The Soundfield Studio

Distortion and Noise – Part One

In some areas of the industry, particularly those involved in the recording, mixing, and mastering of classical music, a knowledge of distortion and noise is critical in terms of eliminating the many different ways, both in the analog and digital domains, where an audio signal may be subject to degradation. The reason? Classical music is at an extremity of the audio engineering world where dynamic range, transparency, phase alignment, and the reproduction of sound stage and ambient space is absolutely critical. Factors like the total harmonic distortion (THD), intermodulation distortion, and signal-to-noise of various electronic components become most critical, and due to these factors many recording engineers of classical music will not compromise for anything but the best AD/DA converters, shielded and balanced cables, transformerless preamps, solid-state microphones with minimal signal-to-noise, passive EQ and/or [digital] 64-bit linear phase EQ, and minimal compression. A clean power supply is also critical. Engineers in this part of the industry are also ahead of the game when it comes to an awareness of dithering routines and the limitations that exist in PCM digital audio, shifting rather toward newer developments such as Sony/Phillips DSD (a dynamical 1-bit methodology called super-audio) and DXD (a sort-of “high-bandwidth” PCM) technology instead.

This awareness I would like to think is a necessity. However, perhaps not in opposition to this, other styles of music have, over many years, become dependent on distortion in its many forms, and consequently such effects have become intrinsic to these musical genres. Rock, metal, punk, grunge, doom, industrial, hardcore rave, and a huge number of stylistic derivatives have used various kinds of distortion to create a more unique and aggressive sonic palette. Distortion in some ways might be considered sonically as an “injection of attitude” as the process not only changes the tone of the signal, but also the dynamics – a kind of compression or squashing of the signal achieved by driving a signal at higher levels through valves, speaker cabinets, against tape et cetera. Terms like overdrive and saturation again relate to this fundamental idea of “squashing” the audio signal.

The more one delves into distortion, the more it appears to be a universe unto itself. From the most subtle harmonic distortion and coloration achieved when using analog electronic components like valve pre-amps and transformer based pre-amps, adjustments in input impedance and/or impedance mis-match, noisy components, different power supplies, to more extreme distortion achieved with FET transistors, overdriving speaker cabinets, valve distortion achieved when adjusting bias, tape saturation, and digital manipulation of phase and pulse-width, all the way through to extreme distortion involving signal rectification, noise modulation synthesis, waveshaping synthesis, signal truncation and rounding, signal bit-reduction, sample-rate reduction, logic bitwise and inequality operations. I generally consider these all as primarily “destructive” processes of signal modification.

When we hear the term distortion perhaps the first thing a lot of us think of is the sound of a distorted electric guitar. But the reality of distortion is that it exists in many different forms and extremities. Milder forms of signal distortion, what is referred to as harmonic distortion, is used in many cases as a way of “warming” or “fattening” a signal, for example when valves are used to add even harmonics, or tape saturation is used to accentuate odd harmonics in a signal. Distortion can also exist in more extreme forms where overdrive and signal rectification result in drastic tonal and dynamic changes in a signal. It often also decreases the signal-to-noise ratio, consequently accentuating the noisiness that exists in a signal. And noise in some ways has become, like distortion, an intrinsic aspect of our association with many contemporary styles of music.

Historically there has been a growing attraction to the use of noise in music composition and music performance. I believe John Cage was not far off the mark when he stated in 1937:

‘I believe that the use of noise to make music will continue and increase until we reach a music produced through the aid of electrical instruments which will make available for musical purposes any and all sounds that can be heard.’ — John Cage, The Future of Music: Credo (1937)

Edgard Varese’s Ionisation (1929-1931) and John Cage’s Cartridge Music (1960) were both influential works toward a growing trend in using noise (i.e. non-pitched sounds) as a central component of a composers sonic palette and compositional intent, as well as a performers artistic practice. This was most evident during the 1980’s when a new wave of noise artists and bands emerged including Merzbow and Ryuichi Sakamoto from Japan and Sonic Youth from the USA. Trent Reznor from Nine Inch Nails is another who has used noise, and also distortion, extensively in his own work – most notably among these practitioners is the use of different colorations of noise.

So where is all of this going? Well recently I have been starting to become more actively involved in live laptop performance, as well as ongoing work in sound design, mixing, and mastering at the studio. I have been actively building tools and instruments that allow me to be more creative both in the studio and in live situations. Teaching instrument design and sound synthesis has started to give me a different perspective on my own practice, and what kinds of sounds and modes of expression I wish to use. My aim has been to document these explorations as I go.

