# Analytical Tools for Group Additive Synthesis

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Page 66 ï~~Analytical Tools for Group A Barry Eaglestone, Department of Computing, University of Bradford, BRADFORD, West Yorkshire BD7 1DP barry@ uk.ac.bradford.computing Sha Mic De; Uni BR, We shat ABSTRACT: Group additive synthesis (GAS sound, cc frequency )nsists and of component amplitude em partials as men velopes. amplitude scaling fa overheads of additive GAS configuration.ctors dal IC grc synthe s NP-c sis, but a omplete effective, Resynth oup env lgorithmi md there if not op technique which performs an show this to be an improvement on previous further research areas for GAS and suggests addi 1 Introduction ReaI-inme additive vnth pi1ic s useful for nrecise definiti I

Page 67 ï~~the number of groups is k and the dissimilarity meas Bruckner [8] has shown this problem to be NP-comple that the existence of a polynomial time-complexity so existence of su Lch an algorithm fc )r them all. Howe, Execution time therefore becomes prohibitive further explanation of NP-completeness see [9,1 for all 0]. Consequently, the best we can hope for i a good' but not necessarily optimum groupin produce 5 Envelope Calculation The envelope should be calculated so it best represe method of envelope computation would be percept-ba geometric computation. 6 The Method of Group Calculation Used The oroblem of grouoing items according to their researchers in the field of classification. The grouping commonly used classification techniques. The particular scheme used is a hierarchical c as follows: Step 1: Each element to be clustered is olacec

Page 68 ï~~T' synthesis similarity, [ 13. 'he process of clustering opens up possibilitie sound representations, for example instead of c spectral envelopes could be grouped to achie' a 6 m Experiments Â~ if the syst have been performed extended t n non-re cover reC However tem.7 -d instrument, several issues concerning the constraints imp addressed. 9 Sun GAS GAS: based shown bmary reduces the higk is NP-complete HCS algorithm n this algorithm h overheads of additive synthesis, bt and therefore intractable. In this p which performs an effective, if not to be an improvement on the previo necessary take into account the perceptual aspec instrument simulation in real-time. References [1] Wessel, D.L. Foundations of C Timbre omtuter Space VIusic. x xt I I as a MUSIcal Massachusetts Control S, The MI7 11