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Framework for Live Algorithms Tim Blackwell Michael Young Goldsmiths College, London Organised Sound 9(2): 123–136

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The context Consider (for now, because its easier) improvised performance i.e. free of compositional directives such as harmony, rhythm, form… Conventionally such improvisations are explorations of timbre and texture

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The context Consider (for now, because its easier) improvised performance i.e. free of compositional directives such as harmony, rhythm, form… Conventionally such improvisations are explorations of timbre and texture

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What is a Live Algorithm?

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A Live Algorithm is Interactive Autonomous Ideas generator Idiosyncratic Comprehensible

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Interactive Sympathetic, supportive, makes appropriate contributions, tacets Autonomous Not merely automatic, mechanical and predictable. Must be comprehensibly interactive and capable of novelty Ideas machine Contradictory, individualistic source of novelty and leadership

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Idiosyncratic Contributions limited by instrument and experience but can be unusual, individualistic Comprehensible Suitable for collaboration, at least by humans. Not opaque, but not too transparent either And, importantly…

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Closure …knows when to stop!

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Principles Expectation of generating form might not be necessary Local events can be structuring For example, spatio-temporal self-organisation depends only on local interactions of a certain complexity and on positive and negative feedback. Here, the space is (interpreted as) a musical/sonic parameter space at some level. Parameterisations possible at micro (sample, grain), mini (note) and meso (phrase) levels.The problem of emergence might necessitate a need a multi-level system

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Knowledge of music rules might not be necessary LA need not be aware of what it is doing In the model, LAs and humans interact with meaningless sounds, populating an inert environment. This builds on a former XY model, which expresses the paradox of interaction (In our nature-inspired systems, The sounds are organised by stigmergy)

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Knowledge of music rules might not be necessary LA need not be aware of what it is doing Desirability of an Interactive Model and a Conceptual Architecture In the model, LAs and humans interact with meaningless sounds, populating an inert environment. This builds on a former XY model, which expresses the paradox of interaction (In our nature-inspired systems, The sounds are organised by stigmergy)

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The XY model

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The model AB

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Conceptual (and Actual?) Architecture P: Listening, analysing Typically thins degrees of freedom; from real time IN -> p(t) -> p i F(p): Ideas engine Patterning in a hidden space H; generative/algorithmic/iterative x i -> x i+1 Q: Interpretation, Playing, synthesizing Typically expands d.o.f.; into real time x i+1 -> q(t) -> OUT

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PfQ Architecture

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Analysis is typically projection from one level to another, higher level. E.g. samples to event parameters p P: (t) -> p(t) -> p i We observe that this projection is determined by cultural, personal, genre- specific and even political forces P might be a map into H and hence hidden state x is a possible parameterisation of the sonic environment.

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Interpretation is the process of relating internal states to event parameterisations, and eventually to sound Q: x i+1 -> q(t) -> OUT A technical complication surrounds the relationship between real and algorithmic time It is unlikely that both will flow at the same rate: the computational update time x i -> x i+1 might not correspond with the desired time interval between events (t), (t+ t... Internal states might be sampled at a given rate irrespective of iterative time or timing information could even derive from x itself Information might be derived from averages over a population {x 1, x 2, x 3,...} All these complications and possibilities are represented by a single interpretative function Q

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Ideas generator F is parameterised by p and determines state flow of hidden variables x F(p): x i -> x i+1 x i+1 determined F, p(t) and x i F need not derive from any musical concern, and this may be advantageous F only concerns patterning and structure

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Autonomous 1. x 0 even if p = 0 2. x = 0 even if p 0 1. This is usual, expresses state flow in a dynamical system 2. Harder to achieve, but could arrange for Q( x [x-dx, x+dx] ) = q. Alternatively, include dissipation and re- energising so that x 0 between injections of energy (determined by p?)

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Idiosyncratic Q and P concern the mappings to and from sound – herein lies the machine's idiosyncrasies and characteristics Can be quite limited, since interactivity and autonomy are the major prerequisites Potentially P, Q may cross levels

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Interactive autonomy + modification of system state Analysis parameters p ensure interaction i.e. affects, but does not fully determine, x For example, p might be an attractor in H. In a dynamic system, x orbits p, but precise trajectory depends on initial conditions Alternatively, hidden variables x can be regarded as parameters which select mappings F x : p -> q The collaborative interface is the asynchronous map Q F x P = M x OUT (t+ t) = M x IN (t)

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Comprehensible: Transparency > Comprehensibilty > Opacity Very transparent if p H, Q = P -1 and dim(H) is small enough. Easy to establish correlations between human (incoming sound, deposited in the environment by a human) and LA (outgoing sound deposited by the LA). Might become too predictable unless enhanced by some stochastic adjustment (a degenerate solution) Very opaque if QFP is very complex and dim(H) is big. Very hard to establish correlations or any measure of causal relations between human and LA. Too unpredictable and therefore not collaborative

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Closure: Raises issues of knowledge of form Could argue that LA should not be deprived of knowing the modus operandi of the performance In humans, closure is influenced by time constraints, visual cues and an increasing capacity to interpret gestures as possible sonic cadences However, in an LA closure might possibly emerge from lower level dynamics e.g. self-organised criticality

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Other desirable properties Memory Dynamical states do not conventionally posses this Short term (repetitions, anticipations based on recognition..) >>> attractor persistence, pheromone trails E.g. Swarm Techtiles, Ant Colony simulations Long term (draws on previous musical engagements) >>> current states could have memories of previous states… E.g. Particle Swarms (particles have a memory and participate in social networks) …AND the sequence of conditions that caused these states (a contextual memory) E.g. ??

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Links with existing research fields: P: -> p Real-time music analysis and informatics Q: x -> Real-time audio synthesis F Generative Music (Neural, Cellular Autonoma, Genetic Algorithms, Swarms

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Links with existing paradigms Live Electronics: ideas engine F replaced by human volition. State flow is adjustment of controlsx Live Coding F = I and Q is adjusted (in software) manually Generative/algorithmic music: Set p = 0 (turn P off) (t) = F(x i ) = F N ( x 0 ) The system is self-contained - the composer chooses F and the initial condition, x(0)

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Reactive Systems In a reactive system, IN will necessarily trigger certain transitions x i -> x i+1 M x = QFP express a causal and necessary chain – a rule-based system It is conjectured that a reactive system might not be sufficient for a Live Algorithm because it is not sufficiently interactive This touches on various issues in cognitive science and machine intelligence Possibly, a large enough rule set might do the job, and might also be indistinguishable from a discrete dynamical system (i.e. an algorithmic model of a continuous DS) It is hard to see how we might achieve this complexity without drawing on inspiration from dynamical, and other natural, systems

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(Our) Experience Swarm Music: Very transparent, P and Q operate at the note level Swarm Granulator: Less transparent, functions largely at the grain level, although some level-crossing

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Swarm Tech-tiles P actually expands into a 2D landscape F integrates ALife and optimisation Q is a rendering of parts of the landscape visited by x Argrophyllax P: FFT analysis f: stochastic function H: Fourier space Q: coefficients of inverse FFT transform Q

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Evaluation Irrelevance of Turing Test? TT is more relevant for the performers than the listeners. A metric: do the performers find the LA to be stucturing? Applicability: The attributes of a LA should be useful in other musical contexts E.g. intelligent effects pedal, synth plug-ins, accompaniment programs, genre improvisation

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