I have often found the creative process mysterious. What drives a creative artist toward an idea? In the case of a sound artist, toward a sound they might envisage? Well I saw Merzbow twice in Perth, and from then I became fascinated with not only noise, but methods of distortion, both analog and digital, and its infinite world both rich and full of possibilities. The difference between analog and digital processes became more apparent to me after using several analog distortion units here at the studio, whilst also practicing as a live laptop artist. I have three hardware units at the studio specifically designed for signal modification – the Evol Audio Fucifier, the Thermionic Culture Vulture (mastering edition), and the Sherman Filterbank. With this mix of valve and solid-state technology, each of these units can effectively generate rich and varied distortions of many different colors and varieties. I can also push these units to extremities, that seemed by comparison to software equivalents to have more “attitude” and “aggression”. By contrast I wanted to devise some methods I could use to “mangle” sounds in the digital world, and create a similar level of attitude. There is a universe of possible combinations and colors in both the analog and digital worlds. I am not going to argue what is better here between analog and digital, except to suggest that they are indeed different, and they should be judged individually based on the unique way in which each respective methodology modifies a signal. I am certainly not interested here in methods involving impulse responses and convolution synthesis aimed at the creation of digital emulations of analog gear. This article focusses specifically on some known digital methodologies aimed primarily at signal distortion, and to experiment to find some extended ways in which to use the computer to compute what it is best at computing: algorithms.

So in a way this write up focusses largely on a small combination of digital methodologies including noise modulation, waveshaping (including logic bitwise and inequality operations), phase distortion, and signal truncation and/or brickwall limiting.

1. Waveshaping

Waveshaping Synthesis is certainly one of the most widely used methods in signal distortion. This process involves running a waveform through a transfer function, and it is this transfer function that “reshapes” the input waveform. The only problem with waveshaping is that the technique can easily introduce aliasing – if you don’t know what that is, it is best to read about it. Most of the time it is best to avoid it. However, as we will see later in this article, we are also going to exploit its possibilities.

The mildest use of waveshaping synthesis is for the purposes of harmonic distortion (or the adding of harmonics). This is achieved through the use of Chebyshev functions of different order (N) as transfer functions. These allows us to generate frequencies up the Nth harmonic of the input waveform. This way we can ensure the highest frequency generated is below the nyquist frequency, hence avoiding aliasing. Each polynomial will generate a new harmonic, and these may be summed together as one likes – for example, to create the effect of introducing even or odd harmonics in a signal to model the coloration valves and tape impart on a signal.

The first five Chebyshev polynomials are:

A second approach to using waveshaping which is again widely documented is the simulating of overdrive. This is achieved with an overall flattening of the transfer function. In the following set of images, we can see what each transfer function does by observing the shape of the respective waveform. As we move through these series of transfer functions, we can see a general flattening of the waveform. In a way we find the process acts as a compressor on the signal, but not in a conventional way!

As we increase the input gain we find the transfer function introduces further harmonics. We can see the process unfolding in the following spectrogram where time passes from left to right. We see new harmonics enter as the gain of the input signal is increased before running through the hyperbolic tangent transfer function.

We can also reverse the effect, similar as to what we might find in signal expansion, by bending the transfer function in the opposite direction.

One of the primary observations I have made from the work of Merzbow is the minimal dynamic range – sounds are generally at the maximum threshold. The distortions are also more extreme, to the point where the sound source is rarely determinate. Could we also say that aliasing is a factor to be encouraged here? Extreme aliasing would certainly go a long way to obscuring the timbral and spectral qualities inherent in a sound source. I hope so, because some of the following examples are going to exploit this!

Lets suggest some possibilities here, as since there is minimal dynamic fluctuation it might also imply lower bit-depths. You could say that if it were possible to overdrive a speaker to the point where it would completely flatten a waveform, it would result in a square wave! (Figure 5). This is also analogous to converting a digital signal to 1-bit PCM signal. Mathematically a square wave can also be generated from a sine wave using the sgn function. It can also be achieved using an inequality like “greater than” or “less than”. This kind of signal is hardly possible to generate in the real physical world. The binary nature of this seems to me to be something computers are naturally adept at, and does not come naturally to the analog world without the use of digital components.

