A Particle System for Musical Composition

ABSTRACT

This paper describes the development of a particle system for musical composition.   It employs a generator as described in William Reeves' seminal 1983 paper on the subject, but one in which the particles are musical themes rather than points of light.  This is distinct from an audio-level particle system such as might be employed effectively in conjunction with granular synthesis, because an audio-level process has no "musical intelligence" in the traditional sense as the term is used in discussing rhythm, melody, harmony or other traditional  musical qualities.

The particle-system uses the author's software, The Transformation Engine, as the musical engine for rendering particles. This allows the particle system to control relatively high-level musical parameters such as melodic contour, metrical placement and harmonic colour, in addition to fundamental parameters such as pitch as loudness.  The musical theme corresponding to an individual particle can therefore evolve musically over the lifetime of the particle as these high-level parameters change. 

PRIOR WORK

There seems to be little interest in applying the particle system paradigm to music composition, as distinct from audio processing. There are a small number of prior works in applying the concept to audio streams based on the granulation technique, but I have been unable to find any in which the particles are a higher level structure than audio grains.

I have recently discovered that the commercial software Plogue Bidule has a very simple particle system that outputs a stream of MIDI notes. The compositional application is limited becuase pitches, velocities and durations are all purely random, but the Bidule environment provides further processing modules which improves the situation somewhat. Still, by comparison with the system presented here it is very simple because the individual particles are simply individual MIDI notes. There is no facility to add continuous control data, pitch bend, or note sequences with rhythmic timing.

Randomness is an essential feature of a particle system. This is becuase such a system was designed to overcome the limitations of more deterministic graphic methods. As Reeves says,

"Particle systems model an object as a cloud of primitive particles that define its volume. Over a period of time, particles are generated into the system, move and change form within the system, and die from the system. The resulting model is able to represent motion, changes of form, and dynamics that are not possible with classical surface-based representations." (Reeves, Computer Graphics, V17,n3, July 1983.)

Why a MIDI Particle System?

In a recent article, Robert Rowe (NYU) makes a distinction between  Symbolic and Sub-symbolic music systems (Split Levels: Symbolic to Sub-symbolic Interactive Music Systems, Contemporary Music Review Vol. 28, No. 1, February 2009, pp. 31–42.) Symbolic systems, such as MIDI, employ a high-level description of musical events and therefore implicitly embody a large amount of musical knoweledge. This implied knowledge is a form of structure which can also be restrictive. Sub-symbolic systems, such as audio stream processing techniques like granulation, operate at a low-level. They imply less particular musical knowledge and so are correspondingly less restrictive. Each system has characteristic advantages and dis-advantages. Obviously, for a project like the compositional particle system described here, it makes a lot more sense to use a symbolic system like MIDI than a sub-symbolic one based on audio stream processing, even though the latter might have some advantages in terms of audio-quality.

MIDI (1983), despite all the complaints of its detractors (The Musicians Make a Standard, CMJ) , has been a remarkably long-lived computing standard. Its worst limitations have mostly been overcome by clever extensions to the standard, and one of its detractor's main complaints - the slow speed and uni-directional nature of its cable interconnection - has been rendered irrelevant by the use of high-speed network and software-only systems. MIDI's longevity says something positive about its success as a symbolic system.

A symbolic MIDI particle system has the advantage that each particle corresponds to a complete high-level entity, usually a musical motif consisting of series of notes (but see the examples below for other uses.)  This means that  each individual particle can represent a musical entity in the composition, for example, an individual strand of counterpoint. It would be very difficult, probably impossible, to program a  granulation system so that each grain corresponded exactly to a musical motif.  Because of the sub-symbolic character of the granulation process there are simply no markers in the data to readily indicate the presence of a symbolic entity such as a motif. Conversely, because of the symbolic character of MIDI and the high-lelvle control offered by the Transformation Engine (Degazio 2003), it is very straightforward for each grain to be represented by a musical motif.

On the minus side, MIDI is limited in the number of grains that can be performed simultaneously. Whereas audio granulation routinely uses grains numbered in the hundreds, and visual particle systems sometimes employ millions of particles, the MIDI system described here is limited to just 64, the number of tracks in the Transformation Engine.

To a large extent however this deficiency is compensated by the complexity of the MIDI particle as compared to an audio grain. While an audio grain is typically only a few dozen milliseconds long, a MIDI particle can consist of an entire musical phrase of several measures duration, or even an entire composition. Typically it is a musical motif of several notes, lasting perhaps a few beats.

There also seems to be a perceptual characteristic that limits this deficiency. It might be called a sort of primitive rule of large numbers. Perceptually, once more than perhaps 3-10 musical  entities are employed the listener perceives them simply as "many." At any rate the perception of a great mass of sonic entities does not seem to be diminished by the small number of particles.




