Generative Music

Nodal Sequencer

I have been developing my “soundscapes” composition technique recenty with the aid of a sequencer called Nodal, which was developed around 2005 at the Faculty of Information Technology at Monash University, Australia.

Traditional sequencers often use a horizontal “piano-roll” style interface with similarities to the classical music stave – in that:

  • Position in the horizontal dimension encodes a sequence of events.
  • Some arbitrary convention (in this case, length in the horizontal dimension) encodes duration.
  • Position in the vertical dimension encodes pitch.

Nodal uses a completely different approach – in Nodal, a sequence of sound “events” is encoded as a network of nodes and edges:

A voice (i.e. an instrument) begins at the triangular symbol and encounters the first node (“a” in the diagram). Node a instructs the voice to “play” a certain pitch. The voice then leaves node a via an edge (the arrowed path), and traverses to node b where the voice is instructed to play another pitch (the same or different). The elapsed time between sounding nodes a and b is proportional to the path length of the edge between them.

In the above example, at node c the network offers two options – the voice can progress to node d, or it can cycle back and return to node b. Which of these possibilities happens is determined by a set of rules encoded in node c.

The possibilities for choosing between paths come in three flavours:

  1. Sequential – the voice will keep count of how many times it has followed a given path, and when a prescribed maximum count is reached, it will switch to following the other path. When a (potentially different) prescribed maximum count is reached on the second path, it will switch back to following the first path again – and so on.
  2. Parallel – the voice creates a copy of itself, such that there are now two voices. Each voice follows one of the possible paths. This can be used (inter alia) to effectively increase the polyphony of the instrument.
  3. Random – The voice “throws a dice” to decide which path to follow. These “dice” do not have to be fair – they can be weighted in favour of one or other option.

My explanation is very much simplified (Nodal can do a lot more) – but having found the sequencer I immediately realised that for someone interested in aleatoric and generative techniques, Nodal could be a power tool in my software collection.

Below are a couple of soundscapes that include a significant amount of Nodal generated sequence. For both pieces, I constrained my treatment of the Nodal generated sequences through application of an arbitary set of rules to the generated output, as follows:

  1. You cannot add any note events.
  2. You cannot change any note pitches.
  3. You can align events in time as required, including quantisation and humanisation.
  4. You can insert silence, and extend event duration into that silence.
  5. You can delete events.
  6. You can freely add any dynamics, or effects such note velocity, pan, width, special effects etc.
  7. The result can be rendered at any desired tempo.

The strictness by which these rules are applied is allowed to vary according to the desired effect.

“The Narrow Road”

The inspiration for this came from three sources:

  • The extra-musical narrative derives from the opening lines of Matsuo Basho‘s work “Oku no Hosomichi” (The Narrow Road to the Deep North), which was written based on a journey undertaken by Bashō in 1689.
  • The style and instrumentation acknowledges “Lux Aeterna” – written for 16-part mixed choir, by György Ligeti in 1966.
  • The generative technique is informed by the Tintinnabuli method invented by the Estonian composer Arvo Pärt.

“The months and days are the travellers of eternity. The years that come and go are also voyagers. Those who float away their lives on ships or who grow old leading horses are forever journeying, and their homes are wherever their travels take them. Many of the men of old died on the road, and I too for years past have been stirred by the sight of a solitary cloud drifting with the wind to ceaseless thoughts of roaming.”

Network for “The Narrow Road”

“A Minor Doodle”

This piece for concert piano came from a more strict implementation of Arvo Pärt’s method, coupled with a more “loose” interpretation of my arbitrary rules. Consequently, it encodes a greater proportion of my personal preference. Nevertheless, I feel that these “doodles” of sequences undeniably reflect their origin in a virtual machine.

Network for “A Minor Doodle”




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