Well, in fact, a square wave only consists of odd integer harmonics as opposed to the sawtooth wave which contains all integer harmonics. So rather than a speaker amp, using this transfer function would be like slamming a signal against tape at an infinite level. Ok that’s not going to happen! And the tape medium would impart its own color and sound anyway, including inherent effects such as wow and flutter.

Lets say that based on this example, we want to turn some of this theory on its head, and what it is we want to achieve in terms of dynamics and tone shaping. We are not going to rule out aliasing. And we are not aiming here to emulate the behavior of valve and speaker components, but rather we want to find distortion methods that are unique to digital processes. I would argue that for some noise artists, it is most critical to “reveal” the noise in a signal. In fact noise is quite common. In mastering, dithering is a process where a small amount of noise is injected into an audio signal to randomize the quantization error created when a file is converted from a higher bit-depth to a lower bit-depth. This is used to avoid the possibility of periodic limit cycles.

Noise is also common on analog signal path. All electronic components exhibit a certain amount of noise. Studio equipment will always have a rating based on their own signal-to-noise ratio.

So how do we “reveal” this noise in a signal? Well we can achieve this by using a waveshaping transfer function where the minimum and maximum peaks occur about the zero-crossing. This kind of transfer function will have the effect of maximising low level fluctuation in the signal. The square wave is one such example, but what other functions have this characteristic about the zero crossing? Refer to Figure 6 for a list. Please note some of these transfer functions result in a waveform that exceeds the -1, +1 domain range, so will require a limiter.

Having the maximal peak and trough about where the zero-crossing normally occurs changes many of the inherent characteristics of the source wave, including the way in which dynamics are perceived. There are some other transfer functions that result in a maximum and minimum around the zero-crossing. For example, logic bitwise operation bit NOT is one.

2. Phase Distortion, Pulse-Width Modulation, and signal Rectification

For standard oscillators, implementing phase distortion on a signal can be achieved in MaxMSP using the kink~ object. However this will only help us when we are distorting the phase of a table lookup oscillator. In order to distort the phase or pulse-width of any signal we must change where the zero-crossing occurs in the waveform. This can be achieved in several ways. The method shown in the MaxMSP patch below describes a process centered yet again around waveshaping. This example uses a waveshape where the zero crossing can be shifted left or right within the domain -1 and +1, causing a distortion in the overall waveform. The maximum and minimum peaks in the waveform remain relative to the original waveform, however the perceived dynamic intensity of the signal is compromised due to an incurred DC offset. The relative distance of the maximal and minimal peak values to the DC offset is what effects the overall perceived dynamic intensity.

This phase distortion or pulse-width modulation is useful when combined with another distortion process. And when we are using a square wave as our transfer function, we can more efficiently perform phase distortion or pulse-width modulation with a comparator like the > or < inequalities, and change the argument from between -1 and +1. For example, x > 0 will result in a different pulse-width than the inequality x > 0.1.

Not too dissimilar to our first example of phase distortion, we have an example below that shows how we may implement rectification of a signal. This algorithm creates significant changes in the resulting waveform.

This process designed here changes the weighting of the waveform in the positive or negative direction (in terms of DC offset). Like in the previous examples, there is some change in the phase or pulse-width of the waveform, but a “rectification” of the signal is evident also. By removing the DC offset with a high-pass filter can bring the signal back to an oscillation about the zero-crossing.

However I did find I could also use this method for more extreme methods of distortion on a signal. With a slight variation on this MaxMSP patch, this following example I could push with values between -10000 and +10000 provided a DC offset filter (high pass) filter is applied. To control the dynamics this also needs to be run through a limiter or a hyperbolic tangent function. This has become one of my preferred methods of signal distortion.

3. Noise Modulation

The concept of noise modulation is where we modulate a signals frequency, amplitude, or phase according to a noisy signal. Generally signals with an equal weighting across all frequency bands does not give effective results, but noisy signals with different weighting curves are significantly more effective. There are different colors of noise – white, pink, red (brownian), blue, violet, and grey. Each of these different colors of noise has a different associated weighting curve. White noise for instance has an equal weighting curve for all frequencies across the spectrum. So for noise modulation I would generally recommend pink, red, blue, violet, and grey noise. For example, here is pink noise ring modulated with a square wave:

And here is white noise being used to modulate the frequency of an input:

4. Hard Limiting vs Soft Limiting

Another handy tool for the laptop noise artist is the brickwall limiter, which implements soft clipping, and a second technique referred to as signal truncation or hard clipping. Both of these techniques effectively have an attack time of zero, and both keep a signal within the ceiling 0dbfs. However both techniques will impart harmonics on a signal. Hard clipping results in aliasing, and soft clipping will not. The brickwall limiter is often used only for mastering in order to increase the perceived level of audio. However in live performance we might want to consider these tools quite differently, and what role they might play.

