The Wavehole, the TR808 and the Xenakis Screen

 The Xenakis screen

The wavehole approach to organising acoustic particles is an adaptation of the Xenakis screen. In Formalized Music Xenakis discusses various methods with which to organise grains of sound. A Xenakian screen is not unlike Gabor’s Matrix (1946). The representation is musical and interpreted differently from the theoretical signals presented in Gabor’s communications literature. The Xenakis screen (Fig.1), is a two dimensional grid which, exists in one moment of time.

 

Each cell of the screen grid, houses a silence or grain event. Thus, each screen can have, depending on its resolution, a sparse or dense population of grains. The population is referred to as a cloud. Each occupied cell has a frequency ∆F and gain ∆G parameter. A Xenakis cloud is the grouped grain topology in one screen at a given moment in ∆t as in Fig.2. The use of the term granular clouds has a slightly different meaning today. It commonly refers to dense groups of particles as a function of time rather than at a given slice of time. The meaning is a lexicalisation of microsound phenomena rather than belonging to mathematical topology. Xenakis treats parameters as dimensions so that together with ∆t screens consist of four dimensions (∆t,∆f,∆g,∆d). Screens sequenced over ∆t form a book (Fig.2).

 

Early on during the ESE design process, several sound particle synthesis techniques where analysed (functionality and usability) in order to determine salient weaknesses and strengths. The systems reviewed were, Pulsar BTDsys in Buzz Machines, Pulsaret (M4L plugin), Hamburg Nuklear and the Csound FOF, Partikkel and VoSim generators. Importantly, the design analyses were not realised in order to criticise any one system but rather to extract valuable empirical design data, in order to, inform new particle synthesiser systems. The design analysis process was a very informative process and one which now I consider essential in arriving at new differentiated musical instruments.

One of the limitations perceived from the design analyses, is the constrained control and organisation of sound particles across the sobject (sound object) and meso-time levels.

Pulsaret

Pulsaret, an M4L Ableton Live plugin, is one of the most versatile microsound environments on the market. It takes an approach that affords the user with particle states, which can be sequenced and morphed using its snap-sequencer. This affords users with 64 steps (loopable), which can be programmed with one of a hundred user-programmed states (Fig.3). The states are snapshots of the synthesiser and are created and stored by the user in the device. The sequencer runs in synchronisation with the hosts master timing, which is based on beat metrics. Each snapshot, is morphed into another (using a user determined morph time), at a tempo and metric set by the user.  

 

 

Pulsar BTDSYS

PulsarBTD offers integer sequences of burst and rests (Roads, C. 2001). Fig.4, Illustrates how the burst parameter has been set to 4 and the rest period to 2 in order to create a pattern of four Pulsarets followed by two equal length silences. This repeats ad-infinitum. The stochastic mask parameter, which is set to 46% adds subtle interruptions to this pattern.

 

 

This implementation does not offer user defined arbitrary masks like in Pulsaret. Furthermore, the only automatic intervention is provided by stochastic control (Stoch Mask), with no possibility of any other user type of generative or procedural modulation of the bursts. This would seem to constrain any wider creative control of pulsars across the temporal boundaries, i.e., an arbitrarily programmable approach which, could be pre-programmed into some type of sequenced matrices. Perhaps even a modification of the temporal topology of the Xenakis screen to control more than just the amplitude of particles. Partikkel offers an arbitrary mechanism based on preprogrammed arrays.

 

Hamburg Nuklear

Nuklear uses arbitrary masks but these are limited to 8 slots thus, excluding the meso and macro time scales (Fig.5).

 

 

FOF

In the FOF stream it is possible to fade in and out every other particle to create the illusion that the fundamental frequency is morphing between octaves. This is achieved by pre-calculating the fundamental frequency required (Rodet, 1984). The fundamental is then built from consecutive layers of sparser streams of FOF particles and summed into one stream. Density is dependent on how many layers are present. The more layers, the higher the fundamental frequency.

 

The advantage of this technique (octaviation) is that one can fade layers in and out of the stream (Fig.6) creating the illusion that the fundamental frequency is morphing between octaves and without the intervening musical intervals. Because the formants in the spectrum are preserved, it affords the production of dramatic gender morphing vocal timbres and the dynamic resizing of perceived acoustic objects. Octaviation is the mechanism by which, Michael Clarke creates the evaporation and coalition of FOF events in his magical Mälarsång. The dynamic movement between temporal boundaries is a key identity (Jaffe, D. 1995) in the sound world created using FOF generators. The limitation however is that FOF generators are limited to octave morph patterns. This is a major limitation of additive microsound systems because in order to create interval patterns which are not octave patterns would require layers to consist of differing quantities of particles. Furthermore, the user does not have control of the individual placement of each FOF particle in time. It is limited to the fading in and out of consecutive events.

 

The drum machine as a temporal programmer

Each PulsarBTD, Partikkel and Nuklear mask layer could be viewed as a mechanism, not unlike the “single row programming” interface of the Roland TR-808 drum machine (Fig.7) . It is a binary switch in which each mask, is an on-off step switch of a particle stream.

 

 

Single drumbeats are technically microsounds in that, they are typically last (tens at most) milliseconds and are emitted at sub-audio rates, which, is perceived as a repeating collection of individual pulses. The drum machine operates in the time-domain. The TR-808 circumvents the limitation of controlling one row layer of drum sounds by using a rotary switch to choose between a numbers of layers (Fig.8).

