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Page 234 ï~~Natural Selection of Musical Identities. Currit rota, urceus exzt.* Per 1artrnann IHi-Yin Jusic 68 West End Launton Oxfordshire OX6 0DG A multidimensional parameter space where each parameter has been 'perceptually linearized' is described. Defining a musical identity by 'genes' controlling the function for each parameter over the lifctzme of the identity, the principle of 'natural selection' - gene mutation - is used to evolve music of increasing complexity. Introduction To support his argument that accumulation of small change is capable of evolving structures of considerable complexity, Richard Dawkins in his book "The Blind Watchmaker" developed a computer program to draw 'creatures' which he refers to as 'biomorphs'. A picture-drawing rule is applied recursively and the emerging biomorph is drawn symmetrically about a left/right axis. The software - LUDWIG - The deaf Cdiposer The software develops musical identities - a group of discrete events where the evolution of it's 'life' is determined by a number of parameter 'genes' defining individual parameter growth over the duration of the group. Each of a selection of parameters has been perceptually linearized and placed as a universal rulebase (unique for each composition) within the software. Perceptual linearisation of parameters Consonance - Dissonance The pitch class sets (as defined in Forte ) are weighted and sorted using a linear dissonance index as the sorting key. There are 223 prime forms of the pitch-class sets from unison to the twelve-tone chord. The degree of dissonance is computed using the following weightings: 1 semitone -- 10 2 semitones --- 5 3 semitones -} 2 4 semitones --} 1 5 semitones -- 1 6 semi tones - 4 ie. the dissonance level of a major (or minor) triad 0,3,7 with interval vector  is 1x2 + lxi + lxi = 4. For the twelve tone chord with the interval vector [12 12 12 12 12 6] the dissonance level is 252. With increasing complexity it seems certain that perception of the dissonance index is non-linear and the function d(x) "252" is used for mapping the linear scale 0.. 1 to dissonance index. "The wheel turns, a jug emerges. (Horace - Ais Poetica) ICMC GLASGOW 1990 PROCEEDINGS 234
Page 235 ï~~Timing - Durations The organisation of musical time is represented by a three dimensional space where the co-ordinates represent TEMPO, REGULARITY and SUBDIVISIONS. TEMPO The ratio between one tempo and another is normally perceived as a simple arithmetic relationship and the mapping used is: tempo(x) = MAX - TEMPO * x. REGULARITY A perceptual index is created where zero represents complete regularity; ie. the distances between all events are identical. When the index equals one, the modification to the regular inter-event times converts to a Poisson process. The index of dispersion of the process equals one. The relationship between the perceptual index and the index of dispersion reflects the great sensitivity felt to irregularities: regu(x) = 64x/64. SUBDIVISIONS The distance left between events after applying the operations above can be subdivided into 1,2,3,4 or 5 equal parts. The function used for mapping these subdivisions is: sdiv(x) = I171471L). Selection of Chord After selecting a chord with the desired dissonance index, all transpositions and inversions are compared to the current chord. The variation with the maximum number of notes in common is selected. If the chords are identical the new chord becomes a transposition of the old. This system ensures that the dissonance 'mutation' is reached with the least possible turbulence. Musical Biomorphs A musical biomorph is uniquely defined by a set of co-ordinates - referred to as 'mernes' - in the parameter space. The evolution of each meme over the life of the biomorph is defined by a corresponding 'gene' allowing a maximum change of Â~10 per cent over the life of the identity. Creation of Musical Biomorphs through reproduction 1. Musical composition as 'evolution of the species'. Each musical biomorph is presented as a child born from an earlier generation. Here the memes from the parent are transferred to the child and exactly one gene - unit controlling growth (+ve, -ve or static) - mutates in each generation. Memes and genes are represented within the software as floating point numbers between zero and one. A gene value of 0.5 gives a static meme, ie. the parameter does not change during the life. A value of one causes a decline. During reproduction the gene mutates by increasing or decreasing by an amount determined by it's distance from equilibrium (0.5). The function controlling gene growth has been chosen to make the value gravitate towards 0.5 - stasis. Each child chosen for parenthood produces 2n children (n = number of parameters) where all genes except one are passed on. Except for the meme corresponding to the mutating gene, all memes are transferred unchanged from lparent to child. This allows for the smooth change required to create a continuum which makes it p)ossible to move from one extreme to another. More importantly it reflects the desire to pass on to the next generation experience gained over a lifetime. 2. Following a selective breeding programme, a musical biomorph corresponding to the composer's need evolves gradually. Setting a limit for the recursive depth of generations allowed, as well as defining almost arbitrary selection criteria, can create biomorp~hs of surp~rising comlplexity and beauty. ICMC GLASGOW 1990 PROCEEDINGS 235
Page 236 ï~~String Quartet To test Ludwig in his present form, I let hir write a late string quartet. Part one is a family tree evolving from an 'Urptlanze'. Part two is a presentation of the different children created in each generation and part three a binary search for equilibrium from two extremes. The three dimensional temporal space proved very difficult to handle and further evolution of the program is required. References Dawkins, R: The Blind Watchmaker Longman 1986, Penguin Books 1988 Forte, A: The Structure of Atonal Music Yale University Press 1973 ICMC GLASGOW 1990 PROCEEDINGS 236