Some of the techniques that are described in mastering go through the role of the brickwall limiter and how to compensate for too much bottom end, by boosting the top end and vice versa. The brickwall limiter is something one can stack audio against, and the more you push any particular sound, the more it emerges. The technique becomes more coloristic and timbral, as the performer can then sculpt the spectrum by adjusting the qualities and timbre of each instrumental layer. So by pushing a sound in level hard against the limiter will have the perceived effect of pushing other sounds out of the mix, and also consequently increasing the harmonic content of that particular sound. This is not something I advise in any normal circumstances, and I would proceed with caution! All I will say is the EQing your layers is recommended, and bandpass EQ curves here are your friend.

 5. Conclusion

So to wrap some of this up, some of my recent laptop noise work has incorporated principals and ideas I have documented here. As far as musical “devices” are concerned, I wanted to outline some of the methods I have used to create more aggressive and abrasive sounds. Waveshaping is without a doubt one of the most significant tools, but I have documented some ideas and suggestions as to how phase distortion, signal rectification, noise modulation, and the brickwall limiter can also be used.

Multidimensional Data Sets: Traversing Sound Synthesis, Sound Sculpture, and Scored Composition

This article documents some of the conceptual developments of some various approaches to using multidimensional data sets as a means of propagating sound, manipulating and sculpting sound, and generating compositional scores. This is not only achieved through a methodology that is reminiscent of some of the systematic matrix procedures employed by composer Peter Maxwell Davies, but also through a generative signal path method conventionally termed Wave Terrain Synthesis. Both methodologies follow in essence the same kind of paradigm – the notion of extracting information through a process of traversing multi-dimensional topography. In this article we look at four documented examples. The first example is concerned  with the organic morphology of modulation synthesis.  The second example documents a dynamical Wave Terrain Synthesis model that responds and adapts in realtime to live audio input. The third example addresses the use of Wave Terrain Synthesis as a method of  controlling another signal processing technique – in this case the independent spatial distribution of 1024 different spectral bands over a multichannel speaker array. The fourth example reflects on the use of matrices in some of the systematic compositional processes of Peter Maxwell Davies, and briefly shows how pitch, rhythm, and articulation matrices can be extended into higher-dimensional structures, and proposes how gesture can be used to create realtime generative scores. The underlying intent here is to find an effective and unified methodology for simultaneously controlling the complex parameter sets of synthesis, spatialisation, and scored composition in live realtime laptop performance.

1. Introduction

The idea of traversing data sets is well established in the realms of sound synthesis and computer music. One only has to consider the concept of wavetable lookup, and we find this method is the basis of generating digital oscillators, audio sampling, Waveshaping Synthesis, audio analysis via FFT or wavelet methodologies and the subsequent resynthesis of this data, Graphical Synthesis, Convolution Reverb, Wave Terrain Synthesis, Head-Related Transfer Functions (HRTF’s) for the binaural treatment of existing sounds, and Multi-Impulse Response techniques found in the MIR-Project. Table lookup procedures for sound synthesis developed not long after the birth of the microcomputer in the mid-1970’s, and it was in 1978 that Rich Gold first coined the term Wave Terrain Synthesis. There have been many advantages to the table lookup procedure – it is considered to be computationally efficient as processing requirements are consistently low, table lookup allow for storing and reloading tables of data, and these structures also allow for not only arithmetically generated values but the ability to  hold data sets of any measurable phenomenon (provided the data range is adequately sufficient). In this way we may “samples” of the real world, be it audio, video, or any other collection of data. In this way a system can easily can describe the complex non-linear behavior of electronic components and other complex phenomenology such as the localized perception of sound in a binaural setting using HRTF’s.