 

 

The above concept could be interpreted like a Xenakis screen, but with one important difference. Each step switch in the TR808 row, can be thought of as a cell containing a sound particle. In the case of the TR808, this is an electronic drum sound. In terms of usability, the TR808‘s rotary layer selector is a method for reducing the clutter of controls in the equipment’s interface. If we substitute this switch with layers in a computer software based implementation, then we get a two dimensional grid as in Fig.9.

 

 

Waveholes

By viewing the screen cells in the time domain instead of the frequency/amplitude domain, we now have a time domain multi layer grid area with which to hypothetically include or exclude layers of single particles-waves events (Fig 10).

 

Using this conceptualisation of the grid, a ESE user can schedule “holes” in the particle-wave stream. Hence the name “Wavehole” filter. It is in effect a single cycle wave mask, which, is tracked in the time domain. The Wavehole filter was conceived and implemented in 2006 and introduced at the Nord Modular workshop in Frandeuax, Belgium in 2007 and subsequently at the British Acoustics Institute conference Reproduced Sound in 2008. The original implementation offered the arbitrary manual programming PWS events controlling amplitude (∆g) with 32 particle slots. At 30Hz this produced a repeating particle pattern lasting 1 second, which limited it to the microsound and sobject time scales. The present implementation in the ESE beta version released on 07/04/2014 can cycle through 1200 waveholes. At 30 Hz a pattern lasts 40 seconds before repeating which gives more than enough scope to morph to other patterns thus varying the states continuously.

 

 

Higher Resolution amplitude scales

Instead of fixed on/off pulses as in the available implementations of the original pulsar masking, the Wavehole filter affords high resolution intermediary states so that, the user can program accurate amplitudes in the particle-wave stream. Each wavehole is variable. Because such as system requires a sample rate master timing reference, in order to synchronise individual events, it is possible to control other parameters of the particle/wave stream such as, the individual spatial location (similar to channel masking in Pulsar synthesis), formant frequency, spectral processing and the rate of emission of the particle-waves (Fig 12).

Arbitrary Masks

By combining both the Xenakis screen and drum programmer concepts, it is possible to afford a flexible method for the arbitrary temporal programming of the PWS. The relatively simple drum machine approach, opens the concept to a wider variety of users because, of the familiarity of the production technique in the electronic and popular music production community. This is a flexible approach to working across multiple-temporal levels and as we have seen before, it is an essential characteristic of microsound. Instead of a two dimensional Cartesian screen, the Wavehole is a one dimensional sobject finite grid, which occurs over ∆t. Each cell can contain a particle, a part or none. The grid’s dimensionality is expanded using layers (Fig.12).

Programming Waveholes patterns

The concept of stochastically distributed grains does not exist in the Wavehole concept, because wavehole patterns loop. The formant noise generator in the current version however, can be used very effectively to generate pseudo-random amplitude patterns. This will be expanded in future versions. The system  has scope for being controlled by any formalistic or procedural method, because, all sliders will be assignable to real-time control, internally to the PWS system or externally via controller protocols such as MIDI or OSC.

 

 

 

Why change the Xenakis screen topology?

Personally, the idea of Xenakis’ screens is conceptually and visually burdensome when applied to particle-formant layers in which particles are subtracted (subtractive microsound) from the stream rather than added (additive microsound) and layered as in FOF and classic granular synthesis. Whereas asynchronous granular synthesis compositional techniques have concentrated on the time, spectral and spatial domains, the ESE view adds the pitch / frequency (fundamental frequency) domain. As such, the linear nature of the drum-machine layer model, is arguably easier to manage because, one can easily treat these perceptually as rhythmic or periodic patterns.

In the Wavehole model they can also be looped and repeated. The inclusion or omission of a particle event is concurrent along the Wavehole pattern rather than, being local only to one screen. The connections between thousand of screens containing clouds of particles, is arguably harder to hold as a mental geometrical structure because, the particles are multiple pointillist events, which occur at the scale of a few thousands of a second. To me the mental model is too diffused. Consequently, in each layer of the PWS / Wavehole concept, there are no structures such as a Xenakian cloud. The topic of micro-temporal perception in relation to microsound composition is certainly an area, which deserves further study and could be seen to fuel new methods for the composition and design of electronic music.

This article was adapted using extracts from my PhD thesis.

 

References

Xenakis, I. (1992). Formalized Music (Revised Edition),Pendragon Press, Stuyvesant NY.

Gabor, D. (1946) “Theory of communication,” J. IEE (London), vol. 93, pp. 429-457, 1946.

Jaffe, D. (1995). Ten Criteria for Evaluating Synthesis Techniques. Computer Music Journal Vol. 19, pp.76–87.

Roads, C. (2001). Composing with Pulsars, AES Journal of the Audio Engineering Society, Volume 49 Number 3, March pp 134-147.

Villez, P. (2008) Composing with Waveholes and Microsounds. Proceedings from Reproduced Sound 24, Vol 30. Pt6, Immersive Audio, 20-21 November 2008. ISBN 1 901656 95 0, ISBN 1478-6095.

Villez, P. (2009) Elementary Signal Engine, Microsound, Vague Terrains. Available: http://vagueterrain.net/journal15/pere-villez/02 retrieved 21rst April 2013 at 13.54.

Clarke, M. (1987) Mälarsång, Refractions (MPSCD003).