Description of the MIDI Particle System - Basic parameters

The basic particle system parameters were adapted from Quartz Composer's simple built-in particle system, which is obviously a slightly-evolved descendant of William Reeve's original design. To summarize Reeve's design, the following are the essential parameters:

1. Overall Flow Intensity (determined by Rate, Variance)

2. Particle Size

3. Particle Lifetime

4. Particle Initial Position

5. Individual Particle Velocity (modified by Attraction, Gravity)

In musical terms these become : 

1. Overall Flow Intensity - same as visual particles except that the driving frame-rate is musically variable to suit various rhythmic situations

2. Particle Size - loudness, i.e. MIDI velocity and breath controller value

3. Particle Lifetime - duration in musical terms (beats)

4. Particle Initial Position - initial pitch location,  (tessitura)

5. Individual Particle Velocity - same as visual particles

MIDI Particle System Settings window

Some experimentation with the MIDI particle brought up a number of differences from a traditional visual particle system. In brief:

1. smaller number of particles - dozens, rather than thousands or millions
2. particles are not uniformly similar
3. greater complexity of individual particle. The particle consists of a musical stream of several notes differentiated by pitch, rhythm, dynamic shaping, articulation and other performance parameters. This is analogous to using a video stream as the particle source in a conventional visual particle system. 
4. shape of the emitter is not relevant (?)
5. particle parameters are more individually shaped

The most important differences arise from the item 1 - the MIDI particle system employs a much smaller number of individual particles. This implies its corollary, that the individual particles have a more "personality."

There are of course also some similarities to visual particle systems:

1. emergent structure 
2. wide variety of behaviours are possible by adjusting a small number of parameters
3. behaviours recall natural processes

DEMONSTRATION

32 Clarinet Orchestra

The "orchestra" used for many of the particle system examples consists of clarinets synthesized additively in Wallander Modelled Instrument's WIVI system . Clarinets were chosen because, like string instruments, they consist of a large family of instruments covering the entire orchestral pitch range with a consistent tone quality. Unlike sampled instruments, the WIVI instruments provide continuous control of dynamics and tone colour, a factor which is essential to the simulation of flow in the MIDI Particle system.

The orchestra consists of:
6 clarinets in high E-flat
6 Clarinets in B-flat
6 Clarinets in A
6 basset horns in F
4 Bass Clarinets in B-flat
4 Contrabass Clarinets in B-flat
----------------------------------------
TOTAL: 32 instruments/particles


EXAMPLES:

1.  slow random drops 
1. - very low flow rate (0 or 1 particle per beat)
2. fairly long beat (300 ticks = about 5 sixteenths)
3. very short particle lifetime

Huron Peeper Crescendo
FrogCroak&DrumCrescendo-0003 - nice illustration of rhythmic randomenss-orderdness
best example is Viemo - Huron Frog Crescendo

* Bubbling Clarinets (BubblingClarinets-0003)  - following some guidelines from Farnell's Designing Sound

Waves - (ThreeClarinetStreamsinWavesV2_0001.aiff)

Random Flow - Beat synchronized (TransitionRandom>Beat_0002.aiff)
Random flow with continuous pitch descent - (Descent-60x60tk3(dfrntSeed)_002.mov

Random Particle flow to four part counterpoint - Prtcls>CounterpointV3_0001.aiff)

Drum rhythm - Randomness to Beat synchronized - (AfricaDrumsConfluenceT3_0001.aiff)

Ant Colony
This example required certain extensions to the Particle algorithm for full effectiveness. In particular, two parameters relating to the selection of MIDI theme were extended with a variance allowance  in order to be randomized on playback. These parameters were (1) the starting position of the theme, and  (2) the time scaling factor.

The first of these has the effect of varying the beginning of each particle's statement of the theme. Without some statistical variation of this parameter each particle begins with an identical opening. Varying the start point is very effective in this example because the 'Theme" is an algorithmically generated random walk (ex. 1) . Varying the start position therefore has the effect of selecting a different segment of the random walk, providing a much more difference set of "themes". The variance of the starting position can be quantized to a musically sensible value, e.g. in this case to 16th notes. THis means that each particle will randomly choose a starting position on a 16th note boundary.

The second parameter varies the playback rate of theme across a wide range, from 1/12 of the original tempo to 24/12 (=2x) the original tempo. This again provides a much more diverse set of particles, very suitable for the representation of the independent paths of hundreds of creatures.

Random Walk - note pitches, with superimposed pitch bend data.

BIBLIOGRAPHY 

Personal Effects: Weaning Interactive Systems from MIDI

Robert Rowe, New York University (robert.rowe@nyu.edu)

https://files.nyu.edu/rr6/public/spark.pdf

[Moore 88] Moore, F. R. (1988). “The dysfunctions of MIDI”, Computer Music Journal, 12(1):19–28..

Wallander, Arne - WIVI Modelled Instruments; www.wallanderinstruments.com