Investigation into the wide variety of multi-dimensional data sets for use with Wave Terrain Synthesis presented many possibilities.One of the main attractions to Wave Terrain Synthesis for the purposes of this research is that the system of traversing these data sets can be easily effective and intuitive to control, especially when mapped to gestural controller input. The fact that the system also is so adaptable for varied applications as the examples will demonstrate, is also leading toward a hope that this research may find an organic, efficient, and unified methodology,  for the simultaneous control of the parameter sets associated with sound synthesis, sound sculpture and manipulation, and generative scored composition.

As a means of clarification, the term sound sculpture is used here to describe the physical act of sculpting a terrain surfaces with physical input much like Dan Overholt explored with the MATRIX interface. Since the terrain largely affects the resulting sound, this then in turn leads to process of the performer “sculpting” the sound generated via this process.

1. Sound Synthesis Morphology

The concept of morphing sound synthesis is a concept that arose during the course of my Masters thesis. Initially I was more concerned in the thesis to observe the characteristic traits and topographies of conventional sound synthesis processes as it could inform and develop a further understanding of the many other kinds of topographies used in Wave Terrain Synthesis. It was only later that it occurred to me that this would open the possibility for an organic and uninhibited way to efficiently morph between different forms of sound synthesis. In this example we take three forms of modulation synthesis and map the associated parameter spaces, keeping in mind that the audio input source will be sinusoidal in most cases. These three synthesis methods discussed are Ring Modulation, Frequency Modulation, and Waveshaping Synthesis.

It is immediately apparent why Frequency Modulation Synthesis creates more sidebands and spectral complexity when one observes the number of undulations found in its associated parameter space in Figure 3. This is significantly more than that of the Ring Modulation (Figure 2) and the Waveshaping parameter space (Figure 4). The terrain structures are generated in MaxMSP utilizing the Jitter matrix processing library. This library allows for traversing not only 2-dimensional matrices, but higher dimensional structures which may be created using the jit.expr object (Figure 1).

Figure 1. Frequency Modulation parameter space curve as generated in MaxMSP

Figure 2. Ring Modulation Synthesis parameter space determined by the equation

Figure 3. Frequency Modulation Synthesis parameter space determined by the two dimensional equation where I = 3

Figure 4. Waveshaping Synthesis parameter space determined by the two dimensional equation where G(x) and H(x) are two Chebychev Polynomials

Previous research has shown that many curves can result in greater spectral complexity. James has suggested that depending on the way the methodology is perceived, Wave Terrain Synthesis could also be described as multi-dimensional Waveshaping Synthesis.

The potential for using terrain surfaces that exhibit random and “noisy” topographies translate to a resulting waveform contour that exhibit these same sorts of characteristics. Previous research has investigated many different terrain curves ranging from finite solutions to constrained Algebraic, Trigonometric, Logarithmic/Exponential, Complex, and composite mathematical functions, to data extracted from analyses of global seafloor and land topography, digital image files, video, perlin noise functions, elliptic functions, recurrence plots, OpenGL NURBS surfaces, fractal and iterative structures, and video feedback.

The concept of morphology in matrix terms involves the interpolating between two or more different states. In linear terms this could be described simply as a crossfade. This can be achieved with the jit.xfade object in MaxMSP (Figure 5)

Figure 5. The use of jit.xfade to morph between terrain structures

Another useful modulation to explore in this process is the spatial distortion and contortion of a terrain structure through the process of 2D wavetable lookup; this is sometimes referred to as spatial remapping.

As one would find in any Wave Terrain Synthesis model, the multidimensional data set needs to be traversed with a trajectory signal that is often comprised of two independent audio signals. Previous research  into Wave Terrain Synthesis has largely focussed on highly periodic trajectory structures as a means of traversing a terrain. Although other kinds of structures have been used including quasi-periodic orbits such as pseudo-phase space plots, chaotic orbits and random orbits.

Figure 6. Two periodic trajectories created using the combinations of sine tones of varied frequency

In this example, and in keeping with the generative methodology used for generating terrain curves, the trajectories used followed periodic structures such as elliptical curves and orbits attributable to the Harmonograph. These have been described by the parametric equations:

Just as one can spatially distort a terrain structure, geometric transformations can be applied to the trajectory resulting in further modulation possibilities – some of these transformations include phase distortion or pulse width modulation and affine transformation which can involve the translation, scaling, and rotation of a trajectory.

