout ‘piano))

  :omn phrases
  :channel 1
  :sound ‘gm
  :program 0)

Here’s that score-definition again. It’s going to be present in the next example so we won’t include the whole script in the Collage-2 because it will be exactly the same.

4-2Collage #1.

This example uses just a single parameter as its source material, but we can attached further parameters, such as note-lengths and dynamics, to align exactly. Here’s the way it’s done:

; using symbols to create collage-like structures #2

(setf ya ‘(c4c2 fs4)
      yb ‘(cs4cs2 g4)
       yc ‘(c4 g4g3)
      yd ‘(g5 c5fs2)
      ye ‘(fs5 cs5cs3)
      yf ‘(g4c2 cs5))

(setf axa ‘(e e) ; e = 1/8  s = 1/16  e. = 1/8.
      xb ‘(-e e)
      xc ‘(-e s e.)
      xd ‘(-s e s)
      xe ‘(s s s s s s)
      xf ‘(-e s s -e))

(setf za ‘(f)
      zb ‘(mp)
      zc ‘(f)
      zd ‘(pp)
      ze ‘(p f mf)
      zf ‘(fff))
setf s-list (rnd-sample 12 ‘(a b c d e f) :seed 2))
; => (b a e b d b b d c c f d)

(setf r-list (assemble-section ‘x s-list))
(setf p-list (assemble-section ‘y s-list))
(setf v-list (assemble-section ‘z s-list))

(setf phrases
 :length r-list
 :pitch p-list
 :velocity v-list

(def-score collage-2 . . .

Remember that the def-score section of this code has been omitted.

4-3Collage #2.

This approach to making texture out of the collage of micro-motifs forms the basis of part of the first movement of my composition for guitar Dreaming Aloud.

4-4 From the first movement of Dreaming Aloud.

Seventeen short motifs of different phrase lengths were derived by the composer from a single pattern of pitches, (c4 g4 fs4 cs5). This pattern is No.53 from Nicholas Slonimsky’s Thesaurus of Scales and Melodic Patterns. The patterns are arranged in a similar way to the example titled Collage-2 only instead of randomising a list of alphabetic symbols a modulated sine wave creates the alphabetic collection. The expression below shows the detail of the two sine waves, the second modulating the first. The function list-plot enables the expression to be drawn on a graphical interface.

 (gen-sine 48 1.9 60 :phase 90 :modulation
         (gen-sine 48 7 0.9))  :point-radius 0 :style :fill)


This kind of graphical representation of complex data can be a powerful tool in the composing process. It is yet another example of the potential of data conversion. Here the wave-form generation produces a collage collection shown below.

(vector-map ‘(a b c d e f g h i j k l m n o p q )
   (gen-sine 48 1.9 60 :phase 90 :modulation
         (gen-sine 48 7 0.9)))

; => (i l o o n n p q g c k q q o b l m a k m e l e i g d f b h o b o a a o j b o q c e i e p o n i o)

Deriving material in this way can have a powerful element of improvisation attached to it. Once the expression is written it can be evaluated and an output ‘read’ (and heard) over and over again – with different but controllable results. The clue to this possibility lies in the changing of arguments and values; and with randomised operations, the change of value in the random seed. The program for such improvisation can be subsumed into a live-coding environment where the composer interacts by changing and evaluating code as part of a real-time process.

Here’s the description of the Live Coding Instrument from the documentation of the Opusmodus CAC system.

4-6LIVE CODING (sometimes referred to as ‘on-the-fly programming’ or ‘just in time programming’) is a programming practice centred upon the use of improvised interactive programming. Live coding is often used to create sound and image based digital media, and is popular now in computer music, combining algorithmic composition with improvisation. OPUSMODUS joins Mac software such as SuperCollider, Chuck, Max and Pure Data in featuring live coding as a lively addition to its composing and improvising possibilities.


References, Links and Further Reading
Bela Bartok: Sonata for Two Pianos and Percussion
Gordon Crosse: Wildboy
Leos Janacek: Mladi Suite for Wind Sextet
Gyorgy Ligeti: String Quartet #1
Nigel Morgan: Active Notation
Nigel Morgan: Array for Solo Violin
Nigel Morgan: Dreaming Aloud for Solo Guitar
Nigel Morgan: Self Portrait for Seven Musicians
Nigel Morgan: Sense of Place for Solo Guitar
Opusmodus: Website
Henry Pousseur: Website
The Scambi Project


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