An effective physical controller for these kinds of transformations requires a multi-sensory device. Hsu has explored the use of the Wacom Tablet for the purposes of drawing trajectory structures, but new technologies are emerging that promise new directions in terms of customisations in multi-sensory and tactile control such as the Arduino, as well as mobile multi-sensory devices such as the Apple iPhone and iPad. Finding effective ways and means of gesture mapping for trajectory motion and how to effectively generate and/or manipulate a terrain surface strikes right at the heart of effectively performing using this method. The choice of physical controller or sensor is critical in being able to effectively map gestural information from a performer. A Polhemus Stylus or similar device provides position and orientation information for a single point in space via a stylus tip, whilst a gesture interface can input many positions since the system tracks multiple features simultaneously. Further investigation will involve experimentation with two dimensional and three dimensional motion sensors to test their complimentary  for traversing multi-dimensionality. This is a topic for further discussion at a later stage.

One can also easily see how the concept of morphing synthesis can be extended to three dimensions or more. With the current implementation if a four dimensional matrix stores two different sound synthesis parameter spaces, it would be possible to modulate between these two forms of sound synthesis at audio rate.

1. Live Interactive, Dynamical, and Feedback-Based Methodology

Performing with the Decibel ensemble at Createworld 2009 in Brisbane we performed one of my own pieces that involved live alto sax and a MaxMSP patch that reprocessed this live acoustic instrument in various ways. The reprocessing involved a Wave Terrain Synthesis patch that would generate dynamical terrain surfaces. In this model the rate of dynamic terrain evolution can be adjusted; effective rates can be achieved of up to 30 frames a second.

One of the attractions to this kind of model was a fascination with evolutionary and dynamical systems. As opposed to the purely generative system found in example one, this second example explores more of an organic system where the structure of the contours are determined by real-world acoustical events, thus creating a relationship between the acoustic instrumentalist and the computer. Rather than the laptop performer determining the structure of all elements, terrain and trajectory, they are not in complete control of the terrain surfaces derived from the live audio input stream.

This model was inspired by Di Scipio’s research, who would use iterative structures for generating terrain curves. Di Scipio describes some of the sounds produced to be reminiscent of boiling water, cracking of rocks and icebanks, the sound of wind, various kinds of sonorous powders, burning materials, certain kinds of insects, thunder, electrical noises, sulphureous or volcanic events, the wind flapping against thin but large plastic plates, and with higher order iterates the audio  would be  reminiscent of a large fire, rain or hail, or frying oil. Instead of using iterative based structures, this model uses a low-pass filter, which is applied to the audio input in order to control the topographical complexity of the terrain surface itself, allowing the laptop performer to control the resulting spectral complexity of the synthesized sounds generated.  On another side of the token, as a means of introducing further complexity, the laptop performer is able to control the amount of audio feedback that occurs within the software; sounds produced by the instrument are fed back into the system and blended with the live input in order to create further complexity in the evolution of the terrain dynamics.

The terrain surfaces are recurrence plots generated in realtime based on the audio input.  Recurrence plots are normally used to reveal non-stationarity of a series as well as to indicate the degree of aperiodicity in a signal.

For the purposes of creating smooth contours for Wave Terrain Synthesis, we look at the use of the recurrence plots without the Boolean stage. In other words, we are interested in a Recurrence Plot of a function f (t) that is described:

Figure 7a. A recurrence plot terrain generated using live audio input with the trajectory superimposed

Figure 7b. The same recurrence plot in Figure 7a plotted in 3D

The trajectories for this instrument were generated by “collecting” fragments of musical phrases by the instrumentalist. By using an attack and release detection mechanism, the phrases are catalogued and replayed in a different order to which they have been played. The is also a pitch detection algorithm used to determine some of the more prominent tones produced, which are then generated in order to create long drone-like passages with the Wave Terrain Synthesis instrument.

Figure 8. A schematic describing the instrument design

1. Spatial Sculpture

One of the propositions for further research in Wave Terrain Synthesis was where this methodology could be used for the control of another process. In this example we will be looking at the use of Wave Terrain Synthesis methodology to control the discrete independent spatialisation of 1024 spectral bands. This methodology may be adapted to any multi-channel speaker configuration, for example 4, 8 or 16 channels. In this way the performer is able to sculpt the localisation of individual frequency bands without a huge amount of parameter control required, so in this way Wave Terrain Synthesis is used as a bridging system allowing one to generate the complex control data required for another system using a far more manageable generative system.

The process is achieved using a windowing technique that scales the relative amplitudes of each spectral bands, which is itself is dependant on the topographical nature of the terrain curve. A flat terrain contour translates to spectral uniformity in all loudpeakers. However as the terrain tips around an axis the spectral distribution starts to separate so that higher frequency moves across to one side of the spatial field, and low frequency to the other.

Figure 8a. Signal equally spectrally distributed out to all loudspeakers

Figure 8b. Signal is distributed out to the loudspeakers in such a way that the sound spectrally shifts from low to high frequency across the room

More interesting results can be achieved with non-linear and curved terrain surfaces, and when a terrain evolves in contour over time.  Introducing undulating terrain surfaces creates very effective evolutional characteristics, and a sense of emersion in terms of the spatial listening experience., even when the source sound is a mono static oscillator.

One can see that there is an obvious benefit in this case to keeping the trajectory elliptical and to map each corner of the terrain with its relative spectral distribution. The trajectory can then be rotated causing a shift in azimuth for all spectral components and their associated localisation.

Spatialisation can also be influenced at audio rates by geometrically influencing the trajectory signal, that is by rotation, scale or translation, or by spatially contorting the terrain surface using the jit.repos object. Chaotic and randomisation can also be introduced in this way.

1. Scored Composition

Peter Maxwell Davies documents a use of pitch matrices and rhythm matrices in the composition of many of his works. in this way he is able to take a source melody and manipulate this with the contour of another. The different permutations that occur through this process create complexities in terms of harmonic and melodic material, thus also influencing the overall tonality.

Davies is known for his use of magic squares as a source of musical materials and as a structural determinant in his works. In his work Ave Maris Stella (1975) he used a 9×9 square numerologically associated with the moon, reduced modulo 9 to produce a Latin square to permute the notes of a plainsong melody with the same name as the piece and to govern the duration of the notes. In Davies’ A Mirror of Whitening Light (1977) he took 8 notes from the plainsong Veni Sancte Spiritus which is arranged into an 8×8 square and then re-arranged according to the magic square of Mercury.

Peter Maxwell Davies would then generate melodic and harmonic material by traversing the matrix using zig-zag formations, spiral formations. One can see how a similar process could be adopted from the methodology attributed to Wave Terrain Synthesis, but instead of extracting audio signals from a matrix, we are retrieving pitch, rhythm, or articulation data. Alternatively, the matrix could refer to a higher level construct in generative composition such as Markov Chains and formal grammars.

Implementing the traversal of pitch, rhythm, and articulation matrices requires a slightly different approach to the procedure, as the traversal should refer to specific cells rather than smooth gradations between cells as is found in Wave Terrain Synthesis. In order to generate zig-zags and spirals we use collections of counters. These constructs can be triggered and manipulated through gesture that control whether or not the generated material is harmonic, melodic, or more textural. The question here is how does one effectively categorize these gestures, and distinguish between these many varied kinds of materials – chords, melody, fast-fluid material, and various kinds of layers and densities. This will be investigated further during the course of this research project. Investigation will also focus on other matrix transformational procedures such as calculating the inverse of a matrix, multiplication of matrices, and other mathematical procedures for creating other permutations of pitch materials. Rhythm and articulation maps are either kept synchronised with their original respective pitch, or can be processed independently through their own procedure.

Matrices in Jitter can also reflect structures greater than two dimensions. So for transpositional pitch matrices this allows for pitch transformation over two or more melodic contours. This research will investigate how effective this might be in terms of modulating tonality.

There are two music scoring systems for MaxMSP that are in development at this time – MaxScore and Lilypad embedded in MaxMSP.

1. Conclusions

This paper is in a way a synthesis of some of the varied methodologies multidimensional data sets could be used for with respect to sound synthesis, control structures, and scored composition.  The focus of this paper to look at how a similar paradigm model can be used for quite significantly different outcomes, and to propose some initial questions as to how effective Wave Terrain Synthesis is as a control method, and also whether or not the system is practical for live gesturally controlled scored composition. The purpose is to encourage interest in this area, and to throw further questions as this paper documents some of the preliminary workings for a larger scale research project.

The underlying intent here is to find an effective and unified methodology for simultaneously controlling the complex parameter sets of synthesis, spatialisation, and scored composition in live realtime laptop performance.